arXiv subjects

Zhuo-Cheng Xiao

Publications and source records attributed to Zhuo-Cheng Xiao.

10 recordsLinked to original sources

arXiv2026

Activation-Flexible ANN-to-SNN Conversion with Finite-State Markov Neurons

Most ANN-to-SNN conversion methods rely on a specific correspondence between the source activation and the spiking neuron dynamics. We propose a finite-state continuous-time Markov chain (CTMC) neuron framework whose stationary spike flux can approximate every continuous nonnegative monotone activation function on a compact interval. For a generalized CTMC family with affine input-dependent transitions, we prove uniform approximation to arbitrary accuracy over this function class and derive an explicit approximation error bound. In practice, two- and three-state CTMCs fit ReLU, sigmoid, softplus, and clipped ReLU on the evaluated input ranges, and we evaluate corresponding MLP conversions for each activation with layerwise rate scaling. Moderate clipping improves the conversion cost-accuracy tradeoff on the MNIST MLP and reduces SynOps by 27% on VGG-11/MNIST at matched ANN-SNN accuracy gap criteria, whereas the trend reverses on VGG-11/CIFAR-10. Mean-field and layerwise diagnostics indicate that finite-window sampling and terminal-layer mismatch are the main residual errors. Overall, our results establish finite-state CTMC neurons as a theoretically grounded framework for activation-flexible ANN-to-SNN conversion beyond fixed activation-neuron correspondences.

cs.NE↗

arXiv2026

Diffusion learning reveals viable parameter manifolds and compensation geometry in biological dynamical systems

Models of complex systems often have many parameters, yet are constrained by far fewer experimentally accessible observables; consequently, similar activity can emerge from coordinated parameter changes. We formalize these compatible parameter sets as \emph{viable parameter manifolds}: the inverse images of target dynamical features under a parameter-to-feature map. The relevant codimension is not the number of reported features, but the effective rank of that map at the target scale. Locally redundant features lower the effective codimension, while poor conditioning, high curvature, or regime mixing degrade learnability. We train conditional score-based diffusion models on simulated parameter--feature pairs and use them as amortized samplers of prior-weighted viable sets. In the Lorenz system, scalar trajectory statistics generate thin viable sheets, and a finite-tolerance conditioning localizes a transition-adjacent corridor. In the Izhikevich neuron model, four firing descriptors lie close to a nearly two-dimensional family of features, and the learned inverse images reveal distinct regular and irregular compensation geometries. In a deterministic ODE reduction of finite spiking networks, the same framework reveals excitatory--inhibitory compensation, timescale--coupling tradeoffs, and viable manifolds across 4--12 parameter dimensions. In this view, robustness, compensation, and hidden parameter dependencies are organized as inverse geometry, with diffusion models providing practical tools for sampling, visualizing, and interrogating that geometry.

q-bio.QM↗

arXiv2026

Finite-state Markovian surrogates for long-time neuronal state distributions and firing rates

Spiking neuronal networks connect cellular and synaptic mechanisms to collective activity, but estimating their long-time statistics often requires costly spike-by-spike simulation. We construct finite-state Markovian surrogates for neuronal populations with one- to three-dimensional intrinsic dynamics. A finite phase-space partition represents each population by its occupancy across single-neuron states, and the firing rate is defined uniformly as probability flux through model-specific spike transitions. We compare two closures: Type I enforces a stationary mean synaptic drive, whereas Type II retains its temporal evolution. In the leaky linear integrate-and-fire (LIF) benchmarks, the Type I estimator is accurate in temporally homogeneous cases but misses rate changes driven by synaptic timescales. In the synaptic-timescale sweep, the Type II estimator achieves small relative errors in most cases. Exponential integrate-and-fire (EIF) results exhibit an analogous qualitative pattern. FitzHugh--Nagumo (FHN) and reduced Hodgkin--Huxley (HH) examples extend the construction from one-dimensional threshold--reset dynamics to continuous trajectories in nonlinear two- and three-dimensional phase spaces. Together, these examples show how the finite-state construction generates model-dependent estimates of long-time state distributions and firing rates without resolving every neuron and spike.

q-bio.NC↗

arXiv2026

Mostly-monocular responses and other visual functions in a multiscale network model of Macaque V1

