{"title":"Comparing Dynamical Models Through Diffeomorphic Vector Field Alignment","authors":"Ruiqi Chen;Giacomo Vedovati;Todd Braver;ShiNung Ching","doi":"10.1162/NECO.a.1526","DOIUrl":"10.1162/NECO.a.1526","url":null,"abstract":"Dynamical systems models such as recurrent neural networks (RNNs) are increasingly popular in theoretical neuroscience as a vehicle for hypothesis generation and data analysis. Evaluating the dynamics in such models is key to understanding their learned generative mechanisms. However, such evaluation is impeded by two major challenges: (1) comparison of learned dynamics across models is difficult because a priori there is no enforced equivalence of their coordinate systems, and (2) identification of mechanistically important low-dimensional motifs (e.g., limit sets) is analytically intractable in high-dimensional nonlinear models such as RNNs. Here, we propose a comprehensive framework to address these two issues, termed diffeomorphic vector field alignment for learned models (DFORM). DFORM learns a nonlinear coordinate transformation between the state spaces of two dynamical systems, which aligns their trajectories in a maximally one-to-one manner. In so doing, DFORM enables an assessment of whether a set of models exhibits topological equivalence, that is, their dynamics are mechanistically similar despite differences in their coordinate systems. A by-product of this methodology is a means to locate dynamical motifs on low-dimensional manifolds embedded within higher-dimensional systems. We verified DFORM’s ability to identify linear and nonlinear coordinate transformations using canonical topologically equivalent systems, RNNs, and systems related by nonlinear flows. DFORM was also shown to provide a quantification of similarity between topologically distinct systems. We then demonstrated that DFORM can locate important dynamical motifs including invariant manifolds and saddle limit sets within high-dimensional models. Finally, using a set of RNN models trained on human functional magnetic resonance imaging recordings, we illustrated that DFORM can identify limit cycles from high-dimensional data-driven models, which agreed well with prior numerical analysis.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"38 6","pages":"1006-1061"},"PeriodicalIF":2.1,"publicationDate":"2026-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147789361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Neural ComputationPub Date : 2026-03-20Epub Date: 2026-06-01DOI: 10.1162/NECO.a.1511
Shubham Choudhary;Paul Masset;Demba Ba
{"title":"Implicit Generative Modeling by Kernel Similarity Matching","authors":"Shubham Choudhary;Paul Masset;Demba Ba","doi":"10.1162/NECO.a.1511","DOIUrl":"10.1162/NECO.a.1511","url":null,"abstract":"Understanding how the brain encodes stimuli has been a fundamental problem in computational neuroscience. Insights into this problem have led to the design and development of artificial neural networks that learn representations by incorporating brain-like learning abilities. Recently, learning representations by capturing similarity among input samples has been studied (Pehlevan et al., 2018) to tackle this problem. This approach, however, has thus far been used only to learn downstream features from an input and has not been studied in the context of a generative paradigm, where one can map the representations back to the input space, incorporating not only bottom-up interactions (stimuli→latent) but also learning features in a top-down manner (latent→stimuli). We investigate a kernel similarity matching framework for generative modeling. Starting with a modified sparse coding objective for learning representations proposed in prior works (Olshausen & Field, 1996; Tolooshams & Ba, 2022), we demonstrate that representation learning in this context is equivalent to maximizing similarity between the input kernel and a latent kernel. We show that an implicit generative model arises from learning the kernel structure in the latent space and show how the framework can be adapted to learn manifold structures, potentially providing insights as to how task representations can be encoded in the brain. To solve the objective, we propose a novel alternate direction method of multipliers (ADMM)–based algorithm and discuss the interpretation of the optimization process. Finally, we discuss how this representation learning problem can lead toward a biologically plausible architecture to learn the model parameters that ties together representation learning using similarity matching (a bottom-up approach) with predictive coding (a top-down approach).","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"38 6","pages":"897-951"},"PeriodicalIF":2.1,"publicationDate":"2026-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147634986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Neural ComputationPub Date : 2026-03-20Epub Date: 2026-06-01DOI: 10.1162/NECO.a.1522
Takuma Sumi;Georgi S. Medvedev
