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.
{"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":"<p><p>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.</p>","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":" ","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}
Dmitri Rachkovskij, Evgeny Osipov, Olexander Volkov, Daswin De Silva, Denis Kleyko
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.
{"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":"<p><p>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.</p>","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":" ","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}
Pascal J Sager, Jan M Deriu, Benjamin F Grewe, Thilo Stadelmann, Christoph von der Malsburg
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.
{"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":"<p><p>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.</p>","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":" ","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}
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.
{"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":"<p><p>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.</p>","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":" ","pages":"499-537"},"PeriodicalIF":2.1,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","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":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"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":"<p><p>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.</p>","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":" ","pages":"573-601"},"PeriodicalIF":2.1,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","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":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xiang Zhang, Chenlin Xu, Zhouxiao Lu, Haonan Wang, Dong Song
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.
{"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":"<p><p>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.</p>","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":" ","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}
Sensory operators are classically modeled using small circuits involving canonical computations, such as energy extraction and gain control. Notwithstanding their utility, circuit models do not provide a unified framework encompassing the variety of effects observed experimentally. We develop a novel, alternative framework that recasts sensory operators in the language of intrinsic geometry. We start from a plausible representation of perceptual processes that is akin to measuring distances over a sensory manifold. We show that this representation is sufficiently expressive to capture a wide range of empirical effects associated with elementary sensory computations. The resulting geometrical framework offers a new perspective on state-of-the-art empirical descriptors of sensory behavior, such as first-order and second-order perceptual kernels. For example, it relates these descriptors to notions of flatness and curvature in perceptual space.
{"title":"Perceptual Processes as Charting Operators.","authors":"Peter Neri","doi":"10.1162/NECO.a.1506","DOIUrl":"https://doi.org/10.1162/NECO.a.1506","url":null,"abstract":"<p><p>Sensory operators are classically modeled using small circuits involving canonical computations, such as energy extraction and gain control. Notwithstanding their utility, circuit models do not provide a unified framework encompassing the variety of effects observed experimentally. We develop a novel, alternative framework that recasts sensory operators in the language of intrinsic geometry. We start from a plausible representation of perceptual processes that is akin to measuring distances over a sensory manifold. We show that this representation is sufficiently expressive to capture a wide range of empirical effects associated with elementary sensory computations. The resulting geometrical framework offers a new perspective on state-of-the-art empirical descriptors of sensory behavior, such as first-order and second-order perceptual kernels. For example, it relates these descriptors to notions of flatness and curvature in perceptual space.</p>","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":" ","pages":"1-54"},"PeriodicalIF":2.1,"publicationDate":"2026-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147366910","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}
Juliana Londono Alvarez;Katherine Morrison;Carina Curto
Neural circuits in the brain perform a variety of essential functions, including input classification, pattern completion, and the generation of rhythms and oscillations that support functions such as breathing and locomotion. There is also substantial evidence that the brain encodes memories and processes information via sequences of neural activity. Traditionally, rhythmic activity and pattern generation have been modeled using coupled oscillators, whereas input classification and pattern completion have been modeled using attractor neural networks. Here, we present a theoretical framework that demonstrates how attractor-based networks can also generate diverse rhythmic patterns, such as those of central pattern generator circuits (CPGs). Additionally, we propose a mechanism for transitioning between patterns. Specifically, we construct a network that can step through a sequence of five different quadruped gaits. It is composed of two dynamically distinct modules: a “counter” network that can count the number of external inputs it receives via a sequence of fixed points and a locomotion network that encodes five different quadruped gaits as limit cycles. A sequence of locomotive gaits is obtained by connecting the counter network with the locomotion network. Specifically, we introduce a new architecture for layering networks that produces fusion attractors, binding pairs of attractors from individual layers. All of this is accomplished within a unified framework of attractor-based models using threshold-linear networks.
{"title":"Attractor-Based Models for Sequences and Pattern Generation in Neural Circuits","authors":"Juliana Londono Alvarez;Katherine Morrison;Carina Curto","doi":"10.1162/NECO.a.1492","DOIUrl":"10.1162/NECO.a.1492","url":null,"abstract":"Neural circuits in the brain perform a variety of essential functions, including input classification, pattern completion, and the generation of rhythms and oscillations that support functions such as breathing and locomotion. There is also substantial evidence that the brain encodes memories and processes information via sequences of neural activity. Traditionally, rhythmic activity and pattern generation have been modeled using coupled oscillators, whereas input classification and pattern completion have been modeled using attractor neural networks. Here, we present a theoretical framework that demonstrates how attractor-based networks can also generate diverse rhythmic patterns, such as those of central pattern generator circuits (CPGs). Additionally, we propose a mechanism for transitioning between patterns. Specifically, we construct a network that can step through a sequence of five different quadruped gaits. It is composed of two dynamically distinct modules: a “counter” network that can count the number of external inputs it receives via a sequence of fixed points and a locomotion network that encodes five different quadruped gaits as limit cycles. A sequence of locomotive gaits is obtained by connecting the counter network with the locomotion network. Specifically, we introduce a new architecture for layering networks that produces fusion attractors, binding pairs of attractors from individual layers. All of this is accomplished within a unified framework of attractor-based models using threshold-linear networks.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"38 3","pages":"257-291"},"PeriodicalIF":2.1,"publicationDate":"2026-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146121133","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}
Presynaptic axon terminals maintain in their cytosol an almost constant level of adenosine triphosphate (ATP) to safeguard neurotransmission during varying workloads. In the study reported in this letter, it is argued that the vesicular release of neurotransmitter and the recycling of transmitter via astrocytes may itself be a mechanism of ATP homeostasis. In a minimal metabolic model of a presynaptic axon bouton, the accumulation of glutamate into vesicles and the activity-dependent supply of its precursor glutamine by astrocytes generated a steady-state level of ATP that was independent of the workload. When the workload increased, an enhanced supply of glutamine raised the rate of ATP production through the conversion of glutamate to the Krebs cycle intermediate α-ketoglutarate. The accumulation and release of glutamate, on the other hand, acted as a leak that diminished ATP production when the workload decreased. The fraction of ATP that the axon spent on the release and recycling of glutamate was small (4.7%), irrespective of the workload. Increasing this fraction enhanced the speed of ATP homeostasis and reduced the futile production of ATP. The model can be extended to axons releasing other, or coreleasing multiple, transmitters. Hence, the activity-dependent formation and release of neurotransmitter may be a universal mechanism of ATP homeostasis.
