A key challenge in visual object recognition is developing models that generalize from limited data while maintaining transparency in their decision making. We propose a biologically inspired model that addresses both issues by classifying images based on transformation-invariant local shape key features. Following the principles of the brain's what and where pathways, each feature is encoded by an image patch and its relative location in polar coordinates, enabling interpretable and robust comparisons between inputs and class prototypes. To mimic human concept learning, prototypes are selected using clustering, improving representativeness and generalization. Results show that our model achieves human-comparable performance, with an error rate between 1% and 2% on the MNIST data set when all training images are used as prototypes. In data-limited scenarios, where only a small number of prototypes are selected, our model consistently outperforms convolutional neural networks (CNNs). To evaluate out-of-distribution generalization, we use prototypes from MNIST and test both models on the ETL-1 data set, which differs in data distribution. Although CNN accuracy drops significantly under these conditions, our model maintains high accuracy, even with few prototypes, demonstrating strong robustness and greater capacity to generalize to unseen distributions, bringing it closer to human-like recognition capabilities.

This letter shows that generative diffusion processes converge to associative memory systems at vanishing noise levels and characterizes the stability, robustness, memorization, and generation dynamics of both model classes. Morse-Smale dynamical systems are shown to be universal approximators of associative memory models, with diffusion processes as their white-noise perturbations. The universal properties of associative memory that follow are used to characterize a generic transition from generation to memory as noise diminishes. The structural stability of Morse-Smale flows-that is, the robustness of their global critical point structure-implies the stability of both trajectories and invariant measures for diffusions in the zero-noise limit. The learning and generation landscapes of these models appear as parameterized families of gradient flows and their stochastic perturbations, and the bifurcation theory for Morse-Smale systems implies that they are generically stable except at isolated parameter values, where enumerable sets of local and global bifurcations govern transitions between stable systems. These landscapes are thus characterized by ordered bifurcation sequences that create, destroy, or alter connections between rest points and are robust under small stochastic or deterministic perturbations. The framework is agnostic to model formulation, which we verify with examples from energy-based models, denoising diffusion models, and classical and modern Hopfield networks. We additionally derive structural stability criteria for Hopfield-type networks and find that simple cases violate them. Collectively, our geometric approach provides insight into the classification, stability, and emergence of memory and generative landscapes.

The action potential constitutes the digital component of the signaling dynamics of neurons. But the biophysical nature of the full-time course of the action potential associated with changes in membrane potential is mathematically distinct from its representation as a discrete set of events that encode when action potentials are triggered in a collection of spike trains. In this letter, we develop from first principles a unified functional-analytic framework for neuronal spike trains, grounded in Schwartz distribution theory. We show how this representation provides an exact operational calculus for convolution, distributional differentiation, and distributional support, which enables closed-form analysis of spike train dynamics without discretization, rate approximation, or smoothing. We then analyze the framework in the context of a two-neuron reciprocal circuit with propagation latencies and refractoriness, deriving exact results for synaptic drive, spike timing sensitivity, and causal admissibility of inputs, quantities that are either ill-defined or require approximation in conventional treatments.

A cornerstone of our understanding of both biological and artificial neural networks is that they store information in the strengths of synaptic connections among the neurons. However, in contrast to the well-established theory for quantifying information encoded by the firing activity of neural networks, there does not exist a framework for quantifying information stored in the network's connection distribution itself. Here, we develop a theoretical framework for synaptic information by using densely connected Hebbian networks performing autoassociative memory tasks and by modeling data patterns to be stored as log-normal distributions. Specifically, we derive analytical approximations for Shannon mutual information between the data and singletons, pairs, and arbitrary n-tuples of synaptic connections within the network. Our framework corroborates well-established insights regarding pattern storage capacity, supports the principle of distributed coding in neural firing activities, and formalizes the heterogeneity inherent in information encoding across synapses in a network. Notably, it discovers synergistic interactions among synapses, revealing that the information encoded jointly by all the synapses exceeds the sum of its parts. Taken together, this study introduces a powerful, interpretable framework for quantitatively understanding information storage in the synapses of neural networks, one that illustrates the duality of synaptic connectivity and neural population activity in learning and memory.

