Neural Computation

Spiking Neural Networks (SNNs) have the potential to replicate the brains computational efficacy by explicitly incorporating action potentials or "spikes", which is not a feature of most artificial neural networks. However, training SNNs is difficult due to the non-differentiable nature of the most common spiking models: integrate-and-fire neurons. This study investigates if some of the difficulty in training SNNs arises from the use of integrate-and-fire neurons, rather than smoother alternatives, like conductance-based neurons. To that end, we considered networks of Morris-Lecar (ML) neurons, a conductance-based neuron model which is differentiable. Networks were built using kinetic synaptic models that smoothly link presynaptic voltage dynamics directly to postsynaptic conductance changes, ensuring that all components remain fully differentiable. Switching to biophysically detailed models of synapses and neurons enabled direct end-to-end training through Backpropagation Through Time (BPTT). Biophysically detailed networks were successfully trained on image classification, regression, and time series prediction tasks. These results demonstrate the feasibility of employing biophysically detailed differentiable point neuron models to create SNNs that function as more accurate paradigms for the study of neural computations and learning. Further, this work confirms that some aspects of the difficulty in translating gradient-based learning algorithms from machine learning may arise from model choice, rather than SNNs being intrinsically difficult to train. 1. Author summaryThe brains information-processing efficiency arises in part from neurons communicating via discrete spikes. Spiking Neural Networks (SNNs) mimic this process at the neuronal level but have been difficult to train as most machine learning algorithms are not directly applicable. Most SNNs use integrate-and-fire neurons, a modelling framework that simplifies spikes into non-differentiable, abrupt voltage changes, which makes them difficult to train with powerful, standard AI training methods that use derivatives to compute gradients (e.g. Backprop). In our work, we asked if this difficulty could be overcome by considering end-to-end differentiable spiking neural networks. We used completely differentiable SNNs using the Morris-Lecar neuron, a biophysically detailed neuron model that produces smooth spikes, along with differentiable kinetic synapses. With the entire network being mathematically differentiable, we found that we could train it directly using standard backpropagation through time on different tasks (regression, classification, and chaotic time series prediction). This work demonstrates that the use of integrate-and-fire models may be limiting applications of machine learning algorithms towards understanding how learning functions in the brain.

The directionality of network information flow dictates how networks process information. A central component of information processing in both biological and artificial neural networks is their ability to perform synergistic integration-a type of computation. We established previously that synergistic integration varies directly with the strength of feedforward information flow. However, the relationships between both recurrent and feedback information flow and synergistic integration remain unknown. To address this, we analyzed the spiking activity of hundreds of neurons in organotypic cultures of mouse cortex. We asked how empirically observed synergistic integration varied with local functional network structure that was categorized into motifs with varying recurrent and feedback information flow. We found that synergistic integration was elevated in motifs with greater recurrent information flow beyond that expected from the local feedforward information flow. Feedback information flow was interrelated with feedforward information flow and was associated with decreased synergistic integration. Our results indicate that synergistic integration is distinctly influenced by the directionality of local information flow. Author SummaryNetworks compute information. That is, they modify inputs to generate distinct outputs. These computations are an important component of network information processing. Knowing how the routing of information in a network influences computation is therefore crucial. Here we asked how a key form of computation--synergistic integration--is related to the direction of local information flow in networks of spiking cortical neurons. Specifically, we asked how information flow between input neurons (i.e., recurrent information flow) and information flow from output neurons to input neurons (i.e., feedback information flow) was related to the amount of synergistic integration performed by output neurons. We found that greater synergistic integration occurred where there was more recurrent information flow. And, lesser synergistic integration occurred where there was more feedback information flow relative to feedforward information flow. These results show that computation, in the form of synergistic integration, is distinctly influenced by the directionality of local information flow. Such work is valuable for predicting where and how network computation occurs and for designing networks with desired computational abilities.

Neural networks seem to be able to handle almost any task they face. This feat involves coping efficiently with different data types, at multiple scales, and with varying statistical properties. Here, we show that this so-called optimal coding can occur at the single-neuron level and does not require adaptation. Differentiator neurons, i.e., neurons that spike whenever there is an increase in the input stimuli, are capable of capturing arbitrary statistics and scale of practically any stimulus they encounter. We show this optimality both analytically and using simulations, which demonstrate how an ideal neuron can handle drastically different probability distributions. While the mechanism we present is an oversimplification of "real" neurons and does not necessarily capture all neuron types, this is also its strength since it can function alongside other neuronal goals such as data manipulation and learning. Depicting the simplicity of neural response to complex stimuli, this result may also indicate a straightforward way to improve current artificial neural networks.

