arXiv subjects

ShiNung Ching

Publications and source records attributed to ShiNung Ching.

At least 19 recordsLinked to original sources

arXiv2026

Scalable iterative Gramian synthesis for control-affine systems

This article presents a scalable implementation of nonlinear Gramian-based control synthesis for control-affine systems, including a minimum energy control construction. These synthesis advances are achieved by addressing key computational bottlenecks inherent to iterative synthesis map formulations, yielding a computational scheme that exhibits rapid convergence and high-precision. The efficacy of this synthesis framework is demonstrated across five canonical nonlinear control systems and 100-dimensional recurrent neural network models, including underactuated systems. Empirical scaling results further indicate that convergence is primarily governed by intrinsic system properties, such as nonlinearity and controllability, rather than by state-space dimensionality. This work provides a practical, scalable computational pathway for translating rigorous nonlinear synthesis theory into high-dimensional control applications.

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arXiv2026

Minimum-Energy Control For Control-Affine Systems

Fixed-horizon minimum-energy control for control-affine systems rarely admits closed-form formulas beyond the linear setting. In this article, under the assumption of unconstrained controls, we derive a fixed-horizon minimum-energy control for a broad class of control-affine systems as a fixed point of a Lagrange multiplier synthesis map. Compared with our earlier general steering synthesis, the present construction is based on a generally non-symmetric Gramian-like matrix and solves the associated $L^2$-energy problem. More specifically, under a comparison estimate criterion and a self-mapping assumption, we prove that the synthesis map has a unique fixed point in the feasible coercive classes, which can be computed via a standard Picard iteration. As a demonstration of concept, we use uniform complete controllability results for linear time-varying systems to derive a bracket-generating condition ensuring complete controllability for time-dependent planar control-affine systems with scalar input, and our minimum energy framework applies under standing assumptions. Special treatment for the unicycle kinematic model is also provided, and numerical examples illustrate the approach's effectiveness.

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arXiv2025

Comparing Dynamical Models Through Diffeomorphic Vector Field Alignment

Dynamical systems models such as recurrent neural networks (RNNs) are increasingly popular in theoretical neuroscience for hypothesis-generation and data analysis. Evaluating the dynamics in such models is key to understanding their learned generative mechanisms. However, such evaluation is impeded by two major challenges: First, comparison of learned dynamics across models is difficult because there is no enforced equivalence of their coordinate systems. Second, identification of mechanistically important low-dimensional motifs (e.g., limit sets) is intractable in high-dimensional nonlinear models such as RNNs. Here, we propose a comprehensive framework to address these two issues, termed Diffeomorphic vector field alignment FOR learned Models (DFORM). DFORM learns a nonlinear coordinate transformation between the state spaces of two dynamical systems, which aligns their trajectories in a maximally one-to-one manner. In so doing, DFORM enables an assessment of whether two models exhibit topological equivalence, i.e., similar mechanisms despite differences in coordinate systems. A byproduct of this method is a means to locate dynamical motifs on low-dimensional manifolds embedded within higher-dimensional systems. We verified DFORM's ability to identify linear and nonlinear coordinate transformations using canonical topologically equivalent systems, RNNs, and systems related by nonlinear flows. DFORM was also shown to provide a quantification of similarity between topologically distinct systems. We then demonstrated that DFORM can locate important dynamical motifs including invariant manifolds and saddle limit sets within high-dimensional models. Finally, using a set of RNN models trained on human functional MRI (fMRI) recordings, we illustrated that DFORM can identify limit cycles from high-dimensional data-driven models, which agreed well with prior numerical analysis.

