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We develop a statistical mechanical approach based on the replica method to study the design space of deep and wide neural networks constrained to meet a large number of training data. Specifically, we analyze the configuration space of the…
Dense Associative Memories or modern Hopfield networks permit storage and reliable retrieval of an exponentially large (in the dimension of feature space) number of memories. At the same time, their naive implementation is non-biological,…
For decades, conventional computers based on the von Neumann architecture have performed computation by repeatedly transferring data between their processing and their memory units, which are physically separated. As computation becomes…
The brain has a great capacity for computation and efficient resolution of complex problems, far surpassing modern computers. Neuromorphic engineering seeks to mimic the basic principles of the brain to develop systems capable of achieving…
We discuss the properties of equilibrium states in an autoassociative memory model storing hierarchically correlated patterns (hereafter, hierarchical patterns). We will show that symmetric mixed states (hereafter, mixed states) are…
Computation in the brain involves multiple types of neurons, yet the organizing principles for how these neurons work together remain unclear. Information theory has offered explanations for how different types of neurons can optimize the…
The instability of mixing in the Kuramoto model of coupled phase oscillators is the key to understanding a range of spatiotemporal patterns, which feature prominently in collective dynamics of systems ranging from neuronal networks, to…
A stable population network is hard to interrupt without any ecological consequences. A communication blockage between patches may destabilize the populations in the ecological network. This work deals with the construction of a safe cut…
We present a computational model based on the CRISP theory (Content Representation, Intrinsic Sequences, and Pattern completion) of the hippocampus that allows to continuously store pattern sequences online in a one-shot fashion. Rather…
Persistence diagrams have been widely used to quantify the underlying features of filtered topological spaces in data visualization. In many applications, computing distances between diagrams is essential; however, computing these distances…
Stochastic renewal processes are ubiquitous across physics, biology, and the social sciences. Here, we show that continuous-time renewal dynamics can naturally produce a mixed discrete-continuous structure, with a macroscopic fraction of…
The nature of yield in amorphous materials under stress has yet to be fully elucidated. In particular, understanding how microscopic rearrangement gives rise to macroscopic structural and rheological signatures in disordered systems is…
High-dimensional neural activity often reside in a low-dimensional subspace, referred to as neural manifolds. Grid cells in the medial entorhinal cortex provide a periodic spatial code that are organized near a toroidal manifold,…
In-memory computing is an emerging computing paradigm that could enable deeplearning inference at significantly higher energy efficiency and reduced latency. The essential idea is to map the synaptic weights corresponding to each layer to…
A synaptic theory of Working Memory (WM) has been developed in the last decade as a possible alternative to the persistent spiking paradigm. In this context, we have developed a neural mass model able to reproduce exactly the dynamics of…
While information processing in complex systems can be described in abstract, general terms, there are cases in which the relation between these computations and the physical substrate of the underlying system is itself of interest.…
Various features of the development of individual living species, including individual humans, are programmed. Is death also programmed, and if yes, how is it implemented and what can be the underlying mechanism providing the inevitability…
Hyperdimensional computing (HDC) is an emerging computational framework that takes inspiration from attributes of neuronal circuits such as hyperdimensionality, fully distributed holographic representation, and (pseudo)randomness. When…
Spiking neural networks excel at event-driven sensing. Yet, maintaining task-relevant context over long timescales both algorithmically and in hardware, while respecting both tight energy and memory budgets, remains a core challenge in the…
A disordered material that cannot relax to equilibrium, such as an amorphous or glassy solid, responds to deformation in a way that depends on its past. In experiments we train a 2D athermal amorphous solid with oscillatory shear, and show…