arXiv subjects

Taro Toyoizumi

Publications and source records attributed to Taro Toyoizumi.

30 records · Page 2Linked to original sources

arXiv2019

Robust random search with scale-free stochastic resetting

A new model of search based on stochastic resetting is introduced, wherein rate of resets depends explicitly on time elapsed since the beginning of the process. It is shown that rate inversely proportional to time leads to paradoxical diffusion which mixes self-similarity and linear growth of the mean square displacement with non-locality and non-Gaussian propagator. It is argued that such resetting protocol offers a general and efficient search-boosting method that does not need to be optimized with respect to the scale of the underlying search problem (e.g., distance to the goal) and is not very sensitive to other search parameters. Both subdiffusive and superdiffusive regimes of the mean squared displacement scaling are demonstrated with more general rate functions.

cond-mat.stat-mech↗

arXiv2017

Reinforced stochastic gradient descent for deep neural network learning

Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the high-dimensional parameter space. Therefore, it is highly desirable to design an efficient algorithm to escape from these saddle points and reach a parameter region of better generalization capabilities. Here, we propose a simple extension of SGD, namely reinforced SGD, which simply adds previous first-order gradients in a stochastic manner with a probability that increases with learning time. As verified in a simple synthetic dataset, this method significantly accelerates learning compared with the original SGD. Surprisingly, it dramatically reduces over-fitting effects, even compared with state-of-the-art adaptive learning algorithm---Adam. For a benchmark handwritten digits dataset, the learning performance is comparable to Adam, yet with an extra advantage of requiring one-fold less computer memory. The reinforced SGD is also compared with SGD with fixed or adaptive momentum parameter and Nesterov's momentum, which shows that the proposed framework is able to reach a similar generalization accuracy with less computational costs. Overall, our method introduces stochastic memory into gradients, which plays an important role in understanding how gradient-based training algorithms can work and its relationship with generalization abilities of deep networks.

cs.LG↗

arXiv2017

Emergence of Lévy walks from second order stochastic optimization

In natural foraging, many organisms seem to perform two different types of motile search: directed search (taxis) and random search. The former is observed when the environment provides cues to guide motion towards a target. The latter involves no apparent memory or information processing and can be mathematically modeled by random walks. We show that both types of search can be generated by a common mechanism in which Lévy flights or Lévy walks emerge from a second-order gradient-based search with noisy observations. No explicit switching mechanism is required -- instead, continuous transitions between the directed and random motions emerge depending on the Hessian matrix of the cost function. For a wide range of scenarios the Lévy tail index is $α=1$, consistent with previous observations in foraging organisms. These results suggest that adopting a second-order optimization method can be a useful strategy to combine efficient features of directed and random search.

cond-mat.stat-mech↗

arXiv2017

Locally embedded presages of global network bursts

Spontaneous, synchronous bursting of neural population is a widely observed phenomenon in nervous networks, which is considered important for functions and dysfunctions of the brain. However, how the global synchrony across a large number of neurons emerges from an initially non-bursting network state is not fully understood. In this study, we develop a new state-space reconstruction method combined with high-resolution recordings of cultured neurons. This method extracts deterministic signatures of upcoming global bursts in "local" dynamics of individual neurons during non-bursting periods. We find that local information within a single-cell time series can compare with or even outperform the global mean field activity for predicting future global bursts. Moreover, the inter-cell variability in the burst predictability is found to reflect the network structure realized in the non-bursting periods. These findings demonstrate the deterministic mechanisms underlying the locally concentrated early-warnings of the global state transition in self-organized networks.

q-bio.NC↗

arXiv2016

Unsupervised feature learning from finite data by message passing: discontinuous versus continuous phase transition

Unsupervised neural network learning extracts hidden features from unlabeled training data. This is used as a pretraining step for further supervised learning in deep networks. Hence, understanding unsupervised learning is of fundamental importance. Here, we study the unsupervised learning from a finite number of data, based on the restricted Boltzmann machine learning. Our study inspires an efficient message passing algorithm to infer the hidden feature, and estimate the entropy of candidate features consistent with the data. Our analysis reveals that the learning requires only a few data if the feature is salient and extensively many if the feature is weak. Moreover, the entropy of candidate features monotonically decreases with data size and becomes negative (i.e., entropy crisis) before the message passing becomes unstable, suggesting a discontinuous phase transition. In terms of convergence time of the message passing algorithm, the unsupervised learning exhibits an easy-hard-easy phenomenon as the training data size increases. All these properties are reproduced in an approximate Hopfield model, with an exception that the entropy crisis is absent, and only continuous phase transition is observed. This key difference is also confirmed in a handwritten digits dataset. This study deepens our understanding of unsupervised learning from a finite number of data, and may provide insights into its role in training deep networks.

cond-mat.dis-nn↗

arXiv2016

Brain State Control by Closed-Loop Environmental Feedback

Brain state regulates sensory processing and motor control for adaptive behavior. Internal mechanisms of brain state control are well studied, but the role of external modulation from the environment is not well understood. Here, we examined the role of closed-loop environmental (CLE) feedback, in comparison to open-loop sensory input, on brain state and behavior in diverse vertebrate systems. In fictively swimming zebrafish, CLE feedback for optomotor stability controlled brain state by reducing coherent neuronal activity. The role of CLE feedback in brain state was also shown in a model of rodent active whisking, where brief interruptions in this feedback enhanced signal-to-noise ratio for detecting touch. Finally, in monkey visual fixation, artificial CLE feedback suppressed stimulus-specific neuronal activity and improved behavioral performance. Our findings show that the environment mediates continuous closed-loop feedback that controls neuronal gain, regulating brain state, and that brain function is an emergent property of brain-environment interactions.

