DAM with MRL improves relational reasoning in MANNs.
problem Limited performance of associative memory networks on complex relational reasoning tasks.
method Distributed Associative Memory architecture with Memory Refreshing Loss.
result Enhanced relation reasoning performance of MANNs on long temporal sequence data.
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.
Heretofore, neural networks with external memory are restricted to single memory with lossy representations of memory interactions. A rich representation of relationships between memory pieces urges a high-order and segregated relational memory. In this paper, we propose to separate the storage of individual experience…
The paper studies scaling laws for associative memory mechanisms.
problem Understanding and optimizing learning and memorization processes.
method High-dimensional matrices of outer products of embeddings, relating to transformer models. Derived scaling laws with sample and parameter sizes. Extensive numerical experiments.
result Precise scaling laws and statistical efficiency of estimators.
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…
LLMs can be tricked into recalling facts based on context clues.
problem Manipulation of LLMs' factual recall through context changes.
method Mathematical exploration of transformers' associative memory properties.
result Transformers use self-attention and value matrix for associative memory.
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.
Sigmoid autoencoders can implement associative memory with certain conditions.
problem Implementing associative memory in neural networks.
method Theoretical analysis of overparameterized sigmoid autoencoders using the NTK and iterative maps.
result Overparameterized sigmoid autoencoders can have attractors in the NTK limit, leading to associative memory.
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.
Transformers can store facts efficiently using associative memories.
problem Understanding how transformers store and recall factual information.
method Proved linear scaling of storage capacities for linear and MLP associative memories, introduced a synthetic task, and analyzed gradient flow.
result Shallow transformers can achieve near optimal storage capacity for factual recall tasks using associative memories.
An associative memory is a framework of content-addressable memory that stores a collection of message vectors (or a dataset) over a neural network while enabling a neurally feasible mechanism to recover any message in the dataset from its noisy version. Designing an associative memory requires addressing two main task…
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.
A model of associative memory is studied, which stores and reliably retrieves many more patterns than the number of neurons in the network. We propose a simple duality between this dense associative memory and neural networks commonly used in deep learning. On the associative memory side of this duality, a family of mo…
The paper explores how gradient descent trains associative memories, revealing oscillations and convergence issues.
problem Training dynamics of associative memories in overparameterized and underparameterized settings.
method Reduction to particle system dynamics, theory, and experiments.
result Oscillatory transitory regimes and benign loss spikes in overparameterized settings, suboptimal memorization in underparameterized settings.
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.
Memory capacity of DAM scales exponentially with feature separation, unaffected by correlations.
problem Understanding how feature correlations impact DAM's capacity.
method Developed an empirical framework to analyze DAM's capacity under varying feature correlations and pattern separations.
result Memory capacity scales exponentially with feature separation, unaffected by correlations.
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…
The Unlearning algorithm improves neural network performance in memory tasks.
problem Improving neural network performance in memory tasks.
method Simplified Unlearning algorithm, structured training data, and new regularization technique for Boltzmann Machines.
result The Unlearning rule outperforms traditional Boltzmann-Machine learning in learning hidden probability distributions.
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.
RCAM-based ensemble combines binary classifiers using similarity and vote scheme.
problem Improving binary classification accuracy through ensemble methods.
method RCAM-based ensemble combining classifiers using similarity and recurrent consult-vote scheme.
result RCAM-based ensemble outperforms individual classifiers and majority voting.
Develops hyperparameter transfer methods for Dense Associative Memories.
problem Challenges in transferring hyperparameters for DenseAMs due to unique architecture and activation functions.
method Derives explicit prescriptions for hyperparameter transfer from small to large models.
result Excellent agreement between theoretical and empirical results.
New cooperative dynamics enhances retrieval performance in neural networks.
problem Understanding emergent computational capabilities in disordered systems.
method Leveraging statistical mechanics, extended neural network architecture for hetero-associative memory.
result Layers trained with less informative datasets develop retrieval regions of the same amplitude, leading to optimal performance.
Sharp limits found for storing and retrieving input-output associations in linear associative memories.
problem Understanding the fundamental limits of storing and retrieving input-output associations in neural networks.
method Study of a minimal linear associative memory model, introducing a decoupled model and using statistical physics to characterize storage capacity.
result Linear associative memory can store up to 1/2 log(p) associations, providing a sharp statistical-physics characterization.
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.
Extends DAMs to Gaussian distributions for efficient pattern storage and retrieval.
problem Limited storage capacity and retrieval methods for non-vector pattern representations.
method Introduces a log-sum-exp energy function over Gaussian distributions, using optimal transport maps for retrieval dynamics.
result Proves exponential storage capacity and provides quantitative retrieval guarantees.
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.
Dense Associative Memories outperform classical networks in robustness and signal processing.
problem Improving neural network performance in adversarial attacks and weak signal processing.
method Relaxing replica symmetry in statistical mechanics of spin glasses to analyze unsupervised and supervised learning.
result Explicit analytical investigation of phase diagrams and storage capacities for Dense Associative Memories.
New algorithms for multitask learning with long-term memory.
problem Learning from tasks partitioned into unknown segments with associated hypotheses.
method Online multitask learning algorithms exploiting segmentation and hypothesis association.
result Regret bounds and efficient algorithms for various hypothesis classes.
