Raffaele Marino;Lorenzo Buffoni;Lorenzo Chicchi;Francesca Di Patti;Diego Febbe;Lorenzo Giambagli;Duccio Fanelli
The Wilson-Cowan model for metapopulation, a neural mass network model, treats different subcortical regions of the brain as connected nodes, with connections representing various types of structural, functional, or effective neuronal connectivity between these regions. Each region comprises interacting populations of excitatory and inhibitory cells, consistent with the standard Wilson-Cowan model. In this article, we show how to incorporate stable attractors into such a metapopulation model’s dynamics. By doing so, we transform the neural mass network model into a biologically inspired learning algorithm capable of solving different classification tasks. We test it on MNIST and Fashion MNIST in combination with convolutional neural networks, as well as on CIFAR-10 and TF-FLOWERS, and in combination with a transformer architecture (BERT) on IMDB, consistently achieving high classification accuracy.
{"title":"Learning in Wilson-Cowan Model for Metapopulation","authors":"Raffaele Marino;Lorenzo Buffoni;Lorenzo Chicchi;Francesca Di Patti;Diego Febbe;Lorenzo Giambagli;Duccio Fanelli","doi":"10.1162/neco_a_01744","DOIUrl":"10.1162/neco_a_01744","url":null,"abstract":"The Wilson-Cowan model for metapopulation, a neural mass network model, treats different subcortical regions of the brain as connected nodes, with connections representing various types of structural, functional, or effective neuronal connectivity between these regions. Each region comprises interacting populations of excitatory and inhibitory cells, consistent with the standard Wilson-Cowan model. In this article, we show how to incorporate stable attractors into such a metapopulation model’s dynamics. By doing so, we transform the neural mass network model into a biologically inspired learning algorithm capable of solving different classification tasks. We test it on MNIST and Fashion MNIST in combination with convolutional neural networks, as well as on CIFAR-10 and TF-FLOWERS, and in combination with a transformer architecture (BERT) on IMDB, consistently achieving high classification accuracy.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"37 4","pages":"701-741"},"PeriodicalIF":2.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143607151","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}
We propose a sparse deep ReLU network (SDRN) estimator of the regression function obtained from regularized empirical risk minimization with a Lipschitz loss function. Our framework can be applied to a variety of regression and classification problems. We establish novel nonasymptotic excess risk bounds for our SDRN estimator when the regression function belongs to a Sobolev space with mixed derivatives. We obtain a new, nearly optimal, risk rate in the sense that the SDRN estimator can achieve nearly the same optimal minimax convergence rate as one-dimensional nonparametric regression with the dimension involved in a logarithm term only when the feature dimension is fixed. The estimator has a slightly slower rate when the dimension grows with the sample size. We show that the depth of the SDRN estimator grows with the sample size in logarithmic order, and the total number of nodes and weights grows in polynomial order of the sample size to have the nearly optimal risk rate. The proposed SDRN can go deeper with fewer parameters to well estimate the regression and overcome the overfitting problem encountered by conventional feedforward neural networks.
