Cognition arises from the coordinated interaction of brain regions with distinct computational roles. Despite improvements in our ability to extract the dynamics underlying circuit computation from population activity recorded in individual areas, understanding how multiple areas jointly support distributed computation remains a challenge. As part of this effort, we propose a multi-region neural dynamics model composed of two building blocks: _i)_ within-region (potentially driven) nonlinear dynamics and _ii)_ communication channels between regions, parameterized through their impulse response. Together, these choices make it possible to learn nonlinear neural population dynamics and understand the flow of information between regions by drawing from the rich literature of linear systems theory. We develop a state noise inversion free variational filtering and learning algorithm for our model and show, through neuroscientifically inspired numerical experiments, how the proposed model can reveal interpretable characterizations of the local computations within and the flow of information between neural populations. We further validate the efficacy of our approach using simultaneous population recordings from areas V1 and V2.

How should feedback influence recurrent neural network (RNN) learning? One way to address the known limitations of backpropagation through time is to directly adjust neural activities during the learning process. However, it remains unclear how to effectively use feedback to shape RNN dynamics. Here, we introduce error forcing (EF), where the network activity is guided orthogonally toward the zero-error manifold during learning. This method contrasts with alternatives like teaching forcing, which impose stronger constraints on neural activity and thus induce larger feedback influence on circuit dynamics. Furthermore, EF can be understood from a Bayesian perspective as a form of approximate dynamic inference. Empirically, EF consistently outperforms other learning algorithms across several tasks and its benefits persist when additional biological constraints are taken into account. Overall, EF is a powerful temporal credit assignment mechanism and a promising candidate model for learning in biological systems.

Despite many successful examples in which probabilistic inference can account for perception, we have little understanding of how the brain represents and uses structured priors that capture the complexity of natural input statistics. Here we construct a recurrent circuit model that can implicitly represent priors over latent variables, and combine them with sensory and contextual sources of information to encode task-specific posteriors. Inspired by the recent success of diffusion models as means of learning and using priors over images, our model uses dendritic nonlinearities optimized for denoising, and stochastic somatic integration with the degree of noise modulated by an oscillating global signal. Combining these elements into a recurrent network yields a stochastic dynamical system that samples from the prior at a rate prescribed by the period of the global oscillator. Additional inputs reflecting sensory or top-down contextual information alter these dynamics to generate samples from the corresponding posterior, with different input gating patterns selecting different inference tasks. We demonstrate that this architecture can sample from low dimensional nonlinear manifolds and multimodal posteriors. Overall, the model provides a new framework for circuit-level representation of probabilistic information, in a format that facilitates flexible inference.

Prediction is a fundamental capability of all living organisms, and has been proposed as an objective for learning sensory representations. Recent work demonstrates that in primate visual systems, prediction is facilitated by neural representations that follow straighter temporal trajectories than their initial photoreceptor encoding, which allows for prediction by linear extrapolation. Inspired by these experimental findings, we develop a self-supervised learning (SSL) objective that explicitly quantifies and promotes straightening. We demonstrate the power of this objective in training deep feedforward neural networks on smoothly-rendered synthetic image sequences that mimic commonly-occurring properties of natural videos. The learned model contains neural embeddings that are predictive, but also factorize the geometric, photometric, and semantic attributes of objects. The representations also prove more robust to noise and adversarial attacks compared to previous SSL methods that optimize for invariance to random augmentations. Moreover, these beneficial properties can be transferred to other training procedures by using the straightening objective as a regularizer, suggesting a broader utility for straightening as a principle for robust unsupervised learning.

Normative models of synaptic plasticity use computational rationales to arrive at predictions of behavioral and network-level adaptive phenomena. In recent years, there has been an explosion of theoretical work in this realm, but experimental confirmation remains limited. In this review, we organize work on normative plasticity models in terms of a set of desiderata that, when satisfied, are designed to ensure that a given model demonstrates a clear link between plasticity and adaptive behavior, is consistent with known biological evidence about neural plasticity and yields specific testable predictions. As a prototype, we include a detailed analysis of the REINFORCE algorithm. We also discuss how new models have begun to improve on the identified criteria and suggest avenues for further development. Overall, we provide a conceptual guide to help develop neural learning theories that are precise, powerful, and experimentally testable.

