Neural Computation

The brain uses recurrent spiking neural networks for higher cognitive functions such as symbolic computations, in particular, mathematical computations. We review the current state of research on spike-based symbolic computations of this type. In addition, we present new results which show that surprisingly small spiking neural networks can perform symbolic computations on bit sequences and numbers and even learn such computations using a biologically plausible learning rule. The resulting networks operate in a rather low firing rate regime, where they could not simply emulate artificial neural networks by encoding continuous values through firing rates. Thus, we propose here a new paradigm for symbolic computation in neural networks that provides concrete hypotheses about the organization of symbolic computations in the brain. The employed spike-based network models are the basis for drastically more energy-efficient computer hardware - neuromorphic hardware. Hence, our results can be seen as creating a bridge from symbolic artificial intelligence to energy-efficient implementation in spike-based neuromorphic hardware.

Neuroscientists rely on distributed spatio-temporal patterns of neural activity to understand how neural units contribute to cognitive functions and behavior. However, the extent to which neural activity reliably indicates a units causal contribution to the behavior is not well understood. To address this issue, we provide a systematic multi-site perturbation framework that captures time-varying causal contributions of elements to a collectively produced outcome. Applying our framework to intuitive toy examples and artificial neuronal networks revealed that recorded activity patterns of neural elements may not be generally informative of their causal contribution due to activity transformations within a network. Overall, our findings emphasize the limitations of inferring causal mechanisms from neural activities and offer a rigorous lesioning framework for elucidating causal neural contributions.

The activity and connectivity of neurons in the primate brain underlying behavior cannot yet be completely specified, but neural networks provide complete models of the connectivity and activity that performs specific tasks and provide insight into the neural computations performed by the primate brain (Fetz and Shupe 2003). Studies of neurons in the monkey cortex have shown that short-term memory of sensory events may be mediated by sustained neural activity. Short-term memory tasks have been modeled with dynamic neural networks using a single continuous variable and a gate input to create a sample-and-hold (SAH) function (Zipser 1991; Maier 2003). Networks trained to perform these short-term memory tasks develop hidden unit activity which resembles that of cortical neurons in monkeys performing memory tasks. We here extend the investigation of single-input SAH networks to networks computing SAH for two continuous-variable inputs that have varying degrees of common mode signal. Results provide insights into computational mechanisms of associative short-term memory of sensory signals with common mode components, such as visual inputs to the two eyes, auditory inputs to the ears and proprioceptive input from multiple muscle spindle afferents. We also examined the attractor states that these SAH networks eventually reach after sufficiently long delay periods and found that these were determined by the shapes of the input-output functions of the hidden units rather than network architecture.

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.

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.

Mechanistic and computational models in neuroscience usually take the form of systems of differential or time-recursive equations. The spatio-temporal behavior of such systems is the subject of dynamical systems theory (DST). DST provides a powerful mathematical toolbox for describing and analyzing neurobiological processes at any level, from molecules to behavior, and has been a mainstay of computational neuroscience for decades. Recently, recurrent neural networks (RNNs) became a popular machine learning tool for studying the nonlinear dynamics underlying neural or behavioral observations. By training RNNs on the same behavioral tasks as employed for animal subjects and dissecting their inner workings, insights and hypotheses about the neuro-computational underpinnings of behavior could be generated. Alternatively, RNNs may be trained directly on the physiological and behavioral time series at hand. Ideally, the once trained RNN would then be able to generate data with the same temporal and geometrical properties as those observed. This is called dynamical systems reconstruction, a burgeoning field in machine learning and nonlinear dynamics. Through this more powerful approach the trained RNN becomes a surrogate for the experimentally probed system, as far as its dynamical and computational properties are concerned. The trained system can then be systematically analyzed, probed and simulated. Here we will review this highly exciting and rapidly expanding field, including recent trends in machine learning that may as yet be less well known in neuroscience. We will also discuss important validation tests, caveats, and requirements of RNN-based dynamical systems reconstruction. Concepts and applications will be illustrated with various examples from neuroscience.

A foundational result in neural computation was proving the firing-rate model of neurons defines a universal function approximator. In this paper I prove it is possible for astrocytes to compute anything neurons can, by extending this original proof to a model of calcium waves in astrocytes. I confirm this in a series of computer simulations. The major limit for astrocytes, it turns out, is not their ability to learn solutions but the computational complexity of their network. I suggest some initial experiments that might be used to confirm these predictions.

