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	<rdf:li rdf:resource="https://implicit-layers-tutorial.org/"/>
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	<rdf:li rdf:resource="http://proceedings.mlr.press/v97/taghvaei19a.html"/>
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  </channel><item rdf:about="https://www.cell.com/neuron/fulltext/S0896-6273(25)00716-0?_returnURL=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS0896627325007160%3Fshowall%3Dtrue">
    <title>It’s not the thought that counts: Allostasis at the core of brain function: Neuron</title>
    <dc:date>2026-06-02T23:33:52+00:00</dc:date>
    <link>https://www.cell.com/neuron/fulltext/S0896-6273(25)00716-0?_returnURL=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS0896627325007160%3Fshowall%3Dtrue</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[n psychology and neuroscience, scientific questions are often framed in terms of mental activity (e.g., cognition, emotion, and perception); however, the brain is an organ with a particular function that only it can fulfill. Converging evidence suggests that this function is allostasis: the predictive regulation of competing demands from internal bodily systems. We review evidence for a distributed allostatic system that organizes whole-brain signaling, scaffolds psychological phenomena, and places bodily regulation at the core of brain structure. We also demonstrate, with an example from Alzheimer’s disease, how an “allostasis-first” perspective might transform hypothesis generation in the context of neurological health and disease. In sum, the common conception that the brain is primarily for thinking, or other cognitive processes, is potentially misleading, and neuroscience may benefit from a theoretical structure that centers on basic questions of how the brain coordinates and efficiently regulates the body.]]></description>
<dc:subject>papers to-read neuroscience control-theory dynamical-systems cognition</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:0eecd28934b3/</dc:identifier>
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<item rdf:about="https://arxiv.org/abs/2410.01576">
    <title>[2410.01576] On incompressible flows in discrete networks and Shnirelman's inequality</title>
    <dc:date>2026-05-10T00:50:27+00:00</dc:date>
    <link>https://arxiv.org/abs/2410.01576</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[Let $f$ and $g$ be two volume-preserving diffeomorphisms on the cube $Q=[0,1]^{\nu}$, $\nu \geq 3$. We show that there is a divergence-free vector field $v \in L^1((0,1);L^p(Q))$ such that $v$ connects $f$ and $g$ through the corresponding flow and $\Vert v \Vert_{L^1_t L^p_x} \leq C_{p,\nu} \Vert f- g \Vert_{L^p_x}$. In particular we show Shnirelman's inequality, cf. [Shnirelman, Generalized fluid flows, their approximation and applications (1994)], for the optimal Hölder exponent $\alpha =1$, thus proving that the metric on the group of volume-preserving diffeomorphisms of $Q$ is equivalent to the $L^2$-distance. To achieve this, we discretise our problem, use some results on flows in discrete networks and then construct a flow in non-discrete space-time out of the discrete solution. ]]></description>
<dc:subject>papers to-read dynamical-systems PDEs</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:0d9ac4075df5/</dc:identifier>
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<item rdf:about="https://arxiv.org/abs/2605.01172">
    <title>[2605.01172] A Theory of Generalization in Deep Learning</title>
    <dc:date>2026-05-10T00:44:31+00:00</dc:date>
    <link>https://arxiv.org/abs/2605.01172</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[We present a non-asymptotic theory of generalization in deep learning where the empirical neural tangent kernel partitions the output space. In directions corresponding to signal, error dissipates rapidly; in the vast orthogonal dimensions corresponding to noise, the kernel's near-zero eigenvalues trap residual error in a test-invisible reservoir. Within the signal channel, minibatch SGD ensures that coherent population signal accumulates via fast linear drift, while idiosyncratic memorization is suppressed into a slow, diffusive random walk. We prove generalization survives even when the kernel evolves \mathcal{O}(1) in operator norm, the full feature-learning regime. This theory naturally explains disparate phenomena in deep learning theory, such as benign overfitting, double descent, implicit bias, and grokking. Lastly, we derive an exact population-risk objective from a single training run with no validation data, for any architecture, loss, or optimizer, and prove that it measures precisely the noise in the signal channel. This objective reduces in practice to an SNR preconditioner on top of Adam, adding one state vector at no extra cost; it accelerates grokking by 5 \times, suppresses memorization in PINNs and implicit neural representations, and improves DPO fine-tuning under noisy preferences while staying 3 \times closer to the reference policy. ]]></description>
<dc:subject>papers to-read learning-theory machine-learning deep-learning dynamical-systems optimization neural-networks generalization-bounds</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:5ed6efa9c148/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:generalization-bounds"/>
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<item rdf:about="https://royalsocietypublishing.org/rspa/article/482/2336/20250413/481461/On-computing-quantum-waves-exactly-from-classical">
    <title>On computing quantum waves exactly from classical action | Proceedings A | The Royal Society</title>
    <dc:date>2026-05-01T15:55:32+00:00</dc:date>
    <link>https://royalsocietypublishing.org/rspa/article/482/2336/20250413/481461/On-computing-quantum-waves-exactly-from-classical</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[We show that the Schrödinger equation can be solved exactly based only on classical least action. Fundamental postulates of quantum mechanics can in turn be derived directly from this construction. The results extend to the relativistic Klein-Gordon, Pauli, and Dirac equations, and suggest a smooth transition between physics across scales. Most quantum mechanics problems have classical versions which involve multiple least action solutions. The associated classical multipaths stem either from the initial position or momentum distribution, or from branch points, generated, e.g. by a multiply connected manifold (double slit experiment), by spatial inequality constraints (particle in a box), or by a singularity (Coulomb potential). We show that the exact Schrödinger wave function can be constructed by combining this classical multi-valued action with the classical density ⁠, computed analytically from along each extremal action path. The construction is general and does not involve any semi-classical approximation. Quantum wave collapse at measurement can be derived from the classical density change. Entanglement corresponds to a sum of classical particle actions mapping to a tensor product of spinors. The results also provide a simpler computational alternative to Feynman path integrals, as they use only a minimal subset of classical paths.

-- Need to read carefully, but I am disposed toward skepticism. For one, no citation to Ed Nelson's stochastic mechanics or to Guerra and Morato's paper on optimal control and quantum mechanics: https://journals.aps.org/prd/abstract/10.1103/PhysRevD.27.1774.]]></description>
<dc:subject>papers to-read physics dynamical-systems quantum-mechanics color-me-skeptical</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:10c52d2df623/</dc:identifier>
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<item rdf:about="https://www.cambridge.org/core/journals/economics-and-philosophy/article/market-as-a-creative-process/4A62A60230535D4A8553A7C26A184F56">
    <title>The Market as a Creative Process | Economics &amp; Philosophy | Cambridge Core</title>
    <dc:date>2026-04-18T21:19:33+00:00</dc:date>
    <link>https://www.cambridge.org/core/journals/economics-and-philosophy/article/market-as-a-creative-process/4A62A60230535D4A8553A7C26A184F56</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[Contributions in modern theoretical physics and chemistry on the behavior of nonlinear systems, exemplified by Ilya Prigogine's work on the thermodynamics of open systems (Prigogine and Stengers, 1984), attract growing attention in economics (Anderson, Arrow, and Pines, 1988; Arthur, 1990; Baumol and Benhabib, 1989; Mirowski, 1990; Radzicki, 1990). Our purpose here is to relate the new orientation in the natural sciences to a particular nonorthodox strand of thought within economics. All that is needed for this purpose is some appreciation of the general thrust of the enterprise, which involves a shift of perspective from the determinism of conventional physics (which presumably inspired the neoclassical research program in economics) to the nonteleological open-endedness, creative, and nondetermined nature of evolutionary processes.]]></description>
<dc:subject>papers to-read economics dynamical-systems complex-systems process-philosophy evolution</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:7f64a7342065/</dc:identifier>
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<item rdf:about="https://structures.uni-heidelberg.de/blog/posts/2026_02/">
    <title>STRUCTURES Blog | Predicting the Future: From Cave Paintings to DynaMix</title>
    <dc:date>2026-04-18T21:18:09+00:00</dc:date>
    <link>https://structures.uni-heidelberg.de/blog/posts/2026_02/</link>
    <dc:creator>mraginsky</dc:creator><dc:subject>blogs dynamical-systems control-theory time-series neural-networks</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:02e81ead7f43/</dc:identifier>
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<item rdf:about="https://arxiv.org/abs/2512.24945">
    <title>[2512.24945] Dynamic response phenotypes and model discrimination in systems and synthetic biology</title>
    <dc:date>2026-01-06T03:50:39+00:00</dc:date>
    <link>https://arxiv.org/abs/2512.24945</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[Biological systems encode function not primarily in steady states, but in the structure of transient responses elicited by time-varying stimuli. Overshoots, biphasic dynamics, adaptation kinetics, fold-change detection, entrainment, and cumulative exposure effects often determine phenotypic outcomes, yet are poorly captured by classical steady-state or dose-response analyses. This paper develops an input-output perspective on such "dynamic phenotypes," emphasizing how qualitative features of transient behavior constrain underlying network architectures independently of detailed parameter values. A central theme is the role of sign structure and interconnection logic, particularly the contrast between monotone systems and architectures containing antagonistic pathways. We show how incoherent feedforward (IFF) motifs provide a simple and recurrent mechanism for generating non-monotonic and adaptive responses across multiple levels of biological organization, from molecular signaling to immune regulation and population dynamics. Conversely, monotonicity imposes sharp impossibility results that can be used to falsify entire classes of models from transient data alone. Beyond step inputs, we highlight how periodic forcing, ramps, and integral-type readouts such as cumulative dose responses offer powerful experimental probes that reveal otherwise hidden structure, separate competing motifs, and expose invariances such as fold-change detection. Throughout, we illustrate how control-theoretic concepts, including monotonicity, equivariance, and input-output analysis, can be used not as engineering metaphors, but as precise mathematical tools for biological model discrimination. Thus we argue for a shift in emphasis from asymptotic behavior to transient and input-driven dynamics as a primary lens for understanding, testing, and reverse-engineering biological networks. ]]></description>
<dc:subject>papers to-read systems-biology control-theory dynamical-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:dbf668c42dc8/</dc:identifier>
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<item rdf:about="https://link.springer.com/article/10.1007/s00332-002-0506-0">
    <title>For Differential Equations with r Parameters, 2r+1 Experiments Are Enough for Identification | Journal of Nonlinear Science</title>
    <dc:date>2025-11-14T03:26:20+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s00332-002-0506-0</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[Given a set of differential equations whose description involves unknown parameters, such as reaction constants in chemical kinetics, and supposing that one may at any time measure the values of some of the variables and possibly choose external inputs to help excite the system, how many experiments are sufficient in order to obtain all the information that is potentially available about the parameters? This paper shows that the best possible answer (assuming exact measurements) is 2r+1 experiments, where r is the number of parameters. Moreover, a generic set of such experiments suffices. ]]></description>
<dc:subject>papers to-read dynamical-systems differential-equations system-identification</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:cb57577cf584/</dc:identifier>
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<item rdf:about="https://arxiv.org/abs/2510.15511">
    <title>[2510.15511] Language Models are Injective and Hence Invertible</title>
    <dc:date>2025-11-05T16:01:19+00:00</dc:date>
