Unified perspective on Hopfield networks with attention module.
problem Understanding and optimizing Hopfield networks with attention mechanisms.
method Study of BM counterparts of modern Hopfield networks and their salient properties.
result Introduction of AttnBM with tractable likelihood and gradient.
Modern Hopfield networks help prevent forgetting in generative models after task changes.
problem How to prevent forgetting in generative models after task changes.
method Introduce intrinsic forgetting as an increase in Hopfield energy after task change, analyze memory replay effectiveness, and validate predictions in experiments.
result High-energy, outlier-like samples are more forgettable than cluster-like samples, and energy-based selection of replay samples mitigates forgetting.
Enhanced Hopfield model boosts memory retrieval capacity.
problem Memory retrieval in modern Hopfield models with limited capacity.
method Introduces a learnable feature map transforming energy function into kernel space, minimizing separation loss for uniform memory distribution.
result Significant reduction in metastable states, enhancing memory capacity and retrieval accuracy.
Sparse Hopfield model improves memory retrieval with fewer connections.
problem Memory retrieval efficiency with fewer connections.
method Sparse extension of Hopfield model, derived from sparse entropic regularizer.
result Sparse Hopfield model achieves tighter error bounds and better performance.
CLuP achieves near optimal ground state energies for positive and negative Hopfield models.
problem Finding near optimal ground state energies for positive and negative Hopfield models.
method Controlled Loosening-up (CLuP) algorithm with fully lifted random duality theory (fl RDT).
result Achieves ground state free energies of 1.77 and 0.33 for positive and negative Hopfield models respectively. ERM uses energy-based selection to improve recursive reasoning.
problem Lack of principled inference mechanism in recursive models.
method Energy-guided Recursive Model (ERM) introduces Hopfield energies for trajectory selection.
result ERM achieves optimal solutions on various puzzles.
Unified framework for non-linear attention using modern Hopfield networks.
problem Improving transformer model's understanding of complex relationships and efficiency.
method Proposes an energy functional based on Modern Hopfield Networks (MNH) to unify linear and non-linear attention mechanisms.
result Context wells encapsulate contextual relationships among tokens, offering a richer representation of non-linear data.
A modern Hopfield network improves deep learning with better memory and attention.
problem Improving memory and attention mechanisms in deep learning.
method Introducing a new Hopfield network with continuous states and a novel update rule.
result The new Hopfield network can store and retrieve patterns efficiently with low errors.
Generative diffusion models mimic biological memory networks, encoding associative dynamics in deep neural weights.
problem Understanding long-term memory mechanisms in neuroscience and AI.
method Interpreting generative diffusion models as energy-based models and comparing them to Hopfield networks.
result Generative diffusion models can encode associative dynamics of Hopfield networks in deep neural weights.
A new theory explains large associative memory with biological plausibility.
problem Large associative memory in neurobiology and machine learning.
method Microscopic theory with hidden neurons and two-body interactions.
result Valid model of large associative memory with biological plausibility.
Analog method solves portfolio optimization problems faster and more efficiently.
problem Accurate covariance matrix estimation and fast optimal portfolio selection for financial applications.
method Two-step process using equilibrium propagation and analog Hopfield networks.
result Fully analog pipeline calculates optimal portfolios in energy-efficient manner.
Stochastic attention learns to retrieve and generate from memory without training.
problem Learning to retrieve and generate from memory efficiently.
method Langevin dynamics on modern Hopfield energy for stochastic attention.
result Stochastic attention can retrieve and generate from memory without training, matching gold standards.
Efficient sparse modern Hopfield models are introduced for memory retrieval and learning tasks.
problem Efficient modern Hopfield models for memory retrieval and learning tasks.
method Nonparametric interpretation of Hopfield models as a regression problem.
result Sparse-structured modern Hopfield models with sub-quadratic complexity.
We propose a modification of the cost function of the Hopfield model whose salient features shine in its Taylor expansion and result in more than pairwise interactions with alternate signs, suggesting a unified framework for handling both with deep learning and network pruning. In our analysis, we heavily rely on the H…
Hebbian learning derived from maximum entropy principles.
problem Storing and retrieving information in neural networks.
method Maximum entropy extremization to derive Hebbian learning rules.
result Hebbian learning rules converge to Hopfield model in the big data limit.
We analyze computational limits of modern Hopfield models based on pattern norms.
problem Understanding the efficiency of modern Hopfield models from a fine-grained complexity perspective.
method Fine-grained complexity analysis and upper bound criterion for pattern norms.
result Below a specific norm threshold, efficient variants of modern Hopfield models exist.
