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The plasticity of the conduction delay between neurons plays a fundamental role in learning. However, the exact underlying mechanisms in the brain for this modulation is still an open problem. Understanding the precise adjustment of…

Biological systems have to build models from their sensory data that allow them to efficiently process previously unseen inputs. Here, we study a neural network learning a linearly separable rule using examples provided by a teacher. We…

A spontaneously active neural system that is capable of continual learning should also be capable of homeostasis of both firing rate and connectivity. Experimental evidence suggests that both types of homeostasis exist, and that…

In both machine learning and in computational neuroscience, plasticity in functional neural networks is frequently expressed as gradient descent on a cost. Often, this imposes symmetry constraints that are difficult to reconcile with local…

In this paper, inspired from our previous algorithm, which was based on the theory of Tsallis statistical mechanics, we develop a new evolving stochastic learning algorithm for neural networks. The new algorithm combines deterministic and…

In "Large Associative Memory Problem in Neurobiology and Machine Learning," Dmitry Krotov and John Hopfield introduced a general technique for the systematic construction of neural ordinary differential equations with non-increasing energy…

In this paper, we present data for the lognormal distributions of spike rates, synaptic weights and intrinsic excitability (gain) for neurons in various brain areas, such as auditory or visual cortex, hippocampus, cerebellum, striatum,…

The human ability to flexibly reason using analogies with domain-general content depends on mechanisms for identifying relations between concepts, and for mapping concepts and their relations across analogs. Building on a recent model of…

Auto-associative neural networks (e.g., the Hopfield model implementing the standard Hebbian prescription) serve as a foundational framework for pattern recognition and associative memory in statistical mechanics. However, their…

Recent advances at the intersection of control theory, neuroscience, and machine learning have revealed novel mechanisms by which dynamical systems perform computation. These advances encompass a wide range of conceptual, mathematical, and…

Convolutional networks are ubiquitous in deep learning. They are particularly useful for images, as they reduce the number of parameters, reduce training time, and increase accuracy. However, as a model of the brain they are seriously…

Deep learning networks generally use non-biological learning methods. By contrast, networks based on more biologically plausible learning, such as Hebbian learning, show comparatively poor performance and difficulties of implementation.…

Learning shared structure across environments facilitates rapid learning and adaptive behavior in neural systems. This has been widely demonstrated and applied in machine learning to train models that are capable of generalizing to novel…

We discuss prototype formation in the Hopfield network. Typically, Hebbian learning with highly correlated states leads to degraded memory performance. We show this type of learning can lead to prototype formation, where unlearned states…

Spike-timing dependent plasticity in biological neural networks has been proven to be important during biological learning process. On the other hand, artificial neural networks use a different way to learn, such as Back-Propagation or…

Modeling stochastic dynamics from discrete observations is a key interdisciplinary challenge. Existing methods often fail to estimate the continuous evolution of probability densities from trajectories or face the curse of dimensionality.…

In neuroscience, classical Hopfield networks are the standard biologically plausible model of long-term memory, relying on Hebbian plasticity for storage and attractor dynamics for recall. In contrast, memory-augmented neural networks in…

Incorporating novelties into deep learning systems remains a challenging problem. Introducing new information to a machine learning system can interfere with previously stored data and potentially alter the global model paradigm, especially…

In this paper, we propose novel learning frameworks to tackle optimal control problems by applying the Pontryagin maximum principle and then solving for a Hamiltonian dynamical system. Applying the Pontryagin maximum principle to the…

Unsupervised structure learning in high-dimensional time series data has attracted a lot of research interests. For example, segmenting and labelling high dimensional time series can be helpful in behavior understanding and medical…