How connectivity structure shapes rich and lazy learning in neural circuits.

In theoretical neuroscience, recent work leverages deep learning tools to explore how some network attributes critically influence its learning dynamics. Notably, initial weight distributions with small (resp. large) variance may yield a rich (resp. lazy) regime, where significant (resp. minor) changes to network states and representation are observed over the course of learning. However, in biology, neural circuit connectivity could exhibit a low-rank structure and therefore differs markedly from the random initializations generally used for these studies. As such, here we investigate how the structure of the initial weights -- in particular their effective rank -- influences the network learning regime. Through both empirical and theoretical analyses, we discover that high-rank initializations typically yield smaller network changes indicative of lazier learning, a finding we also confirm with experimentally-driven initial connectivity in recurrent neural networks. Conversely, low-rank initialization biases learning towards richer learning. Importantly, however, as an exception to this rule, we find lazier learning can still occur with a low-rank initialization that aligns with task and data statistics. Our research highlights the pivotal role of initial weight structures in shaping learning regimes, with implications for metabolic costs of plasticity and risks of catastrophic forgetting.

Evolutionary algorithms as an alternative to backpropagation for supervised training of Biophysical Neural Networks and Neural ODEs.

Training networks consisting of biophysically accurate neuron models could allow for new insights into how brain circuits can organize and solve tasks. We begin by analyzing the extent to which the central algorithm for neural network learning -- stochastic gradient descent through backpropagation (BP) -- can be used to train such networks. We find that properties of biophysically based neural network models needed for accurate modelling such as stiffness, high nonlinearity and long evaluation timeframes relative to spike times makes BP unstable and divergent in a variety of cases. To address these instabilities and inspired by recent work, we investigate the use of "gradient-estimating" evolutionary algorithms (EAs) for training biophysically based neural networks. We find that EAs have several advantages making them desirable over direct BP, including being forward-pass only, robust to noisy and rigid losses, allowing for discrete loss formulations, and potentially facilitating a more global exploration of parameters. We apply our method to train a recurrent network of Morris-Lecar neuron models on a stimulus integration and working memory task, and show how it can succeed in cases where direct BP is inapplicable. To expand on the viability of EAs in general, we apply them to a general neural ODE problem and a stiff neural ODE benchmark and find again that EAs can out-perform direct BP here, especially for the over-parameterized regime. Our findings suggest that biophysical neurons could provide useful benchmarks for testing the limits of BP-adjacent methods, and demonstrate the viability of EAs for training networks with complex components.

A biologically inspired architecture with switching units can learn to generalize across backgrounds.

Humans and other animals navigate different environments effortlessly, their brains rapidly and accurately generalizing across contexts. Despite recent progress in deep learning, this flexibility remains a challenge for many artificial systems. Here, we show how a bio-inspired network motif can explicitly address this issue. We do this using a dataset of MNIST digits of varying transparency, set on one of two backgrounds of different statistics that define two contexts: a pixel-wise noise or a more naturalistic background from the CIFAR-10 dataset. After learning digit classification when both contexts are shown sequentially, we find that both shallow and deep networks have sharply decreased performance when returning to the first background - an instance of the catastrophic forgetting phenomenon known from continual learning. To overcome this, we propose the bottleneck-switching network or switching network for short. This is a bio-inspired architecture analogous to a well-studied network motif in the visual cortex, with additional "switching" units that are activated in the presence of a new background, assuming a priori a contextual signal to turn these units on or off. Intriguingly, only a few of these switching units are sufficient to enable the network to learn the new context without catastrophic forgetting through inhibition of redundant background features. Further, the bottleneck-switching network can generalize to novel contexts similar to contexts it has learned. Importantly, we find that - again as in the underlying biological network motif, recurrently connecting the switching units to network layers is advantageous for context generalization.

Modeling functional cell types in spike train data.

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.

Expressive probabilistic sampling in recurrent neural networks.