Energy Transformer integrates attention, energy models, and associative memory.
problem Lack of clear theoretical foundations in attention mechanisms and straightforward design of energy functions in energy-based models.
method Proposes Energy Transformer, a sequence of attention layers with a specifically engineered energy function.
result Obtained strong results on graph anomaly detection and classification tasks.
STanHop predicts multivariate time series with memory-enhanced capabilities.
problem Predicting multivariate time series with memory-enhanced capabilities.
method Sparse Tandem Hopfield Network (STanHop) with two external memory modules.
result STanHop outperforms dense Hopfield models in memory retrieval error.
Hopfield networks outperform deep-learning methods in portfolio optimization.
problem Optimizing portfolios and managing asset allocation efficiently.
method Application of Hopfield networks to portfolio optimization, using combinatorial purged cross-validation.
result Modern Hopfield Networks perform on par or better than deep-learning methods, with faster training times and better stability.
A new Hopfield model reduces inefficiency in large transformer models.
problem Inefficiency in training large transformer-based models.
method Introduces an Outlier-Efficient Hopfield Model (OutEffHop) to improve model performance.
result Achieves up to 26% reduction in model output norms across four models.
DeepRC uses Hopfield networks and attention to classify immune repertoires.
problem Classifying the vast number of immunosequences of an individual.
method Integrates transformer-like attention into deep learning architectures.
result DeepRC outperforms other methods in predictive performance.
RBM models reveal how hidden unit tail behavior affects pattern reconstruction.
problem Understanding how the tail behavior of hidden units in RBMs influences pattern reconstruction.
method Identified an effective energy function for RBMs and studied its local minima.
result The ability to reconstruct patterns depends on the tail behavior of the hidden unit prior distribution.
A new associative memory uses Sinkhorn divergence for efficient pattern retrieval.
problem Efficiently retrieving patterns from large datasets of weighted point clouds.
method Derived retrieval dynamics as a SHK gradient flow, discretized for a deterministic algorithm.
result Proved basin invariance, geometric convergence, and robust recovery from perturbations.
Multitask algorithms typically use task similarity information as a bias to speed up and improve the performance of learning processes. Tasks are learned jointly, sharing information across them, in order to construct models more accurate than those learned separately over single tasks. In this contribution, we present…
BiSHop tackles tabular data challenges with sparse Hopfield layers.
problem Non-rotationally invariant data structure and feature sparsity in tabular data.
method Sequential column-wise and row-wise processing through interconnected directional learning modules with generalized sparse modern Hopfield layers.
result BiSHop surpasses current SOTA methods with significantly less hyperparameter tuning.
New analysis tightens memory capacity of Hopfield models using spherical codes.
problem Optimizing memory capacity in modern Hopfield models and Kernelized Hopfield Models.
method Connecting Hopfield models to spherical codes in information theory, establishing an optimal capacity bound and a sub-linear algorithm.
result First tight and optimal asymptotic memory capacity for modern Hopfield models, matching known lower bounds.
Hopfield networks improve reaction template prediction for few/zero-shot scenarios.
problem Predicting reaction templates for new molecules in CASP.
method Adapted Hopfield networks to associate reaction templates, molecules, and structural information.
result Significantly improved performance for templates with few or zero training examples.
We study the problem of learning associative memory -- a system which is able to retrieve a remembered pattern based on its distorted or incomplete version. Attractor networks provide a sound model of associative memory: patterns are stored as attractors of the network dynamics and associative retrieval is performed by…
Enhances sequence memory capacity in neural networks.
problem Limited sequence capacity in Hopfield-like neural networks.
method Introducing a nonlinear interaction term and a generalized pseudoinverse rule.
result Significantly increased sequence capacity with novel scaling laws.
In this paper, we address the stability of a broad class of discrete-time hypercomplex-valued Hopfield-type neural networks. To ensure the neural networks belonging to this class always settle down at a stationary state, we introduce novel hypercomplex number systems referred to as real-part associative hypercomplex nu…
V-HMN integrates memory mechanisms for improved image recognition.
problem Limited interpretability and high data requirements of existing vision backbones.
method Brain-inspired hierarchical memory modules with iterative refinement.
result V-HMN achieves strong performance on image classification benchmarks.