    <link>https://arxiv.org/abs/2510.15511</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[Transformer components such as non-linear activations and normalization are inherently non-injective, suggesting that different inputs could map to the same output and prevent exact recovery of the input from a model's representations. In this paper, we challenge this view. First, we prove mathematically that transformer language models mapping discrete input sequences to their corresponding sequence of continuous representations are injective and therefore lossless, a property established at initialization and preserved during training. Second, we confirm this result empirically through billions of collision tests on six state-of-the-art language models, and observe no collisions. Third, we operationalize injectivity: we introduce SipIt, the first algorithm that provably and efficiently reconstructs the exact input text from hidden activations, establishing linear-time guarantees and demonstrating exact invertibility in practice. Overall, our work establishes injectivity as a fundamental and exploitable property of language models, with direct implications for transparency, interpretability, and safe deployment. ]]></description>
<dc:subject>papers to-read large-language-models dynamical-systems neural-networks</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:b44b817515cc/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:large-language-models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:neural-networks"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2508.11990">
    <title>[2508.11990] Universal Learning of Nonlinear Dynamics</title>
    <dc:date>2025-10-22T16:19:25+00:00</dc:date>
    <link>https://arxiv.org/abs/2508.11990</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to the next based on a spectral representation of the system. Using techniques from online convex optimization, we prove vanishing prediction error for any nonlinear dynamical system that has finitely many marginally stable modes, with rates governed by a novel quantitative control-theoretic notion of learnability. The main technical component of our method is a new spectral filtering algorithm for linear dynamical systems, which incorporates past observations and applies to general noisy and marginally stable systems. This significantly generalizes the original spectral filtering algorithm to both asymmetric dynamics as well as incorporating noise correction, and is of independent interest. ]]></description>
<dc:subject>papers to-read system-identification control-theory learning-theory dynamical-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:9164da4f209d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:system-identification"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:learning-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/article/10.1007/s10450-006-9683-8">
    <title>The Symplectic Semigroup and Riccati Differential Equations | Journal of Dynamical and Control Systems</title>
    <dc:date>2025-10-15T15:41:07+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s10450-006-9683-8</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[In this paper, we study close connections that exist between the Riccati operator (differential) equation that arises in linear control systems and the symplectic group and its subsemigroup of symplectic Hamiltonian operators. A canonical triple factorization is derived for the symplectic Hamiltonian operators, and their closure under multiplication is deduced from this property. This semigroup of Hamiltonian operators, which we call the symplectic semigroup, is studied from the viewpoint of Lie semigroup theory, and resulting consequences for the theory of the Riccati equation are delineated. Among other things, these developments provide an elementary proof for the existence of a solution of the Riccati equation for all t ≥ 0 under rather general hypotheses.]]></description>
<dc:subject>papers to-read dynamical-systems control-theory differential-equations symplectic-geometry</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:adfbeaa3393e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:differential-equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:symplectic-geometry"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2509.19601">
    <title>[2509.19601] Modular Machine Learning with Applications to Genetic Circuit Composition</title>
    <dc:date>2025-09-29T01:53:44+00:00</dc:date>
    <link>https://arxiv.org/abs/2509.19601</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[In several applications, including in synthetic biology, one often has input/output data on a system composed of many modules, and although the modules' input/output functions and signals may be unknown, knowledge of the composition architecture can significantly reduce the amount of training data required to learn the system's input/output mapping. Learning the modules' input/output functions is also necessary for designing new systems from different composition architectures. Here, we propose a modular learning framework, which incorporates prior knowledge of the system's compositional structure to (a) identify the composing modules' input/output functions from the system's input/output data and (b) achieve this by using a reduced amount of data compared to what would be required without knowledge of the compositional structure. To achieve this, we introduce the notion of modular identifiability, which allows recovery of modules' input/output functions from a subset of the system's input/output data, and provide theoretical guarantees on a class of systems motivated by genetic circuits. We demonstrate the theory on computational studies showing that a neural network (NNET) that accounts for the compositional structure can learn the composing modules' input/output functions and predict the system's output on inputs outside of the training set distribution. By contrast, a neural network that is agnostic of the structure is unable to predict on inputs that fall outside of the training set distribution. By reducing the need for experimental data and allowing module identification, this framework offers the potential to ease the design of synthetic biological circuits and of multi-module systems more generally. ]]></description>
<dc:subject>papers to-read systems-biology control-theory dynamical-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:cd5e939dcbbb/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:systems-biology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2209.08832">
    <title>[2209.08832] From microscopic to macroscopic scale equations: mean field, hydrodynamic and graph limits</title>
    <dc:date>2025-09-25T13:36:29+00:00</dc:date>
    <link>https://arxiv.org/abs/2209.08832</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[Considering finite particle systems, we elaborate on various ways to pass to the limit as thenumber of agents tends to infinity, either by mean field limit, deriving the Vlasov equation,or by hydrodynamic or graph limit, obtaining the Euler equation. We provide convergenceestimates. We also show how to pass from Liouville to Vlasov or to Euler by taking adequatemoments. Our results encompass and generalize a number of known results of the this http URL a surprising consequence of our analysis, we show that sufficiently regular solutions of anylinear PDE can be approximated by solutions of systems of N particles, to within 1/ log log(N ). ]]></description>
<dc:subject>papers to-read statistical-physics dynamical-systems interacting-particle-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:b2fd1757e956/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:statistical-physics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:interacting-particle-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0235070">
    <title>From graph topology to ODE models for gene regulatory networks | PLOS One</title>
    <dc:date>2025-08-24T17:37:23+00:00</dc:date>
    <link>https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0235070</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[A gene regulatory network can be described at a high level by a directed graph with signed edges, and at a more detailed level by a system of ordinary differential equations (ODEs). The former qualitatively models the causal regulatory interactions between ordered pairs of genes, while the latter quantitatively models the time-varying concentrations of mRNA and proteins. This paper clarifies the connection between the two types of models. We propose a property, called the constant sign property, for a general class of ODE models. The constant sign property characterizes the set of conditions (system parameters, external signals, or internal states) under which an ODE model is consistent with a signed, directed graph. If the constant sign property for an ODE model holds globally for all conditions, then the ODE model has a single signed, directed graph. If the constant sign property for an ODE model only holds locally, which may be more typical, then the ODE model corresponds to different graphs under different sets of conditions. In addition, two versions of constant sign property are given and a relationship between them is proved. As an example, the ODE models that capture the effect of cis-regulatory elements involving protein complex binding, based on the model in the GeneNetWeaver source code, are described in detail and shown to satisfy the global constant sign property with a unique consistent gene regulatory graph. Even a single gene regulatory graph is shown to have many ODE models of GeneNetWeaver type consistent with it due to combinatorial complexity and continuous parameters. Finally the question of how closely data generated by one ODE model can be fit by another ODE model is explored. It is observed that the fit is better if the two models come from the same graph.]]></description>
<dc:subject>papers to-read dynamical-systems systems-biology graph-theory networks genomics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:a9f0df19d6f1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:systems-biology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:genomics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.peterputnam.org/">
    <title>The Peter Putnam Papers</title>
    <dc:date>2025-06-29T16:02:10+00:00</dc:date>
    <link>https://www.peterputnam.org/</link>
    <dc:creator>mraginsky</dc:creator><dc:subject>papers cognition neural-networks dynamical-systems ai</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:e9cc14716bd7/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:cognition"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:ai"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://projecteuclid.org/journals/annals-of-applied-probability/volume-34/issue-1A/Toward-a-mathematical-theory-of-trajectory-inference/10.1214/23-AAP1969.full">
    <title>Toward a mathematical theory of trajectory inference</title>
    <dc:date>2025-02-18T20:00:07+00:00</dc:date>
    <link>https://projecteuclid.org/journals/annals-of-applied-probability/volume-34/issue-1A/Toward-a-mathematical-theory-of-trajectory-inference/10.1214/23-AAP1969.full</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[We devise a theoretical framework and a numerical method to infer trajectories of a stochastic process from samples of its temporal marginals. This problem arises in the analysis of single-cell RNA-sequencing data, which provide high-dimensional measurements of cell states but cannot track the trajectories of the cells over time. We prove that for a class of stochastic processes it is possible to recover the ground truth trajectories from limited samples of the temporal marginals at each time-point, and provide an efficient algorithm to do so in practice. The method we develop, Global Waddington-OT (gWOT), boils down to a smooth convex optimization problem posed globally over all time-points involving entropy-regularized optimal transport. We demonstrate that this problem can be solved efficiently in practice and yields good reconstructions, as we show on several synthetic and real data sets.]]></description>
<dc:subject>papers to-read mathematical-biology dynamical-systems optimal-transportation SDEs</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:64c16c4c14ee/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:mathematical-biology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:optimal-transportation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:SDEs"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2409.12179">
    <title>[2409.12179] Computational Dynamical Systems</title>
    <dc:date>2025-01-20T21:17:07+00:00</dc:date>
    <link>https://arxiv.org/abs/2409.12179</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that 'chaotic' dynamical systems (more precisely, Axiom A systems) and 'integrable' dynamical systems (more generally, measure-preserving systems) cannot robustly simulate universal Turing machines, although such machines can be robustly simulated by other kinds of dynamical systems. Subsequently, we show that any Turing machine that can be encoded into a structurally stable one-dimensional dynamical system must have a decidable halting problem, and moreover an explicit time complexity bound in instances where it does halt. More broadly, our work elucidates what it means for one 'machine' to simulate another, and emphasizes the necessity of defining low-complexity 'encoders' and 'decoders' to translate between the dynamics of the simulation and the system being simulated. We highlight how the notion of a computational dynamical system leads to questions at the intersection of computational complexity theory, dynamical systems theory, and real algebraic geometry. ]]></description>
<dc:subject>papers to-read computation dynamical-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:443b5d7ab1e5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:computation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2406.19861">