{"title":"Nearly Optimal Learning Using Sparse Deep ReLU Networks in Regularized Empirical Risk Minimization With Lipschitz Loss","authors":"Ke Huang;Mingming Liu;Shujie Ma","doi":"10.1162/neco_a_01742","DOIUrl":"10.1162/neco_a_01742","url":null,"abstract":"We propose a sparse deep ReLU network (SDRN) estimator of the regression function obtained from regularized empirical risk minimization with a Lipschitz loss function. Our framework can be applied to a variety of regression and classification problems. We establish novel nonasymptotic excess risk bounds for our SDRN estimator when the regression function belongs to a Sobolev space with mixed derivatives. We obtain a new, nearly optimal, risk rate in the sense that the SDRN estimator can achieve nearly the same optimal minimax convergence rate as one-dimensional nonparametric regression with the dimension involved in a logarithm term only when the feature dimension is fixed. The estimator has a slightly slower rate when the dimension grows with the sample size. We show that the depth of the SDRN estimator grows with the sample size in logarithmic order, and the total number of nodes and weights grows in polynomial order of the sample size to have the nearly optimal risk rate. The proposed SDRN can go deeper with fewer parameters to well estimate the regression and overcome the overfitting problem encountered by conventional feedforward neural networks.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"37 4","pages":"815-870"},"PeriodicalIF":2.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143607153","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}
Neocortical layer 5 thick-tufted pyramidal cells are prone to exhibiting burst firing on receipt of coincident basal and apical dendritic inputs. These inputs carry different information, with basal inputs coming from feedforward sensory pathways and apical inputs coming from diverse sources that provide context in the cortical hierarchy. We explore the information processing possibilities of this burst firing using computer simulations of a noisy compartmental cell model. Simulated data on stochastic burst firing due to brief, simultaneously injected basal and apical currents allow estimation of burst firing probability for different stimulus current amplitudes. Information-theory-based partial information decomposition (PID) is used to quantify the contributions of the apical and basal input streams to the information in the cell output bursting probability. Four different operating regimes are apparent, depending on the relative strengths of the input streams, with output burst probability carrying more or less information that is uniquely contributed by either the basal or apical input, or shared and synergistic information due to the combined streams. We derive and fit transfer functions for these different regimes that describe burst probability over the different ranges of basal and apical input amplitudes. The operating regimes can be classified into distinct modes of information processing, depending on the contribution of apical input to output bursting: apical cooperation, in which both basal and apical inputs are required to generate a burst; apical amplification, in which basal input alone can generate a burst but the burst probability is modulated by apical input; apical drive, in which apical input alone can produce a burst; and apical integration, in which strong apical or basal inputs alone, as well as their combination, can generate bursting. In particular, PID and the transfer function clarify that the apical amplification mode has the features required for contextually modulated information processing.
{"title":"Context-Sensitive Processing in a Model Neocortical Pyramidal Cell With Two Sites of Input Integration","authors":"Bruce P. Graham;Jim W. Kay;William A. Phillips","doi":"10.1162/neco_a_01739","DOIUrl":"10.1162/neco_a_01739","url":null,"abstract":"Neocortical layer 5 thick-tufted pyramidal cells are prone to exhibiting burst firing on receipt of coincident basal and apical dendritic inputs. These inputs carry different information, with basal inputs coming from feedforward sensory pathways and apical inputs coming from diverse sources that provide context in the cortical hierarchy. We explore the information processing possibilities of this burst firing using computer simulations of a noisy compartmental cell model. Simulated data on stochastic burst firing due to brief, simultaneously injected basal and apical currents allow estimation of burst firing probability for different stimulus current amplitudes. Information-theory-based partial information decomposition (PID) is used to quantify the contributions of the apical and basal input streams to the information in the cell output bursting probability. Four different operating regimes are apparent, depending on the relative strengths of the input streams, with output burst probability carrying more or less information that is uniquely contributed by either the basal or apical input, or shared and synergistic information due to the combined streams. We derive and fit transfer functions for these different regimes that describe burst probability over the different ranges of basal and apical input amplitudes. The operating regimes can be classified into distinct modes of information processing, depending on the contribution of apical input to output bursting: apical cooperation, in which both basal and apical inputs are required to generate a burst; apical amplification, in which basal input alone can generate a burst but the burst probability is modulated by apical input; apical drive, in which apical input alone can produce a burst; and apical integration, in which strong apical or basal inputs alone, as well as their combination, can generate bursting. In particular, PID and the transfer function clarify that the apical amplification mode has the features required for contextually modulated information processing.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"37 4","pages":"588-634"},"PeriodicalIF":2.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143607147","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}
Hanna Pankka;Jaakko Lehtinen;Risto J. Ilmoniemi;Timo Roine
Forecasting electroencephalography (EEG) signals, that is, estimating future values of the time series based on the past ones, is essential in many real-time EEG-based applications, such as brain–computer interfaces and closed-loop brain stimulation. As these applications are becoming more and more common, the importance of a good prediction model has increased. Previously, the autoregressive model (AR) has been employed for this task; however, its prediction accuracy tends to fade quickly as multiple steps are predicted. We aim to improve on this by applying probabilistic deep learning to make robust longer-range forecasts. For this, we applied the probabilistic deep neural network model WaveNet to forecast resting-state EEG in theta- (4–7.5 Hz) and alpha-frequency (8–13 Hz) bands and compared it to the AR model. WaveNet reliably predicted EEG signals in both theta and alpha frequencies 150 ms ahead, with mean absolute errors of 1.0 ± 1.1 µV (theta) and 0.9 ± 1.1 µV (alpha), and outperformed the AR model in estimating the signal amplitude and phase. Furthermore, we found that the probabilistic approach offers a way of forecasting even more accurately while effectively discarding uncertain predictions. We demonstrate for the first time that probabilistic deep learning can be used to forecast resting-state EEG time series. In the future, the developed model can enhance the real-time estimation of brain states in brain–computer interfaces and brain stimulation protocols. It may also be useful for answering neuroscientific questions and for diagnostic purposes.