We propose a general framework for solving statistical mechanics of systems with finite size. The approach extends the celebrated variational mean-field approaches using autoregressive neural networks, which support direct sampling and exact calculation of normalized probability of configurations. It computes variation…
Restricted Boltzmann Machines are described by the Gibbs measure of a bipartite spin glass, which in turn corresponds to the one of a generalised Hopfield network. This equivalence allows us to characterise the state of these systems in terms of retrieval capabilities, both at low and high load. We study the paramagnet…
DMs emerge from DenseAMs, transitioning from memorization to generalization.
problem Hindered memory retrieval in DenseAMs due to spurious states.
method Examined diffusion models through the lens of DenseAMs, focusing on their generative process.
result Identified a critical phase in DMs transitioning from memorization to generalization.
We study Generalised Restricted Boltzmann Machines with generic priors for units and weights, interpolating between Boolean and Gaussian variables. We present a complete analysis of the replica symmetric phase diagram of these systems, which can be regarded as Generalised Hopfield models. We underline the role of the r…
A new memory system handles non-stationary environments by self-sizing and retaining memories.
problem Non-stationary environments where memories arrive over time and must be distinguished from noise.
method A self-sizing continual associative memory that generalizes Hopfield's network, handling adaptation and novelty.
result The memory system grows to the intrinsic memory demand of the environment and retains memories without forgetting.
We consider the problem of inferring the interactions between a set of N binary variables from the knowledge of their frequencies and pairwise correlations. The inference framework is based on the Hopfield model, a special case of the Ising model where the interaction matrix is defined through a set of patterns in the …
HopCPT improves conformal prediction for time series with temporal dependencies.
problem Uncertainty quantification in time series data.
method HopCPT, a novel conformal prediction approach for time series that leverages temporal dependencies.
result HopCPT outperforms state-of-the-art methods on multiple real-world time series datasets.
The study revisits Hopfield's associative memory model and calculates its capacity for two specific pattern basins.
problem Determining the capacity of a Hebbian-Hopfield network for storing binary patterns.
method Using fully lifted random duality theory and numerical analysis, the study calculates the capacity for two specific pattern basins.
result Explicit characterizations of the capacity for the AGS and NLT pattern basins, with remarkable fast lifting convergence.
We unify kernel density estimation and empirical Bayes and address a set of problems in unsupervised learning with a geometric interpretation of those methods, rooted in the concentration of measure phenomenon. Kernel density is viewed symbolically as X⇀Y where the rand…
This paper introduces a hierarchical associative memory model with multiple layers.
problem Limitations of traditional associative memory models with only one hidden layer.
method Develops a fully recurrent model with arbitrary layers, including locally connected ones, and a corresponding energy function.
result The model can dynamically assemble memories using weights from lower layers and higher layers' rules.
Learning to remember long sequences remains a challenging task for recurrent neural networks. Register memory and attention mechanisms were both proposed to resolve the issue with either high computational cost to retain memory differentiability, or by discounting the RNN representation learning towards encoding shorte…
New method uses MHN for associative learning in network embedding.
problem Represent nodes in networks as low-dimensional vectors while incorporating topological and structural information.
method Introduces Modern Hopfield Networks (MHN) for associative learning between node content and neighbors.
result Competitive performance on node classification and linkage prediction tasks.
OLS is a special case of Transformer, revealing its linear nature.
problem Understanding the statistical essence of Transformer architecture.
method Algebraic proof and spectral decomposition of covariance matrix.
result Attention mechanism in Transformers is mathematically equivalent to OLS.
A new method uses a frozen language model to improve sample efficiency in reinforcement learning.
problem Improving sample efficiency in reinforcement learning with partially observable environments.
method FROZEN Hopfield network and HELM (History Embedding Language Model) method.
result HELM achieves new state-of-the-art results on Minigrid and Procgen environments.
A new model for sequential memory using temporal predictive coding.
problem Forming accurate memory of sequential stimuli in the brain.
method Proposes a novel PC-based model called temporal predictive coding (tPC).
result Shows that tPC models can accurately memorize and retrieve sequential inputs.
RBMs learn archetypes when trained on blurred copies of them, revealing a critical sample size.
problem Determining the critical sample size for RBMs to learn archetypes.
method Formal equivalence between RBMs and Hopfield networks, statistical-mechanics of disordered systems, Monte Carlo simulations.
result A phase diagram highlights regions where learning can be accomplished.
A neural network learns from examples and optimizes by dreaming.
problem The gap between training data and biological neural networks' experience.
method Inspired by biological learning, a generalized Hopfield network with Hebbian learning and off-line sleeping mechanisms.
result The network learns from examples, generalizes, and optimizes its storage capacity.