    <title>[2406.19861] Operator World Models for Reinforcement Learning</title>
    <dc:date>2025-01-20T02:19:08+00:00</dc:date>
    <link>https://arxiv.org/abs/2406.19861</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[Policy Mirror Descent (PMD) is a powerful and theoretically sound methodology for sequential decision-making. However, it is not directly applicable to Reinforcement Learning (RL) due to the inaccessibility of explicit action-value functions. We address this challenge by introducing a novel approach based on learning a world model of the environment using conditional mean embeddings. Leveraging tools from operator theory we derive a closed-form expression of the action-value function in terms of the world model via simple matrix operations. Combining these estimators with PMD leads to POWR, a new RL algorithm for which we prove convergence rates to the global optimum. Preliminary experiments in finite and infinite state settings support the effectiveness of our method ]]></description>
<dc:subject>papers to-read reinforcement-learning dynamical-systems optimization kernel-methods</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:7f2d5ffec7a5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:reinforcement-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:kernel-methods"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2409.07401">
    <title>[2409.07401] Convergence of continuous-time stochastic gradient descent with applications to linear deep neural networks</title>
    <dc:date>2025-01-07T15:38:32+00:00</dc:date>
    <link>https://arxiv.org/abs/2409.07401</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[We study a continuous-time approximation of the stochastic gradient descent process for minimizing the expected loss in learning problems. The main results establish general sufficient conditions for the convergence, extending the results of Chatterjee (2022) established for (nonstochastic) gradient descent. We show how the main result can be applied to the case of overparametrized linear neural network training. ]]></description>
<dc:subject>papers to-read SDEs optimization gradient-flows learning-theory dynamical-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:5a9d57c53afc/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:SDEs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:gradient-flows"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:learning-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/article/10.1007/BF01202856">
    <title>Optimal interpolating and smoothing functional artificial neural networks (FANNs) based on a generalized fock space framework | Circuits, Systems, and Signal Processing</title>
    <dc:date>2024-12-27T14:03:53+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/BF01202856</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[Functional artificial neural networks (FANNs) are artificial neural networks (ANNs) in which the synaptic weights are “functions” rather than numbers. Thus the signals in such networks are analog, and the action of a synapse on a signal passing through it takes place in the form of a scalar product inL 2 between the functional weight and the signal. In this paper, four classes of FANNs are introduced. They result from the solution of a nonparametric optimization problem in a generalized Fock space (GFS) of abstract Volterra series under interpolating or smoothing input-output training data constraints. Two of these classes of FANNs correspond to the interpolating case and are represented by what we call the (two-layer)optimal interpolating (OI) FANN and theoptimal multilayer neural interpolating (OMNI) FANN. The remaining two classes correspond to the smoothing case. We name their representations as the (two-layer)optimal smoothing (OS) FANN and theoptimal smoothing multilayer artificial neural (OSMAN) FANN. In addition to providing the background and the derivation of these FANNs, this paper presents a novel approach to their implementation. This approach does away with the computationally cumbersome use of functional weights. Instead, the effect of these weights is provided by linear time-invariant differential equation models of which those weights are impulse responses. These are implemented by a linear filter bank. This approach thus leads to simple and meaningful causal realizations of FANNs which we call Dynamical FANNs or simply D-FANNs.]]></description>
<dc:subject>papers to-read neural-networks nonlinear-systems dynamical-systems control-theory filtering</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:05c0de74bb6d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:nonlinear-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:filtering"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2412.07438">
    <title>[2412.07438] Flows of vector fields and the Kalman Theorem</title>
    <dc:date>2024-12-15T21:09:53+00:00</dc:date>
    <link>https://arxiv.org/abs/2412.07438</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[We investigate the relations between the Kalman Theorem and the Chow-Rashevskji Theorem or, more precisely, the general theory of flows tangent to non-integrable distributions. The main results consist of two proofs of the Kalman Theorem, which are alternative to the most common ones and which enlighten the above relations and stimulate generalisations in various directions.]]></description>
<dc:subject>papers to-read control-theory dynamical-systems differential-geometry</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:0a41e9ddec66/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:differential-geometry"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.biorxiv.org/content/10.1101/2020.09.19.304584v1">
    <title>On the Mathematics of RNA Velocity I: Theoretical Analysis | bioRxiv</title>
    <dc:date>2024-12-09T19:23:32+00:00</dc:date>
    <link>https://www.biorxiv.org/content/10.1101/2020.09.19.304584v1</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[The RNA velocity provides a new avenue to study the stemness and lineage of cells in the development in scRNA-seq data analysis. Some promising extensions of it are proposed and the community is experiencing a fast developing period. However, in this stage, it is of prime importance to revisit the whole process of RNA velocity analysis from the mathematical point of view, which will help to understand the rationale and drawbacks of different proposals. The current paper is devoted to this purpose. We present a thorough mathematical study on the RNA velocity model from dynamics to downstream data analysis. We derived the analytical solution of the RNA velocity model from both deterministic and stochastic point of view. We presented the parameter inference framework based on the maximum likelihood estimate. We also derived the continuum limit of different downstream analysis methods, which provides insights on the construction of transition probability matrix, root and endingcells identification, and the development routes finding. The overall analysis aims at providing a mathematical basis for more advanced design and development of RNA velocity type methods in the future.]]></description>
<dc:subject>papers to-read biology systems-biology cells genomics dynamical-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:5e24c4613977/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:biology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:systems-biology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:cells"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:genomics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://proceedings.mlr.press/v211/guanchun23a.html">
    <title>A Dynamical Systems Perspective on Discrete Optimization</title>
    <dc:date>2024-08-22T15:57:20+00:00</dc:date>
    <link>https://proceedings.mlr.press/v211/guanchun23a.html</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[We discuss a dynamical systems perspective on discrete optimization. Departing from the fact that many combinatorial optimization problems can be reformulated as finding low energy spin con- figurations in corresponding Ising models, we derive a penalized rank-two relaxation of the Ising formulation. It turns out that the associated gradient flow dynamics exactly correspond to a type of hardware solvers termed oscillator-based Ising machines. We also analyze the advantage of adding angle penalties by leveraging random rounding techniques. Therefore, our work contributes to a rigorous understanding of oscillator-based Ising machines by drawing connections to the penalty method in constrained optimization and providing a rationale for the introduction of sub-harmonic injection locking. Furthermore, we characterize a class of coupling functions between oscillators, which ensures convergence to discrete solutions. This class of coupling functions avoids explicit penalty terms or rounding schemes, which are prevalent in other formulations. ]]></description>
<dc:subject>papers to-read dynamical-systems optimization statistical-physics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:e7a2328fbf3e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:statistical-physics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2305.17628">
    <title>[2305.17628] Convex operator-theoretic methods in stochastic control</title>
    <dc:date>2024-08-20T11:05:16+00:00</dc:date>
    <link>https://arxiv.org/abs/2305.17628</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[This paper is about operator-theoretic methods for solving nonlinear stochastic optimal control problems to global optimality. These methods leverage on the convex duality between optimally controlled diffusion processes and Hamilton-Jacobi-Bellman (HJB) equations for nonlinear systems in an ergodic Hilbert-Sobolev space. In detail, a generalized Bakry-Emery condition is introduced under which one can establish the global exponential stabilizability of a large class of nonlinear systems. It is shown that this condition is sufficient to ensure the existence of solutions of the ergodic HJB for stochastic optimal control problems on infinite time horizons. Moreover, a novel dynamic programming recursion for bounded linear operators is introduced, which can be used to numerically solve HJB equations by a Galerkin projection. ]]></description>
<dc:subject>papers to-read control-theory dynamical-systems optimization functional-analysis</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:c36d6ed9e02d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:functional-analysis"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2304.03519">
    <title>[2304.03519] Robust data-driven control for nonlinear systems using the Koopman operator</title>
    <dc:date>2024-08-20T10:58:37+00:00</dc:date>
    <link>https://arxiv.org/abs/2304.03519</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[Data-driven analysis and control of dynamical systems have gained a lot of interest in recent years. While the class of linear systems is well studied, theoretical results for nonlinear systems are still rare. In this paper, we present a data-driven controller design method for discrete-time control-affine nonlinear systems. Our approach relies on the Koopman operator, which is a linear but infinite-dimensional operator lifting the nonlinear system to a higher-dimensional space. Particularly, we derive a linear fractional representation of a lifted bilinear system representation based on measured data. Further, we restrict the lifting to finite dimensions, but account for the truncation error using a finite-gain argument. We derive a linear matrix inequality based design procedure to guarantee robust local stability for the resulting bilinear system for all error terms satisfying the finite-gain bound and, thus, also for the underlying nonlinear system. Finally, we apply the developed design method to the nonlinear Van der Pol oscillator. ]]></description>
<dc:subject>papers to-read control-theory dynamical-systems Koopman-operators</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:1b6cb0cfd335/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:Koopman-operators"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2404.18380">
    <title>[2404.18380] Dynamic Global Feedback Stabilization: why do the twist?</title>
    <dc:date>2024-08-13T20:11:02+00:00</dc:date>
    <link>https://arxiv.org/abs/2404.18380</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[We investigate global dynamic feedback stabilization from a topological viewpoint. In particular, we consider the general case of dynamic feedback systems, whereby the total space (which includes the state space of the system and of the controller) is a fibre bundle, and derive conditions on the topology of the bundle that are necessary for various notions of global stabilization to hold. This point of view highlight the importance of distinguishing trivial bundles and twisted bundles in the study of global dynamic feedback stabilization, as we show that dynamic feedback defined on a twisted bundle can stabilize systems that dynamic feedback on trivial bundles cannot. ]]></description>
<dc:subject>papers to-read control-theory dynamical-systems feedback geometry topology</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:1e6f0dfe9c79/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:feedback"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:topology"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/book/10.1007/BFb0036078">
    <title>Control Using Logic-Based Switching | SpringerLink</title>
    <dc:date>2024-08-12T18:51:27+00:00</dc:date>