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arXiv2025

Control of neural field equations with step-function inputs

Wilson-Cowan and Amari-type models capture nonlinear neural population dynamics, providing a fundamental framework for modeling how sensory and other exogenous inputs shape activity in neural tissue. We study the controllability properties of Amari-type neural fields subject to piecewise/constant-in-time inputs. The model describes the time evolution of the polarization of neural tissue within a spatial continuum, with synaptic interactions represented by a convolution kernel. We study the synthesis of piecewise/constant-in-time inputs to achieve two-point boundary-type control objectives, namely, steering neural activity from an initial state to a prescribed target state. This approach is particularly relevant for predicting the emergence of paradoxical neural representations, such as discordant visual illusions that occur in response to overt sensory stimuli. We first present a control synthesis based on the Banach fixed-point theorem, which yields an iterative construction of a constant-in-time input under minimal regularity assumptions on the kernel and transfer function; however, it exhibits practical limitations, even in the linear case. To overcome these challenges, we then develop a generic synthesis framework based on the flow of neural dynamics drift, enabling explicit piecewise constant and constant-in-time inputs. Extensive numerical results in one and two spatial dimensions confirm the effectiveness of the proposed syntheses and demonstrate their superior performance compared to inputs derived from naive linearization at the initial or target states when these states are not equilibria of the drift dynamics. By providing a mathematically rigorous framework for controlling Amari-type neural fields, this work advances our understanding of nonlinear neural population control with potential applications in computational neuroscience, psychophysics, and neurostimulation.

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arXiv2025

Episodically adapted network-based controllers

We consider the problem of distributing a control policy across a network of interconnected units. Distributing controllers in this way has a number of potential advantages, especially in terms of robustness, as the failure of a single unit can be compensated by the activity of others. However, it is not obvious a priori how such network-based controllers should be constructed for any given system and control objective. Here, we propose a synthesis procedure for obtaining dynamical networks that enact well-defined control policies in a model-free manner. We specifically consider an augmented state space consisting of both the plant state and the network states. Solution of an optimization problem in this augmented state space produces a desired objective and specification of the network dynamics. Because of the analytical tractability of this method, we are able to provide convergence and robustness assessments

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arXiv2025

Control analysis and synthesis for general control-affine systems

We study controllability and constructive synthesis for control-affine systems. We introduce trajectory-dependent Gramian maps that extend the linear time-varying Gramian and yield explicit fixed-point synthesis maps. On feasible coercivity classes (uniform eigenvalue lower bounds), the Gramian map is Lipschitz, and under a comparison estimate criterion, synthesis iterates exhibit decay, and the Banach fixed-point theorem gives a unique fixed point that steers the system and satisfies an energy identity. When, in addition, an orthogonality condition holds, this fixed point coincides with the unique global minimum-energy control on the feasible set; if the coercivity bound holds uniformly for all bounded controls, the same conclusion holds on the full bounded-control space. We provide structural conditions on the input matrix that ensure the nonemptiness of the feasible class (and, in fully actuated regimes, equality with the full space) and sufficient conditions for underactuated systems via bounded-amplitude reference controls. Case studies on Hopfield network dynamics illustrate refined estimates that enlarge reachable targets. A trajectory-freezing and compactness step extends the synthesis to general nonlinear control-affine systems. The results yield verifiable controllability criteria with explicit, numerically implementable controllers.

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arXiv2024

On the control of recurrent neural networks using constant inputs

This paper investigates the controllability of a broad class of recurrent neural networks widely used in theoretical neuroscience, including models of large-scale human brain dynamics. Motivated by emerging applications in non-invasive neurostimulation such as transcranial direct current stimulation (tDCS), we study the control synthesis of these networks using constant and piecewise constant inputs. The neural model considered is a continuous-time Hopfield-type system with nonlinear activation functions and arbitrary input matrices representing inter-regional brain interactions. Our main contribution is the formulation and solution of a control synthesis problem for such nonlinear systems using specific solution representations. These representations yield explicit algebraic conditions for synthesizing constant and piecewise constant controls that solve a two-point boundary value problem in state space up to higher-order corrections with respect to the time horizon. In particular, the input is constructed to satisfy a tractable small-time algebraic relation involving the Jacobian of the nonlinear drift, ensuring that the synthesis reduces to verifying conditions on the system matrices. For canonical input matrices that directly actuate $k$ nodes, this implies that the reachable set (with constant inputs) of a given initial state is an affine subspace whose dimension equals the input rank and whose basis can be computed efficiently using a thin QR factorization. Numerical simulations illustrate the theoretical results and demonstrate the effectiveness of the proposed synthesis in guiding the design of brain stimulation protocols for therapeutic and cognitive applications.