For solving tasks such as recognizing a song, answering a question, or inverting a sequence of symbols, cortical microcircuits need to integrate and manipulate information that was dispersed over time during the preceding seconds. Creating biologically realistic models for the underlying computations, especially with spiking neurons and for behaviorally relevant integration time spans, is notoriously difficult. We examine the role of spike frequency adaptation in such computations and find that it has a surprisingly large impact. The inclusion of this well known property of a substantial fraction of neurons in the neocortex -- especially in higher areas of the human neocortex -- moves the performance of spiking neural network models for computations on network inputs that are temporally dispersed from a fairly low level up to the performance level of the human brain.

Recent work has claimed that the emergence of grid cells from trained path-integrator circuits is a more fragile phenomenon than previously reported. In this note we critically assess the main analysis and simulation results underlying this claim, within the proper context of previously published theoretical work. Our assessment reveals that the emergence of grid cells is entirely consistent with this prior theory: hexagonal grid cells robustly emerge precisely when prior theory predicts they should, and dont when prior theory predicts they should not.

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.

Recent work has suggested that feedforward residual neural networks (ResNets) approximate iterative recurrent computations. Iterative computations are useful in many domains, so they might provide good solutions for neural networks to learn. Here we quantify the degree to which ResNets learn iterative solutions and introduce a regularization approach that encourages learning of iterative solutions. Iterative methods are characterized by two properties: iteration and convergence. To quantify these properties, we define three indices of iterative convergence. Consistent with previous work, we show that, even though ResNets can express iterative solutions, they do not learn them when trained conventionally on computer vision tasks. We then introduce regularizations to encourage iterative convergent computation and test whether this provides a useful inductive bias. To make the networks more iterative, we manipulate the degree of weight sharing across layers using soft gradient coupling. This new method provides a form of recurrence regularization and can interpolate smoothly between an ordinary ResNet and a "recurrent" ResNet (i.e., one that uses identical weights across layers and thus could be physically implemented with a recurrent network computing the successive stages iteratively across time). To make the networks more convergent we impose a Lipschitz constraint on the residual functions using spectral normalization. The three indices of iterative convergence reveal that the gradient coupling and the Lipschitz constraint succeed at making the networks iterative and convergent, respectively. However, neither recurrence regularization nor spectral normalization improve classification accuracy on standard visual recognition tasks (MNIST, CIFAR-10, CIFAR-100) or on challenging recognition tasks with partial occlusions (Digitclutter). Iterative convergent computation, in these tasks, does not provide a useful inductive bias for ResNets.

In this paper we introduce a novel Salience Affected Artificial Neural Network (SANN) that models the way neuromodulators such as dopamine and noradrenaline affect neural dynamics in the human brain by being distributed diffusely through neocortical regions. This allows one-time learning to take place through strengthening entire patterns of activation at one go. We present a model that accepts a salience signal, and returns a reverse salience signal. We demonstrate that we can tag an image with salience with only a single training iteration, and that the same image will then produces the highest reverse salience signal during classification. We explore the effects of salience on learning via its effect on the activation functions of each node, as well as on the strength of weights in the network. We demonstrate that a salience signal improves classification accuracy of the specific image that was tagged with salience, as well as all images in the same class, while penalizing images in other classes. Results are validated using 5-fold validation testing on MNIST and Fashion MNIST datasets. This research serves as a proof of concept, and could be the first step towards introducing salience tagging into Deep Learning Networks and robotics.

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.

AO_SCPLOWBSTRACTC_SCPLOWA salient difference between artificial and biological neural networks is the complexity and diversity of individual units in the latter (Tasic et al., 2018). This remarkable diversity is present in the cellular and synaptic dynamics. In this study we focus on the role in learning of one such dynamical mechanism missing from most artificial neural network models, short-term synaptic plasticity (STSP). Biological synapses have dynamics over at least two time scales: a long time scale, which maps well to synaptic changes in artificial neural networks during learning, and the short time scale of STSP, which is typically ignored. Recent studies have shown the utility of such short-term dynamics in a variety of tasks (Masse et al., 2019; Perez-Nieves et al., 2021), and networks trained with such synapses have been shown to better match recorded neuronal activity and animal behavior (Hu et al., 2020). Here, we allow the timescale of STSP in individual neurons to be learned, simultaneously with standard learning of overall synaptic weights. We study learning performance on two predictive tasks, a simple dynamical system and a more complex MNIST pixel sequence. When the number of computational units is similar to the task dimensionality, RNNs with STSP outperform standard RNN and LSTM models. A potential explanation for this improvement is the encoding of activity history in the short-term synaptic dynamics, a biological form of long short-term memory. Beyond a role for synaptic dynamics themselves, we find a reason and a role for their diversity: learned synaptic time constants become heterogeneous across training and contribute to improved prediction performance in feedforward architectures. These results demonstrate how biologically motivated neural dynamics improve performance on the fundamental task of predicting future inputs with limited computational resources, and how learning such predictions drives neural dynamics towards the diversity found in biological brains.