We propose that in order to harness our understanding of neuroscience toward machine learning, we must first have powerful tools for training brain-like models of learning. Although substantial progress has been made toward understanding the dynamics of learning in the brain, neuroscience-derived models of learning have yet to demonstrate the same performance capabilities as methods in deep learning such as gradient descent. Inspired by the successes of machine learning using gradient descent, we demonstrate that models of neuromodulated synaptic plasticity from neuroscience can be trained in Spiking Neural Networks (SNNs) with a framework of learning to learn through gradient descent to address challenging online learning problems. This framework opens a new path toward developing neuroscience inspired online learning algorithms.

Recurrent neural networks (RNNs) have proven to be highly successful in emulating human-like cognitive functions such as working memory. In recent years, RNNs are evolving to incorporate more biophysical realism to produce more plausible predictions on how cognitive tasks are solved in real neural circuits. However, there are major challenges in constructing and training networks with the complex and nonlinear properties of real neurons. A major component of the success of RNNs is that they share the same mathematical base as deep neural networks, permitting highly efficient optimization of model parameters using standard deep learning techniques. To do so, they use abstract representations of neurons which fail to capture the impact of cell-level biophysical and morphologic properties that may benefit network-level function. Expanding task-trained RNNs with biophysical properties such as dendrites and active ionic currents poses substantial challenges, as it moves these models away from the validated training regimes known to be highly effective for RNNs. To address this gap, we developed a biophysically detailed reservoir computing (BRC) framework with the goal of extracting mechanistic insights from biophysical neural models, and propose that these insights can be used to guide model choices that will work for specific categories of cognitive tasks. The BRC network was constructed with synaptically coupled excitatory and inhibitory cells, in which the excitatory cells include multicompartment biophysically active dendrites; motivated by empirical studies suggesting dendrites have desirable computational benefits (e.g. pattern classification and coincidence detection). We trained the BRC network to do a simplified working memory task where it had to maintain the representation of an extrinsic "cue" input. We studied the impact of extrinsic input time constants (fast AMPA vs slow NMDA) and location (dendrite vs soma) on the ability of a network to solve the task. Our results revealed that cue inputs through NMDA receptors are particularly efficient for solving the working memory task. Further, the properties of NMDA receptors are uniquely suited for cue inputs delivered at the dendrite, as networks trained with dendritic AMPA cue inputs failed to solve the task. Detailed examination of the cell and network dynamics that solve the task reveals distinct local network configurations and computing principles for the different types of extrinsic input. Overall, much like the body of mechanistic insights that have underpinned the success of training RNNs, this study lays the groundwork for applying the BRC framework to train biophysically detailed neural models to solve complex human-like cognitive tasks.

The human brain comprises an intricate web of connections that generate complex neural networks capable of storing and processing information. This information depends on multiple factors, including underlying network structure, connectivity, and interactions; and thus, methods to characterize neural networks typically aim to unravel and interpret a combination of these factors. Here, we present four-dimensional (4D) Shannons entropy, a novel quantitative metric of network activity based on the Triple Correlation Uniqueness (TCU) theorem. Triple correlation, which provides a complete and unique characterization of the network, relates three nodes separated by up to four spatiotemporal lags. Here, we evaluate the 4D entropy from the spatiotemporal lag probability distribution function (PDF) of the network activitys triple correlation. Given a spike raster, we compute triple correlation by iterating over time and space. Summing the contributions to the triple correlation over each of the spatial and temporal lag combinations generates a unique 4D spatiotemporal lag distribution, from which we estimate a PDF and compute Shannons entropy. To outline our approach, we first compute 4D Shannons entropy from feedforward motif-class patterns in a simulated spike raster. We then apply this methodology to spiking activity recorded from rat cortical cultures to compare our results to previously published results of pairwise (2D) correlated spectral entropy over time. We find that while first- and second-order metrics of activity (spike rate and cross-correlation) show agreement with previously published results, our 4D entropy computation (which also includes third-order interactions) reveals a greater depth of underlying network organization compared to published pairwise entropy. Ultimately, because our approach is based on the TCU, we propose that 4D Shannons entropy is a more complete tool for neural network characterization. Author SummaryHere, we present a novel entropy metric for neural network characterization, 4D Shannons entropy, based on triple correlation, which measures interactions among up to three neurons in time and space. Per the Triple Correlation Uniqueness (TCU) theorem, our 4D entropy approach is based on a complete and unique characterization of network activity. We first outline the method to obtain 4D Shannons entropy using a simulated spike raster of feedforward three-neuron configurations. We then apply this metric to an open-source, experimental dataset of rat cortical cultures over time to show that while first- and second-order interactions (spike rate and cross-correlation) show similar trends to published results, the TCU-based 4D Shannons entropy metric provides greater insights into later-stage network activity compared to the published pairwise entropy. As this metric is computed from a 4D distribution unique to the network, we propose that utilization of 4D entropy offers a clear advantage compared to currently utilized pairwise entropy metrics for neural network analyses. For this reason, neuroscientific and clinical applications abound - these may include analysis of distinct dynamical states, characterizing responses to medication, and identification of pathological brain networks, such as seizures.

