Study proposes memory-efficient backpropagation for linear layers in neural networks.
problem Significant memory usage in backpropagation through linear layers in neural networks.
method Randomized matrix multiplications to reduce memory usage with a moderate decrease in test accuracy.
result Demonstrated benefits of the proposed method on fine-tuning pre-trained models.
Recurrent neural networks can learn complex transduction problems that require maintaining and actively exploiting a memory of their inputs. Such models traditionally consider memory and input-output functionalities indissolubly entangled. We introduce a novel recurrent architecture based on the conceptual separation b…
Study on memory effects in RNNs learning temporal data.
problem Understanding memory effects in RNNs for temporal data learning.
method Mathematical analysis of continuous-time linear RNNs, focusing on approximation and optimization dynamics.
result Long-term memory requires a large number of neurons and slows down training.
We show that fundamental learning tasks, such as finding an approximate linear separator or linear regression, require memory at least \emph{quadratic} in the dimension, in a natural streaming setting. This implies that such problems cannot be solved (at least in this setting) by scalable memory-efficient streaming alg…
RNN-HAR model improves VaR forecasting with long-memory and non-linear dynamics.
problem Efficiently forecasting Value at Risk (VaR) with long-memory and non-linear realized volatility.
method Loss-based generalized Bayesian inference with Sequential Monte Carlo for model estimation and prediction.
result RNN-HAR model consistently outperforms other VaR forecasting models.
Optimal linear contracts are possible even with memory in Gaussian settings.
problem Can optimal dynamic contracts be linear when agents control memory processes?
method Developed a methodology for non-Markovian and non-semimartingale settings, showed linear contracts are optimal for one-dimensional models.
result Linear contracts are optimal for one-dimensional models with memory, and for radial effort cost functions in higher dimensions.
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.
Linear RNNs exhibit a bias towards shorter memory due to initialization variance.
problem Understanding the performance limitations of RNNs, especially linear ones.
method Kernel regime analysis to show equivalence to 1D-convolutional networks and analyze weightings.
result Linear RNNs with random initialization have a bias towards shorter memory periods.
Nonlinear RNNs' memory capacity varies widely, making it impractical.
problem The usefulness of memory capacity as a metric for linear RNNs is questioned.
method Analysis of random nonlinear RNNs with varying input scales.
result Memory capacity of nonlinear RNNs is arbitrary and impractical.
XLA compiler extension improves memory efficiency for machine learning.
problem Memory constraints limit the scalability of memory-intensive machine learning algorithms.
method Developed an XLA compiler extension that adjusts algorithm data-flow representation to fit memory limits.
result k-nearest neighbour and sparse Gaussian process regression can be run at larger scales.
We consider the problem of performing linear regression over a stream of d-dimensional examples, and show that any algorithm that uses a subquadratic amount of memory exhibits a slower rate of convergence than can be achieved without memory constraints. Specifically, consider a sequence of labeled examples $(a_1,b_1)…
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.
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.
Efficient sampling reduces memory usage for Minimax distance analysis.
problem Quadratic memory requirement for existing Minimax distance methods.
method Proposes a novel sampling technique with linear space complexity.
result Demonstrates significant reduction in memory usage for Minimax distances.
Efficient algorithm predicts unknown linear systems with long-term memory.
problem Predicting unknown and partially observed linear dynamical systems with long-term memory.
method Bounding the generalized Kolmogorov width of the Kalman filter model using spectral methods and conducting tight convex relaxation.
result Competes with Kalman filter in hindsight with only logarithmic regret.
The mathematical model of a linear system with the short memory about own stochastic behavior is proposed. It is assumed that the system is under a continual influence of independent stochastic impulses. In a short memory approximation the expression of the stochastic process is found. An application of the model propo…
We propose a generic algorithmic building block to accelerate training of machine learning models on heterogeneous compute systems. Our scheme allows to efficiently employ compute accelerators such as GPUs and FPGAs for the training of large-scale machine learning models, when the training data exceeds their memory cap…
Kernel-based K-means clustering has gained popularity due to its simplicity and the power of its implicit non-linear representation of the data. A dominant concern is the memory requirement since memory scales as the square of the number of data points. We provide a new analysis of a class of approximate kernel methods…
Learning to solve sequential tasks with recurrent models requires the ability to memorize long sequences and to extract task-relevant features from them. In this paper, we study the memorization subtask from the point of view of the design and training of recurrent neural networks. We propose a new model, the Linear Me…
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.
Algorithm learns linear systems from partial observations with near-optimal rate.
problem Identifying linear dynamical systems from partial observations, especially those with long-term memory.
method Multi-scale low-rank approximation using SVD on Hankel matrices of increasing sizes, combined with Fourier domain concentration bounds.
result Near-optimal rate of $\widetilde O\left(\sqrt\frac{d}{T}
ight)$ in H2 error, with logarithmic dependence on memory length. Improved accuracy in neural networks using CTF memory with RPU.
problem Challenges in achieving high accuracy in neural networks using in-memory computing.
method Exploring the trade-off between conductance change range and linearity in CTF memory for RPU-based matrix operations.
result Achieved accuracy of 97.9% on MNIST dataset, 89.1% and 70.5% on CIFAR-10 and CIFAR-100 datasets.
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…
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.
We extend Kirman's model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman's agent based model is compared to the non-linear stochastic models of long-range memory in financia…
Reservoir Memory Machines solve benchmark tasks faster than Neural Turing Machines.
problem Training Neural Turing Machines is hard and limits their applicability.
method Proposes Reservoir Memory Machines, combining neural network flexibility with Turing machine capabilities, but with faster training via alignment and linear regression.
result Reservoir Memory Machines solve benchmark tasks as well as Neural Turing Machines but are much faster to train.