    <link>https://link.springer.com/book/10.1007/BFb0036078</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[A logic-based switching controller is one whose subsystems include not only familiar dynamical components such as integrators, summers, gains etc. but event-driven logic and associated switches as well. In such a system the predominantly logical component is the supervisor, mode changer, etc. There has been growing interest in recent years in determining what could be gained from utilising "hybrid" controllers of this type. To this end a workshop was held on Block Island with the aim of bringing together individuals to discuss the research and common interest in the field. This volume not only includes contributions from those who were present at Block Island but also additional material from those who were not. Topics covered include: hybrid dynamical systems, control of hard-bound constrained and nonlinear systems, automotive problems involving switching control and system control in the face of large-scale modeling errors. ]]></description>
<dc:subject>books control-theory adaptive-systems dynamical-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:a31bfff8e73a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:books"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:adaptive-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.pnas.org/doi/10.1073/pnas.2311893121">
    <title>The neuron as a direct data-driven controller | PNAS</title>
    <dc:date>2024-06-25T02:10:00+00:00</dc:date>
    <link>https://www.pnas.org/doi/10.1073/pnas.2311893121</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[In the quest to model neuronal function amid gaps in physiological data, a promising strategy is to develop a normative theory that interprets neuronal physiology as optimizing a computational objective. This study extends current normative models, which primarily optimize prediction, by conceptualizing neurons as optimal feedback controllers. We posit that neurons, especially those beyond early sensory areas, steer their environment toward a specific desired state through their output. This environment comprises both synaptically interlinked neurons and external motor sensory feedback loops, enabling neurons to evaluate the effectiveness of their control via synaptic feedback. To model neurons as biologically feasible controllers which implicitly identify loop dynamics, infer latent states, and optimize control we utilize the contemporary direct data-driven control (DD-DC) framework. Our DD-DC neuron model explains various neurophysiological phenomena: the shift from potentiation to depression in spike-timing-dependent plasticity with its asymmetry, the duration and adaptive nature of feedforward and feedback neuronal filters, the imprecision in spike generation under constant stimulation, and the characteristic operational variability and noise in the brain. Our model presents a significant departure from the traditional, feedforward, instant-response McCulloch–Pitts–Rosenblatt neuron, offering a modern, biologically informed fundamental unit for constructing neural networks.]]></description>
<dc:subject>papers to-read neuroscience control-theory dynamical-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:0fe5a5c7ec9e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:neuroscience"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://onlinelibrary.wiley.com/doi/10.1111/ejn.16372">
    <title>Formalising the role of behaviour in neuroscience - Piantadosi - European Journal of Neuroscience - Wiley Online Library</title>
    <dc:date>2024-06-17T19:59:17+00:00</dc:date>
    <link>https://onlinelibrary.wiley.com/doi/10.1111/ejn.16372</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[We develop a mathematical approach to formally proving that certain neural computations and representations exist based on patterns observed in an organism's behaviour. To illustrate, we provide a simple set of conditions under which an ant's ability to determine how far it is from its nest would logically imply neural structures isomorphic to the natural numbers. We generalise these results to arbitrary behaviours and representations and show what mathematical characterisation of neural computation and representation is simplest while being maximally predictive of behaviour. We develop this framework in detail using a path integration example, where an organism's ability to search for its nest in the correct location implies representational structures isomorphic to two-dimensional coordinates under addition. We also study a system for processing a^nb^n strings common in comparative work. Our approach provides an objective way to determine what theory of a physical system is best, addressing a fundamental challenge in neuroscientific inference. These results motivate considering which neurobiological structures have the requisite formal structure and are otherwise physically plausible given relevant physical considerations such as generalisability, information density, thermodynamic stability and energetic cost.

ETA -- on the first read, this paper commits the fallacy of reifying the state representation.]]></description>
<dc:subject>papers to-read neuroscience control-theory dynamical-systems state-space-models</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:b2dcbfcf9013/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:neuroscience"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:state-space-models"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/article/10.1007/s10699-012-9304-9">
    <title>On the Import of Constraints in Complex Dynamical Systems | Foundations of Science</title>
    <dc:date>2024-04-15T02:08:40+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s10699-012-9304-9</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[Complexity arises from interaction dynamics, but its forms are co-determined by the operative constraints within which the dynamics are expressed. The basic interaction dynamics underlying complex systems is mostly well understood. The formation and operation of constraints is often not, and oftener under appreciated. The attempt to reduce constraints to basic interaction fails in key cases. The overall aim of this paper is to highlight the key role played by constraints in shaping the field of complex systems. Following an introduction to constraints (Sect. 1), the paper develops the roles of constraints in specifying forms of complexity (Sect. 2) and illustrates the roles of constraints in formulating the fundamental challenges to understanding posed by complex systems (Sect. 3).]]></description>
<dc:subject>papers to-read dynamical-systems philosophy-of-engineering physics complex-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:5ff28afc08c9/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:philosophy-of-engineering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:physics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:complex-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2402.01032">
    <title>[2402.01032] Repeat After Me: Transformers are Better than State Space Models at Copying</title>
    <dc:date>2024-02-07T16:20:02+00:00</dc:date>
    <link>https://arxiv.org/abs/2402.01032</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[Transformers are the dominant architecture for sequence modeling, but there is growing interest in models that use a fixed-size latent state that does not depend on the sequence length, which we refer to as "generalized state space models" (GSSMs). In this paper we show that while GSSMs are promising in terms of inference-time efficiency, they are limited compared to transformer models on tasks that require copying from the input context. We start with a theoretical analysis of the simple task of string copying and prove that a two layer transformer can copy strings of exponential length while GSSMs are fundamentally limited by their fixed-size latent state. Empirically, we find that transformers outperform GSSMs in terms of efficiency and generalization on synthetic tasks that require copying the context. Finally, we evaluate pretrained large language models and find that transformer models dramatically outperform state space models at copying and retrieving information from context. Taken together, these results suggest a fundamental gap between transformers and GSSMs on tasks of practical interest. ]]></description>
<dc:subject>papers to-read dynamical-systems transformers</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:1297f3039ff1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:transformers"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://ieeexplore.ieee.org/abstract/document/9454440">
    <title>Feedback Maximum Principle for Ensemble Control of Local Continuity Equations: An Application to Supervised Machine Learning | IEEE Journals &amp; Magazine | IEEE Xplore</title>
    <dc:date>2024-01-14T21:02:13+00:00</dc:date>
    <link>https://ieeexplore.ieee.org/abstract/document/9454440</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[We consider an optimal control problem for a system of local continuity equations on a space of probability measures. Such systems can be viewed as macroscopic models of ensembles of non-interacting particles or homotypic individuals, representing several different “populations”. For the stated problem, we propose a necessary conditions of optimality which involve feedback controls inherent to the extremal structure designed via the standard Pontryagin's Maximum Principle. These optimality conditions admit a realization as an iterative algorithm for optimal control. As a motivating case, we discuss an application of the derived optimality condition, and the consequent numeric method to a problem of supervised machine learning via dynamic systems.]]></description>
<dc:subject>papers to-read dynamical-systems control-theory ODEs machine-learning</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:2028fc5e7330/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:ODEs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:machine-learning"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2312.12903">
    <title>[2312.12903] A Minimal Control Family of Dynamical Syetem for Universal Approximation</title>
    <dc:date>2023-12-23T20:19:04+00:00</dc:date>
    <link>https://arxiv.org/abs/2312.12903</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[The universal approximation property (UAP) of neural networks is a fundamental characteristic of deep learning. It is widely recognized that a composition of linear functions and non-linear functions, such as the rectified linear unit (ReLU) activation function, can approximate continuous functions on compact domains. In this paper, we extend this efficacy to the scenario of dynamical systems with controls. We prove that the control family $\mathcal{F}_1 = \mathcal{F}_0 \cup \{ \text{ReLU}(\cdot)\} $ is enough to generate flow maps that can uniformly approximate diffeomorphisms of $\mathbb{R}^d$ on any compact domain, where $\mathcal{F}_0 = \{x \mapsto Ax+b: A\in \mathbb{R}^{d\times d}, b \in \mathbb{R}^d\}$ is the set of linear maps and the dimension $d\ge2$. Since $\mathcal{F}_1$ contains only one nonlinear function and $\mathcal{F}_0$ does not hold the UAP, we call $\mathcal{F}_1$ a minimal control family for UAP. Based on this, some sufficient conditions, such as the affine invariance, on the control family are established and discussed. Our result reveals an underlying connection between the approximation power of neural networks and control systems. ]]></description>
<dc:subject>papers to-read neural-networks dynamical-systems differential-equations control-theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:f238f721525e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:differential-equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2212.13628">
    <title>[2212.13628] Functional Expansions</title>
    <dc:date>2023-11-29T19:11:59+00:00</dc:date>
    <link>https://arxiv.org/abs/2212.13628</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[Path dependence is omnipresent in many disciplines such as engineering, system theory and finance. It reflects the influence of the past on the future, often expressed through functionals. However, non-Markovian problems are often infinite-dimensional, thus challenging from a conceptual and computational perspective. In this work, we shed light on expansions of functionals. First, we treat static expansions made around paths of fixed length and propose a generalization of the Wiener series−the intrinsic value expansion (IVE). In the dynamic case, we revisit the functional Taylor expansion (FTE). The latter connects the functional Itô calculus with the signature to quantify the effect in a functional when a "perturbation" path is concatenated with the source path. In particular, the FTE elegantly separates the functional from future trajectories. The notions of real analyticity and radius of convergence are also extended to the path space. We discuss other dynamic expansions arising from Hilbert projections and the Wiener chaos, and finally show financial applications of the FTE to the pricing and hedging of exotic contingent claims. ]]></description>
<dc:subject>papers have-read stochastic-analysis functional-analysis finance dynamical-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:e14055ffa1bf/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:have-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:stochastic-analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:functional-analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:finance"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://videolectures.net/cyberstat2012_granada/">
    <title>Workshop on Statistical Physics of Inference and Control Theory, Granada 2012 - VideoLectures - VideoLectures.NET</title>
    <dc:date>2023-08-09T21:01:56+00:00</dc:date>
    <link>http://videolectures.net/cyberstat2012_granada/</link>