In this letter, we propose Bayesian Tucker decomposition (BTuD) in which the residuals are supposed to follow. Although we have proposed an algorithm to perform the proposed BTuD, the conventional higher-order orthogonal iteration can generate Tucker decomposition consistent with the present implementation. Using the proposed BTuD, we can perform unsupervised feature selection successfully applied to various synthetic data sets, global coupled maps with randomized coupling strength, and gene expression profiles. Thus, we can conclude that our newly proposed unsupervised feature selection method is promising. In addition to this, BTuD-based unsupervised feature extraction (FE) is expected to coincide with TD-based unsupervised FE that were previously proposed and successfully applied to a wide range of problems.

Predictive coding frameworks suggest neural computations rely on hierarchical error minimization, yet the neural implementation of this inference remains unclear. We propose that cross-frequency coupling (CFC) furnishes fundamental mechanism for this process. Using our laminar neural mass model (LaNMM), we demonstrate that signal-envelope coupling (SEC) an envelope-envelope coupling (EEC) instantiate a hierarchical comparator mechanism. Specifically, SEC generates prediction-error signals by subtracting top-down predictions from bottom-up oscillatory envelopes, while EEC operates at slower timescales to implement gating-a critical mechanism for precision weighting. To establish the face validity and clinical implications of this proposal, we model perturbations of these CFC mechanisms to investigate their roles in pathophysiological and altered neuronal function. In Alzheimer's disease, interneuron dysfunction disrupts the comparator, causing aberrant prediction error amplification in early stages and drastic attenuation in late phases. Conversely, serotonergic psychedelics increase excitatory gain, diminishing the modulatory effect of predictions and causing a failure of sensory attenuation. Collectively, these findings implicate multiscale cross-frequency coupling as a key computational mechanism supporting predictive coding and its disruption in disease.

Although evidence integration to the boundary model has successfully explained a wide range of behavioral and neural data in decision making under uncertainty, how animals learn and optimize the boundary remains unresolved. Here, we propose a model-free reinforcement learning algorithm for perceptual decisions under uncertainty that implements a sequential sampling process with an implicit decision boundary. Our model learns whether to commit to a decision given the available evidence or continue sampling information at a cost. We reproduced the canonical features of perceptual decision making such as dependence of accuracy and reaction time on evidence strength, modulation of speed-accuracy trade-off by payoff regime, and many others. By unifying learning and decision making within the same framework, this model can inspire a new look at the mechanisms of flexibility in context-dependent changes of behavior.

In reinforcement learning (RL), temporal difference (TD) error is known to be related to the firing rate of dopamine neurons. It has been observed that each dopamine neuron does not behave uniformly, but each responds to the TD error in an optimistic or pessimistic manner, interpreted as a kind of distributional RL. To explain such biological data, a heuristic model has also been introduced with learning rates asymmetric for the positive and negative TD errors. However, this heuristic model is not theoretically grounded, and it is unknown whether it can work as an RL algorithm. This letter therefore introduces a novel theoretically grounded model with optimism and pessimism, which is derived from control as inference. In combination with ensemble learning, a distributional value function as a critic is estimated from regularly introduced optimism and pessimism. Based on its central value, a policy in an actor is improved. This proposed algorithm, so-called DROP (distributional and regular optimism and pessimism), is compared on dynamic tasks. Although the heuristic model showed poor learning performance, DROP demonstrated excellent performance in all tasks with high generality. In addition, DROP achieved learning performance comparable to the state-of-the-art algorithms. In other words, it was suggested that DROP is a new model that can elicit the potential contributions of optimism and pessimism.

