The simple linear threshold units used in many artificial neural networks have a limited computational capacity. Famously, a single unit cannot handle non-linearly separable problems like XOR. In contrast, real neurons exhibit complex morphologies as well as active dendritic integration, suggesting that their computational capacities outperform those of simple linear units. Considering specific families of Boolean functions, we empirically examine the computational limits of single units that incorporate more complex dendritic structures. For random Boolean functions, we show that there is a phase transition in learnability as a function of the input dimension, with most random functions below a certain critical dimension being learnable and those above not. This critical dimension is best predicted by the overall size of the dendritic arbor. This demonstrates that real neurons have a far higher computational complexity than is usually considered in neural models, whether in machine learning or computational neuroscience. Furthermore, using architectures that are, respectively, more "apical" or "basal" we show that there are non-trivially disjoint sets of learnable functions by each type of neuron. Importantly, these two types of architectures differ in the robustness and generality of the computations they can perform. The basal-like architecture shows a higher probability of function realization, while the apical-like architecture shows an advantage with fast retraining for different functions. Given the cell-type specificity of morphological characteristics, these results suggest both that different components of the dendritic arbor as well as distinct cell types may have distinct computational roles. In single neurons, morphology sculpts computation, shaping not only what neurons do, but how they learn and adapt. Our analysis offers new directions for neuron-level inductive biases in NeuroAI models using scalable models for neuronal cell-type specific computation.

The modern connectivist framing of neural computation emphasizes the primacy of synaptic communication at the risk of neglecting the influence of the surrounding neuromodulatory environment --- a neuron's 'biophysical context.' Decades of experimental work has established two views of neuromodulatory (NMs) influence: 1) NMs significantly alter circuit dynamics and 2) NMs gate synaptic plasticity, acting as a 'third factor' in learning. Here, we unify these perspectives, proposing that neuromodulation via volume transmission implements a powerful computational principle: context factorization. We derive an endogenously neuromodulated Recurrent Neural Network (e-nmRNN) from a rate reduction of NM release, showing how NM concentrations dynamically factorize network connectivity. This framework reveals how multiplicative NM gating distinctly influences dynamical regimes compared to additive input. Crucially, this context factorization enables targeted online credit assignment: learning rules derived for the e-nmRNN are naturally gated by NM concentrations, localizing updates to relevant contexts. We demonstrate that e-nmRNN dynamics can learn to approximate gradient descent, facilitating rapid in-context adaptation akin to meta-learning. Empirically, e-nmRNNs achieve strong compositional generalization in sequence-to-sequence tasks, outperforming baselines and exhibiting greater hyperparameter robustness. Furthermore, when trained on complex multitasking benchmarks, e-nmRNNs develop emergent properties mirroring biological observations, including modularity, cell-type specialization based on NM release, and distinct neuromodulatory timescales encoding task context. The model's interpretability allows us to reverse engineer these emergent structures. Notably, in reinforcement learning tasks, the e-nmRNN learns to encode context and signals like Reward Prediction Error (RPE) within its neuromodulator dynamics, demonstrating a mechanism for RPE-gated online credit assignment essential for learning how to learn. By bridging biophysical mechanisms with computational principles and empirical validation, our work presents e-nmRNNs as a performant, interpretable model for understanding the computational role of neuromodulation in flexible and compositional learning.

Self-assessment of one’s choices, i.e., confidence, is the topic of many decision neuroscience studies. Computational models of confidence, however, are limited to specific scenarios such as between choices with the same value. Here we present a normative framework for modeling decision confidence that is generalizable to various tasks and experimental setups. We further drive the implications of our model from both theoretical and experimental points of view. Specifically, we show that our model maps to the planning as an inference framework where the objective function is maximizing the gained reward and information entropy of the policy. Moreover, we validate our model on two different psychophysics experiments and show its superiority over other approaches in explaining subjects' confidence reports.

A major goal of computational neuroscience is to build accurate models of the activity of neurons that can be used to interpret their function in circuits. Here, we explore using functional cell types to refine single-cell models by grouping them into functionally relevant classes. Formally, we define a hierarchical generative model for cell types, single-cell parameters, and neural responses, and then derive an expectation-maximization algorithm with variational inference that maximizes the likelihood of the neural recordings. We apply this "simultaneous" method to estimate cell types and fit single-cell models from simulated data, and find that it accurately recovers the ground truth parameters. We then apply our approach to in vitro neural recordings from neurons in mouse primary visual cortex, and find that it yields improved prediction of single-cell activity. We demonstrate that the discovered cell-type clusters are well separated and generalizable, and thus amenable to interpretation. We then compare discovered cluster memberships with locational, morphological, and transcriptomic data. Our findings reveal the potential to improve models of neural responses by explicitly allowing for shared functional properties across neurons.