{"title":"Graphon Signal Processing for Spiking and Biological Neural Networks","authors":"Takuma Sumi;Georgi S. Medvedev","doi":"10.1162/NECO.a.1522","DOIUrl":"10.1162/NECO.a.1522","url":null,"abstract":"Graph signal processing (GSP) extends classical signal processing to signals defined on graphs, enabling filtering, spectral analysis, and sampling of data generated by networks of various kinds. Graphon signal processing (GnSP) develops this framework further by employing the theory of graphons. Graphons are measurable functions on the unit square that represent graphs and limits of convergent graph sequences. The use of graphons provides stability of GSP methods to stochastic variability in network data and improves computational efficiency for very large networks. We use GnSP to address the stimulus identification problem (SIP) in computational and biological neural networks. The SIP is an inverse problem that aims to infer the unknown stimulus sfrom the observed network output f. We first validate the approach in spiking neural network simulations and then analyze calcium imaging recordings. Graphon-based spectral projections yield trial-invariant, low-dimensional embeddings that improve stimulus classification over principal component analysis and discrete GSP baselines. The embeddings remain stable under variations in network stochasticity, providing robustness to different network sizes and noise levels. To the best of our knowledge, this is the first application of GnSP to biological neural networks, opening new avenues for graphon-based analysis in neuroscience.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"38 6","pages":"1090-1115"},"PeriodicalIF":2.1,"publicationDate":"2026-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147789551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Thousand-Brains Systems: Sensorimotor Intelligence for Rapid, Robust Learning and Inference","authors":"Niels Leadholm;Viviane Clay;Scott Knudstrup;Hojae Lee;Jeff Hawkins","doi":"10.1162/NECO.a.1508","DOIUrl":"10.1162/NECO.a.1508","url":null,"abstract":"Current AI systems achieve impressive performance on many tasks, yet they lack core attributes of biological intelligence, including rapid, continual learning, representations grounded in sensorimotor interactions, and structured knowledge that enables efficient generalization. Neuroscience theory suggests that mammals evolved flexible intelligence through the replication of a semi-independent, sensorimotor module, a functional unit known as a cortical column. To address the disparity between biological and artificial intelligence, Thousand Brains systems were proposed as a means of mirroring the architecture of cortical columns and their interactions. In our current work, we evaluate the unique properties of Monty, the first implementation of a Thousand Brains system. We focus on 3D object perception and, in particular, the combined task of object recognition and pose estimation. Utilizing the YCB data set of household objects, we first assess Monty’s use of sensorimotor learning to build structured representations, finding that these enable robust generalization. These representations include an emphasis on classifying objects by their global shape, as well as a natural ability to detect object symmetries. We then explore Monty’s use of model-free and model-based policies to enable rapid inference by supporting principled movements. We find that such policies complement Monty’s modular architecture, a design that can accommodate communication between modules to further accelerate inference speed via a novel voting algorithm. Finally, we examine Monty’s use of associative, Hebbian-like binding to enable rapid, continual, and computationally efficient learning, properties that compare favorably to current deep learning architectures. While Monty is still in a nascent stage of development, these findings support Thousand Brains systems as a powerful and promising new approach to AI and reinforce the importance of sensorimotor learning for developing intelligent systems.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"38 6","pages":"845-896"},"PeriodicalIF":2.1,"publicationDate":"2026-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11541257","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147635088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Neural ComputationPub Date : 2026-03-17Epub Date: 2026-03-24DOI: 10.1162/NECO.a.1502
Dmitri Rachkovskij;Evgeny Osipov;Olexander Volkov;Daswin De Silva;Denis Kleyko
{"title":"Multiclass Linear Perceptrons With Multiplicative Margins","authors":"Dmitri Rachkovskij;Evgeny Osipov;Olexander Volkov;Daswin De Silva;Denis Kleyko","doi":"10.1162/NECO.a.1502","DOIUrl":"10.1162/NECO.a.1502","url":null,"abstract":"This article introduces a family of multiclass linear perceptron classifiers with a multiplicative margin mechanism (MMPerc), as an alternative to standard margin-free and additive margin perceptrons. The multiplicative formulation enforces classification confidence by requiring the true class score to exceed that of competing classes by a specified fraction of itself rather than by a fixed additive threshold. This avoids dependence on score magnitudes arising from varied norms of data and class weight vectors. We propose several architectural and algorithmic variants of MMPerc, derive associated loss functions and mistake bounds for both linearly separable and nonseparable data, and analyze key design considerations, including bias, margin threshold selection, and training modes. Extensive experiments on synthetic and real data sets show that MMPerc classifiers typically outperform the standard perceptron, as well as classic baselines such as support vector machines and ridge classifiers. Owing to their simplicity, minimalistic design, and computational efficiency, MMPerc classifiers are promising candidates for conventional machine learning tasks, linear evaluation of deep neural networks, integration with hyperdimensional computing and vector symbolic architecture representations, and deployment in resource-constrained applications.