Active inference, a neutrally inspired model for inferring actions based on the free energy principle (FEP), has been proposed as a unifying framework for understanding perception, action, and learning in the brain. Active inference has previously been used to model ecologically important tasks such as navigation and planning, but scaling it to solve complex large-scale problems in real-world environments has remained a challenge. Inspired by the existence of multiscale hierarchical representations in the brain, we propose a model for planning actions based on hierarchical active inference. Our approach combines a hierarchical model of the environment with successor representations for efficient planning. We present results demonstrating (1) how lower-level successor representations can be used to learn higher-level abstract states, (2) how planning based on active inference at the lower level can be used to bootstrap and learn higher-level abstract actions, and (3) how these learned higher-level abstract states and actions can facilitate efficient planning. We illustrate the performance of the approach on several planning and reinforcement learning (RL) problems, including a variant of the well-known four rooms task, a key-based navigation task, a partially observable planning problem, the mountain car problem, and PointMaze, a family of navigation tasks with continuous state and action spaces. Our results represent, to our knowledge, the first application of learned hierarchical state and action abstractions to active inference in FEP-based theories of brain function.

Evaluating the variability of posterior estimates is a key aspect of Bayesian model assessment. In this study, we focus on the posterior covariance matrix W, defined through the log likelihoods of individual observations. Previous studies, notably MacEachern and Peruggia (2002) and Thomas et al. (2018), examined the role of the principal space of W in Bayesian sensitivity analysis. Here, we show that the principal space of W is also central to frequentist evaluation, using the recently proposed Bayesian infinitesimal jackknife (Bayesian IJ) approximation (Giordano & Broderick, 2023) as a key tool. We further clarify the relationship between W and the Fisher kernel, showing that a modified version of the Fisher kernel can be viewed as an approximation to W. Moreover, the matrix W itself can be interpreted as a reproducing kernel, which we refer to as the W-kernel. Based on this connection, we investigate the relation between the W-kernel formulation in the data space and the classical asymptotic formulation in the parameter space. We also introduce the matrix Z, which is effectively dual to W in the sense of PCA; this formulation provides another perspective on the relationship between W and classical asymptotic theory. In the appendixes, we explore approximate bootstrap methods for posterior means and show that projection onto the principal space of W facilitates frequentist evaluation when higher-order terms are included. In addition, we introduce incomplete Cholesky decomposition as an efficient method for computing the principal space of W and discuss the concept of representative subsets of observations.

This letter introduces a novel method for discrete-sequence classification within the hyperdimensional computing (HDC) paradigm. The method, inspired by the concept of hidden Markov models (HMM), implements mechanisms that effectively address the major challenges arising in analyzing sequences generated by real-world processes, such as variable length, misalignment, symbol repetitions, omissions, or insertions. All algebraic transformations of input data in HMM-based sequence classification are replaced by bitwise operations on appropriately derived hyperdimensional binary vectors (hypervectors). The proposed hypervector transformation pipeline mirrors the algebraic manipulations of the HMM paradigm and involves a procedure that prevents information decay when processing longer sequences. Since only binary bit-wise operations on hypervectors are used in computations, the proposed method is well suited for hardware implementation, especially in the form of custom in-memory computing VLSI devices. The experimental evaluation of the proposed method, conducted on both artificial and real-world data sets, demonstrates its superiority over existing HDC-based sequence analysis approaches, yielding noticeable gains in classification accuracy. We also demonstrate that the proposed approach, like most HDC-based sequence classification methods, is robust against adverse physical, internal, or external factors that induce bit flips in the underlying hardware, which could entirely corrupt the outcomes of classical sequence-analysis methods, such as HMMs.