In recent years, many researchers have proposed new models for synaptic plasticity in the brain based on principles of machine learning. The central motivation has been the development of learning algorithms that are able to learn difficult tasks while qualifying as "biologically plausible". However, the concept of a biologically plausible learning algorithm is only heuristically defined as an algorithm that is potentially implementable by biological neural networks. Further, claims that neural circuits could implement any given algorithm typically rest on an amorphous concept of "locality" (both in space and time). As a result, it is unclear what many proposed local learning algorithms actually predict biologically, and which of these are consequently good candidates for experimental investigation. Here, we address this lack of clarity by proposing formal and operational definitions of locality. Specifically, we define different classes of locality, each of which makes clear what quantities cannot be included in a learning rule if an algorithm is to qualify as local with respect to a given (biological) constraint. We subsequently use this framework to distill testable predictions from various classes of biologically plausible synaptic plasticity models that are robust to arbitrary choices about neural network architecture. Therefore, our framework can be used to guide claims of biological plausibility and to identify potential means of experimentally falsifying a proposed learning algorithm for the brain.

Understanding how the brain constructs statistical models of the sensory world remains a longstanding challenge for computational neuroscience. Here, we derive an unsupervised local synaptic plasticity rule that trains neural circuits to infer latent structure from sensory stimuli via a novel loss function for approximate online Bayesian inference. The learning algorithm is driven by a local error signal computed between two factors that jointly contribute to neural activity: stimulus drive and internal predictions --- the network's 'impression' of the stimulus. Physiologically, we associate these two components with the basal and apical dendrites of pyramidal neurons, respectively. We show that learning can be implemented online, is capable of capturing temporal dependencies in continuous input streams, and generalizes to hierarchical architectures. Furthermore, we demonstrate both analytically and empirically that the algorithm is more data-efficient than a three-factor plasticity alternative, enabling it to learn statistics of high-dimensional, naturalistic inputs. Overall, the model provides a bridge from mechanistic accounts of synaptic plasticity to algorithmic descriptions of unsupervised probabilistic learning and inference.

Many features of human and animal behavior can be understood in the framework of Bayesian inference and optimal decision making, but the biological substrate of such processes is not fully understood. Neural sampling provides a flexible code for probabilistic inference in high dimensions and explains key features of sensory responses under experimental manipulations of uncertainty. However, since it encodes uncertainty implicitly, across time and neurons, it remains unclear how such representations can be used for decision making. Here we propose a spiking network model that maps neural samples of a task-specific marginal distribution into an instantaneous representation of uncertainty via a procedure inspired by online kernel density estimation, so that its output can be readily used for decision making. Our model is consistent with experimental results at the level of single neurons and populations, and makes predictions for how neural responses and decisions could be modulated by uncertainty and prior biases. More generally, our work brings together conflicting perspectives on probabilistic brain computation.

Identifying the common structure of neural dynamics across subjects is key for extracting unifying principles of brain computation and for many brain machine interface applications. Here, we propose a novel probabilistic approach for aligning stimulus-evoked responses from multiple animals in a common low dimensional manifold and use hierarchical inference to identify which stimulus drives neural activity in any given trial. Our probabilistic decoder is robust to a range of features of the neural responses and significantly outperforms existing neural alignment procedures. When applied to recordings from the mouse olfactory bulb, our approach reveals low-dimensional population dynamics that are odor specific and have consistent structure across animals. Thus, our decoder can be used for increasing the robustness and scalability of neural-based chemical detection.

Recent technological advances in systems neuroscience have led to a shift away from using simple tasks, with low-dimensional, well-controlled stimuli, towards trying to understand neural activity during naturalistic behavior. However, with the increase in number and complexity of task-relevant features, standard analyses such as estimating tuning functions become challenging. Here, we use a Poisson generalized additive model (P-GAM) with spline nonlinearities and an exponential link function to map a large number of task variables (input stimuli, behavioral outputs, or activity of other neurons, modeled as discrete events or continuous variables) into spike counts. We develop efficient procedures for parameter learning by optimizing a generalized cross-validation score and infer marginal confidence bounds for the contribution of each feature to neural responses. This allows us to robustly identify a minimal set of task features that each neuron is responsive to, circumventing computationally demanding model comparison. We show that our estimation procedure outperforms traditional regularized GLMs in terms of both fit quality and computing time. When applied to neural recordings from monkeys performing a virtual reality spatial navigation task, P-GAM reveals mixed selectivity and preferential coupling between neurons with similar tuning.

