Active inference offers a first principle account of sentient behavior, from which special and important cases—for example, reinforcement learning, active learning, Bayes optimal inference, Bayes optimal design—can be derived. Active inference finesses the exploitation-exploration dilemma in relation to prior preferences by placing information gain on the same footing as reward or value. In brief,

Backdoor data poisoning attacks add mislabeled examples to the training set, with an embedded backdoor pattern, so that the classifier learns to classify to a target class whenever the backdoor pattern is present in a test sample. Here, we address posttraining detection of scene-plausible perceptible backdoors, a type of backdoor attack that can be relatively easily fashioned, particularly against

It is of great interest to characterize the spiking activity of individual neurons in a cell ensemble. Many different mechanisms, such as synaptic coupling and the spiking activity of itself and its neighbors, drive a cell's firing properties. Though this is a widely studied modeling problem, there is still room to develop modeling solutions by simplifications embedded in previous models. The first

We propose a novel biologically plausible solution to the credit assignment problem motivated by observations in the ventral visual pathway and trained deep neural networks. In both, representations of objects in the same category become progressively more similar, while objects belonging to different categories become less similar. We use this observation to motivate a layer-specific learning goal

Pairwise similarities and dissimilarities between data points are often obtained more easily than full labels of data in real-world classification problems. To make use of such pairwise information, an empirical risk minimization approach has been proposed, where an unbiased estimator of the classification risk is computed from only pairwise similarities and unlabeled data. However, this approach has

This letter introduces a new framework for quantifying predictive uncertainty for both data and models that rely on projecting the data into a gaussian reproducing kernel Hilbert space (RKHS) and transforming the data probability density function (PDF) in a way that quantifies the flow of its gradient as a topological potential field quantified at all points in the sample space. This enables the decomposition

The relationship between complex brain oscillations and the dynamics of individual neurons is poorly understood. Here we utilize maximum caliber, a dynamical inference principle, to build a minimal yet general model of the collective (mean field) dynamics of large populations of neurons. In agreement with previous experimental observations, we describe a simple, testable mechanism, involving only a

The expected free energy (EFE) is a central quantity in the theory of active inference. It is the quantity that all active inference agents are mandated to minimize through action, and its decomposition into extrinsic and intrinsic value terms is key to the balance of exploration and exploitation that active inference agents evince. Despite its importance, the mathematical origins of this quantity

Surprise-based learning allows agents to rapidly adapt to nonstationary stochastic environments characterized by sudden changes. We show that exact Bayesian inference in a hierarchical model gives rise to a surprise-modulated trade-off between forgetting old observations and integrating them with the new ones. The modulation depends on a probability ratio, which we call the Bayes factor surprise, that

Hopfield neural networks have been extended using hypercomplex numbers. The algebra of bicomplex numbers, also referred to as commutative quaternions, is a number system of dimension 4. Since the multiplication is commutative, many notions and theories of linear algebra, such as determinant, are available, unlike quaternions. A bicomplex-valued Hopfield neural network (BHNN) has been proposed as a

Our goal is to understand and optimize human concept learning by predicting the ease of learning of a particular exemplar or category. We propose a method for estimating ease values, quantitative measures of ease of learning, as an alternative to conducting costly empirical training studies. Our method combines a psychological embedding of domain exemplars with a pragmatic categorization model. The

Spike trains with negative interspike interval (ISI) correlations, in which long/short ISIs are more likely followed by short/long ISIs, are common in many neurons. They can be described by stochastic models with a spike-triggered adaptation variable. We analyze a phenomenon in these models where such statistically dependent ISI sequences arise in tandem with quasi-statistically independent and identically

Formation of stimulus equivalence classes has been recently modeled through equivalence projective simulation (EPS), a modified version of a projective simulation (PS) learning agent. PS is endowed with an episodic memory that resembles the internal representation in the brain and the concept of cognitive maps. PS flexibility and interpretability enable the EPS model and, consequently the model we

We propose a novel neural model with lateral interaction for learning tasks. The model consists of two functional fields: an elementary field to extract features and a high-level field to store and recognize patterns. Each field is composed of some neurons with lateral interaction, and the neurons in different fields are connected by the rules of synaptic plasticity. The model is established on the

The positive-negative axis of emotional valence has long been recognized as fundamental to adaptive behavior, but its origin and underlying function have largely eluded formal theorizing and computational modeling. Using deep active inference, a hierarchical inference scheme that rests on inverting a model of how sensory data are generated, we develop a principled Bayesian model of emotional valence