Nature endows networks of spiking neurons in the brain with innate computing capabilities. But it has remained an open problem how the genome achieves that. Experimental data imply that the genome encodes synaptic connection probabilities between neurons depending on their genetic types and spatial distance. We show that this low-dimensional parameterization suffices for programming fundamental computing capabilities into networks of spiking neurons. However, this method is only effective if the network employs a substantial number of different neuron types. This provides an intriguing answer to the open question why the brain employs so many neuron types, many more than were used so far in neural network models. Neural networks whose computational function is induced through their connectivity structure, rather than through synaptic plasticity, are distinguished by short wire length and robustness to weight perturbations. These neural networks features are not only essential for the brain, but also for energy-efficient neuromorphic hardware. Significance statementFundamental computing capabilities of neural networks in the brain are innate, i.e., they do not depend on experience-dependent plasticity. Examples are the capability to recognize odors of poisonous food, and the capability to stand up and walk right after birth. But it has remained unknown how the genetic code can achieve that. A prominent aspect of neural networks of the brain that is under genetic control is the connection probability between neurons of different types. We show that this low-dimensional code suffices for inducing substantial innate computing capabilities in neural networks, provided they have -like the brain- a fair number of different neuron types. Hence under this condition structure can induce computational function in neural networks.

AO_SCPLOWBSTRACTC_SCPLOWOne of the most compelling ideas for bridging neuroscience and artificial neural networks is the establishment of a framework based on three main components: network architecture, optimization mechanism, and loss (or objective) function to be minimized. While the first two components have been extensively explored, the definition of a loss or objective function in neuroscience has been addressed less thoroughly, often from perspectives such as predictive coding. In this work, we propose an elementary loss function grounded in the comparison of neuronal responses to two signals: an external one, used for learning, and an internal one, reflecting the acquired knowledge. The loss function is thus simply the basic difference between the two, which, in terms of logical signals, corresponds to a well-known non-linearly separable function: the XOR function. We illustrate with a computational example how a binarized image recognition algorithm can be straightforwardly implemented in an autoencoder, and we show how a neuronal motif organized around an inhibitory neuron could implement such XOR operation and provide a feedback signal that makes optimization possible.

The brains faculty to assimilate and retain information, continually updating its memory while limiting the loss of valuable past knowledge, remains largely a mystery. We address this challenge related to continuous learning in the context of associative memory networks, where the sequential storage of correlated patterns typically requires non-local learning rules or external memory systems. Our work demonstrates how incorporating biologically-inspired inhibitory plasticity enables networks to autonomously explore their attractor landscape. The algorithm presented here allows for the autonomous retrieval of stored patterns, enabling the progressive incorporation of correlated memories. This mechanism is reminiscent of memory consolidation during sleep-like states in biological systems. The resulting framework provides insights into how neural circuits might maintain memories through purely local interactions, and takes a step forward towards a more biologically plausible mechanism for continuous learning. Author summaryCatastrophic forgetting - when acquiring new knowledge seriously degrades previously learned information - remains a fundamental challenge in machine learning, affecting systems from simple associative networks to complex language models. One widely studied approach to mitigate forgetting is memory rehearsal, in which prior stored information are periodically replayed, an idea supported by neurophysiological evidence of memory consolidation during sleep. In this work, we show that networks with plastic inhibitory connections can spontaneously recall stored memories without external guidance. This built-in retrieval mechanism allows for the incorporation of new memories while preserving older ones, opening a path toward a biologically inspired solution to the problem of catastrophic forgetting.