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arXiv2024

Synergistic pathways of modulation enable robust task packing within neural dynamics

Understanding how brain networks learn and manage multiple tasks simultaneously is of interest in both neuroscience and artificial intelligence. In this regard, a recent research thread in theoretical neuroscience has focused on how recurrent neural network models and their internal dynamics enact multi-task learning. To manage different tasks requires a mechanism to convey information about task identity or context into the model, which from a biological perspective may involve mechanisms of neuromodulation. In this study, we use recurrent network models to probe the distinctions between two forms of contextual modulation of neural dynamics, at the level of neuronal excitability and at the level of synaptic strength. We characterize these mechanisms in terms of their functional outcomes, focusing on their robustness to context ambiguity and, relatedly, their efficiency with respect to packing multiple tasks into finite size networks. We also demonstrate distinction between these mechanisms at the level of the neuronal dynamics they induce. Together, these characterizations indicate complementarity and synergy in how these mechanisms act, potentially over multiple time-scales, toward enhancing robustness of multi-task learning.

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arXiv2024

DFORM: Diffeomorphic vector field alignment for assessing dynamics across learned models

Dynamical system models such as Recurrent Neural Networks (RNNs) have become increasingly popular as hypothesis-generating tools in scientific research. Evaluating the dynamics in such networks is key to understanding their learned generative mechanisms. However, comparison of learned dynamics across models is challenging due to their inherent nonlinearity and because a priori there is no enforced equivalence of their coordinate systems. Here, we propose the DFORM (Diffeomorphic vector field alignment for comparing dynamics across learned models) framework. DFORM learns a nonlinear coordinate transformation which provides a continuous, maximally one-to-one mapping between the trajectories of learned models, thus approximating a diffeomorphism between them. The mismatch between DFORM-transformed vector fields defines the orbital similarity between two models, thus providing a generalization of the concepts of smooth orbital and topological equivalence. As an example, we apply DFORM to models trained on a canonical neuroscience task, showing that learned dynamics may be functionally similar, despite overt differences in attractor landscapes.

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arXiv2023

Strong anti-Hebbian plasticity alters the convexity of network attractor landscapes

In this paper, we study recurrent neural networks in the presence of pairwise learning rules. We are specifically interested in how the attractor landscapes of such networks become altered as a function of the strength and nature (Hebbian vs. anti-Hebbian) of learning, which may have a bearing on the ability of such rules to mediate large-scale optimization problems. Through formal analysis, we show that a transition from Hebbian to anti-Hebbian learning brings about a pitchfork bifurcation that destroys convexity in the network attractor landscape. In larger-scale settings, this implies that anti-Hebbian plasticity will bring about multiple stable equilibria, and such effects may be outsized at interconnection or `choke' points. Furthermore, attractor landscapes are more sensitive to slower learning rates than faster ones. These results provide insight into the types of objective functions that can be encoded via different pairwise plasticity rules.

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arXiv2023

Astrocytes as a mechanism for meta-plasticity and contextually-guided network function

