Low precision weights, activations, and gradients have been proposed as a way to improve the computational efficiency and memory footprint of deep neural networks. Recently, low precision networks have even shown to be more robust to adversarial attacks. However, typical implementations of low precision DNNs use unifor…
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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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48 results for “stochastic precision”
Stochastic Coordinate Minimization with Progressive Precision for Stochastic Convex Optimizationstat.ML
Optimizes CM for stochastic convex optimization with progressive precision.
problem Stochastic nature of objective function in convex optimization.
method Iterative coordinate minimization with optimal precision control.
result Order-optimal regret performance for strongly convex and nonsmooth functions.
SPEQ improves quantized neural networks by stochastic precision sharing and cosine similarity loss.
problem Improving quantized deep neural networks for edge devices.
method SPEQ combines stochastic precision sharing and cosine similarity loss for knowledge distillation.
result SPEQ outperforms existing methods in various tasks.
Paper explores low-precision SGLD for neural networks, reducing costs without sacrificing performance.
problem Infeasibility of low-precision sampling in large-scale scenarios.
method Developed low-precision SGLD with quantization function and full-precision gradient accumulators.
result Low-precision SGLD achieves comparable performance to full-precision SGLD with only 8 bits.
This paper improves low-precision sampling using SGHMC for deep learning models.
problem Enhancing training efficiency of deep neural networks with low-precision training.
method Investigates low-precision sampling via Stochastic Gradient Hamiltonian Monte Carlo (SGHMC) for both log-concave and non-log-concave distributions.
result Low-precision SGHMC achieves quadratic improvement in error compared to SGLD for non-log-concave distributions.
Gradient descent stagnates in low-precision, but unbiased rounding schemes improve convergence.
problem Stagnation of gradient descent in low-precision computation.
method Proposed unbiased stochastic rounding schemes that trade zero bias for larger probability of preserving small gradients.
result Unbiased rounding methods typically improve convergence rate of gradient descent for convex problems.
Low-precision streaming PCA estimates the leading eigenvector with limited precision.
problem Estimating the leading eigenvector in a streaming setting with limited precision.
method Oja's algorithm with linear and nonlinear stochastic quantization.
result A batched version of the quantized variants achieves the lower bound on quantization error up to logarithmic factors.
Training of large-scale deep neural networks is often constrained by the available computational resources. We study the effect of limited precision data representation and computation on neural network training. Within the context of low-precision fixed-point computations, we observe the rounding scheme to play a cruc…
Gradient descent with biased rounding errors converges faster under certain conditions.
problem Stagnation or negative impact of rounding errors in neural network training with low precision.
method Analysis of gradient descent with stochastic fixed-point rounding errors under the Polyak-Lojasiewicz inequality.
result Biased rounding errors can improve convergence rates, especially when the Polyak-Lojasiewicz inequality holds.
BOSH optimizes functions with stochastic evaluations more efficiently and precisely.
problem Optimizing functions with noisy evaluations can lead to suboptimal solutions.
method BOSH uses a hierarchical Gaussian process to generate a growing pool of realizations.
result BOSH provides more efficient and higher-precision optimization than standard BO.
Low precision operations can provide scalability, memory savings, portability, and energy efficiency. This paper proposes SWALP, an approach to low precision training that averages low-precision SGD iterates with a modified learning rate schedule. SWALP is easy to implement and can match the performance of full-precisi…
The paper addresses numerical integration issues in SV models, proposing a fast regime switching algorithm.
problem Numerical integration challenges in SV models, especially with high precision and low computational time.
method Proposes a fast regime switching algorithm to determine when higher precision arithmetic is needed.
result Shows that numerical quadratures need to be carefully chosen based on model parameters and parameter values.
We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence structure in the model. Incorporating sparsity in the precision matrix allows the Gaus…
Rex solves the inverse problem for ODE/SDE solvers, improving precision and stability.
problem Inversion of ODE/SDE solvers is inaccurate and impractical for precision applications.
method Rex uses Lawson methods to convert explicit Runge-Kutta schemes into algebraically reversible ones.
result Rex achieves near-machine-precision reconstruction and improves generative models.
