Related papers: Mixed states in a sparsely encoded associative mem…
The faithful storage and coherent manipulation of quantum states with matter-systems enable the construction of large-scale quantum networks based on quantum repeater. To achieve useful communication rates, highly multimode quantum memories…
Large language models demonstrate remarkable ability in factual recall, yet the fundamental limits of storing and retrieving input--output associations with neural networks remain unclear. We study these limits in a minimal setting: a…
This work focuses on the training dynamics of one associative memory module storing outer products of token embeddings. We reduce this problem to the study of a system of particles, which interact according to properties of the data…
We investigate the minimal number of failures that can partition a system where processes communicate both through shared memory and by message passing. We prove that this number precisely captures the resilience that can be achieved by…
Matrix product operators allow efficient descriptions (or realizations) of states on a 1D lattice. We consider the task of learning a realization of minimal dimension from copies of an unknown state, such that the resulting operator is…
Associative memories in the brain receive and store patterns of activity registered by the sensory neurons, and are able to retrieve them when necessary. Due to their importance in human intelligence, computational models of associative…
Multiprocess systems, including grid systems, multiprocessors and multicore computers, incorporate a variety of specialized hardware and software mechanisms, which speed computation, but result in complex memory behavior. As a consequence,…
We prove that a general upper bound on the maximal mutual information of quantum channels is saturated in the case of Pauli channels with an arbitrary degree of memory. For a subset of such channels we explicitly identify the optimal signal…
We present a \emph{pairwise normal form} for finite-state shared memory concurrent programs: all variables are shared between exactly two processes, and the guards on transitions are conjunctions of conditions over this pairwise shared…
Qualitatively, some real networks in the brain could be characterized as 'small worlds', in the sense that the structure of their connections is intermediate between the extremes of an orderly geometric arrangement and of a…
Non-locality is a fundamental trait of quantum many-body systems, both at the level of pure states, as well as at the level of mixed states. Due to non-locality, mixed states of any two subsystems are correlated in a stronger way than what…
Memory layers use a trainable key-value lookup mechanism to add extra parameters to a model without increasing FLOPs. Conceptually, sparsely activated memory layers complement compute-heavy dense feed-forward layers, providing dedicated…
Chimera states and bump states are collective synchronization phenomena observed independently (at different parameter regions) in networks of coupled nonlinear oscillators. And while chimera states are characterized by coexistence of…
With a statistical measure of distance, we derive a classical uncertainty relation for processes traversing nonequilibrium states both transiently and irreversibly. The geometric uncertainty associated with dynamical histories that we…
Sparse codes in neuroscience have been suggested to offer certain computational advantages over other neural representations of sensory data. To explore this viewpoint, a sparse code is used to represent natural images in an optimal control…
Bounds analogous to entropic uncertainty relations allow one to design practical tests to detect quantum entanglement by a collective measurement performed on several copies of the state analyzed. This approach, initially worked out for…
We study a pulse-coupled dynamics of excitable elements in uncorrelated scale-free networks. Regimes of self-sustained activity are found for homogeneous and inhomogeneous couplings, in which the system displays a wide variety of behaviors,…
We present a model to describe the concentration-dependent growth of protein filaments. Our model contains two states, a low entropy/high affinity ordered state and a high entropy/low affinity disordered state. Consistent with experiments,…
Calculation of topological order parameters, such as the topological entropy and topological mutual information, are used to determine whether states possess topological order. Their calculation is expected to give reliable results when the…
A scheme for generating the maximally entangled mixed state of two atoms on-resonance asymmetrically coupled to a single mode optical cavity field is presented. The part frontier of both maximally entangled mixed states and maximal Bell…