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. Our analysis offers new directions for neuronlevel inductive biases in NeuroAI models using scalable models for neuronal cell-type specific computation.

Artificial neural networks constitute simplified computational models of neural circuits that might help understand how the biological brain solves and represents complex tasks. Previous research revealed that recurrent neural networks (RNNs) with 48 hidden units show human-level performance in restless four-armed bandit tasks but differ from humans with respect to the task strategy employed. Here we systematically examined the impact of network capacity (no. of hidden units) on computational mechanisms and performance. Computational modeling was applied to investigate and compare network behavior between capacity levels as well as between RNNs and human learners. Using a task frequently employed in human cognitive neuroscience work as well as in animal systems neuroscience work, we show that high-capacity networks displayed increased directed exploration and attenuated random exploration relative to low-capacity networks. RNNs with 576 hidden units approached "human-like" exploration strategies, but the overall switch rate and the level of perseveration still deviated from human learners. In the context of the resource-rational framework, which posits a trade-off between reward and policy complexity, human learners may devote more resources to solving the task, albeit without performance benefits over RNNs. Taken together, this work reveals the importance of network capacity on exploration strategies during reinforcement learning and therefore contributes to the goal of building neural networks that behave "human-like" to possibly gain insights into computational mechanisms in human brains.

Most recurrent neural networks (RNNs) do not include a fundamental constraint of real neural circuits: Dales Law, which implies that neurons must be excitatory (E) or inhibitory (I). Dales Law is generally absent from RNNs because simply partitioning a standard networks units into E and I populations impairs learning. However, here we extend a recent feedforward bio-inspired EI network architecture, named Dales ANNs, to recurrent networks, and demonstrate that good performance is possible while respecting Dales Law. This begs the question: What makes some forms of EI network learn poorly and others learn well? And, why does the simple approach of incorporating Dales Law impair learning? Historically the answer was thought to be the sign constraints on EI network parameters, and this was a motivation behind Dales ANNs. However, here we show the spectral properties of the recurrent weight matrix at initialisation are more impactful on network performance than sign constraints. We find that simple EI partitioning results in a singular value distribution that is multimodal and dispersed, whereas standard RNNs have an unimodal, more clustered singular value distribution, as do recurrent Dales ANNs. We also show that the spectral properties and performance of partitioned EI networks are worse for small networks with fewer I units, and we present normalised SVD entropy as a measure of spectrum pathology that correlates with performance. Overall, this work sheds light on a long-standing mystery in neuroscience-inspired AI and computational neuroscience, paving the way for greater alignment between neural networks and biology.

Biological neuronal networks (BNNs) are a source of inspiration and analogy making for researchers that focus on artificial neuronal networks (ANNs). Moreover, neuroscientists increasingly use ANNs as a model for the brain. Despite certain similarities between these two types of networks, important differences can be discerned. First, biological neural networks are sculpted by evolution and the constraints that it entails, whereas artificial neural networks are engineered to solve particular tasks. Second, the network topology of these systems, apart from some analogies that can be drawn, exhibits pronounced differences. Here, we examine strategies to construct recurrent neural networks (RNNs) that instantiate the network topology of brains of different species. We refer to such RNNs as bio-instantiated. We investigate the performance of bio-instantiated RNNs in terms of: i) the prediction performance itself, that is, the capacity of the network to minimize the desired function at hand in test data, and ii) speed of training, that is, how fast during training the network reaches its optimal performance. We examine bio-instantiated RNNs in working memory tasks where task-relevant information must be tracked as a sequence of events unfolds in time. We highlight the strategies that can be used to construct RNNs with the network topology found in BNNs, without sacrificing performance. Despite that we observe no enhancement of performance when compared to randomly wired RNNs, our approach demonstrates how empirical neural network data can be used for constructing RNNs, thus, facilitating further experimentation with biologically realistic network topologies, in contexts where such aspect is desired.