{"title":"Enhanced EEG Forecasting: A Probabilistic Deep Learning Approach","authors":"Hanna Pankka;Jaakko Lehtinen;Risto J. Ilmoniemi;Timo Roine","doi":"10.1162/neco_a_01743","DOIUrl":"10.1162/neco_a_01743","url":null,"abstract":"Forecasting electroencephalography (EEG) signals, that is, estimating future values of the time series based on the past ones, is essential in many real-time EEG-based applications, such as brain–computer interfaces and closed-loop brain stimulation. As these applications are becoming more and more common, the importance of a good prediction model has increased. Previously, the autoregressive model (AR) has been employed for this task; however, its prediction accuracy tends to fade quickly as multiple steps are predicted. We aim to improve on this by applying probabilistic deep learning to make robust longer-range forecasts. For this, we applied the probabilistic deep neural network model WaveNet to forecast resting-state EEG in theta- (4–7.5 Hz) and alpha-frequency (8–13 Hz) bands and compared it to the AR model. WaveNet reliably predicted EEG signals in both theta and alpha frequencies 150 ms ahead, with mean absolute errors of 1.0 ± 1.1 µV (theta) and 0.9 ± 1.1 µV (alpha), and outperformed the AR model in estimating the signal amplitude and phase. Furthermore, we found that the probabilistic approach offers a way of forecasting even more accurately while effectively discarding uncertain predictions. We demonstrate for the first time that probabilistic deep learning can be used to forecast resting-state EEG time series. In the future, the developed model can enhance the real-time estimation of brain states in brain–computer interfaces and brain stimulation protocols. It may also be useful for answering neuroscientific questions and for diagnostic purposes.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"37 4","pages":"793-814"},"PeriodicalIF":2.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143607149","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}
From biological and artificial network perspectives, researchers have started acknowledging astrocytes as computational units mediating neural processes. Here, we propose a novel biologically inspired neuron-astrocyte network model for image recognition, one of the first attempts at implementing astrocytes in spiking neuron networks (SNNs) using a standard data set. The architecture for image recognition has three primary units: the preprocessing unit for converting the image pixels into spiking patterns, the neuron-astrocyte network forming bipartite (neural connections) and tripartite synapses (neural and astrocytic connections), and the classifier unit. In the astrocyte-mediated SNNs, an astrocyte integrates neural signals following the simplified Postnov model. It then modulates the integrate-and-fire (IF) neurons via gliotransmission, thereby strengthening the synaptic connections of the neurons within the astrocytic territory. We develop an architecture derived from a baseline SNN model for unsupervised digit classification. The spiking neuron-astrocyte networks (SNANs) display better network performance with an optimal variance-bias trade-off than SNN alone. We demonstrate that astrocytes promote faster learning, support memory formation and recognition, and provide a simplified network architecture. Our proposed SNAN can serve as a benchmark for future researchers on astrocyte implementation in artificial networks, particularly in neuromorphic systems, for its simplified design.