Astrocytes are a ubiquitous and enigmatic type of non-neuronal cell and are found in the brain of all vertebrates. While traditionally viewed as being supportive of neurons, it is increasingly recognized that astrocytes may play a more direct and active role in brain function and neural computation. On account of their sensitivity to a host of physiological covariates and ability to modulate neuronal activity and connectivity on slower time scales, astrocytes may be particularly well poised to modulate the dynamics of neural circuits in functionally salient ways. In the current paper, we seek to capture these features via actionable abstractions within computational models of neuron-astrocyte interaction. Specifically, we engage how nested feedback loops of neuron-astrocyte interaction, acting over separated time-scales may endow astrocytes with the capability to enable learning in context-dependent settings, where fluctuations in task parameters may occur much more slowly than within-task requirements. We pose a general model of neuron-synapse-astrocyte interaction and use formal analysis to characterize how astrocytic modulation may constitute a form of meta-plasticity, altering the ways in which synapses and neurons adapt as a function of time. We then embed this model in a bandit-based reinforcement learning task environment, and show how the presence of time-scale separated astrocytic modulation enables learning over multiple fluctuating contexts. Indeed, these networks learn far more reliably versus dynamically homogeneous networks and conventional non-network-based bandit algorithms. Our results indicate how the presence of neuron-astrocyte interaction in the brain may benefit learning over different time-scales and the conveyance of task-relevant contextual information onto circuit dynamics.

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arXiv2022

Contextual guidance: An integrated theory for astrocytes function in brain circuits and behavior

The participation of astrocytes in brain computation was formally hypothesized in 1992, coinciding with the discovery that these glial cells display a complex form of Ca2+ excitability. This fostered conceptual advances centered on the notion of reciprocal interactions between neurons and astrocytes, which permitted a critical leap forward in uncovering many roles of astrocytes in brain circuits, and signaled the rise of a major new force in neuroscience: that of glial biology. In the past decade, a multitude of unconventional and disparate functions of astrocytes have been documented that are not predicted by these canonical models and that are challenging to piece together into a holistic and parsimonious picture. This highlights a disconnect between the rapidly evolving field of astrocyte biology and the conceptual frameworks guiding it, and emphasizes the need for a careful reconsideration of how we theorize the functional position of astrocytes in brain circuitry. Here, we propose a unifying, highly transferable, data-driven, and computationally-relevant conceptual framework for astrocyte biology, which we coin contextual guidance. It describes astrocytes as contextual gates that decode multiple environmental factors to shape neural circuitry in an adaptive, state-dependent fashion. This paradigm is organically inclusive of all fundamental features of astrocytes, many of which have remained unaccounted for in previous theories. We find that this new concept provides an intuitive and powerful theoretical space to improve our understanding of brain function and computational models thereof across scales because it depicts astrocytes as a hub for circumstantial inputs into relevant specialized circuits that permits adaptive behaviors at the network and organism level.

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arXiv2022

Representation Learning for Context-Dependent Decision-Making

Humans are capable of adjusting to changing environments flexibly and quickly. Empirical evidence has revealed that representation learning plays a crucial role in endowing humans with such a capability. Inspired by this observation, we study representation learning in the sequential decision-making scenario with contextual changes. We propose an online algorithm that is able to learn and transfer context-dependent representations and show that it significantly outperforms the existing ones that do not learn representations adaptively. As a case study, we apply our algorithm to the Wisconsin Card Sorting Task, a well-established test for the mental flexibility of humans in sequential decision-making. By comparing our algorithm with the standard Q-learning and Deep-Q learning algorithms, we demonstrate the benefits of adaptive representation learning.

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arXiv2022

Non-Stationary Representation Learning in Sequential Linear Bandits

In this paper, we study representation learning for multi-task decision-making in non-stationary environments. We consider the framework of sequential linear bandits, where the agent performs a series of tasks drawn from distinct sets associated with different environments. The embeddings of tasks in each set share a low-dimensional feature extractor called representation, and representations are different across sets. We propose an online algorithm that facilitates efficient decision-making by learning and transferring non-stationary representations in an adaptive fashion. We prove that our algorithm significantly outperforms the existing ones that treat tasks independently. We also conduct experiments using both synthetic and real data to validate our theoretical insights and demonstrate the efficacy of our algorithm.

