相关论文: Comment on ``Capacity of the Hopfield model''
Recent studies point to the potential storage of a large number of patterns in the celebrated Hopfield associative memory model, well beyond the limits obtained previously. We investigate the properties of new fixed points to discover that…
We generalize the computation of the capacity of exponential Hopfield model from Lucibello and M\'ezard (2024) to more generic pattern ensembles, including binary patterns and patterns generated from a hidden manifold model.
We estimate the critical capacity of the zero-temperature Hopfield model by using a novel and rigorous method. The probability of having a stable fixed point is one when $\alpha\le 0.113$ for a large number of neurons. This result is an…
We investigate the computational limits of the memory retrieval dynamics of modern Hopfield models from the fine-grained complexity analysis. Our key contribution is the characterization of a phase transition behavior in the efficiency of…
The storage capacity of the extremely diluted Hopfield Model is studied by using Monte Carlo techniques. In this work, instead of diluting the synapses according to a given distribution, the dilution of the synapses is obtained…
The Hopfield model is a pioneering neural network model with associative memory retrieval. The analytical solution of the model in mean field limit revealed that memories can be retrieved without any error up to a finite storage capacity of…
We present a nonparametric interpretation for deep learning compatible modern Hopfield models and utilize this new perspective to debut efficient variants. Our key contribution stems from interpreting the memory storage and retrieval…
We use a formal correspondence between thermodynamics and inference, where the number of samples can be thought of as the inverse temperature, to study a quantity called ``learning capacity'' which is a measure of the effective…
In [7] Krotov and Hopfield suggest a generalized version of the well-known Hopfield model of associative memory. In their version they consider a polynomial interaction function and claim that this increases the storage capacity of the…
Recent research has established a connection between modern Hopfield networks (HNs) and transformer attention heads, with guarantees of exponential storage capacity. However, these models still face challenges scaling storage efficiently.…
This note clarifies some confusions (and perhaps throws out more) around model-based reinforcement learning and their theoretical understanding in the context of deep RL. Main topics of discussion are (1) how to reconcile model-based RL's…
In this paper we introduce and exploit the real replica approach for a minimal generalization of the Hopfield model, by assuming the learned patterns to be distributed accordingly to a standard unit Gaussian. We consider the high storage…
On-device machine learning is often constrained by limited storage, particularly in continuous data collection scenarios. This paper presents an empirical study on storage-aware learning, focusing on the trade-off between data quantity and…
This reply tries to rectify some misunderstandings that are in our opinion contained in the Comment by Campostrini and Rossi, <hep-lat 99407008> on our paper <hep-lat 9407003>.
In this article I resolve formally the apparent paradox that arises in the context of the computational model of resistance exercise introduced in my previous work. Contrary to intuition, the model seems to allow for a localized increase in…
In this work we introduce and investigate the properties of the "relativistic" Hopfield model endowed with temporally correlated patterns. First, we review the "relativistic" Hopfield model and we briefly describe the experimental evidence…
We provide a surprising answer to a question raised in S. Ahmad and A.C. Lazer [2], and extend the results of that paper.
We study a class of Hopfield models where the memories are represented by a mixture of Gaussian and binary variables and the neurons are Ising spins. We study the properties of this family of models as the relative weight of the two kinds…
It has been suggested that adversarial examples cause deep learning models to make incorrect predictions with high confidence. In this work, we take the opposite stance: an overly confident model is more likely to be vulnerable to…
In this reply we show that the criticisms raised by J. Noronha are based on a misapplication of the model we have proposed in [A. Jaouadi, M. Telmini, E. Charron, Phys. Rev. A 83, 023616 (2011)]. Here we explicitly discuss the range of…