{"title":"Spiking Neuron-Astrocyte Networks for Image Recognition","authors":"Jhunlyn Lorenzo;Juan-Antonio Rico-Gallego;Stéphane Binczak;Sabir Jacquir","doi":"10.1162/neco_a_01740","DOIUrl":"10.1162/neco_a_01740","url":null,"abstract":"From biological and artificial network perspectives, researchers have started acknowledging astrocytes as computational units mediating neural processes. Here, we propose a novel biologically inspired neuron-astrocyte network model for image recognition, one of the first attempts at implementing astrocytes in spiking neuron networks (SNNs) using a standard data set. The architecture for image recognition has three primary units: the preprocessing unit for converting the image pixels into spiking patterns, the neuron-astrocyte network forming bipartite (neural connections) and tripartite synapses (neural and astrocytic connections), and the classifier unit. In the astrocyte-mediated SNNs, an astrocyte integrates neural signals following the simplified Postnov model. It then modulates the integrate-and-fire (IF) neurons via gliotransmission, thereby strengthening the synaptic connections of the neurons within the astrocytic territory. We develop an architecture derived from a baseline SNN model for unsupervised digit classification. The spiking neuron-astrocyte networks (SNANs) display better network performance with an optimal variance-bias trade-off than SNN alone. We demonstrate that astrocytes promote faster learning, support memory formation and recognition, and provide a simplified network architecture. Our proposed SNAN can serve as a benchmark for future researchers on astrocyte implementation in artificial networks, particularly in neuromorphic systems, for its simplified design.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"37 4","pages":"635-665"},"PeriodicalIF":2.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143607154","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}
Attractor neural networks consider that neural information is stored as stationary states of a dynamical system formed by a large number of interconnected neurons. The attractor property empowers a neural system to encode information robustly, but it also incurs the difficulty of rapid update of network states, which can impair information update and search in the brain. To overcome this difficulty, a solution is to include adaptation in the attractor network dynamics, whereby the adaptation serves as a slow negative feedback mechanism to destabilize what are otherwise permanently stable states. In such a way, the neural system can, on one hand, represent information reliably using attractor states, and on the other hand, perform computations wherever rapid state updating is involved. Previous studies have shown that continuous attractor neural networks with adaptation (A-CANNs) exhibit rich dynamical behaviors accounting for various brain functions. In this review, we present a comprehensive view of the rich diverse dynamics of A-CANNs. Moreover, we provide a unified mathematical framework to understand these different dynamical behaviors and briefly discuss their biological implications.
{"title":"Dynamics of Continuous Attractor Neural Networks With Spike Frequency Adaptation","authors":"Yujun Li;Tianhao Chu;Si Wu","doi":"10.1162/neco_a_01757","DOIUrl":"10.1162/neco_a_01757","url":null,"abstract":"Attractor neural networks consider that neural information is stored as stationary states of a dynamical system formed by a large number of interconnected neurons. The attractor property empowers a neural system to encode information robustly, but it also incurs the difficulty of rapid update of network states, which can impair information update and search in the brain. To overcome this difficulty, a solution is to include adaptation in the attractor network dynamics, whereby the adaptation serves as a slow negative feedback mechanism to destabilize what are otherwise permanently stable states. In such a way, the neural system can, on one hand, represent information reliably using attractor states, and on the other hand, perform computations wherever rapid state updating is involved. Previous studies have shown that continuous attractor neural networks with adaptation (A-CANNs) exhibit rich dynamical behaviors accounting for various brain functions. In this review, we present a comprehensive view of the rich diverse dynamics of A-CANNs. Moreover, we provide a unified mathematical framework to understand these different dynamical behaviors and briefly discuss their biological implications.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"37 6","pages":"1057-1101"},"PeriodicalIF":2.7,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144026069","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}
Spiking neural networks (SNNs) provide an energy-efficient alternative to traditional artificial neural networks, leveraging diverse neural encoding schemes such as rate, time-to-first-spike (TTFS), and population-based binary codes. Each encoding method offers distinct advantages: TTFS enables rapid and precise transmission with minimal energy use, rate encoding provides robust signal representation, and binary population encoding aligns well with digital hardware implementations. This letter introduces a set of neural microcircuits based on leaky integrate-and-fire neurons that enable translation between these encoding schemes. We propose two applications showcasing the utility of these microcircuits. First, we demonstrate a number comparison operation that significantly reduces spike transmission by switching from rate to TTFS encoding. Second, we present a high-bandwidth neural transmitter capable of encoding and transmitting binary population-encoded data through a single axon and reconstructing it at the target site. Additionally, we conduct a detailed analysis of these microcircuits, providing quantitative metrics to assess their efficiency in terms of neuron count, synaptic complexity, spike overhead, and runtime. Our findings highlight the potential of LIF neuron microcircuits in computational neuroscience and neuromorphic computing, offering a pathway to more interpretable and efficient SNN designs.
