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Inspired by detailed modelling of biological neurons, spiking neural networks (SNNs) are investigated as biologically plausible and high-performance models of neural computation. The sparse and binary communication between spiking neurons potentially enables powerful and energy-efficient neural networks. The performance of SNNs, however, has remained lacking compared with artificial neural networks. Here we demonstrate how an activity-regularizing surrogate gradient combined with recurrent networks of tunable and adaptive spiking neurons yields the state of the art for SNNs on challenging benchmarks in the time domain, such as speech and gesture recognition. This also exceeds the performance of standard classical recurrent neural networks and approaches that of the best modern artificial neural networks. As these SNNs exhibit sparse spiking, we show that they are theoretically one to three orders of magnitude more computationally efficient compared to recurrent neural networks with similar performance. Together, this positions SNNs as an attractive solution for AI hardware implementations. The use of sparse signals in spiking neural networks, modelled on biological neurons, offers in principle a highly efficient approach for artificial neural networks when implemented on neuromorphic hardware, but new training approaches are needed to improve performance. Using a new type of activity-regularizing surrogate gradient for backpropagation combined with recurrent networks of tunable and adaptive spiking neurons, state-of-the-art performance for spiking neural networks is demonstrated on benchmarks in the time domain.

Predictive coding is a prominent theoretical framework for understanding hierarchical sensory processing in the brain, yet how it could be implemented in networks of cortical neurons is still unclear. While most existing studies have taken a hand-wiring approach to creating microcircuits that match experimental results, recent work in rate-based artificial neural networks revealed that suitable cortical connectivity might result from self-organisation given some fundamental computational principle, such as energy efficiency. As no corresponding approach has studied this in more plausible networks of spiking neurons, we here investigate whether predictive coding properties in a multi-compartment spiking neural network can emerge from energy optimisation. We find that a model trained with an energy objective in addition to a task-relevant objective is able to reconstruct internal representations given top-down expectation signals alone. Additionally, neurons in the energy-optimised model show differential responses to expected versus unexpected stimuli, qualitatively similar to experimental evidence for predictive coding. These findings indicate that predictive-coding-like behaviour might be an emergent property of energy optimisation, providing a new perspective on how predictive coding could be achieved in the cortex.

This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data set generated by a sophisticated financial model, and runs the trained ANN as an agent of the original solver in a fast and efficient way. We test this approach on three different types of solvers, including the analytic solution for the Black-Scholes equation, the COS method for the Heston stochastic volatility model and Brent's iterative root-finding method for the calculation of implied volatilities. The numerical results show that the ANN solver can reduce the computing time significantly.

Many cognitive problems can be decomposed into series of subproblems that are solved sequentially by the brain. When subproblems are solved, relevant intermediate results need to be stored by neurons and propagated to the next subproblem, until the overarching goal has been completed. We will here consider visual tasks, which can be decomposed into sequences of elemental visual operations. Experimental evidence suggests that intermediate results of the elemental operations are stored in working memory as an enhancement of neural activity in the visual cortex. The focus of enhanced activity is then available for subsequent operations to act upon. The main question at stake is how the elemental operations and their sequencing can emerge in neural networks that are trained with only rewards, in a reinforcement learning setting. We here propose a new recurrent neural network architecture that can learn composite visual tasks that require the application of successive elemental operations. Specifically, we selected three tasks for which electrophysiological recordings of monkeys’ visual cortex are available. To train the networks, we used RELEARNN, a biologically plausible four-factor Hebbian learning rule, which is local both in time and space. We report that networks learn elemental operations, such as contour grouping and visual search, and execute sequences of operations, solely based on the characteristics of the visual stimuli and the reward structure of a task. After training was completed, the activity of the units of the neural network elicited by behaviorally relevant image items was stronger than that elicited by irrelevant ones, just as has been observed in the visual cortex of monkeys solving the same tasks. Relevant information that needed to be exchanged between subroutines was maintained as a focus of enhanced activity and passed on to the subsequent subroutines. Our results demonstrate how a biologically plausible learning rule can train a recurrent neural network on multistep visual tasks.

The acquisition of knowledge and skills does not occur in isolation but learning experiences amalgamate within and across domains. The process through which learning can accelerate over time is referred to as learning-to-learn or meta-learning. While meta-learning can be implemented in recurrent neural networks, these networks tend to be trained with architectures that are not easily interpretable or mappable to the brain and with learning rules that are biologically implausible. Specifically, these rules have often employed backpropagation-through-time, which relies on information that is unavailable at synapses that are undergoing plasticity in the brain. Previous studies that exclusively used local information for their weight updates had a limited capacity to integrate information over long timespans and could not easily learn-to-learn. Here, we propose a novel gated memory network named RECOLLECT, which can flexibly retain or forget information by means of a single memory gate and is trained with a biologically plausible trial-and-error-learning that requires only local information. We demonstrate that RECOLLECT successfully learns to represent task-relevant information over increasingly long memory delays in a pro-/anti-saccade task, and that it learns to flush its memory at the end of a trial. Moreover, we show that RECOLLECT can learn-to-learn an effective policy on a reversal bandit task. Finally, we show that the solutions acquired by RECOLLECT resemble how animals learn similar tasks.