In sampling-based Bayesian models of brain function, neural activities are assumed to be samples from probability distributions that the brain uses for probabilistic computation. However, a comprehensive understanding of how mechanistic models of neural dynamics can sample from arbitrary distributions is still lacking. We use tools from functional analysis and stochastic differential equations to explore the minimum architectural requirements for $\textit{recurrent}$ neural circuits to sample from complex distributions. We first consider the traditional sampling model consisting of a network of neurons whose outputs directly represent the samples (sampler-only network). We argue that synaptic current and firing-rate dynamics in the traditional model have limited capacity to sample from a complex probability distribution. We show that the firing rate dynamics of a recurrent neural circuit with a separate set of output units can sample from an arbitrary probability distribution. We call such circuits reservoir-sampler networks (RSNs). We propose an efficient training procedure based on denoising score matching that finds recurrent and output weights such that the RSN implements Langevin sampling. We empirically demonstrate our model's ability to sample from several complex data distributions using the proposed neural dynamics and discuss its applicability to developing the next generation of sampling-based brain models.

From lazy to rich to exclusive task representations in neural networks and neural codes.

Neural circuits-both in the brain and in "artificial" neural network models-learn to solve a remarkable variety of tasks, and there is a great current opportunity to use neural networks as models for brain function. Key to this endeavor is the ability to characterize the representations formed by both artificial and biological brains. Here, we investigate this potential through the lens of recently developing theory that characterizes neural networks as "lazy" or "rich" depending on the approach they use to solve tasks: lazy networks solve tasks by making small changes in connectivity, while rich networks solve tasks by significantly modifying weights throughout the network (including "hidden layers"). We further elucidate rich networks through the lens of compression and "neural collapse", ideas that have recently been of significant interest to neuroscience and machine learning. We then show how these ideas apply to a domain of increasing importance to both fields: extracting latent structures through self-supervised learning.

Modeling functional cell types in spike train data.

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.

Heterogeneity in Neuronal Dynamics Is Learned by Gradient Descent for Temporal Processing Tasks.

Individual neurons in the brain have complex intrinsic dynamics that are highly diverse. We hypothesize that the complex dynamics produced by networks of complex and heterogeneous neurons may contribute to the brain's ability to process and respond to temporally complex data. To study the role of complex and heterogeneous neuronal dynamics in network computation, we develop a rate-based neuronal model, the generalized-leaky-integrate-and-fire-rate (GLIFR) model, which is a rate equivalent of the generalized-leaky-integrate-and-fire model. The GLIFR model has multiple dynamical mechanisms, which add to the complexity of its activity while maintaining differentiability. We focus on the role of after-spike currents, currents induced or modulated by neuronal spikes, in producing rich temporal dynamics. We use machine learning techniques to learn both synaptic weights and parameters underlying intrinsic dynamics to solve temporal tasks. The GLIFR model allows the use of standard gradient descent techniques rather than surrogate gradient descent, which has been used in spiking neural networks. After establishing the ability to optimize parameters using gradient descent in single neurons, we ask how networks of GLIFR neurons learn and perform on temporally challenging tasks, such as sequential MNIST. We find that these networks learn diverse parameters, which gives rise to diversity in neuronal dynamics, as demonstrated by clustering of neuronal parameters. GLIFR networks have mixed performance when compared to vanilla recurrent neural networks, with higher performance in pixel-by-pixel MNIST but lower in line-by-line MNIST. However, they appear to be more robust to random silencing. We find that the ability to learn heterogeneity and the presence of after-spike currents contribute to these gains in performance. Our work demonstrates both the computational robustness of neuronal complexity and diversity in networks and a feasible method of training such models using exact gradients.

MouseNet: A biologically constrained convolutional neural network model for the mouse visual cortex.

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.

A scale-dependent measure of system dimensionality.