This study explores whether predictive coding (PC) inspired Deep Neural Networks can serve as biologically plausible neural network models of the brain. We compared two PC-inspired training objectives, a predictive and a contrastive approach, to a supervised baseline in a simple Recurrent Neural Network (RNN) architecture. We evaluated the models on key signatures of PC, including mismatch responses, formation of priors, and learning of semantic information. Our results show that the PC-inspired models, especially a locally trained predictive model, exhibited these PC-like behaviors better than a Supervised or an Untrained RNN. Further, we found that activity regularization evokes mismatch response-like effects across all models, suggesting it may serve as a proxy for the energy-saving principles of PC. Finally, we find that Gain Control (an important mechanism in the PC framework) can be implemented using weight regularization. Overall, our findings indicate that PC-inspired models are able to capture important computational principles of predictive processing in the brain, and can serve as a promising foundation for building biologically plausible artificial neural networks. This work contributes to our understanding of the relationship between artificial and biological neural networks, and highlights the potential of PC-inspired algorithms for advancing brain modelling as well as brain-inspired machine learning.

The human brain readily learns tasks in sequence without forgetting previous ones. Artificial neural networks (ANNs), on the other hand, need to be modified to achieve similar performance. While effective, many algorithms that accomplish this are based on weight importance methods that do not correspond to biological mechanisms. Here we introduce a simple, biologically plausible, method for enabling effective continual learning in ANNs. We show that it is possible to learn a weight-dependent plasticity function that prevents catastrophic forgetting over multiple tasks. We highlight the effectiveness of our method by evaluating it on a set of MNIST classification tasks. We further find that the use of our method promotes synaptic multi-modality, similar to that seen in biology.

The process of making inference on networks of spiking neurons is crucial to decipher the underlying mechanisms of neural computation. Mean-field theory simplifies the interactions between neurons to produce macroscopic network behavior, facilitating the study of information processing and computation within the brain. In this study, we perform inference on a mean-field model of spiking neurons to gain insight into likely parameter values, uniqueness and degeneracies, and also to explore how well the statistical relationship between parameters is maintained by traversing across scales. We benchmark against state-of-the-art optimization and Bayesian estimation algorithms to identify their strengths and weaknesses in our analysis. We show that when confronted with dynamical noise or in the case of missing data in the presence of bistability, generating probability distributions using deep neural density estimators outperforms other algorithms, such as adaptive Monte Carlo sampling. However, this class of deep generative models may result in an overestimation of uncertainty and correlation between parameters. Nevertheless, this issue can be improved by incorporating time-delay embedding. Moreover, we show that training deep Neural ODEs on spiking neurons enables the inference of system dynamics from microscopic states. In summary, this work demonstrates the enhanced accuracy and efficiency of inference on networks of spiking neurons when deep learning is harnessed to solve inverse problems in neural computation.

The goal of theoretical neuroscience is to develop models that help us better understand biological intelligence. Such models range broadly in complexity and biological detail. For example, task-optimized recurrent neural networks (RNNs) have generated hypotheses about how the brain may perform various computations, but these models typically assume a fixed weight matrix representing the synaptic connectivity between neurons. From decades of neuroscience research, we know that synaptic weights are constantly changing, controlled in part by chemicals such as neuromodulators. In this work we explore the computational implications of synaptic gain scaling, a form of neuromodulation, using task-optimized low-rank RNNs. In our neuromodulated RNN (NM-RNN) model, a neuromodulatory subnetwork outputs a low-dimensional neuromodulatory signal that dynamically scales the low-rank recurrent weights of an output-generating RNN. In empirical experiments, we find that the structured flexibility in the NM-RNN allows it to both train and generalize with a higher degree of accuracy than low-rank RNNs on a set of canonical tasks. Additionally, via theoretical analyses we show how neuromodulatory gain scaling endows networks with gating mechanisms commonly found in artificial RNNs. We end by analyzing the low-rank dynamics of trai ned NM-RNNs, to show how task computations are distributed.

Biological neurons integrate their inputs on dendrites using a diverse range of non-linear functions. However the majority of artificial neural networks (ANNs) ignore biological neurons structural complexity and instead use simplified point neurons. Can dendritic properties add value to ANNs? In this paper we investigate this question in the context of continual learning, an area where ANNs suffer from catastrophic forgetting (i.e., ANNs are unable to learn new information without erasing what they previously learned). We propose that dendritic properties can help neurons learn context-specific patterns and invoke highly sparse context-specific subnetworks. Within a continual learning scenario, these task-specific subnetworks interfere minimally with each other and, as a result, the network remembers previous tasks significantly better than standard ANNs. We then show that by combining dendritic networks with Synaptic Intelligence (a biologically motivated method for complex weights) we can achieve significant resilience to catastrophic forgetting, more than either technique can achieve on its own. Our neuron model is directly inspired by the biophysics of sustained depolarization following dendritic NMDA spikes. Our research sheds light on how biological properties of neurons can be used to solve scenarios that are typically impossible for traditional ANNs to solve.