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arXiv2021

Efficient state and parameter estimation for high-dimensional nonlinear system identification with application to MEG brain network modeling

System identification poses a significant bottleneck to characterizing and controlling complex systems. This challenge is greatest when both the system states and parameters are not directly accessible leading to a dual-estimation problem. Current approaches to such problems are limited in their ability to scale with many-parameter systems as often occurs in networks. In the current work, we present a new, computationally efficient approach to treat large dual-estimation problems. Our approach consists of directly integrating pseudo-optimal state estimation (the Extended Kalman Filter) into a dual-optimization objective, leaving a differentiable cost/error function of only in terms of the unknown system parameters which we solve using numerical gradient/Hessian methods. Intuitively, our approach consists of solving for the parameters that generate the most accurate state estimator (Extended Kalman Filter). We demonstrate that our approach is at least as accurate in state and parameter estimation as joint Kalman Filters (Extended/Unscented), despite lower complexity. We demonstrate the utility of our approach by inverting anatomically-detailed individualized brain models from human magnetoencephalography (MEG) data.

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arXiv2021

Slow manifolds in recurrent networks encode working memory efficiently and robustly

Working memory is a cognitive function involving the storage and manipulation of latent information over brief intervals of time, thus making it crucial for context-dependent computation. Here, we use a top-down modeling approach to examine network-level mechanisms of working memory, an enigmatic issue and central topic of study in neuroscience and machine intelligence. We train thousands of recurrent neural networks on a working memory task and then perform dynamical systems analysis on the ensuing optimized networks, wherein we find that four distinct dynamical mechanisms can emerge. In particular, we show the prevalence of a mechanism in which memories are encoded along slow stable manifolds in the network state space, leading to a phasic neuronal activation profile during memory periods. In contrast to mechanisms in which memories are directly encoded at stable attractors, these networks naturally forget stimuli over time. Despite this seeming functional disadvantage, they are more efficient in terms of how they leverage their attractor landscape and paradoxically, are considerably more robust to noise. Our results provide new dynamical hypotheses regarding how working memory function is encoded in both natural and artificial neural networks.

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arXiv2015

Analysis of Recurrent Linear Networks for Enabling Compressed Sensing of Time-Varying Signals

Recent interest has developed around the problem of dynamic compressed sensing, or the recovery of time-varying, sparse signals from limited observations. In this paper, we study how the dynamics of recurrent networks, formulated as general dynamical systems, mediate the recoverability of such signals. We specifically consider the problem of recovering a high-dimensional network input, over time, from observation of only a subset of the network states (i.e., the network output). Our goal is to ascertain how the network dynamics lead to performance advantages, particularly in scenarios where both the input and output are corrupted by disturbance and noise, respectively. For this scenario, we develop bounds on the recovery performance in terms of the dynamics. Conditions for exact recovery in the absence of noise are also formulated. Through several examples, we use the results to highlight how different network characteristics may trade off toward enabling dynamic compressed sensing and how such tradeoffs may manifest naturally in certain classes of neuronal networks.

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arXiv2014

Input Novelty as a Control Metric for Time Varying Linear Systems

This paper introduces a framework for quantitative characterization of the controllability of time-varying linear systems (or networks) in terms of input novelty. The motivation for such an approach comes from the study of biophysical sensory networks in the brain, wherein responsiveness to both energy and salience (or novelty) are presumably critical for mediating behavior and function. Here, we use an inner product to define the angular separation of the current input with respect to the past input history. Then, by constraining input energy, we define a non-convex optimal control problem to obtain the minimally novel input that effects a given state transfer. We provide analytical conditions for existence and uniqueness in continuous-time, as well as an explicit closed-form expression for the solution. In discrete time, we show that a relaxed convex optimization formulation provides the global optimal solution of the original non-convex problem. Finally, we show how the minimum novelty control can be used as a metric to study control properties of large scale recurrent neuronal networks and other complex linear systems. In particular, we highlight unique aspects of a system's controllability that are captured through the novelty-based metric. The result suggests that a multifaceted approach, combining energy-based analysis with other specific metrics, may be useful for obtaining more complete controllability characterizations.

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