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"38 4","pages":"602-650"},"PeriodicalIF":2.1,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147366897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Neural ComputationPub Date : 2026-03-17Epub Date: 2026-03-24DOI: 10.1162/NECO.a.1504
Matteo Saponati;Martin Vinck
{"title":"Inhibitory Feedback Enables Predictive Learning of Multiple Sequences in Neural Networks","authors":"Matteo Saponati;Martin Vinck","doi":"10.1162/NECO.a.1504","DOIUrl":"10.1162/NECO.a.1504","url":null,"abstract":"Anticipating future events is a key computational task for neuronal networks. Experimental evidence suggests that reliable temporal sequences in neural activity play a functional role in the association and anticipation of events in time. However, how neurons can differentiate and anticipate multiple spike sequences remains largely unknown. We implement a learning rule based on predictive processing, where neurons exclusively fire for the initial, unpredictable inputs in a spiking sequence, leading to an efficient representation with reduced postsynaptic firing. Combining this mechanism with inhibitory feedback leads to sparse firing in the network, enabling neurons to selectively anticipate different sequences in the input. We demonstrate that intermediate levels of inhibition are optimal to decorrelate neuronal activity and to enable the prediction of future inputs. Notably, each sequence is independently encoded in the sparse, anticipatory firing of the network. Overall, our results demonstrate that the interplay of self-supervised predictive learning rules and inhibitory feedback enables fast and efficient classification of different input sequences.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"38 4","pages":"471-498"},"PeriodicalIF":2.1,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147366926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Neural ComputationPub Date : 2026-03-17Epub Date: 2026-03-24DOI: 10.1162/NECO.a.1505
Pascal J. Sager;Jan M. Deriu;Benjamin F. Grewe;Thilo Stadelmann;Christoph von der Malsburg
{"title":"The Cooperative Network Architecture: Learning Structured Networks as Representation of Sensory Patterns","authors":"Pascal J. Sager;Jan M. Deriu;Benjamin F. Grewe;Thilo Stadelmann;Christoph von der Malsburg","doi":"10.1162/NECO.a.1505","DOIUrl":"10.1162/NECO.a.1505","url":null,"abstract":"We introduce the cooperative network architecture (CNA), a model that represents sensory signals using structured, recurrently connected networks of neurons, termed “nets.” Nets are dynamically assembled from overlapping net fragments, which are learned based on statistical regularities in sensory input. This architecture offers robustness to noise, deformation, and generalization to out-of-distribution data, addressing challenges in current vision systems from a novel perspective. We demonstrate that net fragments can be learned without supervision and flexibly recombined to encode novel patterns, enabling figure completion and resilience to noise. Our findings establish CNA as a promising paradigm for developing neural representations that integrate local feature processing with global structure formation, providing a foundation for future research on invariant object recognition.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"38 4","pages":"538-572"},"PeriodicalIF":2.1,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147367235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Neural ComputationPub Date : 2026-03-17Epub Date: 2026-03-24DOI: 10.1162/NECO.a.1503
Takashi Kanamaru;Kazuyuki Aihara
{"title":"Force Learning in Balanced Cortical E-I Networks","authors":"Takashi Kanamaru;Kazuyuki Aihara","doi":"10.1162/NECO.a.1503","DOIUrl":"10.1162/NECO.a.1503","url":null,"abstract":"Force learning is a learning method for generating various types of complex dynamics in recurrent neural networks (RNNs), which is related to the reservoir computing (RC). RC uses an RNN called reservoir whose synaptic weights are randomly generated and fixed during learning. Force learning trains these synaptic weights inside the reservoir networks. Although force learning can be used as an effective tool for machine learning, possibilities of its realization in the brain are not often discussed. Here, in order to consider the possibilities of its realization in the brain, force learning is applied to an