Neuronal networks in rodent primary visual cortex (V1) can generate oscillations in different frequency bands depending on the network state and the level of visual stimulation. High-frequency gamma rhythms, for example, dominate the network's spontaneous activity in adult mice but are attenuated upon visual stimulation, during which the network switches to the beta band instead. The spontaneous local

This work addresses the problem of network pruning and proposes a novel joint training method based on a multiobjective optimization model. Most of the state-of-the-art pruning methods rely on user experience for selecting the sparsity ratio of the weight matrices or tensors, and thus suffer from severe performance reduction with inappropriate user-defined parameters. Moreover, networks might be inferior

Brains process information in spiking neural networks. Their intricate connections shape the diverse functions these networks perform. Yet how network connectivity relates to function is poorly understood, and the functional capabilities of models of spiking networks are still rudimentary. The lack of both theoretical insight and practical algorithms to find the necessary connectivity poses a major

We study the learning dynamics and the representations emerging in recurrent neural networks (RNNs) trained to integrate one or multiple temporal signals. Combining analytical and numerical investigations, we characterize the conditions under which an RNN with n neurons learns to integrate D(≪n) scalar signals of arbitrary duration. We show, for linear, ReLU, and sigmoidal neurons, that the internal

Spatial Monte Carlo integration (SMCI) is an extension of standard Monte Carlo integration and can approximate expectations on Markov random fields with high accuracy. SMCI was applied to pairwise Boltzmann machine (PBM) learning, achieving superior results over those of some existing methods. The approximation level of SMCI can be altered, and it was proved that a higher-order approximation of SMCI

A new network with super-approximation power is introduced. This network is built with Floor (⌊x⌋) or ReLU (max{0,x}) activation function in each neuron; hence, we call such networks Floor-ReLU networks. For any hyperparameters N∈N+ and L∈N+, we show that Floor-ReLU networks with width max{d,5N+13} and depth 64dL+3 can uniformly approximate a Hölder function f on [0,1]d with an approximation error

Sustained attention is a cognitive ability to maintain task focus over extended periods of time (Mackworth, 1948; Chun, Golomb, & Turk-Browne, 2011). In this study, scalp electroencephalography (EEG) signals were processed in real time using a 32 dry-electrode system during a sustained visual attention task. An attention training paradigm was implemented, as designed in DeBettencourt, Cohen, Lee, Norman

In this note, I study how the precision of a binary classifier depends on the ratio r of positive to negative cases in the test set, as well as the classifier's true and false-positive rates. This relationship allows prediction of how the precision-recall curve will change with r, which seems not to be well known. It also allows prediction of how Fβ and the precision gain and recall gain measures of

Empirical estimates of the dimensionality of neural population activity are often much lower than the population size. Similar phenomena are also observed in trained and designed neural network models. These experimental and computational results suggest that mapping low-dimensional dynamics to high-dimensional neural space is a common feature of cortical computation. Despite the ubiquity of this observation

Stable concurrent learning and control of dynamical systems is the subject of adaptive control. Despite being an established field with many practical applications and a rich theory, much of the development in adaptive control for nonlinear systems revolves around a few key algorithms. By exploiting strong connections between classical adaptive nonlinear control techniques and recent progress in optimization

Our work focuses on unsupervised and generative methods that address the following goals: (1) learning unsupervised generative representations that discover latent factors controlling image semantic attributes, (2) studying how this ability to control attributes formally relates to the issue of latent factor disentanglement, clarifying related but dissimilar concepts that had been confounded in the

Active inference is a first principle account of how autonomous agents operate in dynamic, nonstationary environments. This problem is also considered in reinforcement learning, but limited work exists on comparing the two approaches on the same discrete-state environments. In this letter, we provide (1) an accessible overview of the discrete-state formulation of active inference, highlighting natural

Recent work suggests that changing convolutional neural network (CNN) architecture by introducing a bottleneck in the second layer can yield changes in learned function. To understand this relationship fully requires a way of quantitatively comparing trained networks. The fields of electrophysiology and psychophysics have developed a wealth of methods for characterizing visual systems that permit such

A central theme in computational neuroscience is determining the neural correlates of efficient and accurate coding of sensory signals. Diversity, or heterogeneity, of intrinsic neural attributes is known to exist in many brain areas and is thought to significantly affect neural coding. Recent theoretical and experimental work has argued that in uncoupled networks, coding is most accurate at intermediate

This article proposes a methodology to extract a low-dimensional integrate-and-fire model from an arbitrarily detailed single-compartment biophysical model. The method aims at relating the modulation of maximal conductance parameters in the biophysical model to the modulation of parameters in the proposed integrate-and-fire model. The approach is illustrated on two well-documented examples of cellular

