arXiv subjects

Zexin Sun

Publications and source records attributed to Zexin Sun.

7 recordsLinked to original sources

arXiv2024

Structure and Control of Biology-inspired Networks

There is increasing interest in developing the theoretical foundations of networked control systems that illuminate how brain networks function so as to enable sensory perception, control of movement, memory and all the operations that are needed for animals to survive. The present paper proposes a biologically inspired network model featuring dynamic connections regulated by Hebbian learning. Drawing on the machinery of graph theory and classical control we show that our novel nonlinear model exhibits such biologically plausible features as bounded evolution, stability, resilience, and a kind of structural stability -- meaning that perturbations of the model parameters leave the essential properties of the model in tact. The proposed network model involves generalized cactus graphs with multiple control input nodes, and it is shown that the properties of the network are resilient to various changes in network topology provided these changes preserve the generalized cactus structure. A particular example described in what follows is an idealized network model of the visual system of a macaque monkey. The model displays resilience to network disruptions such as might occur in a living organism due to disease or injury. A different model of the same type provides an example of a system that can perform data classification.

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arXiv2024

Koopman-based Deep Learning for Nonlinear System Estimation

Nonlinear differential equations are encountered as models of fluid flow, spiking neurons, and many other systems of interest in the real world. Common features of these systems are that their behaviors are difficult to describe exactly and invariably unmodeled dynamics present challenges in making precise predictions. In this paper, we present a novel data-driven linear estimator based on Koopman operator theory to extract meaningful finite-dimensional representations of complex non-linear systems. The Koopman model is used together with deep reinforcement networks that learn the optimal stepwise actions to predict future states of nonlinear systems. Our estimator is also adaptive to a diffeomorphic transformation of the estimated nonlinear system, which enables it to compute optimal state estimates without re-learning.

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arXiv2023

Neuromimetic Dynamic Networks with Hebbian Learning

Leveraging recent advances in neuroscience and control theory, this paper presents a neuromimetic network model with dynamic symmetric connections governed by Hebbian learning rules. Formal analysis grounded in graph theory and classical control establishes that this biologically plausible model exhibits boundedness, stability, and structural controllability given a generalized sym-cactus structure with multiple control nodes. We prove the necessity of this topology when there are distributed control inputs. Simulations using a 14-node generalized sym-cactus network with two input types validate the model's effectiveness in capturing key neural dynamics.

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arXiv2023

Model Predictive Control for Neuromimetic Quantized Systems

Based on our recent research on neural heuristic quantization systems, we propose an emulation problem consistent with the neuromimetic paradigm. This optimal quantization problem can be solved with model predictive control (MPC) by deriving the conditions under which the quantized system can guarantee (asymptotic) stability during emulation by optimizing a Lyapunov-like objective function. The neuromimetic model features large numbers of discrete inputs, and the optimization involves integer variables. The approach in the paper begins by solving an optimization using model predictive control (MPC) and then using a neural network to train the data generated in this process and applying Fincke and Pohst's sphere decoding algorithm to narrow down the search for the optimal solution.

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arXiv2023

Emulation Learning for Neuromimetic Systems

Building on our recent research on neural heuristic quantization systems, results on learning quantized motions and resilience to channel dropouts are reported. We propose a general emulation problem consistent with the neuromimetic paradigm. This optimal quantization problem can be solved by model predictive control (MPC), but because the optimization step involves integer programming, the approach suffers from combinatorial complexity when the number of input channels becomes large. Even if we collect data points to train a neural network simultaneously, collection of training data and the training itself are still time-consuming. Therefore, we propose a general Deep Q Network (DQN) algorithm that can not only learn the trajectory but also exhibit the advantages of resilience to channel dropout. Furthermore, to transfer the model to other emulation problems, a mapping-based transfer learning approach can be used directly on the current model to obtain the optimal direction for the new emulation problems.

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arXiv2022

Neuromimetic Linear Systems -- Resilience and Learning

Building on our recent work on {\em neuromimetic control theory}, new results on resilience and neuro-inspired quantization are reported. The term neuromimetic refers to the models having features that are characteristic of the neurobiology of biological motor control. As in previous work, the focus is on what we call {\em overcomplete} linear systems that are characterized by larger numbers of input and output channels than the dimensions of the state. The specific contributions of the present paper include a proposed {\em resilient} observer whose operation tolerates output channel intermittency and even complete dropouts. Tying these ideas together with our previous work on resilient stability, a resilient separation principle is established. We also propose a {\em principled quantization} in which control signals are encoded as simple discrete inputs which act collectively through the many channels of input that are the hallmarks of the overcomplete models. Aligned with the neuromimetic paradigm, an {\em emulation} problem is proposed and this in turn defines an optimal quantization problem. Several possible solutions are discussed including direct combinatorial optimization, a Hebbian-like iterative learning algorithm, and a deep Q-learning (DQN) approach. For the problems being considered, machine learning approaches to optimization provide valuable insights regarding comparisons between optimal and nearby suboptimal solutions. These are useful in understanding the kinds of resilience to intermittency and channel dropouts that were earlier demonstrated for continuous systems.

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arXiv2021

Neuromimetic Control -- A Linear Model Paradigm

Stylized models of the neurodynamics that underpin sensory motor control in animals are proposed and studied. The voluntary motions of animals are typically initiated by high level intentions created in the primary cortex through a combination of perceptions of the current state of the environment along with memories of past reactions to similar states. Muscle movements are produced as a result of neural processes in which the parallel activity of large multiplicities of neurons generate signals that collectively lead to desired actions. Essential to coordinated muscle movement are intentionality, prediction, regions of the cortex dealing with misperceptions of sensory cues, and a significant level of resilience with respect to disruptions in the neural pathways through which signals must propagate. While linear models of feedback control systems have been well studied over decades, this paper proposes and analyzes a class of models whose aims are to capture some of the essential features of neural control of movement. Whereas most linear models of feedback systems entail a state component whose dimension is higher than the number of inputs or outputs, the work that follows will treat models in which the numbers of input and output channels greatly exceed the state dimension. While we begin by considering continuous time systems, the aim will be to treat systems whose evolution involves classes of inputs that emulate neural spike trains. Within the proposed class of models, the paper will study resilience to channel dropouts, the ways in which noise and uncertainty can be mitigated by an appropriate notion of consensus among noisy inputs, and finally, by a simple model in which binary activations of a multiplicity of input channels produce a dynamic response that closely approximates the dynamics of a prescribed linear system whose inputs are continuous functions of time.

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