In data assimilation, observations are fused with simulations to obtain an accurate estimate of the state and parameters for a given physical system. Combining data with a model, however, while accurately estimating uncertainty, is computationally expensive and infeasible to run in real-time for complex systems. Here, we present a novel particle filter methodology, the Deep Latent Space Particle filter or D-LSPF , that uses neural network-based surrogate models to overcome this computational challenge. The D-LSPF enables filtering in the low-dimensional latent space obtained using Wasserstein AEs with modified vision transformer layers for dimensionality reduction and transformers for parameterized latent space time stepping. As we demonstrate on three test cases, including leak localization in multi-phase pipe flow and seabed identification for fully nonlinear water waves, the D-LSPF runs orders of magnitude faster than a high-fidelity particle filter and 3-5 times faster than alternative methods while being up to an order of magnitude more accurate. The D-LSPF thus enables real-time data assimilation with uncertainty quantification for the test cases demonstrated in this paper.

Intelligence is our ability to learn appropriate responses to new stimuli and situations. Neurons in association cortex are thought to be essential for this ability. During learning these neurons become tuned to relevant features and start to represent them with persistent activity during memory delays. This learning process is not well understood. Here we develop a biologically plausible learning scheme that explains how trial-and-error learning induces neuronal selectivity and working memory representations for task-relevant information. We propose that the response selection stage sends attentional feedback signals to earlier processing levels, forming synaptic tags at those connections responsible for the stimulus-response mapping. Globally released neuromodulators then interact with tagged synapses to determine their plasticity. The resulting learning rule endows neural networks with the capacity to create new working memory representations of task relevant information as persistent activity. It is remarkably generic: it explains how association neurons learn to store task-relevant information for linear as well as non-linear stimulus-response mappings, how they become tuned to category boundaries or analog variables, depending on the task demands, and how they learn to integrate probabilistic evidence for perceptual decisions.

Predictive coding provides a computational paradigm for modeling perceptual processing as the construction of representations accounting for causes of sensory inputs. Here, we developed a scalable, deep network architecture for predictive coding that is trained using a gated Hebbian learning rule and mimics the feedforward and feedback connectivity of the cortex. After training on image datasets, the models formed latent representations in higher areas that allowed reconstruction of the original images. We analyzed low- and high-level properties such as orientation selectivity, object selectivity and sparseness of neuronal populations in the model. As reported experimentally, image selectivity increased systematically across ascending areas in the model hierarchy. Depending on the strength of regularization factors, sparseness also increased from lower to higher areas. The results suggest a rationale as to why experimental results on sparseness across the cortical hierarchy have been inconsistent. Finally, representations for different object classes became more distinguishable from lower to higher areas. Thus, deep neural networks trained using a gated Hebbian formulation of predictive coding can reproduce several properties associated with neuronal responses along the visual cortical hierarchy.

Predictive coding (PC) is an influential theory in neuroscience, which suggests the existence of a cortical architecture that is constantly generating and updating predictive representations of sensory inputs. Owing to its hierarchical and generative nature, PC has inspired many computational models of perception in the literature. However, the biological plausibility of existing models has not been sufficiently explored due to their use of artificial neurons that approximate neural activity with firing rates in the continuous time domain and propagate signals synchronously. Therefore, we developed a spiking neural network for predictive coding (SNN-PC), in which neurons communicate using event-driven and asynchronous spikes. Adopting the hierarchical structure and Hebbian learning algorithms from previous PC neural network models, SNN-PC introduces two novel features: (1) a fast feedforward sweep from the input to higher areas, which generates a spatially reduced and abstract representation of input (i.e., a neural code for the gist of a scene) and provides a neurobiological alternative to an arbitrary choice of priors; and (2) a separation of positive and negative error-computing neurons, which counters the biological implausibility of a bi-directional error neuron with a very high baseline firing rate. After training with the MNIST handwritten digit dataset, SNN-PC developed hierarchical internal representations and was able to reconstruct samples it had not seen during training. SNN-PC suggests biologically plausible mechanisms by which the brain may perform perceptual inference and learning in an unsupervised manner. In addition, it may be used in neuromorphic applications that can utilize its energy-efficient, event-driven, local learning, and parallel information processing nature.

Artificial Neural Networks (ANNs) are bio-inspired models of neural computation that have proven highly effective. Still, ANNs lack a natural notion of time, and neural units in ANNs exchange analog values in a frame-based manner, a computationally and energetically inefficient form of communication. This contrasts sharply with biological neurons that communicate sparingly and efficiently using isomorphic binary spikes. While Spiking Neural Networks (SNNs) can be constructed by replacing the units of an ANN with spiking neurons (Cao et al., 2015; Diehl et al., 2015) to obtain reasonable performance, these SNNs use Poisson spiking mechanisms with exceedingly high firing rates compared to their biological counterparts. Here we show how spiking neurons that employ a form of neural coding can be used to construct SNNs that match high-performance ANNs and match or exceed state-of-the-art in SNNs on important benchmarks, while requiring firing rates compatible with biological findings. For this, we use spike-based coding based on the firing rate limiting adaptation phenomenon observed in biological spiking neurons. This phenomenon can be captured in fast adapting spiking neuron models, for which we derive the effective transfer function. Neural units in ANNs trained with this transfer function can be substituted directly with adaptive spiking neurons, and the resulting Adaptive SNNs (AdSNNs) can carry out competitive classification in deep neural networks without further modifications. Adaptive spike-based coding additionally allows for the dynamic control of neural coding precision: we show empirically how a simple model of arousal in AdSNNs further halves the average required firing rate and this notion naturally extends to other forms of attention as studied in neuroscience. AdSNNs thus hold promise as a novel and sparsely active model for neural computation that naturally fits to temporally continuous and asynchronous applications.