Neural populations encode the sensory world imperfectly: their capacity is limited by the number of neurons, availability of metabolic and other biophysical resources, and intrinsic noise. The brain is presumably shaped by these limitations, improving efficiency by discarding some aspects of incoming sensory streams, while preferentially preserving commonly occurring, behaviorally-relevant information. Here we construct a stochastic recurrent neural circuit model that can learn efficient, task-specific sensory codes using a novel form of reward-modulated Hebbian synaptic plasticity. We illustrate the flexibility of the model by training an initially unstructured neural network to solve two different tasks: stimulus estimation, and stimulus discrimination. The network achieves high performance in both tasks by appropriately allocating resources and using its recurrent circuitry to best compensate for different levels of noise. We also show how the interaction between stimulus priors and task structure dictates the emergent network representations.

We present a framework for compactly summarizing many recent results in efficient and/or biologically plausible online training of recurrent neural networks (RNN). The framework organizes algorithms according to several criteria: (a) past vs. future facing, (b) tensor structure, (c) stochastic vs. deterministic, and (d) closed form vs. numerical. These axes reveal latent conceptual connections among several recent advances in online learning. Furthermore, we provide novel mathematical intuitions for their degree of success. Testing these algorithms on two parametric task families shows that performances cluster according to our criteria. Although a similar clustering is also observed for pairwise gradient alignment, alignment with exact methods does not explain ultimate performance. This suggests the need for better comparison metrics.

Humans and animals are capable of flexibly switching between a multitude of tasks, each requiring rapid, sensory-informed decision making. Incoming stimuli are processed by a hierarchy of neural circuits consisting of millions of neurons with diverse feature selectivity. At any given moment, only a small subset of these carry task-relevant information. In principle, downstream processing stages could identify the relevant neurons through supervised learning, but this would require many example trials. Such extensive learning periods are inconsistent with the observed flexibility of humans or animals, who can adjust to changes in task parameters or structure almost immediately. Here, we propose a novel solution based on functionally-targeted stochastic modulation. It has been observed that trial-to-trial neural activity is modulated by a shared, low-dimensional, stochastic signal that introduces task-irrelevant noise. Counter-intuitively this noise is preferentially targeted towards task-informative neurons, corrupting the encoded signal. However, we hypothesize that this modulation offers a solution to the identification problem, labeling task-informative neurons so as to facilitate decoding. We simulate an encoding population of spiking neurons whose rates are modulated by a shared stochastic signal, and show that a linear decoder with readout weights approximating neuron-specific modulation strength can achieve near-optimal accuracy. Such a decoder allows fast and flexible task-dependent information routing without relying on hardwired knowledge of the task-informative neurons (as in maximum likelihood) or unrealistically many supervised training trials (as in regression).

Experience constantly shapes neural circuits through a variety of plasticity mechanisms. While the functional roles of some plasticity mechanisms are well-understood, it remains unclear how changes in neural excitability contribute to learning. Here, we develop a normative interpretation of intrinsic plasticity (IP) as a key component of unsupervised learning. We introduce a novel generative mixture model that accounts for the class-specific statistics of stimulus intensities, and we derive a neural circuit that learns the input classes and their intensities. We will analytically show that inference and learning for our generative model can be achieved by a neural circuit with intensity-sensitive neurons equipped with a specific form of IP. Numerical experiments verify our analytical derivations and show robust behavior for artificial and natural stimuli. Our results link IP to non-trivial input statistics, in particular the statistics of stimulus intensities for classes to which a neuron is sensitive. More generally, our work paves the way toward new classification algorithms that are robust to intensity variations.

Jointly characterizing neural responses in terms of several external variables promises novel insights into circuit function, but remains computationally prohibitive in practice. Here we use gaussian process (GP) priors and exploit recent advances in fast GP inference and learning based on Kronecker methods, to efficiently estimate multidimensional nonlinear tuning functions. Our estimator require considerably less data than traditional methods and further provides principled uncertainty estimates. We apply these tools to hippocampal recordings during open field exploration and use them to characterize the joint dependence of CA1 responses on the position of the animal and several other variables, including the animal's speed, direction of motion, and network oscillations.Our results provide an unprecedentedly detailed quantification of the tuning of hippocampal neurons. The model's generality suggests that our approach can be used to estimate neural response properties in other brain regions.