    <dc:creator>mraginsky</dc:creator><dc:subject>statistical-physics inference information control-theory learning dynamical-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:030cd6bd49c8/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:statistical-physics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:information"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/chapter/10.1007/3-540-36589-3_17">
    <title>Controllability, integrability and ergodicity | SpringerLink</title>
    <dc:date>2023-07-13T21:43:09+00:00</dc:date>
    <link>https://link.springer.com/chapter/10.1007/3-540-36589-3_17</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[Systems preserving a smooth measure on the phase space, such as Hamiltonian systems of classical dynamics or incompressible flows of fluid dynamics attract a lot of interest in control theory. I describe some work on the notion of controllability in systems that are measure-preserving and possess drift. Relationship between controllability, a fundamental concept in control theory, and the concepts of integrability and ergodicity, fundamental in dynamical systems theory is addressed. The basic idea is that studying reccurence (or ergodic) properties of trajectories of the drift is key to establishing necessary and sufficient conditions for controllability in such systems. The benefit of this approach is that controllability proofs contain a constructive procedure for control.]]></description>
<dc:subject>papers to-read control-theory dynamical-systems ergodic-theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:25c08d304c7f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:ergodic-theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2305.18288">
    <title>[2305.18288] Linearizability of flows by embeddings</title>
    <dc:date>2023-05-30T02:42:46+00:00</dc:date>
    <link>https://arxiv.org/abs/2305.18288</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[We consider the problem of determining the class of continuous-time dynamical systems that can be globally linearized in the sense of admitting an embedding into a linear flow on a finite-dimensional Euclidean space. We obtain necessary and sufficient conditions for the existence of linearizing embeddings of compact invariant sets and basins of attraction. Our results reveal relationships between linearizability, symmetry, topology, and invariant manifold theory that impose fundamental limitations on algorithms from the ``applied Koopman operator theory'' literature. ]]></description>
<dc:subject>papers to-read dynamical-systems Koopman-operators</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:b93cc5516ec1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:Koopman-operators"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.sciencedirect.com/science/article/abs/pii/S1389041709000163?casa_token=8dkZ1O1iNBcAAAAA:gnuocqU5jszqBuwnBv1BYYua466pUhmQXOokW-3DOCA_-v5GNHpSCvptgCXuxYcYizauW6_Qzt8">
    <title>On strong anticipation - ScienceDirect</title>
    <dc:date>2023-05-04T16:41:49+00:00</dc:date>
    <link>https://www.sciencedirect.com/science/article/abs/pii/S1389041709000163?casa_token=8dkZ1O1iNBcAAAAA:gnuocqU5jszqBuwnBv1BYYua466pUhmQXOokW-3DOCA_-v5GNHpSCvptgCXuxYcYizauW6_Qzt8</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[We examine Dubois’s [Dubois, D., 2003. Mathematical foundations of discrete and functional systems with strong and weak anticipations. Lecture Notes in Computer Science 2684, 110–132.] distinction between weak anticipation and strong anticipation. Anticipation is weak if it arises from a model of the system via internal simulations. Anticipation is strong if it arises from the system itself via lawful regularities embedded in the system’s ordinary mode of functioning. The assumption of weak anticipation dominates cognitive science and neuroscience and in particular the study of perception and action. The assumption of strong anticipation, however, seems to be required by anticipation’s ubiquity. It is, for example, characteristic of homeostatic processes at the level of the organism, organs, and cells. We develop the formal distinction between strong and weak anticipation by elaboration of anticipating synchronization, a phenomenon arising from time delays in appropriately coupled dynamical systems. The elaboration is conducted in respect to (a) strictly physical systems, (b) the defining features of circadian rhythms, often viewed as paradigmatic of biological behavior based in internal models, (c) Pavlovian learning, and (d) forward models in motor control. We identify the common thread of strongly anticipatory systems and argue for its significance in furthering understanding of notions such as “internal”, “model” and “prediction”.]]></description>
<dc:subject>papers to-read control-theory dynamical-systems ecological-psychology cognitive-science</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:a614ef1065ba/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:ecological-psychology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:cognitive-science"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2301.06632">
    <title>[2301.06632] Asymptotic normality and optimality in nonsmooth stochastic approximation</title>
    <dc:date>2023-01-18T09:05:44+00:00</dc:date>
    <link>https://arxiv.org/abs/2301.06632</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[In their seminal work, Polyak and Juditsky showed that stochastic approximation algorithms for solving smooth equations enjoy a central limit theorem. Moreover, it has since been argued that the asymptotic covariance of the method is best possible among any estimation procedure in a local minimax sense of Hájek and Le Cam. A long-standing open question in this line of work is whether similar guarantees hold for important non-smooth problems, such as stochastic nonlinear programming or stochastic variational inequalities. In this work, we show that this is indeed the case. ]]></description>
<dc:subject>papers to-read heard-the-talk optimization dynamical-systems nonsmooth-geometry stratification-theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:c9232da98331/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:heard-the-talk"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:nonsmooth-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:stratification-theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2206.04030">
    <title>[2206.04030] High-dimensional limit theorems for SGD: Effective dynamics and critical scaling</title>
    <dc:date>2023-01-16T09:27:07+00:00</dc:date>
    <link>https://arxiv.org/abs/2206.04030</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[We study the scaling limits of stochastic gradient descent (SGD) with constant step-size in the high-dimensional regime. We prove limit theorems for the trajectories of summary statistics (i.e., finite-dimensional functions) of SGD as the dimension goes to infinity. Our approach allows one to choose the summary statistics that are tracked, the initialization, and the step-size. It yields both ballistic (ODE) and diffusive (SDE) limits, with the limit depending dramatically on the former choices. We show a critical scaling regime for the step-size, below which the effective ballistic dynamics matches gradient flow for the population loss, but at which, a new correction term appears which changes the phase diagram. About the fixed points of this effective dynamics, the corresponding diffusive limits can be quite complex and even degenerate. We demonstrate our approach on popular examples including estimation for spiked matrix and tensor models and classification via two-layer networks for binary and XOR-type Gaussian mixture models. These examples exhibit surprising phenomena including multimodal timescales to convergence as well as convergence to sub-optimal solutions with probability bounded away from zero from random (e.g., Gaussian) initializations. At the same time, we demonstrate the benefit of overparametrization by showing that the latter probability goes to zero as the second layer width grows. ]]></description>
<dc:subject>papers to-read heard-the-talk optimization dynamical-systems machine-learning gradient-flows</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:1e2cc35c0d94/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:heard-the-talk"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:gradient-flows"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2205.14027">
    <title>[2205.14027] Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spaces</title>
    <dc:date>2022-10-25T12:31:35+00:00</dc:date>
    <link>https://arxiv.org/abs/2205.14027</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[    We study a class of dynamical systems modelled as Markov chains that admit an invariant distribution via the corresponding transfer, or Koopman, operator. While data-driven algorithms to reconstruct such operators are well known, their relationship with statistical learning is largely unexplored. We formalize a framework to learn the Koopman operator from finite data trajectories of the dynamical system. We consider the restriction of this operator to a reproducing kernel Hilbert space and introduce a notion of risk, from which different estimators naturally arise. We link the risk with the estimation of the spectral decomposition of the Koopman operator. These observations motivate a reduced-rank operator regression (RRR) estimator. We derive learning bounds for the proposed estimator, holding both in i.i.d. and non i.i.d. settings, the latter in terms of mixing coefficients. Our results suggest RRR might be beneficial over other widely used estimators as confirmed in numerical experiments both for forecasting and mode decomposition. 

]]></description>
<dc:subject>papers to-read heard-the-talk machine-learning kernel-methods dynamical-systems Koopman-operators</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:d99604a1f5bb/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:heard-the-talk"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:kernel-methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:Koopman-operators"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://proceedings.mlr.press/v119/zhuang20a.html">
    <title>Adaptive Checkpoint Adjoint Method for Gradient Estimation in Neural ODE</title>
    <dc:date>2022-10-22T15:36:25+00:00</dc:date>
    <link>https://proceedings.mlr.press/v119/zhuang20a.html</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[The empirical performance of neural ordinary differential equations (NODEs) is significantly inferior to discrete-layer models on benchmark tasks (e.g. image classification). We demonstrate an explanation is the inaccuracy of existing gradient estimation methods: the adjoint method has numerical errors in reverse-mode integration; the naive method suffers from a redundantly deep computation graph. We propose the Adaptive Checkpoint Adjoint (ACA) method: ACA applies a trajectory checkpoint strategy which records the forward- mode trajectory as the reverse-mode trajectory to guarantee accuracy; ACA deletes redundant components for shallow computation graphs; and ACA supports adaptive solvers. On image classification tasks, compared with the adjoint and naive method, ACA achieves half the error rate in half the training time; NODE trained with ACA outperforms ResNet in both accuracy and test-retest reliability. On time-series modeling, ACA outperforms competing methods. Furthermore, NODE with ACA can incorporate physical knowledge to achieve better accuracy. ]]></description>
<dc:subject>papers to-read neural-networks machine-learning ODEs dynamical-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:566a12bbe273/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:ODEs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/article/10.1007/s10485-019-09565-x">
    <title>Dynamical Systems and Sheaves | SpringerLink</title>
    <dc:date>2022-10-03T02:57:57+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s10485-019-09565-x</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as ‘machines’ with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special cases include continuous and discrete dynamical systems (e.g. Moore machines). Additionally, morphisms between the different types of systems allow their translation in a common framework. A central goal is to understand the systems that result from arbitrary interconnection of component subsystems, possibly of different types, as well as establish conditions that ensure totality and determinism compositionally. The fundamental categorical tools used here include lax monoidal functors, which provide a language of compositionality, as well as sheaf theory, which flexibly captures the crucial notion of time.]]></description>
<dc:subject>to-read type-theory control-theory categories dynamical-systems functional-programming logic papers</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:3ee6ce48d6c5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:type-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:categories"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:functional-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:logic"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1710.10258">
    <title>[1710.10258] Temporal Type Theory: A topos-theoretic approach to systems and behavior</title>
    <dc:date>2022-10-03T02:50:36+00:00</dc:date>
    <link>https://arxiv.org/abs/1710.10258</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[    This book introduces a temporal type theory, the first of its kind as far as we know. It is based on a standard core, and as such it can be formalized in a proof assistant such as Coq or Lean by adding a number of axioms. Well-known temporal logics---such as Linear and Metric Temporal Logic (LTL and MTL)---embed within the logic of temporal type theory.