Not only have deep networks become standard in machine learning, they are increasingly of interest in neuroscience as models of cortical computation that capture relationships between structural and functional properties. In addition they are a useful target of theoretical research into the properties of network computation. Deep networks typically have a serial or approximately serial organization across layers, and this is often mirrored in models that purport to represent computation in mammalian brains. There are, however, multiple examples of parallel pathways in mammalian brains. In some cases, such as the mouse, the entire visual system appears arranged in a largely parallel, rather than serial fashion. While these pathways may be formed by differing cost functions that drive different computations, here we present a new mathematical analysis of learning dynamics in networks that have parallel computational pathways driven by the same cost function. We use the approximation of deep linear networks with large hidden layer sizes to show that, as the depth of the parallel pathways increases, different features of the training set (defined by the singular values of the input-output correlation) will typically concentrate in one of the pathways. This result is derived analytically and demonstrated with numerical simulation. Thus, rather than sharing stimulus and task features across multiple pathways, parallel network architectures learn to produce sharply diversified representations with specialized and specific pathways, a mechanism which may hold important consequences for codes in both biological and artificial systems.

Convolutional neural networks trained on object recognition derive inspiration from the neural architecture of the visual system in mammals, and have been used as models of the feedforward computation performed in the primate ventral stream. In contrast to the deep hierarchical organization of primates, the visual system of the mouse has a shallower arrangement. Since mice and primates are both capable of visually guided behavior, this raises questions about the role of architecture in neural computation. In this work, we introduce a novel framework for building a biologically constrained convolutional neural network model of the mouse visual cortex. The architecture and structural parameters of the network are derived from experimental measurements, specifically the 100-micrometer resolution interareal connectome, the estimates of numbers of neurons in each area and cortical layer, and the statistics of connections between cortical layers. This network is constructed to support detailed task-optimized models of mouse visual cortex, with neural populations that can be compared to specific corresponding populations in the mouse brain. Using a well-studied image classification task as our working example, we demonstrate the computational capability of this mouse-sized network. Given its relatively small size, MouseNet achieves roughly 2/3rds the performance level on ImageNet as VGG16. In combination with the large scale Allen Brain Observatory Visual Coding dataset, we use representational similarity analysis to quantify the extent to which MouseNet recapitulates the neural representation in mouse visual cortex. Importantly, we provide evidence that optimizing for task performance does not improve similarity to the corresponding biological system beyond a certain point. We demonstrate that the distributions of some physiological quantities are closer to the observed distributions in the mouse brain after task training. We encourage the use of the MouseNet architecture by making the code freely available.

How well do deep neural networks fare as models of mouse visual cortex? A majority of research to date suggests results far more mixed than those produced in the modeling of primate visual cortex. Here, we perform a large-scale benchmarking of dozens of deep neural network models in mouse visual cortex with both representational similarity analysis and neural regression. Using the Allen Brain Observatory's 2-photon calcium-imaging dataset of activity in over 6,000 reliable rodent visual cortical neurons recorded in response to natural scenes, we replicate previous findings and resolve previous discrepancies, ultimately demonstrating that modern neural networks can in fact be used to explain activity in the mouse visual cortex to a more reasonable degree than previously suggested. Using our benchmark as an atlas, we offer preliminary answers to overarching questions about levels of analysis (e.g. do models that better predict the representations of individual neurons also predict representational similarity across neural populations?); questions about the properties of models that best predict the visual system overall (e.g. is convolution or category-supervision necessary to better predict neural activity?); and questions about the mapping between biological and artificial representations (e.g. does the information processing hierarchy in deep nets match the anatomical hierarchy of mouse visual cortex?). Along the way, we catalogue a number of models (including vision transformers, MLP-Mixers, normalization free networks, Taskonomy encoders and self-supervised models) outside the traditional circuit of convolutional object recognition. Taken together, our results provide a reference point for future ventures in the deep neural network modeling of mouse visual cortex, hinting at novel combinations of mapping method, architecture, and task to more fully characterize the computational motifs of visual representation in a species so central to neuroscience, but with a perceptual physiology and ecology markedly different from the ones we study in primates.