{"title":"Local Glutamate-Glutamine Cycling Underlies Presynaptic ATP Homeostasis","authors":"Reinoud Maex","doi":"10.1162/NECO.a.1490","DOIUrl":"10.1162/NECO.a.1490","url":null,"abstract":"Presynaptic axon terminals maintain in their cytosol an almost constant level of adenosine triphosphate (ATP) to safeguard neurotransmission during varying workloads. In the study reported in this letter, it is argued that the vesicular release of neurotransmitter and the recycling of transmitter via astrocytes may itself be a mechanism of ATP homeostasis. In a minimal metabolic model of a presynaptic axon bouton, the accumulation of glutamate into vesicles and the activity-dependent supply of its precursor glutamine by astrocytes generated a steady-state level of ATP that was independent of the workload. When the workload increased, an enhanced supply of glutamine raised the rate of ATP production through the conversion of glutamate to the Krebs cycle intermediate α-ketoglutarate. The accumulation and release of glutamate, on the other hand, acted as a leak that diminished ATP production when the workload decreased. The fraction of ATP that the axon spent on the release and recycling of glutamate was small (4.7%), irrespective of the workload. Increasing this fraction enhanced the speed of ATP homeostasis and reduced the futile production of ATP. The model can be extended to axons releasing other, or coreleasing multiple, transmitters. Hence, the activity-dependent formation and release of neurotransmitter may be a universal mechanism of ATP homeostasis.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"38 3","pages":"403-438"},"PeriodicalIF":2.1,"publicationDate":"2026-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146121152","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}
Active inference is a process theory of perception, learning, and decision making that is applied to a range of research fields, including neuroscience, robotics, psychology, and machine learning. Active inference rests on an objective function called the expected free energy, which can be justified by the intuitive plausibility of its formulations—for example, the risk plus ambiguity and information gain/pragmatic value formulations. This letter seeks to formalize the problem of deriving these formulations from a single root expected free energy definition—the unification problem. Then we analyze two approaches to defining expected free energy. More precisely, the expected free energy is either defined as (1) the risk over observations plus ambiguity or (2) the risk over states plus ambiguity. In the first setting, no rigorous mathematical justification for the expected free energy has been proposed to date, but all the formulations can be recovered from it by assuming that the likelihood of target distribution T(o|s) is the likelihood of the generative model P(o|s). Importantly, under this likelihood constraint, if the likelihood is lossless,1 then prior preferences over observations can be defined arbitrarily. However, in the more general case of partially observable Markov decision processes (POMDPs), we demonstrate that the likelihood constraint effectively restricts the set of valid prior preferences over observations. Indeed, only a limited class of prior preferences over observations is compatible with the likelihood mapping of the generative model. In the second setting, a justification of the root expected free energy definition exists, but this setting only accounts for two formulations: the risk over states plus ambiguity and entropy plus expected energy formulations. We conclude with a discussion of the conditions under which a unification of expected free energy formulations has been proposed in the literature by appeal to the free energy principle in the specific context of systems without random fluctuations.
{"title":"Reframing the Expected Free Energy: Four Formulations and a Unification","authors":"Théophile Champion;Howard Bowman;Dimitrije Marković;Marek Grześ","doi":"10.1162/NECO.a.1491","DOIUrl":"10.1162/NECO.a.1491","url":null,"abstract":"Active inference is a process theory of perception, learning, and decision making that is applied to a range of research fields, including neuroscience, robotics, psychology, and machine learning. Active inference rests on an objective function called the expected free energy, which can be justified by the intuitive plausibility of its formulations—for example, the risk plus ambiguity and information gain/pragmatic value formulations. This letter seeks to formalize the problem of deriving these formulations from a single root expected free energy definition—the unification problem. Then we analyze two approaches to defining expected free energy. More precisely, the expected free energy is either defined as (1) the risk over observations plus ambiguity or (2) the risk over states plus ambiguity. In the first setting, no rigorous mathematical justification for the expected free energy has been proposed to date, but all the formulations can be recovered from it by assuming that the likelihood of target distribution T(o|s) is the likelihood of the generative model P(o|s). Importantly, under this likelihood constraint, if the likelihood is lossless,1 then prior preferences over observations can be defined arbitrarily. However, in the more general case of partially observable Markov decision processes (POMDPs), we demonstrate that the likelihood constraint effectively restricts the set of valid prior preferences over observations. Indeed, only a limited class of prior preferences over observations is compatible with the likelihood mapping of the generative model. In the second setting, a justification of the root expected free energy definition exists, but this setting only accounts for two formulations: the risk over states plus ambiguity and entropy plus expected energy formulations. We conclude with a discussion of the conditions under which a unification of expected free energy formulations has been proposed in the literature by appeal to the free energy principle in the specific context of systems without random fluctuations.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":"38 3","pages":"439-469"},"PeriodicalIF":2.1,"publicationDate":"2026-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146121225","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}