Stochasticity and limited precision of synaptic weights in neural network models are key aspects of both biological and hardware modeling of learning processes. Here we show that a neural network model with stochastic binary weights naturally gives prominence to exponentially rare dense regions of solutions with a numb…
We present a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small noise formulae for option prices. Our main tool is the theory of regularity structures, which we use in the form of [Bayer et al; A regularity structure for rough vola…
KrADagrad: Kronecker Approximation-Domination Gradient Preconditioned Stochastic Optimizationstat.ML
A new optimization method reduces memory and compute requirements for deep learning.
problem Memory and compute constraints in second-order stochastic optimizers for deep learning.
method Proposes KrAD, a novel factorization to approximate inverse Fisher matrix without inversion, leading to KrADagrad.
result Improves performance over Shampoo for 32-bit precision and comparable/generalization on real datasets.
RONM method reduces regret in stochastic convex bandits with decreasing noise.
problem Stochastic convex bandit problem with decreasing noise.
method Regularized Online Newton Method (RONM) based on Online Newton Method (ONM).
result RONM achieves polylogarithmic regret in time horizon n.
Stochastic optimization's success linked to heavy-tailed noise.
problem Understanding stochastic optimization's success mechanisms.
method Modeling stochastic optimization as random recurrence relations, analyzing multiplicative noise and heavy-tailed behavior.
result Multiplicative noise leads to heavy-tailed stationary behavior in optimization parameters.
Paper proposes efficient algorithms for bandit problems with costly sampling.
problem Maximizing expectation function over a finite set with high sampling cost.
method Proposes naive and adaptive stochastic bandit algorithms for PAC solution.
result Adaptive algorithm outperforms naive in terms of number of samples.
Low-precision computation is often used to lower the time and energy cost of machine learning, and recently hardware accelerators have been developed to support it. Still, it has been used primarily for inference - not training. Previous low-precision training algorithms suffered from a fundamental tradeoff: as the num…
Stochastic dividend discount models (Hurley and Johnson, 1994 and 1998, Yao, 1997) present expressions for the expected value of stock prices when future dividends evolve according to some random scheme. In this paper we try to offer a more precise view on this issue proposing a closed-form formula for the variance of …
The stochastic gradient descent (SGD) optimization algorithm plays a central role in a series of machine learning applications. The scientific literature provides a vast amount of upper error bounds for the SGD method. Much less attention as been paid to proving lower error bounds for the SGD method. It is the key cont…
We propose a stochastic modified equations (SME) for modeling the asynchronous stochastic gradient descent (ASGD) algorithms. The resulting SME of Langevin type extracts more information about the ASGD dynamics and elucidates the relationship between different types of stochastic gradient algorithms. We show the conver…
We develop the mathematical foundations of the stochastic modified equations (SME) framework for analyzing the dynamics of stochastic gradient algorithms, where the latter is approximated by a class of stochastic differential equations with small noise parameters. We prove that this approximation can be understood math…
Mixed-precision CA-SGD for generalized linear models on GPUs
problem SGD communication bottleneck
method Mixed-precision CA-SGD
result Matches FP32 SGD loss within 0.5% on various problems
It is well-known that the precision of data, hyperparameters, and internal representations employed in learning systems directly impacts its energy, throughput, and latency. The precision requirements for the training algorithm are also important for systems that learn on-the-fly. Prior work has shown that the data and…
The problem of maximizing precision at the top of a ranked list, often dubbed Precision@k (prec@k), finds relevance in myriad learning applications such as ranking, multi-label classification, and learning with severe label imbalance. However, despite its popularity, there exist significant gaps in our understanding of…
Neural networks with low-precision weights and activations offer compelling efficiency advantages over their full-precision equivalents. The two most frequently discussed benefits of quantization are reduced memory consumption, and a faster forward pass when implemented with efficient bitwise operations. We propose a t…
Differentiable learning via SGD and GD can simulate various learning problems, depending on precision and minibatch size.
problem Understanding the power of differentiable learning via SGD and GD compared to statistical query (SQ) learning.
method Comparing the learning power of SGD and GD on population and empirical losses with statistical query learning.
result The learning power of SGD and GD depends on the precision of gradient calculations relative to the minibatch size or sample size.