Identifying phase coupling from electrophysiological signals recorded by multiple electrodes, such as electroencephalogram (EEG) and electrocorticography (ECoG), helps neuroscientists and clinicians understand underlying brain structures or mechanisms. From a statistical perspective, these signals are multidimensional circular measurements that are correlated with one another and can be effectively modeled using a torus graph model designed for circular random variables. Using the torus graph model avoids the issue of detecting spurious correlations. However, the naive estimation of this model tends to lead to a dense network structure that is difficult to interpret. Therefore, to enhance the interpretability of the brain network structure, this review proposes a sparse estimation method for the torus graph model using regularized score matching combined with information criteria. In numerical simulations, our method successfully recovered the true dependence structure from a synthetic data set. Furthermore, we present analyses of two real data sets, one involving human EEG and the other marmoset ECoG, demonstrating that our method can be widely applied to phase-coupling analysis across different types of neural data. We found that when we used our proposed method, the modularity of the estimated network structure revealed more resolved brain structures and demonstrated differences in trends among individuals.

Meditative experience has long been associated with conceptual attenuation, reduced reactivity to phenomena, increased present moment perception, and more pleasant experience. However, the computational mechanisms underlying such meditative deconstruction are not well understood, with no formal computational models available to explicate how deconstruction alters perception and action during meditation. Using the active inference framework, I demonstrate that the phenomenology of deconstruction-in terms of conceptual attenuation, reduced reactivity, and shorter temporal scale perception-naturally emerges from the dynamics of hierarchical inference when the deconstructive notion of letting go is cast as a reduction in precision of beliefs about hidden states at a specific level of the generative model. I present a formal hierarchical three-level generative model and simulate deconstruction as an intervention in a facial recognition task, where the agent selects a letting-go policy when perceived affective valence becomes excessively negative. The results demonstrate that the capacity to deconstruct permits agents to self-regulate experienced affect via letting go. The model offers a novel perspective within the paradigm of computational phenomenology on conceptual attenuation, equanimity, stillness, and affect during meditative deconstruction.

When an event occurs that is similar to a previous experience, the original episodic memory can be modified with new information (updating) or a new memory can be encoded separately (differentiation). Prediction errors, the deviation between expected and actual stimuli, are believed to mediate the competition between updating and differentiation, but the underlying mechanisms remain unclear. Here, we present a new analysis of experiments examining recognition memory and cued recall of similar conversations. We find that the original version is recognized more confidently than the modified version, the recognition confidence for modified versions shows a U-shaped dependence on the prediction error, and larger prediction errors lead to participants' more frequently recalling two versions. These results can be accounted for by a computational model based on a modified Hopfield network, which encodes the original and modified versions sequentially and weights the encoding of new patterns based on the prediction error. The model shows that (1) similar new memories interfere with previous ones (updating), while dissimilar ones are stored separately (differentiation); (2) interference from similar representations leads to reduced memory accuracy and lower-confidence recognition; and (3) modulation of the encoding strength is critical for accounting for the experimental data. Our modeling results show that prediction-error-driven competition between updating and differentiation can emerge from intrinsic network dynamics alone.

In many domain adaptation tasks, the source and target domains share an identical feature space, so the domain gap arises only from the distributional shift. In practice; however, new-target-only features (e.g., sensors added after training) often become available at test time, violating the shared feature space assumption and invalidating most existing methods. We address this setting with Label-Aware and Graph-Based Fused Gromov-Wasserstein Optimal Transport (LAGB-FGW), focusing on a transductive domain adaptation scenario, in which the entire unlabeled target data set is available during training, and predictions are jointly inferred for all target samples. LAGB-FGW (1) embeds label discrepancy directly into the source metric, (2) constructs a K-NN graph on the full target feature space to capture structure introduced by the additional features, and (3) jointly solves standard Optimal Transport (OT) and Gromov-Wasserstein OT, thereby transferring labels using both the common and the additional features. We validate LAGB-FGW on four synthetic benchmarks and the HAR70+ human-activity data set, and LAGB-FGW consistently outperforms all baselines, highlighting the advantage of combining source label information with graph-based structural cues when additional target features are available only at test time.