    The types in this theory represent "behavior types". The language is rich enough to allow one to define arbitrary hybrid dynamical systems, which are mixtures of continuous dynamics---e.g. as described by a differential equation---and discrete jumps. In particular, the derivative of a continuous real-valued function is internally defined.
    We construct a semantics for the temporal type theory in the topos of sheaves on a translation-invariant quotient of the standard interval domain. In fact, domain theory plays a recurring role in both the semantics and the type theory. 

]]></description>
<dc:subject>books to-read type-theory control-theory categories dynamical-systems functional-programming logic</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:66d37e1343ca/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:books"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:type-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:categories"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:functional-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:logic"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.ams.org/journals/bull/2019-56-01/S0273-0979-2018-01650-9/">
    <title>Isabelle Gallagher, &quot;From Newton to Navier–Stokes, or how to connect fluid mechanics equations from microscopic to macroscopic scales&quot;</title>
    <dc:date>2022-08-10T16:52:28+00:00</dc:date>
    <link>https://www.ams.org/journals/bull/2019-56-01/S0273-0979-2018-01650-9/</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[In this survey we present an overview of some mathematical results concerning the passage from the microscopic description of fluids via Newton’s laws to the macroscopic description via the Navier–Stokes equations. ]]></description>
<dc:subject>papers to-read fluid-mechanics dynamical-systems physics PDEs</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:21aa3d116955/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:fluid-mechanics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:physics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:PDEs"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2204.12786">
    <title>[2204.12786] Machines of finite depth: towards a formalization of neural networks</title>
    <dc:date>2022-08-02T16:31:20+00:00</dc:date>
    <link>https://arxiv.org/abs/2204.12786</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[We provide a unifying framework where artificial neural networks and their architectures can be formally described as particular cases of a general mathematical construction--machines of finite depth. Unlike neural networks, machines have a precise definition, from which several properties follow naturally. Machines of finite depth are modular (they can be combined), efficiently computable and differentiable. The backward pass of a machine is again a machine and can be computed without overhead using the same procedure as the forward pass. We prove this statement theoretically and practically, via a unified implementation that generalizes several classical architectures--dense, convolutional, and recurrent neural networks with a rich shortcut structure--and their respective backpropagation rules. ]]></description>
<dc:subject>papers to-read neural-networks computation dynamical-systems systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:bf8b501d87fa/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:computation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://eudml.org/doc/208885">
    <title>EUDML  |  Some optimal control applications of real-analytic stratifications and desingularization</title>
    <dc:date>2022-08-02T16:25:50+00:00</dc:date>
    <link>https://eudml.org/doc/208885</link>
    <dc:creator>mraginsky</dc:creator><dc:subject>papers to-read geometry control-theory dynamical-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:8b178b043c07/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2204.11900">
    <title>[2204.11900] Towards a Geometry and Analysis for Bayesian Mechanics</title>
    <dc:date>2022-08-02T16:23:25+00:00</dc:date>
    <link>https://arxiv.org/abs/2204.11900</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[In this paper, a simple case of Bayesian mechanics under the free energy principle is formulated in axiomatic terms. We argue that any dynamical system with constraints on its dynamics necessarily looks as though it is performing inference against these constraints, and that in a non-isolated system, such constraints imply external environmental variables embedding the system. Using aspects of classical dynamical systems theory in statistical mechanics, we show that this inference is equivalent to a gradient ascent on the Shannon entropy functional, recovering an approximate Bayesian inference under a locally ergodic probability measure on the state space. We also use some geometric notions from dynamical systems theory—namely, that the constraints constitute a gauge degree of freedom—to elaborate on how the desire to stay self-organised can be read as a gauge force acting on the system. In doing so, a number of results of independent interest are given. Overall, we provide a related, but alternative, formalism to those driven purely by descriptions of random dynamical systems, and take a further step towards a comprehensive statement of the physics of self-organisation in formal mathematical language. ]]></description>
<dc:subject>papers to-read Bayesian-inference differential-geometry complex-systems adaptive-systems dynamical-systems statistical-physics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:d21d4b8939d5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:Bayesian-inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:differential-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:complex-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:adaptive-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:statistical-physics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/article/10.1007/BF00933032">
    <title>Stochastic systems in Riemannian manifolds | SpringerLink</title>
    <dc:date>2022-08-02T16:04:50+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/BF00933032</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[A formulation of stochastic systems in a Riemannian manifold is given by stochastic differential equations in the tangent bundle of the manifold. Brownian motion is constructed in a compact Riemannian manifold as well as the horizontal lift of this process to the bundle of orthonormal frames. The solution of some stochastic differential equations in the tangent bundle of the manifold is defined by the transformation of the measure for the manifold-valued Brownian motion by a suitable Radon-Nikodym derivative. Real-valued stochastic integrals are defined for this Brownian motion using parallelism along the Brownian paths. A stochastic control problem is formulated and solved for these stochastic systems where a suitable convexity condition is assumed.]]></description>
<dc:subject>papers to-read stochastic-analysis differential-geometry SDEs dynamical-systems probability</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:b60dbee2d2c8/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:stochastic-analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:differential-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:SDEs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:probability"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://royalsocietypublishing.org/doi/10.1098/rsif.2012.0869">
    <title>The algorithmic origins of life | Journal of The Royal Society Interface</title>
    <dc:date>2022-08-02T16:00:01+00:00</dc:date>
    <link>https://royalsocietypublishing.org/doi/10.1098/rsif.2012.0869</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[Although it has been notoriously difficult to pin down precisely what is it that makes life so distinctive and remarkable, there is general agreement that its informational aspect is one key property, perhaps the key property. The unique informational narrative of living systems suggests that life may be characterized by context-dependent causal influences, and, in particular, that top-down (or downward) causation—where higher levels influence and constrain the dynamics of lower levels in organizational hierarchies—may be a major contributor to the hierarchal structure of living systems. Here, we propose that the emergence of life may correspond to a physical transition associated with a shift in the causal structure, where information gains direct and context-dependent causal efficacy over the matter in which it is instantiated. Such a transition may be akin to more traditional physical transitions (e.g. thermodynamic phase transitions), with the crucial distinction that determining which phase (non-life or life) a given system is in requires dynamical information and therefore can only be inferred by identifying causal architecture. We discuss some novel research directions based on this hypothesis, including potential measures of such a transition that may be amenable to laboratory study, and how the proposed mechanism corresponds to the onset of the unique mode of (algorithmic) information processing characteristic of living systems.]]></description>
<dc:subject>papers to-read biogenesis information-theory algorithms causality control-theory dynamical-systems cybernetics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:053e8aa6fdff/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:biogenesis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:information-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:causality"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:cybernetics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2207.12395">
    <title>[2207.12395] Statistical Inference with Stochastic Gradient Algorithms</title>
    <dc:date>2022-07-26T21:02:05+00:00</dc:date>
    <link>https://arxiv.org/abs/2207.12395</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[Stochastic gradient algorithms are widely used for both optimization and sampling in large-scale learning and inference problems. However, in practice, tuning these algorithms is typically done using heuristics and trial-and-error rather than rigorous, generalizable theory. To address this gap between theory and practice, we novel insights into the effect of tuning parameters by characterizing the large-sample behavior of iterates of a very general class of preconditioned stochastic gradient algorithms with fixed step size. In the optimization setting, our results show that iterate averaging with a large fixed step size can result in statistically efficient approximation of the (local) M-estimator. In the sampling context, our results show that with appropriate choices of tuning parameters, the limiting stationary covariance can match either the Bernstein--von Mises limit of the posterior, adjustments to the posterior for model misspecification, or the asymptotic distribution of the MLE; and that with a naive tuning the limit corresponds to none of these. Moreover, we argue that an essentially independent sample from the stationary distribution can be obtained after a fixed number of passes over the dataset. We validate our asymptotic results in realistic finite-sample regimes via several experiments using simulated and real data. Overall, we demonstrate that properly tuned stochastic gradient algorithms with constant step size offer a computationally efficient and statistically robust approach to obtaining point estimates or posterior-like samples. ]]></description>
<dc:subject>papers to-read statistical-learning optimization dynamical-systems sampling</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:2223fcf2d3c3/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:statistical-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:sampling"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/article/10.1007/s00365-021-09549-y">
    <title>The Barron Space and the Flow-Induced Function Spaces for Neural Network Models | SpringerLink</title>
    <dc:date>2022-06-28T19:54:59+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s00365-021-09549-y</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[One of the key issues in the analysis of machine learning models is to identify the appropriate function space and norm for the model. This is the set of functions endowed with a quantity which can control the approximation and estimation errors by a particular machine learning model. In this paper, we address this issue for two representative neural network models: the two-layer networks and the residual neural networks. We define the Barron space and show that it is the right space for two-layer neural network models in the sense that optimal direct and inverse approximation theorems hold for functions in the Barron space. For residual neural network models, we construct the so-called flow-induced function space and prove direct and inverse approximation theorems for this space. In addition, we show that the Rademacher complexity for bounded sets under these norms has the optimal upper bounds.]]></description>
<dc:subject>papers have-read neural-networks dynamical-systems machine-learning approximation-theory function-approximation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:cd69a86cb403/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:have-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:approximation-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:function-approximation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2206.06227">
    <title>[2206.06227] Convergence for score-based generative modeling with polynomial complexity</title>
    <dc:date>2022-06-14T09:48:03+00:00</dc:date>