Biological synaptic plasticity exhibits nonlinearities that are not accounted for by classic Hebbian learning rules. Here, we introduce a simple family of generalized nonlinear Hebbian learning rules. We study the computations implemented by their dynamics in the simple setting of a neuron receiving feedforward inputs. These nonlinear Hebbian rules allow a neuron to learn tensor decompositions of its higher- order input correlations. The particular input correlation decomposed and the form of the decomposition depend on the location of nonlinearities in the plasticity rule. For simple, biologically motivated parameters, the neuron learns eigenvectors of higher-order input correlation tensors. We prove that tensor eigenvectors are attractors and determine their basins of attraction. We calculate the volume of those basins, showing that the dominant eigenvector has the largest basin of attraction. We then study arbitrary learning rules and find that any learning rule that admits a finite Taylor expansion into the neural input and output also has stable equilibria at generalized eigenvectors of higher-order input correlation tensors. Nonlinearities in synaptic plasticity thus allow a neuron to encode higher-order input correlations in a simple fashion.

Neural computation is determined by neurons' dynamics and circuit connectivity. Uncertain and dynamic environments may require neural hardware to adapt to different computational tasks, each requiring different connectivity configurations. At the same time, connectivity is subject to a variety of constraints, placing limits on the possible computations a given neural circuit can perform. Here we examine the hypothesis that the organization of neural circuitry favors computational flexibility: that it makes many computational solutions available, given physiological constraints. From this hypothesis, we develop models of connectivity degree distributions based on constraints on a neuron's total synaptic weight. To test these models, we examine reconstructions of the mushroom bodies from the first instar larva and adult Drosophila melanogaster. We perform a Bayesian model comparison for two constraint models and a random wiring null model. Overall, we find that flexibility under a homeostatically fixed total synaptic weight describes Kenyon cell connectivity better than other models, suggesting a principle shaping the apparently random structure of Kenyon cell wiring. Furthermore, we find evidence that larval Kenyon cells are more flexible earlier in development, suggesting a mechanism whereby neural circuits begin as flexible systems that develop into specialized computational circuits.

Partially inspired by features of computation in visual cortex, deep neural networks compute hierarchical representations of their inputs. While these networks have been highly successful in machine learning, it is still unclear to what extent they can aid our understanding of cortical function. Several groups have developed metrics that provide a quantitative comparison between representations computed by networks and representations measured in cortex. At the same time, neuroscience is well into an unprecedented phase of large-scale data collection, as evidenced by projects such as the Allen Brain Observatory. Despite the magnitude of these efforts, in a given experiment only a fraction of units are recorded, limiting the information available about the cortical representation. Moreover, only a finite number of stimuli can be shown to an animal over the course of a realistic experiment. These limitations raise the question of how and whether metrics that compare representations of deep networks are meaningful on these data sets. Here, we empirically quantify the capabilities and limitations of these metrics due to limited image and neuron sample spaces. We find that the comparison procedure is robust to different choices of stimuli set and the level of sub-sampling that one might expect in a large scale brain survey with thousands of neurons. Using these results, we compare the representations measured in the Allen Brain Observatory in response to natural image presentations. We show that the visual cortical areas are relatively high order representations (in that they map to deeper layers of convolutional neural networks). Furthermore, we see evidence of a broad, more parallel organization rather than a sequential hierarchy, with the primary area VisP (V1) being lower order relative to the other areas.

The dimensionality of a network's collective activity is of increasing interest in neuroscience. This is because dimensionality provides a compact measure of how coordinated network-wide activity is, in terms of the number of modes (or degrees of freedom) that it can independently explore. A low number of modes suggests a compressed low dimensional neural code and reveals interpretable dynamics [1], while findings of high dimension may suggest flexible computations [2, 3]. Here, we address the fundamental question of how dimensionality is related to connectivity, in both autonomous and stimulus-driven networks. Working with a simple spiking network model, we derive three main findings. First, the dimensionality of global activity patterns can be strongly, and systematically, regulated by local connectivity structures. Second, the dimensionality is a better indicator than average correlations in determining how constrained neural activity is. Third, stimulus evoked neural activity interacts systematically with neural connectivity patterns, leading to network responses of either greater or lesser dimensionality than the stimulus.

Despite advances in experimental techniques and accumulation of large datasets concerning the composition and properties of the cortex, quantitative modeling of cortical circuits under in-vivo-like conditions remains challenging. Here we report and publicly release a biophysically detailed circuit model of layer 4 in the mouse primary visual cortex, receiving thalamo-cortical visual inputs. The 45,000-neuron model was subjected to a battery of visual stimuli, and results were compared to published work and new in vivo experiments. Simulations reproduced a variety of observations, including effects of optogenetic perturbations. Critical to the agreement between responses in silico and in vivo were the rules of functional synaptic connectivity between neurons. Interestingly, after extreme simplification the model still performed satisfactorily on many measurements, although quantitative agreement with experiments suffered. These results emphasize the importance of functional rules of cortical wiring and enable a next generation of data-driven models of in vivo neural activity and computations.