excitatory and inhibitory (E-I) network that models the cerebral cortex. A multimodule network composed of excitatory and inhibitory neurons is defined, and a readout is put outside, similar to a conventional reservoir. The output of this network is calculated at the readout as a linear combination of the filtered average firing rates of the excitatory neurons in the modules. Feedback connections that provide output back to the excitatory neurons in the modules with random strength are also added to this network. This network typically shows transitive chaotic synchronization, in which synchronizing modules are rearranged chaotically and intermittently. Under such conditions, our E-I network is trained to generate sinusoidal periodic signals for simplicity with force learning. When adjusting the E-I activity, it is observed that the efficiency of force learning is maximized at an optimal E-I balance near an edge of chaos. These results imply that the cooperation of excitatory and inhibitory neurons is required when force learning works effectively in the brain, although usual reservoir networks don’t distinguish these two kinds of neurons.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"38 4","pages":"573-601"},"PeriodicalIF":2.1,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11455132","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147366928","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Neural ComputationPub Date : 2026-03-17Epub Date: 2026-03-24DOI: 10.1162/NECO.a.1507
Richard W. Prager;Richard Apps
{"title":"Potential for Reinforcement Learning in the Cerebellum","authors":"Richard W. Prager;Richard Apps","doi":"10.1162/NECO.a.1507","DOIUrl":"10.1162/NECO.a.1507","url":null,"abstract":"This article explores how simple reinforcement learning algorithms might be implemented by the anatomy of the cerebellum. In doing this, we highlight which anatomical and physiological details are most important for assessing algorithmic fit, and we discuss which algorithm components are easiest to accommodate in a neural system. We describe hypothetical cerebellar implementations of four reinforcement learning algorithms and discuss the anatomical plausibility of the various components required. We show how one of the algorithms can learn to generate short sequences of actions without continuous information on the resulting changes to the environment. We finish with simulations that illustrate the way that the algorithms learn to solve the problem of balancing an inverted pendulum, commonly known as the cart-pole problem. We highlight two physiological features: reward signals and combining information across time, that indicate that some sort of reinforcement learning adaptation may be taking place. We also describe why the commonly used algorithmic feature, an eligibility trace, presents particular problems to implement in known neural anatomy.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"38 4","pages":"499-537"},"PeriodicalIF":2.1,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11455135","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147367212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Neural ComputationPub Date : 2026-03-17Epub Date: 2026-03-24DOI: 10.1162/NECO.a.1501
Xiang Zhang;Chenlin Xu;Zhouxiao Lu;Haonan Wang;Dong Song
{"title":"ReBaCCA-ss: Relevance-Balanced Continuum Correlation Analysis With Smoothing and Surrogating for Quantifying Similarity Between Population Spiking Activities","authors":"Xiang Zhang;Chenlin Xu;Zhouxiao Lu;Haonan Wang;Dong Song","doi":"10.1162/NECO.a.1501","DOIUrl":"10.1162/NECO.a.1501","url":null,"abstract":"Quantifying similarity between population spike patterns is essential for understanding how neural dynamics encode information. Traditional approaches, which combine kernel smoothing, principal component analysis, and canonical correlation analysis (CCA), have limitations: smoothing kernel bandwidths are often empirically chosen, CCA maximizes alignment between patterns without considering the variance explained within patterns, and baseline correlations from stochastic spiking are rarely corrected. We introduce ReBaCCA-ss (relevance-balanced continuum correlation analysis with smoothing and surrogating), a novel framework that addresses these challenges through three innovations: (1) balancing alignment and variance explanation via continuum canonical correlation, (2) correcting for noise using surrogate spike trains, and (3) selecting the optimal kernel bandwidth by maximizing the difference between true and surrogate correlations. ReBaCCA-ss is validated on both simulated data and hippocampal recordings from rats performing a delayed nonmatch-to-sample task. It reliably identifies spatiotemporal similarities between spike patterns. Combined with multidimensional scaling, ReBaCCA-ss reveals structured neural representations across trials, events, sessions, and animals, offering a powerful tool for neural population analysis.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"38 4","pages":"651-680"},"PeriodicalIF":2.1,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147367240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}