    <link>https://arxiv.org/abs/2206.06227</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[Score-based generative modeling (SGM) is a highly successful approach for learning a probability distribution from data and generating further samples. We prove the first polynomial convergence guarantees for the core mechanic behind SGM: drawing samples from a probability density p given a score estimate (an estimate of ∇lnp) that is accurate in L2(p). Compared to previous works, we do not incur error that grows exponentially in time or that suffers from a curse of dimensionality. Our guarantee works for any smooth distribution and depends polynomially on its log-Sobolev constant. Using our guarantee, we give a theoretical analysis of score-based generative modeling, which transforms white-noise input into samples from a learned data distribution given score estimates at different noise scales. Our analysis gives theoretical grounding to the observation that an annealed procedure is required in practice to generate good samples, as our proof depends essentially on using annealing to obtain a warm start at each step. Moreover, we show that a predictor-corrector algorithm gives better convergence than using either portion alone. ]]></description>
<dc:subject>papers to-read generative-models SDEs learning-theory optimization dynamical-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:3ba5042fb111/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:generative-models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:SDEs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:learning-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2205.09241">
    <title>[2205.09241] Neural ODE Control for Trajectory Approximation of Continuity Equation</title>
    <dc:date>2022-05-23T15:18:53+00:00</dc:date>
    <link>https://arxiv.org/abs/2205.09241</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[We consider the controllability problem for the continuity equation, corresponding to neural ordinary differential equations (ODEs), which describes how a probability measure is pushedforward by the flow. We show that the controlled continuity equation has very strong controllability properties. Particularly, a given solution of the continuity equation corresponding to a bounded Lipschitz vector field defines a trajectory on the set of probability measures. For this trajectory, we show that there exist piecewise constant training weights for a neural ODE such that the solution of the continuity equation corresponding to the neural ODE is arbitrarily close to it. As a corollary to this result, we establish that the continuity equation of the neural ODE is approximately controllable on the set of compactly supported probability measures that are absolutely continuous with respect to the Lebesgue measure. ]]></description>
<dc:subject>papers to-read control-theory dynamical-systems ODEs SDEs neural-networks machine-learning</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:0389d5764128/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:ODEs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:SDEs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:machine-learning"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2101.12606">
    <title>[2101.12606] Dissipativity and optimal control</title>
    <dc:date>2022-03-22T20:14:20+00:00</dc:date>
    <link>https://arxiv.org/abs/2101.12606</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[The close link between dissipativity and optimal control is already apparent in Jan C. Willems' first papers on the subject. In recent years, research on this link has been revived with a particular focus on nonlinear problems and applications in model predictive control (MPC). This paper surveys these recent developments and some of Willems' and other authors' earlier results. ]]></description>
<dc:subject>papers to-read optimization control-theory dynamical-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:2e7dcf0b4bf5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2104.05278">
    <title>[2104.05278] Neural ODE control for classification, approximation and transport</title>
    <dc:date>2021-07-14T17:31:29+00:00</dc:date>
    <link>https://arxiv.org/abs/2104.05278</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[

    We analyze Neural Ordinary Differential Equations (NODEs) from a control theoretical perspective to address some of the main properties and paradigms of Deep Learning (DL), in particular, data classification and universal approximation. These objectives are tackled and achieved from the perspective of the simultaneous control of systems of NODEs. For instance, in the context of classification, each item to be classified corresponds to a different initial datum for the control problem of the NODE, to be classified, all of them by the same common control, to the location (a subdomain of the euclidean space) associated to each label. Our proofs are genuinely nonlinear and constructive, allowing us to estimate the complexity of the control strategies we develop. The nonlinear nature of the activation functions governing the dynamics of NODEs under consideration plays a key role in our proofs, since it allows deforming half of the phase space while the other half remains invariant, a property that classical models in mechanics do not fulfill. This very property allows to build elementary controls inducing specific dynamics and transformations whose concatenation, along with properly chosen hyperplanes, allows achieving our goals in finitely many steps. The nonlinearity of the dynamics is assumed to be Lipschitz. Therefore, our results apply also in the particular case of the ReLU activation function. We also present the counterparts in the context of the control of neural transport equations, establishing a link between optimal transport and deep neural networks. ]]></description>
<dc:subject>papers to-read neural-networks ODEs dynamical-systems control-theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:5bafc70f1ac0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:ODEs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2006.10330">
    <title>[2006.10330] A Shooting Formulation of Deep Learning</title>
    <dc:date>2021-05-03T22:22:04+00:00</dc:date>
    <link>https://arxiv.org/abs/2006.10330</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[Continuous-depth neural networks can be viewed as deep limits of discrete neural networks whose dynamics resemble a discretization of an ordinary differential equation (ODE). Although important steps have been taken to realize the advantages of such continuous formulations, most current techniques are not truly continuous-depth as they assume \textit{identical} layers. Indeed, existing works throw into relief the myriad difficulties presented by an infinite-dimensional parameter space in learning a continuous-depth neural ODE. To this end, we introduce a shooting formulation which shifts the perspective from parameterizing a network layer-by-layer to parameterizing over optimal networks described only by a set of initial conditions. For scalability, we propose a novel particle-ensemble parametrization which fully specifies the optimal weight trajectory of the continuous-depth neural network. Our experiments show that our particle-ensemble shooting formulation can achieve competitive performance, especially on long-range forecasting tasks. Finally, though the current work is inspired by continuous-depth neural networks, the particle-ensemble shooting formulation also applies to discrete-time networks and may lead to a new fertile area of research in deep learning parametrization. ]]></description>
<dc:subject>papers to-read machine-learning neural-networks ODEs control-theory dynamical-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:6f5ab0d954eb/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:ODEs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2002.08071">
    <title>[2002.08071] Dissecting Neural ODEs</title>
    <dc:date>2021-05-03T22:21:23+00:00</dc:date>
    <link>https://arxiv.org/abs/2002.08071</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[Continuous deep learning architectures have recently re-emerged as Neural Ordinary Differential Equations (Neural ODEs). This infinite-depth approach theoretically bridges the gap between deep learning and dynamical systems, offering a novel perspective. However, deciphering the inner working of these models is still an open challenge, as most applications apply them as generic black-box modules. In this work we "open the box", further developing the continuous-depth formulation with the aim of clarifying the influence of several design choices on the underlying dynamics. ]]></description>
<dc:subject>papers have-read machine-learning neural-networks ODEs dynamical-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:a6cb7a07ee6d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:have-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:ODEs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.pnas.org/content/116/21/10537">
    <title>Fundamental bounds on learning performance in neural circuits | PNAS</title>
    <dc:date>2021-04-14T15:36:43+00:00</dc:date>
    <link>https://www.pnas.org/content/116/21/10537</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[How does the size of a neural circuit influence its learning performance? Larger brains tend to be found in species with higher cognitive function and learning ability. Intuitively, we expect the learning capacity of a neural circuit to grow with the number of neurons and synapses. We show how adding apparently redundant neurons and connections to a network can make a task more learnable. Consequently, large neural circuits can either devote connectivity to generating complex behaviors or exploit this connectivity to achieve faster and more precise learning of simpler behaviors. However, we show that in a biologically relevant setting where synapses introduce an unavoidable amount of noise, there is an optimal size of network for a given task. Above the optimal network size, the addition of neurons and synaptic connections starts to impede learning performance. This suggests that the size of brain circuits may be constrained by the need to learn efficiently with unreliable synapses and provides a hypothesis for why some neurological learning deficits are associated with hyperconnectivity. Our analysis is independent of specific learning rules and uncovers fundamental relationships between learning rate, task performance, network size, and intrinsic noise in neural circuits.]]></description>
<dc:subject>papers to-read neuroscience neural-networks learning control-theory dynamical-systems biology</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:05d5179c4894/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:neuroscience"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:biology"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.pnas.org/content/70/10/2974">
    <title>A Theory of the Epigenesis of Neuronal Networks by Selective Stabilization of Synapses | PNAS</title>
    <dc:date>2021-04-14T15:13:41+00:00</dc:date>
    <link>https://www.pnas.org/content/70/10/2974</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[A formalism is introduced to represent the connective organization of an evolving neuronal network and the effects of environment on this organization by stabilization or degeneration of labile synapses associated with functioning. Learning, or the acquisition of an associative property, is related to a characteristic variability of the connective organization: the interaction of the environment with the genetic program is printed as a particular pattern of such organization through neuronal functioning. An application of the theory to the development of the neuromuscular junction is proposed and the basic selective aspect of learning emphasized.]]></description>
<dc:subject>papers to-read neuroscience biology learning control-theory dynamical-systems neural-networks</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:0715924cac17/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:neuroscience"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:biology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:neural-networks"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2104.05508">
    <title>[2104.05508] Noether: The More Things Change, the More Stay the Same</title>
    <dc:date>2021-04-14T15:03:31+00:00</dc:date>
    <link>https://arxiv.org/abs/2104.05508</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[Symmetries have proven to be important ingredients in the analysis of neural networks. So far their use has mostly been implicit or seemingly coincidental.
We undertake a systematic study of the role that symmetry plays. In particular, we clarify how symmetry interacts with the learning algorithm. The key ingredient in our study is played by Noether's celebrated theorem which, informally speaking, states that symmetry leads to conserved quantities (e.g., conservation of energy or conservation of momentum). In the realm of neural networks under gradient descent, model symmetries imply restrictions on the gradient path. E.g., we show that symmetry of activation functions leads to boundedness of weight matrices, for the specific case of linear activations it leads to balance equations of consecutive layers, data augmentation leads to gradient paths that have "momentum"-type restrictions, and time symmetry leads to a version of the Neural Tangent Kernel.
Symmetry alone does not specify the optimization path, but the more symmetries are contained in the model the more restrictions are imposed on the path. Since symmetry also implies over-parametrization, this in effect implies that some part of this over-parametrization is cancelled out by the existence of the conserved quantities.