A fundamental problem in science is uncovering the effective number of degrees of freedom in a complex system: its dimensionality. A system's dimensionality depends on its spatiotemporal scale. Here, we introduce a scale-dependent generalization of a classic enumeration of latent variables, the participation ratio. We demonstrate how the scale-dependent participation ratio identifies the appropriate dimension at local, intermediate, and global scales in several systems such as the Lorenz attractor, hidden Markov models, and switching linear dynamical systems. We show analytically how, at different limiting scales, the scale-dependent participation ratio relates to well-established measures of dimensionality. This measure applied in neural population recordings across multiple brain areas and brain states shows fundamental trends in the dimensionality of neural activity-for example, in behaviorally engaged versus spontaneous states. Our novel method unifies widely used measures of dimensionality and applies broadly to multivariate data across several fields of science.

Network structure mediates functional reorganization induced by optogenetic stimulation of non-human primate sensorimotor cortex.

Because aberrant network-level functional connectivity underlies a variety of neural disorders, the ability to induce targeted functional reorganization would be a profound development toward therapies for neural disorders. Brain stimulation has been shown to induce large-scale network-wide functional connectivity changes (FCC), but the mapping from stimulation to the induced changes is unclear. Here, we develop a model which jointly considers the stimulation protocol and the cortical network structure to accurately predict network-wide FCC in response to optogenetic stimulation of non-human primate primary sensorimotor cortex. We observe that the network structure has a much stronger effect than the stimulation protocol on the resulting FCC. We also observe that the mappings from these input features to the FCC diverge over frequency bands and successive stimulations. Our framework represents a paradigm shift for targeted neural stimulation and can be used to interrogate, improve, and develop stimulation-based interventions for neural disorders.

Single Circuit in V1 Capable of Switching Contexts During Movement Using an Inhibitory Population as a Switch.

As animals adapt to their environments, their brains are tasked with processing stimuli in different sensory contexts. Whether these computations are context dependent or independent, they are all implemented in the same neural tissue. A crucial question is what neural architectures can respond flexibly to a range of stimulus conditions and switch between them. This is a particular case of flexible architecture that permits multiple related computations within a single circuit. Here, we address this question in the specific case of the visual system circuitry, focusing on context integration, defined as the integration of feedforward and surround information across visual space. We show that a biologically inspired microcircuit with multiple inhibitory cell types can switch between visual processing of the static context and the moving context. In our model, the VIP population acts as the switch and modulates the visual circuit through a disinhibitory motif. Moreover, the VIP population is efficient, requiring only a relatively small number of neurons to switch contexts. This circuit eliminates noise in videos by using appropriate lateral connections for contextual spatiotemporal surround modulation, having superior denoising performance compared to circuits where only one context is learned. Our findings shed light on a minimally complex architecture that is capable of switching between two naturalistic contexts using few switching units.

Learning dynamics of deep linear networks with multiple pathways.

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 with both linear and non-linear networks. 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.

Cell-type-specific neuromodulation guides synaptic credit assignment in a spiking neural network.

Brains learn tasks via experience-driven differential adjustment of their myriad individual synaptic connections, but the mechanisms that target appropriate adjustment to particular connections remain deeply enigmatic. While Hebbian synaptic plasticity, synaptic eligibility traces, and top-down feedback signals surely contribute to solving this synaptic credit-assignment problem, alone, they appear to be insufficient. Inspired by new genetic perspectives on neuronal signaling architectures, here, we present a normative theory for synaptic learning, where we predict that neurons communicate their contribution to the learning outcome to nearby neurons via cell-type-specific local neuromodulation. Computational tests suggest that neuron-type diversity and neuron-type-specific local neuromodulation may be critical pieces of the biological credit-assignment puzzle. They also suggest algorithms for improved artificial neural network learning efficiency.

Identification of Multiple Noise Sources Improves Estimation of Neural Responses across Stimulus Conditions.