Kernel clustering algorithm improved for large datasets using incomplete Cholesky factorization.
problem Large memory usage in kernel-based clustering for large-scale datasets.
method Approximate the kernel matrix using incomplete Cholesky factorization and apply linear k-means clustering. result The proposed method achieves similar performance to kernel k-means clustering but handles large-scale datasets efficiently. 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.
We introduce a new sub-linear space sketch---the Weight-Median Sketch---for learning compressed linear classifiers over data streams while supporting the efficient recovery of large-magnitude weights in the model. This enables memory-limited execution of several statistical analyses over streams, including online featu…
AlphaGrad optimizes memory usage in RL algorithms by normalizing gradients.
problem Memory overhead and hyperparameter complexity in adaptive optimizers.
method Tensor-wise L2 normalization followed by a smooth hyperbolic tangent transformation controlled by a single parameter.
result AlphaGrad provides enhanced training stability and competitive performance in various RL algorithms.
Deep RNNs compute American option prices and deltas efficiently.
problem Computing prices and deltas of high-dimensional American options.
method Two deep RNNs, one for price and one for delta, learn over spacetime.
result Linear time and constant memory cost compared to feedforward networks.
SliceOut speeds up deep learning training without sacrificing accuracy.
problem Frequent model re-training and large model training workloads in deep learning.
method SliceOut uses dropout-inspired scheme to drop contiguous sets of units at random, leveraging GPU memory layout.
result 10-40% speedups and memory reduction with minimal accuracy loss.
Linear recurrent networks explain reinforcement learning performance in partially observable settings.
problem Understanding why linear recurrent networks work in reinforcement learning with partial observability.
method Constructed and studied two linear filters for HMMs and action-controlled HMMs.
result Linear filters serve as sufficient statistics and reduce state ambiguity, explaining empirical reinforcement learning success.
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.
LITE efficiently estimates Gaussian PoM with linear time and memory complexity.
problem Estimating the probability of maximality (PoM) of Gaussian vectors efficiently.
method LITE: entropy-regularized UCB approach for almost-linear time and memory complexity.
result Achieves state-of-the-art accuracy with significantly faster performance than existing methods.
Research on long-range memory in financial and social systems using various models.
problem Understanding the nature of long-range memory in socioeconomic systems.
method Various Markov processes including point processes, stochastic differential equations, and agent-based models.
result New estimators of self-similarity and long-range memory for non-Gaussian systems are needed.
Linformer reduces transformer complexity to linear, improving efficiency.
problem High cost of training and deploying large transformer models for long sequences.
method Approximates self-attention with low-rank matrix, proposing Linformer with O(n) complexity. result Linformer performs similarly to standard transformers but is more memory- and time-efficient.
CoLA automates efficient numerical linear algebra for complex matrix structures.
problem Efficiently solving large-scale linear algebra problems with complex matrix structures.
method Combining linear operator abstraction with compositional dispatch rules.
result Automatic and efficient numerical algorithms for various linear algebra operations.
A new algorithm reduces memory usage for deep learning models.
problem Training deep learning models requires significant memory.
method Dynamic Tensor Rematerialization (DTR) is a greedy online algorithm that dynamically plans recomputations.
result DTR achieves comparable performance to optimal static checkpointing with only a small memory budget.
Sketchy reduces memory and compute requirements for adaptive regularization in deep learning.
problem Prohibitive memory and running time for adaptive regularization methods in deep learning.
method Low-rank sketching approach using Frequent Directions (FD) to reduce memory and compute requirements.
result Efficient interpolation between resource requirements and degradation in regret guarantees with rank k. AuON is a linear-time optimizer that improves upon Muon's performance without approximate orthogonal matrices.
problem High memory and computational costs of orthogonal momentum updates.
method AuON uses normalized nonlinear scaling and a 'emergency brake' to handle exploding attention logits.
result AuON achieves strong performance without approximate orthogonal matrices, preserving structural alignment and reconditioning.
It is widely accepted that there is strong persistence in the volatility of financial time series. The origin of the observed persistence, or long-range memory, is still an open problem as the observed phenomenon could be a spurious effect. Earlier we have proposed the consentaneous model of the financial markets based…
In recent years, we have witnessed an increased interest in temporal modeling of patient records from large scale Electronic Health Records (EHR). While simpler RNN models have been used for such problems, memory networks, which in other domains were found to generalize well, are underutilized. Traditional memory netwo…
Introduces Exponentially Weighted Signature for better path representation.
problem Uniform treatment of historical information in signatures.
method Generalizes EFM signature to bounded linear operators, enabling contextualised temporal weighting.
result EWS is the unique solution to a linear controlled differential equation and generalizes state-space models.
New method combines long-memory reservoirs for accurate dengue forecasting from short data.
problem Accurate dengue forecasting from short, noisy, non-stationary, and nonlinear data.
method Fractional ESN and Wavelet ESN frameworks integrating long-term memory.
result fESN and wESN outperform baselines in multiple dengue datasets and forecasting horizons.
The origin of the long-range memory in the non-equilibrium systems is still an open problem as the phenomenon can be reproduced using models based on Markov processes. In these cases a notion of spurious memory is introduced. A good example of Markov processes with spurious memory is stochastic process driven by a non-…
Study shows how to balance memory and learning efficiency in continual learning.
problem Balancing memory and learning efficiency in continual learning.
method Structural regularization with Hessian-based regularization.
result Structural regularization improves statistical performance at the cost of increased memory complexity.
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.