A major obstacle to understanding neural coding and computation is the fact that experimental recordings typically sample only a small fraction of the neurons in a circuit. Measured neural properties are skewed by interactions between recorded neurons and the "hidden" portion of the network. To properly interpret neural data and determine how biological structure gives rise to neural circuit function, we thus need a better understanding of the relationships between measured effective neural properties and the true underlying physiological properties. Here, we focus on how the effective spatiotemporal dynamics of the synaptic interactions between neurons are reshaped by coupling to unobserved neurons. We find that the effective interactions from a pre-synaptic neuron r' to a post-synaptic neuron r can be decomposed into a sum of the true interaction from r' to r plus corrections from every directed path from r' to r through unobserved neurons. Importantly, the resulting formula reveals when the hidden units have-or do not have-major effects on reshaping the interactions among observed neurons. As a particular example of interest, we derive a formula for the impact of hidden units in random networks with "strong" coupling-connection weights that scale with [Formula: see text], where N is the network size, precisely the scaling observed in recent experiments. With this quantitative relationship between measured and true interactions, we can study how network properties shape effective interactions, which properties are relevant for neural computations, and how to manipulate effective interactions.

Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural activity arises from the structure of neural connectivity and intrinsic neural dynamics. This problem of structure-driven activity has drawn major interest in computational neuroscience. Existing methods for relating activity and architecture in spiking networks rely on linearizing activity around a central operating point and thus fail to capture the nonlinear responses of individual neurons that are the hallmark of neural information processing. Here, we overcome this limitation and present a new relationship between connectivity and activity in networks of nonlinear spiking neurons by developing a diagrammatic fluctuation expansion based on statistical field theory. We explicitly show how recurrent network structure produces pairwise and higher-order correlated activity, and how nonlinearities impact the networks' spiking activity. Our findings open new avenues to investigating how single-neuron nonlinearities-including those of different cell types-combine with connectivity to shape population activity and function.

We investigate the dynamics of a deterministic finite-sized network of synaptically coupled spiking neurons and present a formalism for computing the network statistics in a perturbative expansion. The small parameter for the expansion is the inverse number of neurons in the network. The network dynamics are fully characterized by a neuron population density that obeys a conservation law analogous to the Klimontovich equation in the kinetic theory of plasmas. The Klimontovich equation does not possess well-behaved solutions but can be recast in terms of a coupled system of well-behaved moment equations, known as a moment hierarchy. The moment hierarchy is impossible to solve but in the mean field limit of an infinite number of neurons, it reduces to a single well-behaved conservation law for the mean neuron density. For a large but finite system, the moment hierarchy can be truncated perturbatively with the inverse system size as a small parameter but the resulting set of reduced moment equations that are still very difficult to solve. However, the entire moment hierarchy can also be re-expressed in terms of a functional probability distribution of the neuron density. The moments can then be computed perturbatively using methods from statistical field theory. Here we derive the complete mean field theory and the lowest order second moment corrections for physiologically relevant quantities. Although we focus on finite-size corrections, our method can be used to compute perturbative expansions in any parameter.

The manner in which different distributions of synaptic weights onto cortical neurons shape their spiking activity remains open. To characterize a homogeneous neuronal population, we use the master equation for generalized leaky integrate-and-fire neurons with shot-noise synapses. We develop fast semi-analytic numerical methods to solve this equation for either current or conductance synapses, with and without synaptic depression. We show that its solutions match simulations of equivalent neuronal networks better than those of the Fokker-Planck equation and we compute bounds on the network response to non-instantaneous synapses. We apply these methods to study different synaptic weight distributions in feed-forward networks. We characterize the synaptic amplitude distributions using a set of measures, called tail weight numbers, designed to quantify the preponderance of very strong synapses. Even if synaptic amplitude distributions are equated for both the total current and average synaptic weight, distributions with sparse but strong synapses produce higher responses for small inputs, leading to a larger operating range. Furthermore, despite their small number, such synapses enable the network to respond faster and with more stability in the face of external fluctuations.

Population rate or activity equations are the foundation of a common approach to modeling for neural networks. These equations provide mean field dynamics for the firing rate or activity of neurons within a network given some connectivity. The shortcoming of these equations is that they take into account only the average firing rate, while leaving out higher-order statistics like correlations between firing. A stochastic theory of neural networks that includes statistics at all orders was recently formulated. We describe how this theory yields a systematic extension to population rate equations by introducing equations for correlations and appropriate coupling terms. Each level of the approximation yields closed equations; they depend only on the mean and specific correlations of interest, without an ad hoc criterion for doing so. We show in an example of an all-to-all connected network how our system of generalized activity equations captures phenomena missed by the mean field rate equations alone.