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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

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3773110146 · Jun 202019922001200920172026
48 results for Memory Capacity

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.

Generalizes memory and forecasting capacities for nonlinear recurrent networks with dependent inputs.

problem Understanding memory and forecasting capabilities in networks with dependent inputs.
method Formulated bounds for memory and forecasting capacities in terms of network size and input properties.
result Proved that memory capacity for linear recurrent networks with independent inputs is given by the rank of the controllability matrix.

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.

Study characterizes memory capacity of quantum reservoirs using transmon qubits.

problem Understanding the memory capacity of quantum reservoirs built with transmon qubits.
method Characterized memory capacity of quantum reservoirs using transmon qubits from IBM, focusing on NMSE and topology complexity.
result Found a peak in memory capacity for configurations with n-1 self-loops, suggesting optimal design for forecasting tasks.

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.

The memory capacity of linear echo state networks is accurately calculated using new numerical methods.

problem Numerical evaluations of memory capacity in recurrent neural networks often contradict theoretical bounds.
method Developed robust numerical approaches exploiting MC neutrality with respect to the input mask matrix.
result Memory curves fully agree with theory when using the proposed methods.

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.

Derives an empirical capacity model for self-attention neural networks.

problem Theoretical capacity of large transformer models is not fully utilized by current optimization algorithms.
method Analyzes memory capacity of transformers using synthetic training data and common training algorithms.
result Derives an empirical capacity model (ECM) for a generic transformer.

In this paper, the echo state network (ESN) memory capacity, which represents the amount of input data an ESN can store, is analyzed for a new type of deep ESNs. In particular, two deep ESN architectures are studied. First, a parallel deep ESN is proposed in which multiple reservoirs are connected in parallel allowing …

2019-06-11abs ↗pdf ↗

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.

gLSTM improves graph neural networks by increasing storage capacity to prevent over-squashing.

problem Over-squashing in GNNs collapses information from a large receptive field into a single vector, creating an information bottleneck.
method Introduced a new synthetic task to measure over-squashing and adapted ideas from sequence modeling to develop gLSTM, a novel GNN architecture with improved capacity.
result gLSTM architecture demonstrates strong performance on synthetic and real-world graph benchmarks, mitigating over-squashing.

This paper describes an improvement in Deep Q-learning called Reverse Experience Replay (also RER) that solves the problem of sparse rewards and helps to deal with reward maximizing tasks by sampling transitions successively in reverse order. On tasks with enough experience for training and enough Experience Replay mem…

2019-10-19abs ↗pdf ↗

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.

Sparse codes improve optimal control tasks with correlated inputs.

problem Optimal control tasks with correlated feature inputs.
method Used a sparse code to represent natural images in an optimal control task solved with neuro-dynamic programming.
result An over-complete sparse code increases memory capacity and learning speed beyond a complete code.

It has been known for a long time that the classical spherical perceptrons can be used as storage memories. Seminal work of Gardner, \cite{Gar88}, started an analytical study of perceptrons storage abilities. Many of the Gardner's predictions obtained through statistical mechanics tools have been rigorously justified. …

2013-06-17abs ↗pdf ↗

New neural networks model complex phenomena with fewer parameters.

problem Challenges in studying higher-order interactions in neural networks.
method Introducing curved neural networks using the maximum entropy principle.
result Curved neural networks accelerate memory retrieval and exhibit explosive phase transitions.

The brain optimizes memory by forgetting what's predictable, improving generalization.

problem Memory consolidation struggles with representational drift, semanticisation, and offline replay.
method Proposes predictive forgetting as a mechanism to optimize generalization by reducing complexity.
result Predictive forgetting improves information-theoretic generalization bounds on stored representations.

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.

Study capacity constraints in continual learning with a simple model.

problem Understanding optimal resource allocation for agents with limited memory and compute resources.
method Analyzes a capacity-constrained linear-quadratic-Gaussian (LQG) sequential prediction problem and demonstrates optimal capacity allocation strategies.
result Derives a solution to the capacity-constrained LQG sequential prediction problem and shows how to optimally allocate capacity across sub-problems in the steady state.

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.

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.

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.

We present an end-to-end trained memory system that quickly adapts to new data and generates samples like them. Inspired by Kanerva's sparse distributed memory, it has a robust distributed reading and writing mechanism. The memory is analytically tractable, which enables optimal on-line compression via a Bayesian updat…

2018-04-05abs ↗pdf ↗

Service-induced congestion in memory-constrained LLM serving

problem Service-induced congestion in memory-constrained large language model (LLM) serving
method Developing a discrete-time dynamical model of memory-constrained LLM inference
result The system converges to a unique worst-case limit cycle that is asymptotically stable outside a Lebesgue-measure-zero exact-capture set, with throughput losses as large as 50%.

A variety of large-scale machine learning problems can be cast as instances of constrained submodular maximization. Existing approaches for distributed submodular maximization have a critical drawback: The capacity - number of instances that can fit in memory - must grow with the data set size. In practice, while one c…

2016-05-31abs ↗pdf ↗

Stable Hadamard Memory improves reinforcement learning by efficiently managing memory.

problem Memory models struggle in partially observable reinforcement learning environments.
method Introduces a novel memory model using the Hadamard product for efficient memory management and updates.
result Significantly outperforms state-of-the-art memory-based methods on challenging benchmarks.

We propose a new method to study the internal memory used by reinforcement learning policies. We estimate the amount of relevant past information by estimating mutual information between behavior histories and the current action of an agent. We perform this estimation in the passive setting, that is, we do not interven…

2016-11-21abs ↗pdf ↗

New framework captures long-term decision dependence in online learning.

problem Long-term dependence on past decisions in online learning.
method Introduces Online Convex Optimization with Unbounded Memory (OCO-UMB) and pp-effective memory capacity.
result Proves O(HpT)O(\sqrt{H_p T}) upper bound on policy regret and matching lower bound.

An ideal cognitively-inspired memory system would compress and organize incoming items. The Kanerva Machine (Wu et al, 2018) is a Bayesian model that naturally implements online memory compression. However, the organization of the Kanerva Machine is limited by its use of a single Gaussian random matrix for storage. Her…

2020-02-06abs ↗pdf ↗

Following the recent work on capacity allocation, we formulate the conjecture that the shattering problem in deep neural networks can only be avoided if the capacity propagation through layers has a non-degenerate continuous limit when the number of layers tends to infinity. This allows us to study a number of commonly…

2019-03-11abs ↗pdf ↗

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.

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.

The paper analyzes the performance of delay-based reservoir computing using eigenvalue analysis.

problem Quantifying the performance of delay-based reservoir computing.
method Eigenvalue analysis of the dynamical system to predict reservoir computing performance.
result The performance of a reservoir computing system can be predicted by analyzing the small signal response and eigenvalue spectrum.

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.

Global Memory Augmentation (GMAT) improves Transformer performance on long documents.

problem Large memory requirements of Transformer pairwise dot-product attention for long sequences.
method Integrates a dense global memory of length M into sparse Transformer blocks.
result Significant improvement on various tasks, including synthetic tasks, masked language modeling, and reading comprehension.

The computation of convolution layers in deep neural networks typically rely on high performance routines that trade space for time by using additional memory (either for packing purposes or required as part of the algorithm) to improve performance. The problems with such an approach are two-fold. First, these routines…

2018-09-20abs ↗pdf ↗

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.

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.