arXiv research

Deep neural networks with memory learn reduced equations from partial data.

The usual derivation of the Fokker-Planck partial differential eqn. assumes the Chapman-Kolmogorov equation for a Markov process. Starting instead with an Ito stochastic differential equation we argue that finitely many states of memory are allowed in Kolmogorov's two pdes, K1 (the backward time pde) and K2 (the Fokker…

Recurrent neural networks (RNNs) are an effective representation of control policies for a wide range of reinforcement and imitation learning problems. RNN policies, however, are particularly difficult to explain, understand, and analyze due to their use of continuous-valued memory vectors and observation features. In …

Study on natural actor-critic for POMDPs with finite memory.

Study language generation with limited memory, showing different impacts on achievable densities and convergence.

We study finite sample properties of estimators of power-law cross-correlations -- detrended cross-correlation analysis (DCCA), height cross-correlation analysis (HXA) and detrending moving-average cross-correlation analysis (DMCA) -- with a special focus on short-term memory bias as well as power-law coherency. Presen…

CoNNTrA trains DNNs with low-power, low-memory constraints.

A bridge between continuous signals and discrete Ising spins for associative memory.

Embed-KCPD segments text without labels, outperforming baselines.

New algorithms improve GP inference without approximations, achieving better results.

New algorithms for constrained online optimization with memory and predictions.

Deep Neural Networks(DNNs) require huge GPU memory when training on modern image/video databases. Unfortunately, the GPU memory is physically finite, which limits the image resolutions and batch sizes that could be used in training for better DNN performance. Unlike solutions that require physically upgrade GPUs, the G…

We present an extended version of the recently proposed "LLOB" model for the dynamics of latent liquidity in financial markets. By allowing for finite cancellation and deposition rates within a continuous reaction-diffusion setup, we account for finite memory effects on the dynamics of the latent order book. We compute…

We propose an explicit recursive method to approximate a power-law with a finite sum of weighted exponentials. Applications to moving averages with long memory are discussed in relationship with stochastic volatility models.

A new associative memory uses Sinkhorn divergence for efficient pattern retrieval.

Novel algorithms improve efficiency of finite width NTK computation.

We study how the round-off (or discretization) error changes the statistical properties of a Gaussian long memory process. We show that the autocovariance and the spectral density of the discretized process are asymptotically rescaled by a factor smaller than one, and we compute exactly this scaling factor. Consequentl…

Recurrent neural networks are a widely used class of neural architectures. They have, however, two shortcomings. First, it is difficult to understand what exactly they learn. Second, they tend to work poorly on sequences requiring long-term memorization, despite having this capacity in principle. We aim to address both…

New algorithms for multitask learning with long-term memory.

SRG improves optimization efficiency with reduced memory and computation overhead.

Reservoir computers (RCs) and recurrent neural networks (RNNs) can mimic any finite-state automaton in theory, and some workers demonstrated that this can hold in practice. We test the capability of generalized linear models, RCs, and Long Short-Term Memory (LSTM) RNN architectures to predict the stochastic processes g…

Interbank markets are fundamental for bank liquidity management. In this paper, we introduce a model of interbank trading with memory. Our model reproduces features of preferential trading patterns in the e-MID market recently empirically observed through the method of statistically validated networks. The memory mecha…

A new method stabilizes deep reinforcement learning by using QGraphs to retain replay memory information.

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

Subbagging estimation for big data reduces memory usage while maintaining statistical consistency.

Technological progress is leading to proliferation and diversification of trading venues, thus increasing the relevance of the long-standing question of market fragmentation versus consolidation. To address this issue quantitatively, we analyse systems of adaptive traders that choose where to trade based on their previ…

We introduce a simple analysis of the structural complexity of infinite-memory processes built from random samples of stationary, ergodic finite-memory component processes. Such processes are familiar from the well known multi-arm Bandit problem. We contrast our analysis with computation-theoretic and statistical infer…

Study identifies three quantization regimes for ReLU networks.

Efficient algorithm predicts unknown linear systems with long-term memory.

We consider the problem of estimating from sample paths the absolute spectral gap $γ_*$ of a reversible, irreducible and aperiodic Markov chain $(X_t)_{t \in \mathbb{N}}$ over a finite state space $Ω$. We propose the ${\tt UCPI}$ (Upper Confidence Power Iteration) algorithm for this problem, a low-complexity algorithm …

Next-gen reservoir computers fail to predict complex processes, highlighting need for better architectures.

Variance reduction has been commonly used in stochastic optimization. It relies crucially on the assumption that the data set is finite. However, when the data are imputed with random noise as in data augmentation, the perturbed data set be- comes essentially infinite. Recently, the stochastic MISO (S-MISO) algorithm i…

Study pricing derivatives in markets with long-range dependence and jumps.

Deep neural networks solve stochastic control problems with delay.

Despite their attractiveness, popular perception is that techniques for nonparametric function approximation do not scale to streaming data due to an intractable growth in the amount of storage they require. To solve this problem in a memory-affordable way, we propose an online technique based on functional stochastic …

New algorithms find near-stationary points in convex optimization.

Proposes a novel SAM operator for separate item and relational memories.

Agents learn and control complex mechanical systems through shared memories.

The paper tackles scalability issues in Graph Representation Learning.

In this paper, we propose a dual memory structure for reinforcement learning algorithms with replay memory. The dual memory consists of a main memory that stores various data and a cache memory that manages the data and trains the reinforcement learning agent efficiently. Experimental results show that the dual memory …

This study investigates self-organizing dynamics in a stochastic exponential DAM model using Temporal Complexity.

SRMC framework reduces Monte Carlo variance by history-based sampling in high-dimensional spaces.

Stable Hadamard Memory improves reinforcement learning by efficiently managing memory.

We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility jump models, e.g. in Bates model. In such models the option price is determined as the solution of a partial integro-differential equation. The scheme is fourth order accurate in space and second order accurate in ti…

New memory allocation scheme improves image generation performance.

DAM with MRL improves relational reasoning in MANNs.

Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on fi…

Smooth calibration improves forecast reliability even with leaked information.