Visual signals from the two eyes merge gradually as they pass through the primary visual cortex (V1). Here we use a computational model of Macaque V1 to study the first stage of this integration along the magnocellular pathway, in layer 4C$α$, aiming to infer neuroanatomical origins of binocular response. It is known that neurons in layer 4C$α$ are predominantly monocular, though some do exhibit varying degrees of binocularity. We find (1) the emergence of narrow binocular strips along borders of ocular dominance columns (ODC), a finding that aligns with experiments; (2) most consistent with data is when $10-30\%$ of interactions near ODC boundaries are cross-columnar; and (3) feedback from layer 6 is largely monocular. These results were obtained through systematic hypothesis testing using a multiscale model that is orders of magnitude faster than its biologically-detailed predecessors. We propose that multiscale modeling can be an effective tool for bridging anatomy and function.

q-bio.NC↗

arXiv2026

Numerical analysis for leaky-integrate-fire networks under Euler-Maruyama

Leaky integrate-and-fire (LIF) networks are standard reduced models for spike-based neural dynamics and a natural substrate for neuromorphic computation. We study time-driven Euler--Maruyama simulation of current-based LIF networks with exponentially decaying synapses and instantaneous resets. Because diffusion acts through the synaptic current rather than directly through the voltage, numerical error is concentrated at threshold events. It is therefore driven by spike-time perturbations and by grid-induced spike-count mismatch. For layered feedforward networks, under suitable density, rate, regularity, and one-step boundary-layer assumptions, we prove finite-horizon strong and weak error bounds. For the strong error, we first condition on spike histories that match up to the observation horizon. On this matched event, we combine a conditional single-spike hitting-time comparison with direct averaging of the induced synaptic-impact kernel against the boundary flux of crossing speeds. This yields matched-trajectory mean-square strong error of order $h$ up to polylogarithmic factors. We then control spike-count mismatch separately by local rate, dense-spike, and spike-time-tail bounds. For weak error, we use an averaged backward-semigroup argument. Assuming a backward transmission problem and one-step rate, strip, and factorial-moment controls for the numerical marginals, we obtain weak order $1$ for smooth spike-map-compatible observables, with constants explicit in rate and weight bounds. We also outline deterministic and noisy recurrent extensions, motivated by a Lyapunov-exponent formula that couples the stationary threshold flux to the reset saltation factor. These results distinguish single-trial spike-train fidelity from observable-level accuracy and clarify which notion of numerical accuracy is most relevant for mechanistic spiking models and spike-based computation.

math.NA↗

arXiv2024

Minimizing information loss reduces spiking neuronal networks to differential equations

Spiking neuronal networks (SNNs) are widely used in computational neuroscience, from biologically realistic modeling of local cortical networks to phenomenological modeling of the whole brain. Despite their prevalence, a systematic mathematical theory for finite-sized SNNs remains elusive, even for idealized homogeneous networks. The primary challenges are twofold: 1) the rich, parameter-sensitive SNN dynamics, and 2) the singularity and irreversibility of spikes. These challenges pose significant difficulties when relating SNNs to systems of differential equations, leading previous studies to impose additional assumptions or to focus on individual dynamic regimes. In this study, we introduce a Markov approximation of homogeneous SNN dynamics to minimize information loss when translating SNNs into ordinary differential equations. Our only assumption for the Markov approximation is the fast self-decorrelation of synaptic conductances. The system of ordinary differential equations derived from the Markov model effectively captures high-frequency partial synchrony and the metastability of finite-neuron networks produced by interacting excitatory and inhibitory populations. Besides accurately predicting dynamical statistics, such as firing rates, our theory also quantitatively captures the geometry of attractors and bifurcation structures of SNNs. Thus, our work provides a comprehensive mathematical framework that can systematically map parameters of single-neuron physiology, network coupling, and external stimuli to homogeneous SNN dynamics.

q-bio.NC↗

arXiv2022

Learning biological neuronal networks with artificial neural networks: neural oscillations

First-principles-based modelings have been extremely successful in providing crucial insights and predictions for complex biological functions and phenomena. However, they can be hard to build and expensive to simulate for complex living systems. On the other hand, modern data-driven methods thrive at modeling many types of high-dimensional and noisy data. Still, the training and interpretation of these data-driven models remain challenging. Here, we combine the two types of methods to model stochastic neuronal network oscillations. Specifically, we develop a class of first-principles-based artificial neural networks to provide faithful surrogates to the high-dimensional, nonlinear oscillatory dynamics produced by neural circuits in the brain. Furthermore, when the training data set is enlarged within a range of parameter choices, the artificial neural networks become generalizable to these parameters, covering cases in distinctly different dynamical regimes. In all, our work opens a new avenue for modeling complex neuronal network dynamics with artificial neural networks.