1The brain consists of many interconnected networks with time-varying activity. There are multiple sources of noise and variation yet activity has to eventually converge to a stable state for its computations to make sense. We approached this from a control-theory perspective by applying contraction analysis to recurrent neural networks. This allowed us to find mechanisms for achieving stability in multiple connected networks with biologically realistic dynamics, including synaptic plasticity and time-varying inputs. These mechanisms included anti-Hebbian plasticity, synaptic sparsity and excitatory-inhibitory balance. We leveraged these findings to construct networks that could perform functionally relevant computations in the presence of noise and disturbance. Our work provides a blueprint for how to construct stable plastic and distributed networks.

Recurrent Neural Networks (RNNs) are commonly used models to study neural computation. However, a comprehensive understanding of how dynamics in RNNs emerge from the underlying connectivity is largely lacking. Previous work derived such an understanding for RNNs fulfilling very specific constraints on their connectivity, but it is unclear whether the resulting insights apply more generally. Here we study how network dynamics are related to network connectivity in RNNs trained without any specific constraints on several tasks previously employed in neuroscience. Despite the apparent high-dimensional connectivity of these RNNs, we show that a low-dimensional, functionally relevant subspace of the weight matrix can be found through the identification of operative dimensions, which we define as components of the connectivity whose removal has a large influence on local RNN dynamics. We find that a weight matrix built from only a few operative dimensions is sufficient for the RNNs to operate with the original performance, implying that much of the high-dimensional structure of the trained connectivity is functionally irrelevant. The existence of a low-dimensional, operative subspace in the weight matrix simplifies the challenge of linking connectivity to network dynamics and suggests that independent network functions may be placed in specific, separate subspaces of the weight matrix to avoid catastrophic forgetting in continual learning.

Neural decoding is a widely-used machine learning technique for investigating how behavior, perception and cognition are represented in neural activity. However without careful application data leakage can occur, where information from the test set contaminates the training set, leading to biased estimates of decoding performance and potentially invalidating biological conclusions. Here we use simulated and biological datasets to demonstrate how both supervised and unsupervised data preprocessing, including dimensionality reduction, can introduce leakage in neural decoding studies. We reveal that in some cases leakage can paradoxically decrease decoding performance relative to unbiased estimates, and we provide theoretical analyses explaining how this occurs. We demonstrate that, for autocorrelated neural time series, standard k-fold cross-validation can dramatically overstate performance. Finally we provide detailed recommendations for avoiding data leakage in neural decoding.

Bow-tie or hourglass architecture is commonly found in biological neural networks. Recently, artificial neural networks with bow-tie architecture have been widely used in various machine-learning applications. However, it is unclear how bow-tie architecture in neural circuits can be formed. We address this by training multi-layer neural network models to perform classification tasks. We demonstrate that during network learning and structural changes, non-negative connections amplify error signals and quench neural activity particularly in the hidden layer, resulting in the emergence of the networks bow-tie architecture. We further show that such architecture has low wiring cost, robust to network size, and generalizable to different discrimination tasks. Overall, our work suggests a possible mechanism for the emergence of bow-tie neural architecture and its functional advantages.

Learning in the brains cerebral cortex is widely attributed to synaptic plasticity among cortical neurons. However, a growing body of evidence suggests that alternative processes, such as modulation of intrinsic excitability or gating by subcortical inputs, may also serve as important learning mechanisms. We developed the Bias Adaptive Neural Firing Framework (BANFF) as a simplified model of such phenomena embodied by a learnable bias current for each neuron of a rate-based network. Here, we extend this framework to spiking neural networks. We show that learning such biases enables one recurrent spiking neural network with fixed and random synaptic weights to perform well on nine tasks spanning classification, regression, and closed-loop dynamical systems mimicry. The network learnt a unique bias set for each task, and unlike recurrent synapse-based learning, new learning did not interfere with previous learning. The network was robust to non-stationary F-I curves (spike frequency adaptation), and biases could be learned with a learning algorithm (e-prop) that is more biologically plausible than stock gradient descent. Overall, we show that the BANFF can be extended from rate-based to spiking neural networks, maintaining good multi-task performance with a single network of spiking neurons.