{"title":"Neural Code Translation With LIF Neuron Microcircuits","authors":"Ville Karlsson;Joni Kämäräinen","doi":"10.1162/neco_a_01754","DOIUrl":"10.1162/neco_a_01754","url":null,"abstract":"Spiking neural networks (SNNs) provide an energy-efficient alternative to traditional artificial neural networks, leveraging diverse neural encoding schemes such as rate, time-to-first-spike (TTFS), and population-based binary codes. Each encoding method offers distinct advantages: TTFS enables rapid and precise transmission with minimal energy use, rate encoding provides robust signal representation, and binary population encoding aligns well with digital hardware implementations. This letter introduces a set of neural microcircuits based on leaky integrate-and-fire neurons that enable translation between these encoding schemes. We propose two applications showcasing the utility of these microcircuits. First, we demonstrate a number comparison operation that significantly reduces spike transmission by switching from rate to TTFS encoding. Second, we present a high-bandwidth neural transmitter capable of encoding and transmitting binary population-encoded data through a single axon and reconstructing it at the target site. Additionally, we conduct a detailed analysis of these microcircuits, providing quantitative metrics to assess their efficiency in terms of neuron count, synaptic complexity, spike overhead, and runtime. Our findings highlight the potential of LIF neuron microcircuits in computational neuroscience and neuromorphic computing, offering a pathway to more interpretable and efficient SNN designs.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"37 6","pages":"1124-1153"},"PeriodicalIF":2.7,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144046411","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}
The study of brain activity spans diverse scales and levels of description and requires the development of computational models alongside experimental investigations to explore integrations across scales. The high dimensionality of spiking networks presents challenges for understanding their dynamics. To tackle this, a mean-field formulation offers a potential approach for dimensionality reduction while retaining essential elements. Here, we focus on a previously developed mean-field model of adaptive exponential integrate and fire (AdEx) networks used in various research work. We observe qualitative similarities in the bifurcation structure but quantitative differences in mean firing rates between the mean-field model and AdEx spiking network simulations. Even if the mean-field model does not accurately predict phase shift during transients and oscillatory input, it generally captures the qualitative dynamics of the spiking network’s response to both constant and varying inputs. Finally, we offer an overview of the dynamical properties of the AdExMF to assist future users in interpreting their results of simulations.
{"title":"Dynamics and Bifurcation Structure of a Mean-Field Model of Adaptive Exponential Integrate-and-Fire Networks","authors":"Lionel Kusch;Damien Depannemaecker;Alain Destexhe;Viktor Jirsa","doi":"10.1162/neco_a_01758","DOIUrl":"10.1162/neco_a_01758","url":null,"abstract":"The study of brain activity spans diverse scales and levels of description and requires the development of computational models alongside experimental investigations to explore integrations across scales. The high dimensionality of spiking networks presents challenges for understanding their dynamics. To tackle this, a mean-field formulation offers a potential approach for dimensionality reduction while retaining essential elements. Here, we focus on a previously developed mean-field model of adaptive exponential integrate and fire (AdEx) networks used in various research work. We observe qualitative similarities in the bifurcation structure but quantitative differences in mean firing rates between the mean-field model and AdEx spiking network simulations. Even if the mean-field model does not accurately predict phase shift during transients and oscillatory input, it generally captures the qualitative dynamics of the spiking network’s response to both constant and varying inputs. Finally, we offer an overview of the dynamical properties of the AdExMF to assist future users in interpreting their results of simulations.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"37 6","pages":"1102-1123"},"PeriodicalIF":2.7,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144045166","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}
This letter presents a nonassociative algebraic framework for the representation and computation of information items in high-dimensional space. This framework is consistent with the principles of spatial computing and with the empirical findings in cognitive science about memory. Computations are performed through a process of multiplication-like binding and nonassociative interference-like bundling. Models that rely on associative bundling typically lose order information, which necessitates the use of auxiliary order structures, such as position markers, to represent sequential information that is important for cognitive tasks. In contrast, the nonassociative bundling proposed allows the construction of sparse representations of arbitrarily long sequences that maintain their temporal structure across arbitrary lengths. In this operation, noise is a constituent element of the representation of order information rather than a means of obscuring it. The nonassociative nature of the proposed framework results in the representation of a single sequence by two distinct states. The L-state, generated through left-associative bundling, continuously updates and emphasizes a recency effect, while the R-state, formed through right-associative bundling, encodes finite sequences or chunks, capturing a primacy effect. The construction of these states may be associated with activity in the prefrontal cortex in relation to short-term memory and hippocampal encoding in long-term memory, respectively. The accuracy of retrieval is contingent on a decision-making process that is based on the mutual information between the memory states and the cue. The model is able to replicate the serial position curve, which reflects the empirical recency and primacy effects observed in cognitive experiments.