We discuss stability analysis for uncertain stochastic neural networks (SNNs) with time delay in this letter. By constructing a suitable Lyapunov-Krasovskii functional (LKF) and utilizing Wirtinger inequalities for estimating the integral inequalities, the delay-dependent stochastic stability conditions are derived in terms of linear matrix inequalities (LMIs). We discuss the parameter uncertainties

Mild traumatic brain injury (mTBI) presents a significant health concern with potential persisting deficits that can last decades. Although a growing body of literature improves our understanding of the brain network response and corresponding underlying cellular alterations after injury, the effects of cellular disruptions on local circuitry after mTBI are poorly understood. Our group recently reported

The intrinsic electrophysiological properties of single neurons can be described by a broad spectrum of models, from realistic Hodgkin-Huxley-type models with numerous detailed mechanisms to the phenomenological models. The adaptive exponential integrate-and-fire (AdEx) model has emerged as a convenient middle-ground model. With a low computational cost but keeping biophysical interpretation of the

Working memory is essential: it serves to guide intelligent behavior of humans and nonhuman primates when task-relevant stimuli are no longer present to the senses. Moreover, complex tasks often require that multiple working memory representations can be flexibly and independently maintained, prioritized, and updated according to changing task demands. Thus far, neural network models of working memory

Nonlinear interactions in the dendritic tree play a key role in neural computation. Nevertheless, modeling frameworks aimed at the construction of large-scale, functional spiking neural networks, such as the Neural Engineering Framework, tend to assume a linear superposition of postsynaptic currents. In this letter, we present a series of extensions to the Neural Engineering Framework that facilitate

Recent advances in weakly supervised classification allow us to train a classifier from only positive and unlabeled (PU) data. However, existing PU classification methods typically require an accurate estimate of the class-prior probability, a critical bottleneck particularly for high-dimensional data. This problem has been commonly addressed by applying principal component analysis in advance, but

We investigate a latent variable model for multinomial classification inspired by recent capsule architectures for visual object recognition (Sabour, Frosst, & Hinton, 2017). Capsule architectures use vectors of hidden unit activities to encode the pose of visual objects in an image, and they use the lengths of these vectors to encode the probabilities that objects are present. Probabilities from different

Backpropagation (BP) is the cornerstone of today's deep learning algorithms, but it is inefficient partially because of backward locking, which means updating the weights of one layer locks the weight updates in the other layers. Consequently, it is challenging to apply parallel computing or a pipeline structure to update the weights in different layers simultaneously. In this letter, we introduce

Stemming from information-theoretic learning, the correntropy criterion and its applications to machine learning tasks have been extensively studied and explored. Its application to regression problems leads to the robustness-enhanced regression paradigm: correntropy-based regression. Having drawn a great variety of successful real-world applications, its theoretical properties have also been investigated

This letter proposes a new idea to improve learning efficiency in reinforcement learning (RL) with the actor-critic method used as a muscle controller for posture stabilization of the human arm. Actor-critic RL (ACRL) is used for simulations to realize posture controls in humans or robots using muscle tension control. However, it requires very high computational costs to acquire a better muscle control

Testing under what conditions a product satisfies the desired properties is a fundamental problem in manufacturing industry. If the condition and the property are respectively regarded as the input and the output of a black-box function, this task can be interpreted as the problem called level set estimation (LSE): the problem of identifying input regions such that the function value is above (or below)

The ability to encode and manipulate data structures with distributed neural representations could qualitatively enhance the capabilities of traditional neural networks by supporting rule-based symbolic reasoning, a central property of cognition. Here we show how this may be accomplished within the framework of Vector Symbolic Architectures (VSAs) (Plate, 1991; Gayler, 1998; Kanerva, 1996), whereby

Pruning is an effective way to slim and speed up convolutional neural networks. Generally previous work directly pruned neural networks in the original feature space without considering the correlation of neurons. We argue that such a way of pruning still keeps some redundancy in the pruned networks. In this letter, we proposed to prune in the intermediate space in which the correlation of neurons

We develop theoretical foundations of resonator networks, a new type of recurrent neural network introduced in Frady, Kent, Olshausen, and Sommer (2020), a companion article in this issue, to solve a high-dimensional vector factorization problem arising in Vector Symbolic Architectures. Given a composite vector formed by the Hadamard product between a discrete set of high-dimensional vectors, a resonator

The brain may be considered as a synchronized dynamic network with several coherent dynamical units. However, concerns remain whether synchronizability is a stable state in the brain networks. If so, which index can best reveal the synchronizability in brain networks? To answer these questions, we tested the application of the spectral graph theory and the Shannon entropy as alternative approaches