A venerable history of classical work on autoassociative memory has significantly shaped our understanding of several features of the hippocampus, and most prominently of its CA3 area, in relation to memory storage and retrieval. However, existing theories of hippocampal memory processing ignore a key biological constraint affecting memory storage in neural circuits: the bounded dynamical range of synapses. Recent treatments based on the notion of metaplasticity provide a powerful model for individual bounded synapses; however, their implications for the ability of the hippocampus to retrieve memories well and the dynamics of neurons associated with that retrieval are both unknown. Here, we develop a theoretical framework for memory storage and recall with bounded synapses. We formulate the recall of a previously stored pattern from a noisy recall cue and limited-capacity (and therefore lossy) synapses as a probabilistic inference problem, and derive neural dynamics that implement approximate inference algorithms to solve this problem efficiently. In particular, for binary synapses with metaplastic states, we demonstrate for the first time that memories can be efficiently read out with biologically plausible network dynamics that are completely constrained by the synaptic plasticity rule, and the statistics of the stored patterns and of the recall cue. Our theory organises into a coherent framework a wide range of existing data about the regulation of excitability, feedback inhibition, and network oscillations in area CA3, and makes novel and directly testable predictions that can guide future experiments.

It has long been recognised that statistical dependencies in neuronal activity need to be taken into account when decoding stimuli encoded in a neural population. Less studied, though equally pernicious, is the need to take account of dependencies between synaptic weights when decoding patterns previously encoded in an auto-associative memory. We show that activity-dependent learning generically produces such correlations, and failing to take them into account in the dynamics of memory retrieval leads to catastrophically poor recall. We derive optimal network dynamics for recall in the face of synaptic correlations caused by a range of synaptic plasticity rules. These dynamics involve well-studied circuit motifs, such as forms of feedback inhibition and experimentally observed dendritic nonlinearities. We therefore show how addressing the problem of synaptic correlations leads to a novel functional account of key biophysical features of the neural substrate.

Feedforward inhibition and synaptic scaling are important adaptive processes that control the total input a neuron can receive from its afferents. While often studied in isolation, the two have been reported to co-occur in various brain regions. The functional implications of their interactions remain unclear, however. Based on a probabilistic modeling approach, we show here that fast feedforward inhibition and synaptic scaling interact synergistically during unsupervised learning. In technical terms, we model the input to a neural circuit using a normalized mixture model with Poisson noise. We demonstrate analytically and numerically that, in the presence of lateral inhibition introducing competition between different neurons, Hebbian plasticity and synaptic scaling approximate the optimal maximum likelihood solutions for this model. Our results suggest that, beyond its conventional use as a mechanism to remove undesired pattern variations, input normalization can make typical neural interaction and learning rules optimal on the stimulus subspace defined through feedforward inhibition. Furthermore, learning within this subspace is more efficient in practice, as it helps avoid locally optimal solutions. Our results suggest a close connection between feedforward inhibition and synaptic scaling which may have important functional implications for general cortical processing.

Storing a new pattern in a palimpsest memory system comes at the cost of interfering with the memory traces of previously stored items. Knowing the age of a pattern thus becomes critical for recalling it faithfully. This implies that there should be a tight coupling between estimates of age, as a form of familiarity, and the neural dynamics of recollection, something which current theories omit. Using a normative model of autoassociative memory, we show that a dual memory system, consisting of two interacting modules for familiarity and recollection, has best performance for both recollection and recognition. This finding provides a new window onto actively contentious psychological and neural aspects of recognition memory.

Although models based on independent component analysis (ICA) have been successful in explaining various properties of sensory coding in the cortex, it remains unclear how networks of spiking neurons using realistic plasticity rules can realize such computation. Here, we propose a biologically plausible mechanism for ICA-like learning with spiking neurons. Our model combines spike-timing dependent plasticity and synaptic scaling with an intrinsic plasticity rule that regulates neuronal excitability to maximize information transmission. We show that a stochastically spiking neuron learns one independent component for inputs encoded either as rates or using spike-spike correlations. Furthermore, different independent components can be recovered, when the activity of different neurons is decorrelated by adaptive lateral inhibition.