{"title":"Memory States From Almost Nothing: Representing and Computing in a Nonassociative Algebra","authors":"Stefan Reimann","doi":"10.1162/neco_a_01755","DOIUrl":"10.1162/neco_a_01755","url":null,"abstract":"This letter presents a nonassociative algebraic framework for the representation and computation of information items in high-dimensional space. This framework is consistent with the principles of spatial computing and with the empirical findings in cognitive science about memory. Computations are performed through a process of multiplication-like binding and nonassociative interference-like bundling. Models that rely on associative bundling typically lose order information, which necessitates the use of auxiliary order structures, such as position markers, to represent sequential information that is important for cognitive tasks. In contrast, the nonassociative bundling proposed allows the construction of sparse representations of arbitrarily long sequences that maintain their temporal structure across arbitrary lengths. In this operation, noise is a constituent element of the representation of order information rather than a means of obscuring it. The nonassociative nature of the proposed framework results in the representation of a single sequence by two distinct states. The L-state, generated through left-associative bundling, continuously updates and emphasizes a recency effect, while the R-state, formed through right-associative bundling, encodes finite sequences or chunks, capturing a primacy effect. The construction of these states may be associated with activity in the prefrontal cortex in relation to short-term memory and hippocampal encoding in long-term memory, respectively. The accuracy of retrieval is contingent on a decision-making process that is based on the mutual information between the memory states and the cue. The model is able to replicate the serial position curve, which reflects the empirical recency and primacy effects observed in cognitive experiments.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"37 6","pages":"1154-1170"},"PeriodicalIF":2.7,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144057372","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}
Recently, tensor singular value decomposition (t-SVD)–based methods were proposed to solve the low-rank tensor completion (LRTC) problem, which has achieved unprecedented success on image and video inpainting tasks. The t-SVD is limited to process third-order tensors. When faced with higher-order tensors, it reshapes them into third-order tensors, leading to the destruction of interdimensional correlations. To address this limitation, this letter introduces a tproductinduced Tucker decomposition (tTucker) model that replaces the mode product in Tucker decomposition with t-product, which jointly extends the ideas of t-SVD and high-order SVD. This letter defines the rank of the tTucker decomposition and presents an LRTC model that minimizes the induced Schatten-p norm. An efficient alternating direction multiplier method (ADMM) algorithm is developed to optimize the proposed LRTC model, and its effectiveness is demonstrated through experiments conducted on both synthetic and real data sets, showcasing excellent performance.
{"title":"Low-Rank, High-Order Tensor Completion via t- Product-Induced Tucker (tTucker) Decomposition","authors":"Yaodong Li;Jun Tan;Peilin Yang;Guoxu Zhou;Qibin Zhao","doi":"10.1162/neco_a_01756","DOIUrl":"10.1162/neco_a_01756","url":null,"abstract":"Recently, tensor singular value decomposition (t-SVD)–based methods were proposed to solve the low-rank tensor completion (LRTC) problem, which has achieved unprecedented success on image and video inpainting tasks. The t-SVD is limited to process third-order tensors. When faced with higher-order tensors, it reshapes them into third-order tensors, leading to the destruction of interdimensional correlations. To address this limitation, this letter introduces a tproductinduced Tucker decomposition (tTucker) model that replaces the mode product in Tucker decomposition with t-product, which jointly extends the ideas of t-SVD and high-order SVD. This letter defines the rank of the tTucker decomposition and presents an LRTC model that minimizes the induced Schatten-p norm. An efficient alternating direction multiplier method (ADMM) algorithm is developed to optimize the proposed LRTC model, and its effectiveness is demonstrated through experiments conducted on both synthetic and real data sets, showcasing excellent performance.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"37 6","pages":"1171-1192"},"PeriodicalIF":2.7,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144029302","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：