Classic behavioral studies have identified an inverted-U relationship between arousal and performance, while neurophysiology studies have shown that the arousal-related neuromodulator norepinephrine (NE) increases the signal-to-noise ratio (SNR) of neural responses to extrinsic inputs. More recently, abstract computational models suggest that arousal signals uncertainty in predictive internal models and increases the influence of new observations. Here, I present the arousal-regulated filter (ARF), a novel computational model of neural state estimation designed to bridge abstract algorithms, behavioral findings, and basic neural mechanisms. According to the ARF, arousal selectively amplifies feedforward synapses relative to recurrent synapses, consistent with findings from neurophysiology. Computationally, the ARF integrates predictions of an internal model, implemented in recurrent connections, with extrinsic observations, relayed by feedforward projections, to adaptively track dynamic systems. The ARF resembles a Kalman filter but replaces dynamic updating of the Kalman gain matrix with modulation of a scalar gain parameter influenced by arousal, and incorporates a potentially nonlinear activation function. Computational simulations demonstrate ARFs versatility across binary, multi-unit categorical, and continuous neural network architectures that track diffusion and drift-diffusion processes. When the internal model is aligned with environmental dynamics, arousal exhibits an inverted-U relationship with accuracy due to a bias-variance tradeoff, consistent with behavioral results. However, when the internal model is misaligned with the true dynamics (i.e. the true state is unpredictable), increased arousal monotonically improves accuracy. Optimal arousal levels vary systematically, being lower in noisy sensory contexts and higher in volatile environments or when unmodeled dynamics exist. Thus, the ARF provides a unifying framework that links abstract computational algorithms, behavioral phenomena, and neurophysiological mechanisms. The model also offers potential insights into the computational effects of altered arousal states in mental health conditions, with potential implications for new approaches to assessment and treatment. Author SummaryTo effectively navigate the world, the brain must integrate internal predictions with new sensory information. One factor believed to affect this balance is arousal, which controls alertness and attentiveness to new information. Models of the effect of arousal on the brain have tended to be either very abstract (concerning abstract mathematical algorithms) or very concrete (concerning the effect of arousal-related neurotransmitters like norepinephrine on electrical activity in neurons), but the link between these two levels of analysis has not been fully clear. In this study, I introduce the arousal-regulated filter (ARF), a new model designed to bridge abstract computation and concrete neural mechanisms. The model proposes that arousal modulates the influence of new information by altering the balance of different types of neural connections. Through a series of computer simulations of different neural networks, I show that moderate arousal provides a balance between accuracy and responsiveness, which may be disrupted by overly low or high arousal. Overall, this work may help integrate previous theories of arousal and help understand disruptions of arousal in mental illness such as anxiety and posttraumatic stress disorder (PTSD).

In theory, neurons modelled as single layer perceptrons can implement all linearly separable computations. In practice, however, these computations may require arbitrarily precise synaptic weights. This is a strong constraint since both, biological neurons and their artificial counterparts, have to cope with limited precision. Here, we explore how the non-linear processing in dendrites helps overcoming this constraint. We start by finding a class of computations which requires increasing precision with the number of inputs in a perceptron and show that it can be implemented without this constraint in a neuron with sub-linear subunits. Then, we complement this analytical study by a simulation of a biophysical neuron model with two passive dendrites and a soma, and show that it can implement this computation. This works demonstrates a new role of dendrites in neural computation: by distributing the computation across independent subunits, the same computation can be performed more efficiently with less precise tuning of the synaptic weights. We hope that this works not only offers new insight into the importance of dendrites for biological neurons, but also paves the way for new, more efficient architectures of artificial neuromorphic chips. Author SummaryIn theory, we know how much neurons can compute, in practice, the number of possible synaptic weights values limits their computation capacity. Such a limitation holds true for artificial and synthetic neurons. We introduce here a computation where the required means evolve significantly with the number of inputs, this poses a problem as neurons receive multiple thousands of inputs. We study here how the neurons receptive element-called dendrites-can mitigate such a problem. We show that, without dendrites, the largest synaptic weight need to be multiple orders of magnitude larger than the smallest to implement the computation. Yet a neuron with dendrites implements the same computation with constant synaptic weights whatever the number of inputs. This study paves the way for the use of dendritic neurons in a new generation of artificial neural network and neuromorphic chips with a considerably better cost-benefit balance.

In the search for biologically plausible but mathematically precise theories of learning in the brain, recent studies have begun to investigate how key assumptions underlying algorithms for supervised learning in artificial neural networks can be relaxed in biologically plausible ways. Turning to unsupervised learning, we develop biologically more plausible variants of the restricted Boltzmann machine (RBM), and benchmark their performance on MNIST. We show that RBMs with asymmetric connectivity can still be successfully trained with contrastive divergence, even if no two units are reciprocally connected. Furthermore, RBMs are able to learn if the forward, visible-to-hidden layer weights are kept constant and only the backward, hidden-to-visible layer weights are updated. These findings indicate that neural networks with biologically plausible connectivity support contrastive learning.