q-bio.NC↗

arXiv2016

Clustering of neural codewords revealed by a first-order phase transition

A network of neurons in the central nervous system collectively represents information by its spiking activity states. Typically observed states, i.e., codewords, occupy only a limited portion of the state space due to constraints imposed by network interactions. Geometrical organization of codewords in the state space, critical for neural information processing, is poorly understood due to its high dimensionality. Here, we explore the organization of neural codewords using retinal data by computing the entropy of codewords as a function of Hamming distance from a particular reference codeword. Specifically, we report that the retinal codewords in the state space are divided into multiple distinct clusters separated by entropy-gaps, and that this structure is shared with well-known associative memory networks in a recallable phase. Our analysis also elucidates a special nature of the all-silent state. The all-silent state is surrounded by the densest cluster of codewords and located within a reachable distance from most codewords. This codeword-space structure quantitatively predicts typical deviation of a state-trajectory from its initial state. Altogether, our findings reveal a non-trivial heterogeneous structure of the codeword-space that shapes information representation in a biological network.

q-bio.NC↗

arXiv2015

Advanced Mean Field Theory of Restricted Boltzmann Machine

Learning in restricted Boltzmann machine is typically hard due to the computation of gradients of log-likelihood function. To describe the network state statistics of the restricted Boltzmann machine, we develop an advanced mean field theory based on the Bethe approximation. Our theory provides an efficient message passing based method that evaluates not only the partition function (free energy) but also its gradients without requiring statistical sampling. The results are compared with those obtained by the computationally expensive sampling based method.

cond-mat.stat-mech↗

arXiv2015

Structure of attractors in randomly connected networks

The deterministic dynamics of randomly connected neural networks are studied, where a state of binary neurons evolves according to a discreet-time synchronous update rule. We give a theoretical support that the overlap of systems' states between the current and a previous time develops in time according to a Markovian stochastic process in large networks. This Markovian process predicts how often a network revisits one of previously visited states, depending on the system size. The state concentration probability, i.e., the probability that two distinct states co-evolve to the same state, is utilized to analytically derive various characteristics that quantify attractors' structure. The analytical predictions about the total number of attractors, the typical cycle length, and the number of states belonging to all attractive cycles match well with numerical simulations for relatively large system sizes.

cond-mat.stat-mech↗

arXiv2013

State Concentration Exponent as a Measure of Quickness in Kauffman-type Networks

We study the dynamics of randomly connected networks composed of binary Boolean elements and those composed of binary majority vote elements. We elucidate their differences in both sparsely and densely connected cases. The quickness of large network dynamics is usually quantified by the length of transient paths, an analytically intractable measure. For discrete-time dynamics of networks of binary elements, we address this dilemma with an alternative unified framework by using a concept termed state concentration, defined as the exponent of the average number of t-step ancestors in state transition graphs. The state transition graph is defined by nodes corresponding to network states and directed links corresponding to transitions. Using this exponent, we interrogate the dynamics of random Boolean and majority vote networks. We find that extremely sparse Boolean networks and majority vote networks with arbitrary density achieve quickness, owing in part to long-tailed in-degree distributions. As a corollary, only relatively dense majority vote networks can achieve both quickness and robustness.

cond-mat.dis-nn↗

arXiv2012

Nearly extensive sequential memory lifetime achieved by coupled nonlinear neurons

Many cognitive processes rely on the ability of the brain to hold sequences of events in short-term memory. Recent studies have revealed that such memory can be read out from the transient dynamics of a network of neurons. However, the memory performance of such a network in buffering past information has only been rigorously estimated in networks of linear neurons. When signal gain is kept low, so that neurons operate primarily in the linear part of their response nonlinearity, the memory lifetime is bounded by the square root of the network size. In this work, I demonstrate that it is possible to achieve a memory lifetime almost proportional to the network size, "an extensive memory lifetime", when the nonlinearity of neurons is appropriately utilized. The analysis of neural activity revealed that nonlinear dynamics prevented the accumulation of noise by partially removing noise in each time step. With this error-correcting mechanism, I demonstrate that a memory lifetime of order $N/\log N$ can be achieved.

q-bio.NC↗

arXiv2005

Optimal Spike-Timing Dependent Plasticity for Precise Action Potential Firing

In timing-based neural codes, neurons have to emit action potentials at precise moments in time. We use a supervised learning paradigm to derive a synaptic update rule that optimizes via gradient ascent the likelihood of postsynaptic firing at one or several desired firing times. We find that the optimal strategy of up- and downregulating synaptic efficacies can be described by a two-phase learning window similar to that of Spike-Timing Dependent Plasticity (STDP). If the presynaptic spike arrives before the desired postsynaptic spike timing, our optimal learning rule predicts that the synapse should become potentiated. The dependence of the potentiation on spike timing directly reflects the time course of an excitatory postsynaptic potential. The presence and amplitude of depression of synaptic efficacies for reversed spike timing depends on how constraints are implemented in the optimization problem. Two different constraints, i.e., control of postsynaptic rates or control of temporal locality,are discussed.

q-bio.NC↗