Symmetry can therefore be thought of as one further important tool in understanding the performance of neural networks under gradient descent. ]]></description>
<dc:subject>papers to-read deep-learning neural-networks gradient-flows dynamical-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:2b1bc90b677e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:deep-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:gradient-flows"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://openreview.net/forum?id=BJe55gBtvH">
    <title>Depth-Width Trade-offs for ReLU Networks via Sharkovsky's Theorem | OpenReview</title>
    <dc:date>2021-02-19T17:28:30+00:00</dc:date>
    <link>https://openreview.net/forum?id=BJe55gBtvH</link>
    <dc:creator>mraginsky</dc:creator><dc:subject>papers to-read neural-networks deep-learning dynamical-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:c2760284dafa/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:deep-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.frontiersin.org/articles/10.3389/fphys.2020.00200/full">
    <title>Frontiers | Homeostasis: The Underappreciated and Far Too Often Ignored Central Organizing Principle of Physiology | Physiology</title>
    <dc:date>2021-01-02T02:48:56+00:00</dc:date>
    <link>https://www.frontiersin.org/articles/10.3389/fphys.2020.00200/full</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[The grand challenge to physiology, as was first described in an essay published in the inaugural issue of Frontiers in Physiology in 2010, remains to integrate function from molecules to intact organisms. In order to make sense of the vast volume of information derived from, and increasingly dependent upon, reductionist approaches, a greater emphasis must be placed on the traditional integrated and more holistic approaches developed by the scientists who gave birth to physiology as an intellectual discipline. Our understanding of physiological regulation has evolved over time from the Greek idea of body humors, through Claude Bernard’s “milieu intérieur,” to Walter Cannon’s formulation of the concept of “homeostasis” and the application of control theory (feedback and feedforward regulation) to explain how a constant internal environment is achieved. Homeostasis has become the central unifying concept of physiology and is defined as a self-regulating process by which an organism can maintain internal stability while adjusting to changing external conditions. Homeostasis is not static and unvarying; it is a dynamic process that can change internal conditions as required to survive external challenges. It is also important to note that homeostatic regulation is not merely the product of a single negative feedback cycle but reflects the complex interaction of multiple feedback systems that can be modified by higher control centers. This hierarchical control and feedback redundancy results in a finer level of control and a greater flexibility that enables the organism to adapt to changing environmental conditions. The health and vitality of the organism can be said to be the end result of homeostatic regulation. An understanding of normal physiology is not possible without an appreciation of this concept. Conversely, it follows that disruption of homeostatic mechanisms is what leads to disease, and effective therapy must be directed toward re-establishing these homeostatic conditions. Therefore, it is the purpose of this essay to describe the evolution of our understanding of homeostasis and the role of physiological regulation and dysregulation in health and disease.
]]></description>
<dc:subject>to-read papers cybernetics physiology biology control-theory dynamical-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:70dfcf02ea25/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:cybernetics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:physiology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:biology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://implicit-layers-tutorial.org/">
    <title>Deep Implicit Layers - Neural ODEs, Deep Equilibirum Models, and Beyond</title>
    <dc:date>2020-12-07T16:23:42+00:00</dc:date>
    <link>https://implicit-layers-tutorial.org/</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[This web page is the companion website to our NeurIPS 2020 tutorial, created by Zico Kolter, David Duvenaud, and Matt Johnson. The page constain notes to accompany our tutorial (all created via Colab notebooks, which you can experiment with as you like), as well as links to our video presentation as slides. This web page will be under development until the official scheduled time of the tutorial (December 7, 1:30pm PT), and may undergo additional changes after that time.]]></description>
<dc:subject>machine-learning neural-networks deep-learning dynamical-systems ODEs generative-models</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:9e151207031f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:deep-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:ODEs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:generative-models"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2007.06007">
    <title>[2007.06007] Universal Approximation Power of Deep Neural Networks via Nonlinear Control Theory</title>
    <dc:date>2020-08-19T18:45:41+00:00</dc:date>
    <link>https://arxiv.org/abs/2007.06007</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[ In this paper, we explain the universal approximation capabilities of deep neural networks through geometric nonlinear control. Inspired by recent work establishing links between residual networks and control systems, we provide a general sufficient condition for a residual network to have the power of universal approximation by asking the activation function, or one of its derivatives, to satisfy a quadratic differential equation. Many activation functions used in practice satisfy this assumption, exactly or approximately, and we show this property to be sufficient for an adequately deep neural network with n states to approximate arbitrarily well any continuous function defined on a compact subset of R^n. We further show this result to hold for very simple architectures, where the weights only need to assume two values. The key technical contribution consists of relating the universal approximation problem to controllability of an ensemble of control systems corresponding to a residual network, and to leverage classical Lie algebraic techniques to characterize controllability. ]]></description>
<dc:subject>papers to-read deep-learning neural-networks dynamical-systems control-theory differential-equations</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:50632fd10d08/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:deep-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:differential-equations"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1807.08351">
    <title>[1807.08351] Data Assimilation: The Schrödinger Perspective</title>
    <dc:date>2020-07-20T20:22:22+00:00</dc:date>
    <link>https://arxiv.org/abs/1807.08351</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using probabilistic particle-based algorithms. In addition to surveying recent developments for discrete- and continuous-time data assimilation, both in terms of mathematical foundations and algorithmic implementations, we also provide a unifying framework from the perspective of coupling of measures, and Schrödinger's boundary value problem for stochastic processes in particular. ]]></description>
<dc:subject>papers have-read filtering MCMC Bayesian-inference dynamical-systems PDEs stochastic-control</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:86d2f91d7b18/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:have-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:MCMC"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:Bayesian-inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:PDEs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:stochastic-control"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://proceedings.mlr.press/v97/taghvaei19a.html">
    <title>Accelerated Flow for Probability Distributions</title>
    <dc:date>2020-07-20T20:19:46+00:00</dc:date>
    <link>http://proceedings.mlr.press/v97/taghvaei19a.html</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[This paper presents a methodology and numerical algorithms for constructing accelerated gradient flows on the space of probability distributions. In particular, we extend the recent variational formulation of accelerated methods in (Wibisono et al., 2016) from vector valued variables to probability distributions. The variational problem is modeled as a mean-field optimal control problem. A quantitative estimate on the asymptotic convergence rate is provided based on a Lyapunov function construction, when the objective functional is displacement convex. An important special case is considered where the objective functional is the relative entropy. For this case, two numerical approximations are presented to implement the Hamilton’s equations as a system of N interacting particles. The algorithm is numerically illustrated and compared with the MCMC and Hamiltonian MCMC algorithms. ]]></description>
<dc:subject>papers to-read machine-learning sampling dynamical-systems</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:d3babed75d43/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:sampling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2005.10963">
    <title>[2005.10963] Stochastic control liasons: Richard Sinkhorn meets Gaspard Monge on a Schroedinger bridge</title>
    <dc:date>2020-07-20T20:18:38+00:00</dc:date>
    <link>https://arxiv.org/abs/2005.10963</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[ In 1931/32, Schroedinger studied a hot gas Gedankenexperiment, an instance of large deviations of the empirical distribution and an early example of the so-called maximum entropy inference method. This so-called Schroedinger bridge problem (SBP) was recently recognized as a regularization of the Monge-Kantorovich Optimal Mass Transport (OMT), leading to effective computation of the latter. Specifically, OMT with quadratic cost may be viewed as a zero-temperature limit of SBP, which amounts to minimization of the Helmholtz's free energy over probability distributions constrained to possess given marginals. The problem features a delicate compromise, mediated by a temperature parameter, between minimizing the internal energy and maximizing the entropy. These concepts are central to a rapidly expanding area of modern science dealing with the so-called {\em Sinkhorn algorithm} which appears as a special case of an algorithm first studied by the French analyst Robert Fortet in 1938/40 specifically for Schroedinger bridges. Due to the constraint on end-point distributions, dynamic programming is not a suitable tool to attack these problems. Instead, Fortet's iterative algorithm and its discrete counterpart, the Sinkhorn iteration, permit computation by iteratively solving the so-called {\em Schroedinger system}. In both the continuous as well as the discrete-time and space settings, {\em stochastic control} provides a reformulation and dynamic versions of these problems. The formalism behind these control problems have attracted attention as they lead to a variety of new applications in spacecraft guidance, control of robot or biological swarms, sensing, active cooling, network routing as well as in computer and data science. This multifacet and versatile framework, intertwining SBP and OMT, provides the substrate for a historical and technical overview of the field taken up in this paper. ]]></description>
<dc:subject>papers to-read stochastic-control optimal-transportation dynamical-systems dynamic-programming PDEs</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:7f29f1ad8914/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:stochastic-control"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:optimal-transportation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamic-programming"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:PDEs"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/math/9906212">
    <title>[math/9906212] Proof of the gradient conjecture of R. Thom</title>
    <dc:date>2020-07-20T20:17:35+00:00</dc:date>
    <link>https://arxiv.org/abs/math/9906212</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[Let x(t) be a trajectory of the gradient of a real analytic function and suppose that x_0 is a limit point of x(t). We prove the gradient conjecture of R. Thom which states that the secants of x(t) at x_0 have a limit. Actually we show a stronger statement: the radial projection of x(t) from x_0 onto the unit sphere has finite length. ]]></description>
<dc:subject>papers to-read dynamical-systems differential-equations geometry</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:d521a6357ac3/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:differential-equations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:geometry"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2006.06462">
    <title>[2006.06462] Deep Differential System Stability -- Learning advanced computations from examples</title>
    <dc:date>2020-07-20T20:17:00+00:00</dc:date>
    <link>https://arxiv.org/abs/2006.06462</link>
    <dc:creator>mraginsky</dc:creator><description><![CDATA[ Can advanced mathematical computations be learned from examples? Using transformers over large generated datasets, we train models to learn properties of differential systems, such as local stability, behavior at infinity and controllability. We achieve near perfect estimates of qualitative characteristics of the systems, and good approximations of numerical quantities, demonstrating that neural networks can learn advanced theorems and complex computations without built-in mathematical knowledge. 

-- I am skeptical, so usual caveats apply]]></description>
<dc:subject>papers to-read machine-learning deep-learning dynamical-systems control-theory state-space-models stability</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:mraginsky/b:ca3ba9610638/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:papers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:to-read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:deep-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:control-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:state-space-models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:mraginsky/t:stability"/>
</rdf:Bag></taxo:topics>
</item>
</rdf:RDF>