arXiv subjects

Joanna Tyrcha

Publications and source records attributed to Joanna Tyrcha.

7 recordsLinked to original sources

arXiv2025

Glassy dynamics near the interpolation transition in deep recurrent networks

We examine learning dynamics in deep recurrent networks, focusing on the behavior near the boundary in the depth-width plane separating under- from over-parametrized networks, known as the interpolation transition. The training data are Bach chorales in 4-part harmony, and the learning is by stochastic gradient descent with a cross-entropy loss function. We find critical slowing down of the learning approaching the transition from the overparametrized side: For a given network depth, learning times to reach small training loss values appear to diverge proportional to $1/(w - w_c)$ as the width w approaches a (loss-dependent) critical value $w_c$. We identify the zero-loss limit of this value with the interpolation transition. We also study aging (the slowing down of fluctuations as the time since the beginning of learning increases). Taking a system that has been learning for a time $τ_w$, we measure the subsequent mean-square fluctuations of the weight values at times $τ> τ_w$. In the underparametrized phase, we find that they are well-described by a single function of $τ/τ_w$. While this scaling holds approximately at short times at the transition and in the overparametrized phase, it breaks down at longer times when the training loss gets close to the lower limit imposed by the stochastic gradient descent dynamics. Both this kind of aging and the critical slowing down are also found in certain spin glass models, suggesting that those models contain the most essential features of the learning dynamics.

cond-mat.dis-nn↗

arXiv2018

Stochastic activation in a genetic switch model

We study a biological autoregulation process, involving a protein that enhances its own transcription, in a parameter region where bistability would be present in the absence of fluctuations. We calculate the rate of fluctuation-induced rare transitions between locally-stable states using a path integral formulation and Master and Chapman-Kolmogorov equations. As in simpler models for rare transitions, the rate has the form of the exponential of a quantity $S_0$ (a "barrier") multiplied by a prefactor $η$. We calculate $S_0$ and $η$ first in the bursting limit (where the ratio $γ$ of the protein and mRNA lifetimes is very large). In this limit, the calculation can be done almost entirely analytically, and the results are in good agreement with simulations. For finite $γ$ numerical calculations are generally required. However, $S_0$ can be calculated analytically to first order in $1/γ$, and the result agrees well with the full numerical calculation for all $γ> 1$. Employing a method used previously on other problems, we find we can account qualitatively for the way the prefactor $η$ varies with $γ$, but its value is 15-20% higher than that inferred from simulations.

physics.bio-ph↗

arXiv2014

Belief-Propagation and replicas for inference and learning in a kinetic Ising model with hidden spins

We propose a new algorithm for inferring the state of hidden spins and reconstructing the connections in a synchronous kinetic Ising model, given the observed history. Focusing on the case in which the hidden spins are conditionally independent of each other given the state of observable spins, we show that calculating the likelihood of the data can be simplified by introducing a set of replicated auxiliary spins. Belief Propagation (BP) and Susceptibility Propagation (SusP) can then be used to infer the states of hidden variables and learn the couplings. We study the convergence and performance of this algorithm for networks with both Gaussian-distributed and binary bonds. We also study how the algorithm behaves as the fraction of hidden nodes and the amount of data are changed, showing that it outperforms the TAP equations for reconstructing the connections.

cond-mat.dis-nn↗

arXiv2013

The Effect of Nonstationarity on Models Inferred from Neural Data

Neurons subject to a common non-stationary input may exhibit a correlated firing behavior. Correlations in the statistics of neural spike trains also arise as the effect of interaction between neurons. Here we show that these two situations can be distinguished, with machine learning techniques, provided the data are rich enough. In order to do this, we study the problem of inferring a kinetic Ising model, stationary or nonstationary, from the available data. We apply the inference procedure to two data sets: one from salamander retinal ganglion cells and the other from a realistic computational cortical network model. We show that many aspects of the concerted activity of the salamander retinal neurons can be traced simply to the external input. A model of non-interacting neurons subject to a non-stationary external field outperforms a model with stationary input with couplings between neurons, even accounting for the differences in the number of model parameters. When couplings are added to the non-stationary model, for the retinal data, little is gained: the inferred couplings are generally not significant. Likewise, the distribution of the sizes of sets of neurons that spike simultaneously and the frequency of spike patterns as function of their rank (Zipf plots) are well-explained by an independent-neuron model with time-dependent external input, and adding connections to such a model does not offer significant improvement. For the cortical model data, robust couplings, well correlated with the real connections, can be inferred using the non-stationary model. Adding connections to this model slightly improves the agreement with the data for the probability of synchronous spikes but hardly affects the Zipf plot.

q-bio.QM↗

arXiv2013

Network Inference with Hidden Units

We derive learning rules for finding the connections between units in stochastic dynamical networks from the recorded history of a ``visible'' subset of the units. We consider two models. In both of them, the visible units are binary and stochastic. In one model the ``hidden'' units are continuous-valued, with sigmoidal activation functions, and in the other they are binary and stochastic like the visible ones. We derive exact learning rules for both cases. For the stochastic case, performing the exact calculation requires, in general, repeated summations over an number of configurations that grows exponentially with the size of the system and the data length, which is not feasible for large systems. We derive a mean field theory, based on a factorized ansatz for the distribution of hidden-unit states, which offers an attractive alternative for large systems. We present the results of some numerical calculations that illustrate key features of the two models and, for the stochastic case, the exact and approximate calculations.

cond-mat.dis-nn↗

arXiv2011

Ising Models for Inferring Network Structure From Spike Data

Now that spike trains from many neurons can be recorded simultaneously, there is a need for methods to decode these data to learn about the networks that these neurons are part of. One approach to this problem is to adjust the parameters of a simple model network to make its spike trains resemble the data as much as possible. The connections in the model network can then give us an idea of how the real neurons that generated the data are connected and how they influence each other. In this chapter we describe how to do this for the simplest kind of model: an Ising network. We derive algorithms for finding the best model connection strengths for fitting a given data set, as well as faster approximate algorithms based on mean field theory. We test the performance of these algorithms on data from model networks and experiments.

q-bio.QM↗

arXiv2009

The Ising Model for Neural Data: Model Quality and Approximate Methods for Extracting Functional Connectivity

We study pairwise Ising models for describing the statistics of multi-neuron spike trains, using data from a simulated cortical network. We explore efficient ways of finding the optimal couplings in these models and examine their statistical properties. To do this, we extract the optimal couplings for subsets of size up to 200 neurons, essentially exactly, using Boltzmann learning. We then study the quality of several approximate methods for finding the couplings by comparing their results with those found from Boltzmann learning. Two of these methods- inversion of the TAP equations and an approximation proposed by Sessak and Monasson- are remarkably accurate. Using these approximations for larger subsets of neurons, we find that extracting couplings using data from a subset smaller than the full network tends systematically to overestimate their magnitude. This effect is described qualitatively by infinite-range spin glass theory for the normal phase. We also show that a globally-correlated input to the neurons in the network lead to a small increase in the average coupling. However, the pair-to-pair variation of the couplings is much larger than this and reflects intrinsic properties of the network. Finally, we study the quality of these models by comparing their entropies with that of the data. We find that they perform well for small subsets of the neurons in the network, but the fit quality starts to deteriorate as the subset size grows, signalling the need to include higher order correlations to describe the statistics of large networks.

q-bio.QM↗