In this study, we integrated neural encoding and decoding into a unified framework for spatial information processing in the brain. Specifically, the neural representations of self-location in the hippocampus (HPC) and entorhinal cortex (EC) play crucial roles in spatial navigation. Intriguingly, these neural representations in these neighboring brain areas show stark differences. Whereas the place

Measuring functional connectivity from fMRI recordings is important in understanding processing in cortical networks. However, because the brain's connection pattern is complex, currently used methods are prone to producing false functional connections. We introduce differential covariance analysis, a new method that uses derivatives of the signal for estimating functional connectivity. We generated

Spiking neural networks (SNNs) with the event-driven manner of transmitting spikes consume ultra-low power on neuromorphic chips. However, training deep SNNs is still challenging compared to convolutional neural networks (CNNs). The SNN training algorithms have not achieved the same performance as CNNs. In this letter, we aim to understand the intrinsic limitations of SNN training to design better

Hierarchical sparse coding (HSC) is a powerful model to efficiently represent multidimensional, structured data such as images. The simplest solution to solve this computationally hard problem is to decompose it into independent layer-wise subproblems. However, neuroscientific evidence would suggest interconnecting these subproblems as in predictive coding (PC) theory, which adds top-down connections

Recent remarkable advances in experimental techniques have provided a background for inferring neuronal couplings from point process data that include a great number of neurons. Here, we propose a systematic procedure for pre- and postprocessing generic point process data in an objective manner to handle data in the framework of a binary simple statistical model, the Ising or generalized McCulloch–Pitts

According to the neuromuscular model of virtual trajectory control, the postures and movements of limbs are performed by shifting the equilibrium positions determined by agonist and antagonist muscle activities. In this study, we develop virtual trajectory control for the reaching movements of a multi-joint arm, introducing a proportional-derivative feedback control scheme. In virtual trajectory control

Marked point process models have recently been used to capture the coding properties of neural populations from multiunit electrophysiological recordings without spike sorting. These clusterless models have been shown in some instances to better describe the firing properties of neural populations than collections of receptive field models for sorted neurons and to lead to better decoding results.

A complex-valued Hopfield neural network (CHNN) with a multistate activation function is a multistate model of neural associative memory. The weight parameters need a lot of memory resources. Twin-multistate activation functions were introduced to quaternion- and bicomplex-valued Hopfield neural networks. Since their architectures are much more complicated than that of CHNN, the architecture should

The cerebellum is known to have an important role in sensing and execution of precise time intervals, but the mechanism by which arbitrary time intervals can be recognized and replicated with high precision is unknown. We propose a computational model in which precise time intervals can be identified from the pattern of individual spike activity in a population of parallel fibers in the cerebellar

A reflex is a simple closed-loop control approach that tries to minimize an error but fails to do so because it will always react too late. An adaptive algorithm can use this error to learn a forward model with the help of predictive cues. For example, a driver learns to improve steering by looking ahead to avoid steering in the last minute. In order to process complex cues such as the road ahead,

This letter proves that a ReLU network can approximate any continuous function with arbitrary precision by means of piecewise linear or constant approximations. For univariate function f(x), we use the composite of ReLUs to produce a line segment; all of the subnetworks of line segments comprise a ReLU network, which is a piecewise linear approximation to f(x). For multivariate function f(x), ReLU

This letter considers a class of biologically plausible cost functions for neural networks, where the same cost function is minimized by both neural activity and plasticity. We show that such cost functions can be cast as a variational bound on model evidence under an implicit generative model. Using generative models based on partially observed Markov decision processes (POMDP), we show that neural

Fox and Lu introduced a Langevin framework for discrete-time stochastic models of randomly gated ion channels such as the Hodgkin-Huxley (HH) system. They derived a Fokker-Planck equation with state-dependent diffusion tensor D and suggested a Langevin formulation with noise coefficient matrix S such that SS⊤=D. Subsequently, several authors introduced a variety of Langevin equations for the HH system

In this letter, we study an active learning problem for maximizing an unknown linear function with high-dimensional binary features. This problem is notoriously complex but arises in many important contexts. When the sampling budget, that is, the number of possible function evaluations, is smaller than the number of dimensions, it tends to be impossible to identify all of the optimal binary features

In this letter, we study a class of the regularized regression algorithms when the sampling process is unbounded. By choosing different loss functions, the learning algorithms can include a wide range of commonly used algorithms for regression. Unlike the prior work on theoretical analysis of unbounded sampling, no constraint on the output variables is specified in our setting. By an elegant error