CICLAD efficiently mines frequent closed itemsets from data streams with minimal memory usage.
problem Mining frequent closed itemsets from data streams is resource-intensive.
method CICLAD is an intersection-based sliding-window FCI miner that optimizes memory usage while maintaining performance.
result CICLAD achieves significantly lower memory footprint compared to existing methods.
Linear memory stores associations up to a logarithmic scale, but listwise retrieval can handle a quadratic scale.
problem How many key-value associations can a linear memory store?
method Analyzed linear memory models for top-1 and listwise retrieval, proving phase transitions and developing asymptotic theories.
result Linear memory has a logarithmic capacity for top-1 retrieval and a quadratic capacity for listwise retrieval.
Muon spectral optimizer outperforms SGD in associative memory tasks.
problem Understanding the advantage of spectral optimizers in learning associative memory.
method Linear associative memory problem, Gaussian inputs and outputs, power law frequency distribution, thresholded gradient approximation.
result Muon significantly outperforms SGD in storage capacity and recovery rates.
A bridge between continuous signals and discrete Ising spins for associative memory.
problem Associative memory in continuous-signal-driven Ising spin systems.
method Multilayer Ising framework with PCA whitening and SimHash projection, coupled to pseudo-inverse memory couplings.
result Finite-size scaling of operational storage capacity with αc(N)=αc(∞)−cN−1/2, approaching αc(∞)≈0.50. Deep Convolutional features extracted from a comprehensive labeled dataset, contain substantial representations which could be effectively used in a new domain. Despite the fact that generic features achieved good results in many visual tasks, fine-tuning is required for pretrained deep CNN models to be more effective …
Muon outperforms GD in associative memory learning by balancing frequency components.
problem Training dynamics and scaling behavior of Muon in associative memory learning.
method Study of Muon in a linear associative memory model with softmax retrieval and hierarchical frequency spectrum over query-answer pairs.
result Muon achieves exponential speedup over GD in noiseless case and superior scaling efficiency in noisy case.
Deep models store facts in geometric embeddings, not just associative memory.
problem Understanding how deep models store and utilize atomic facts.
method Identified geometric memory, contrasting with associative lookup.
result Geometric memory transforms hard reasoning into easy tasks.
One stylized feature of financial volatility impacting the modeling process is long memory. This paper examines long memory for alternative risk measures, observed absolute and squared returns for Daily REITs and compares the findings for a non- REIT equity index. The paper utilizes a variety of tests for long memory f…
Partially observable environments present an important open challenge in the domain of sequential control learning with delayed rewards. Despite numerous attempts during the two last decades, the majority of reinforcement learning algorithms and associated approximate models, applied to this context, still assume Marko…
In this paper, we introduce a novel layer designed to be used as the output of pre-trained neural networks in the context of classification. Based on Associative Memories, this layer can help design Deep Neural Networks which support incremental learning and that can be (partially) trained in real time on embedded devi…
A new framework for efficient sequence maps using Bayesian filtering and covariance.
problem Designing efficient recurrent sequence maps from explicit memory assumptions.
method Design-model framework, exact Bayesian filtering, query-dependent readout, linear-Gaussian instantiation.
result Improved robustness and retrieval performance across various benchmarks.
It is generally accepted that many time series of practical interest exhibit strong dependence, i.e., long memory. For such series, the sample autocorrelations decay slowly and log-log periodogram plots indicate a straight-line relationship. This necessitates a class of models for describing such behavior. A popular cl…
This paper proposes a new approach to Transformers by integrating hierarchical associative memory with MetaFormers.
problem Theoretical framework for Transformers and MLP-Mixers remains underdeveloped.
method Integrating hierarchical associative memory with MetaFormers to create a parallelized MLP-Mixer.
result Symmetry-breaking effects improve the performance of the MLP-Mixer in image recognition tasks.
HAMN combines CF models to improve drug repositioning.
problem Efficient drug repositioning with cold start problem.
method Hybrid Attentional Memory Network (HAMN) integrating memory and attention mechanisms.
result HAMN outperforms other models in drug repositioning tasks.
The concepts of unitary evolution matrices and associative memory have boosted the field of Recurrent Neural Networks (RNN) to state-of-the-art performance in a variety of sequential tasks. However, RNN still have a limited capacity to manipulate long-term memory. To bypass this weakness the most successful application…
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.
We present a recurrent neural network memory that uses sparse coding to create a combinatoric encoding of sequential inputs. Using several examples, we show that the network can associate distant causes and effects in a discrete stochastic process, predict partially-observable higher-order sequences, and enable a DQN a…
This study investigates self-organizing dynamics in a stochastic exponential DAM model using Temporal Complexity.
problem Understanding self-organizing behavior in artificial neural systems.
method Investigation of a stochastic exponential DAM model through Temporal Complexity analysis.
result The model exhibits regimes of complex intermittency with nontrivial temporal correlations and scale-free behavior.
Transformers recall from long distributions with statistical guarantees.
problem Designing Transformers that can recall from arbitrarily long, distributional contexts.
method Recast associative memory as probability measures, decomposing the task into recall and prediction.
result A shallow measure-theoretic Transformer learns the recall-and-predict map under spectral assumptions.
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.