Most models of neural responses are constructed to reproduce the average response to inputs but lack the flexibility to capture observed variability in responses. The origins and structure of this variability have significant implications for how information is encoded and processed in the nervous system, both by limiting information that can be conveyed and by determining processing strategies that are favorable for minimizing its negative effects. Here, we present a new modeling framework that incorporates multiple sources of noise to better capture observed features of neural response variability across stimulus conditions. We apply this model to retinal ganglion cells at two different ambient light levels and demonstrate that it captures the full distribution of responses. Further, the model reveals light level-dependent changes that could not be seen with previous models, showing both large changes in rectification of nonlinear circuit elements and systematic differences in the contributions of different noise sources under different conditions.

Autoencoder networks extract latent variables and encode these variables in their connectomes.

Advances in electron microscopy and data processing techniques are leading to increasingly large and complete microscale connectomes. At the same time, advances in artificial neural networks have produced model systems that perform comparably rich computations with perfectly specified connectivity. This raises an exciting scientific opportunity for the study of both biological and artificial neural networks: to infer the underlying circuit function from the structure of its connectivity. A potential roadblock, however, is that - even with well constrained neural dynamics - there are in principle many different connectomes that could support a given computation. Here, we define a tractable setting in which the problem of inferring circuit function from circuit connectivity can be analyzed in detail: the function of input compression and reconstruction, in an autoencoder network with a single hidden layer. Here, in general there is substantial ambiguity in the weights that can produce the same circuit function, because largely arbitrary changes to input weights can be undone by applying the inverse modifications to the output weights. However, we use mathematical arguments and simulations to show that adding simple, biologically motivated regularization of connectivity resolves this ambiguity in an interesting way: weights are constrained such that the latent variable structure underlying the inputs can be extracted from the weights by using nonlinear dimensionality reduction methods.

Predictive learning as a network mechanism for extracting low-dimensional latent space representations.

Artificial neural networks have recently achieved many successes in solving sequential processing and planning tasks. Their success is often ascribed to the emergence of the task's low-dimensional latent structure in the network activity - i.e., in the learned neural representations. Here, we investigate the hypothesis that a means for generating representations with easily accessed low-dimensional latent structure, possibly reflecting an underlying semantic organization, is through learning to predict observations about the world. Specifically, we ask whether and when network mechanisms for sensory prediction coincide with those for extracting the underlying latent variables. Using a recurrent neural network model trained to predict a sequence of observations we show that network dynamics exhibit low-dimensional but nonlinearly transformed representations of sensory inputs that map the latent structure of the sensory environment. We quantify these results using nonlinear measures of intrinsic dimensionality and linear decodability of latent variables, and provide mathematical arguments for why such useful predictive representations emerge. We focus throughout on how our results can aid the analysis and interpretation of experimental data.

Nonlinear convergence boosts information coding in circuits with parallel outputs.

Neural circuits are structured with layers of converging and diverging connectivity and selectivity-inducing nonlinearities at neurons and synapses. These components have the potential to hamper an accurate encoding of the circuit inputs. Past computational studies have optimized the nonlinearities of single neurons, or connection weights in networks, to maximize encoded information, but have not grappled with the simultaneous impact of convergent circuit structure and nonlinear response functions for efficient coding. Our approach is to compare model circuits with different combinations of convergence, divergence, and nonlinear neurons to discover how interactions between these components affect coding efficiency. We find that a convergent circuit with divergent parallel pathways can encode more information with nonlinear subunits than with linear subunits, despite the compressive loss induced by the convergence and the nonlinearities when considered separately.

Network Dynamics Governed by Lyapunov Functions: From Memory to Classification.

In 1982, John Hopfield published a neural network model for memory retrieval, a model that became a cornerstone in theoretical neuroscience. In a recent paper, Krotov and Hopfield built on these early studies and showed how a network that incorporates a biologically plausible learning rule governed by a Lyapunov function can effectively perform classification tasks.

Dimensionality in recurrent spiking networks: Global trends in activity and local origins in connectivity.

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.