nlin.AO↗

arXiv2022

Multi-band oscillations emerge from a simple spiking network

In the brain, coherent neuronal activities often appear simultaneously in multiple frequency bands, e.g., as combinations of alpha (8-12 Hz), beta (12.5-30 Hz), gamma (30-120 Hz) oscillations, among others. These rhythms are believed to underlie information processing and cognitive functions and have been subjected to intense experimental and theoretical scrutiny. Computational modeling has provided a framework for the emergence of network-level oscillatory behavior from the interaction of spiking neurons. However, due to the strong nonlinear interactions between highly recurrent spiking populations, the interplay between cortical rhythms in multiple frequency bands has rarely been theoretically investigated. Many studies invoke multiple physiological timescales or oscillatory inputs to produce rhythms in multi-bands. Here we demonstrate the emergence of multi-band oscillations in a simple network consisting of one excitatory and one inhibitory neuronal population driven by constant input. First, we construct a data-driven, Poincaré section theory for robust numerical observations of single-frequency oscillations bifurcating into multiple bands. Then we develop model reductions of the stochastic, nonlinear, high-dimensional neuronal network to capture the appearance of multi-band dynamics and the underlying bifurcations theoretically. Furthermore, when viewed within the reduced state space, our analysis reveals conserved geometrical features of the bifurcations on low-dimensional dynamical manifolds. These results suggest a simple geometric mechanism behind the emergence of multi-band oscillations without appealing to oscillatory inputs or multiple synaptic or neuronal timescales. Thus our work points to unexplored regimes of stochastic competition between excitation and inhibition behind the generation of dynamic, patterned neuronal activities.

q-bio.NC↗

arXiv2021

A data-informed mean-field approach to mapping of cortical parameter landscapes

Constraining the many biological parameters that govern cortical dynamics is computationally and conceptually difficult because of the curse of dimensionality. This paper addresses these challenges by proposing (1) a novel data-informed mean-field (MF) approach to efficiently map the parameter space of network models; and (2) an organizing principle for studying parameter space that enables the extraction biologically meaningful relations from this high-dimensional data. We illustrate these ideas using a large-scale network model of the Macaque primary visual cortex. Of the 10-20 model parameters, we identify 7 that are especially poorly constrained, and use the MF algorithm in (1) to discover the firing rate contours in this 7D parameter cube. Defining a "biologically plausible" region to consist of parameters that exhibit spontaneous Excitatory and Inhibitory firing rates compatible with experimental values, we find that this region is a slightly thickened codimension-1 submanifold. An implication of this finding is that while plausible regimes depend sensitively on parameters, they are also robust and flexible provided one compensates appropriately when parameters are varied. Our organizing principle for conceptualizing parameter dependence is to focus on certain 2D parameter planes that govern lateral inhibition: Intersecting these planes with the biologically plausible region leads to very simple geometric structures which, when suitably scaled, have a universal character independent of where the intersections are taken. In addition to elucidating the geometry of the plausible region, this invariance suggests useful approximate scaling relations. Our study offers, for the first time, a complete characterization of the set of all biologically plausible parameters for a detailed cortical model, which has been out of reach due to the high dimensionality of parameter space.

q-bio.NC↗

arXiv2021

Model Reduction Captures Stochastic Gamma Oscillations on Low-Dimensional Manifolds

Gamma frequency oscillations (25-140 Hz), observed in the neural activities within many brain regions, have long been regarded as a physiological basis underlying many brain functions, such as memory and attention. Among numerous theoretical and computational modeling studies, gamma oscillations have been found in biologically realistic spiking network models of the primary visual cortex. However, due to its high dimensionality and strong nonlinearity, it is generally difficult to perform detailed theoretical analysis of the emergent gamma dynamics. Here we propose a suite of Markovian model reduction methods with varying levels of complexity and applied it to spiking network models exhibiting heterogeneous dynamical regimes, ranging from homogeneous firing to strong synchrony in the gamma band. The reduced models not only successfully reproduce gamma band oscillations in the full model, but also exhibit the same dynamical features as we vary parameters. Most remarkably, the invariant measure of the coarse-grained Markov process reveals a two-dimensional surface in state space upon which the gamma dynamics mainly resides. Our results suggest that the statistical features of gamma oscillations strongly depend on the subthreshold neuronal distributions. Because of the generality of the Markovian assumptions, our dimensional reduction methods offer a powerful toolbox for theoretical examinations of many other complex cortical spatio-temporal behaviors observed in both neurophysiological experiments and numerical simulations.

q-bio.NC↗