Reduced precision computation for deep neural networks is one of the key areas addressing the widening compute gap driven by an exponential growth in model size. In recent years, deep learning training has largely migrated to 16-bit precision, with significant gains in performance and energy efficiency. However, attemp…
Designing a deep neural network (DNN) with good generalization capability is a complex process especially when the weights are severely quantized. Model averaging is a promising approach for achieving the good generalization capability of DNNs, especially when the loss surface for training contains many sharp minima. W…
We propose a new stochastic L-BFGS algorithm and prove a linear convergence rate for strongly convex and smooth functions. Our algorithm draws heavily from a recent stochastic variant of L-BFGS proposed in Byrd et al. (2014) as well as a recent approach to variance reduction for stochastic gradient descent from Johnson…
We develop a scalable method for Bayesian neural networks with stochastic differential equations.
problem Uncertainty quantification in deep neural networks.
method Gradient-based stochastic variational inference in continuous-depth Bayesian neural networks.
result Gradient estimator with zero variance as the approximation improves.
The Straight-Through Estimator (STE) is widely used for back-propagating gradients through the quantization function, but the STE technique lacks a complete theoretical understanding. We propose an alternative methodology called alpha-blending (AB), which quantizes neural networks to low-precision using stochastic grad…
We study local complexity measures for stochastic convex optimization problems, providing a local minimax theory analogous to that of Hájek and Le Cam for classical statistical problems. We give complementary optimality results, developing fully online methods that adaptively achieve optimal convergence guarantees. Our…
We introduce an asymptotic small noise expansion, a so called vol-of-vol expansion, for potentially infinite dimensional and rough stochastic volatility models. Thereby we extend the scope of existing results for finite dimensional models and validate claims for infinite dimensional models. Furthermore we provide new, …
This paper focuses on stochastic orders and its applications : policy limits and deductibles. Further, many applications and some examples are given : comparison of two families of copulas, individual and collective risk model, reinsurance contracts and dependent portfolios increase risk. More precisely, we propose a n…
There is widespread sentiment that it is not possible to effectively utilize fast gradient methods (e.g. Nesterov's acceleration, conjugate gradient, heavy ball) for the purposes of stochastic optimization due to their instability and error accumulation, a notion made precise in d'Aspremont 2008 and Devolder, Glineur, …
A framework detects where constitutive models fail in elastography, improving clinical interpretation.
problem Assuming constitutive models correctly describe soft tissue mechanics leads to misleading results.
method Probabilistic framework treating stress as a latent variable, comparing it to assumed model predictions.
result Inferred precision field identifies invalid regions with high accuracy, improving model validity.
Study on the smoothness of solutions to a specific type of stochastic differential equation.
problem Regularity of solutions to mean-field -SDEs.
method Analysis of first and second order Fréchet differentiability in the random initial condition.
result Established the Fréchet differentiability of the solution and specified the corresponding equations.
In this paper, we propose a unified view of gradient-based algorithms for stochastic convex composite optimization by extending the concept of estimate sequence introduced by Nesterov. More precisely, we interpret a large class of stochastic optimization methods as procedures that iteratively minimize a surrogate of th…
We propose a correlated stochastic process of which the novel non-Gaussian probability mass function is constructed by exactly solving moment generating function. The calculation of cumulants and auto-correlation shows that the process is convergent and scale invariant in the large but finite number limit. We demonstra…
Generative adversarial networks (GANs) transform latent vectors into visually plausible images. It is generally thought that the original GAN formulation gives no out-of-the-box method to reverse the mapping, projecting images back into latent space. We introduce a simple, gradient-based technique called stochastic cli…
New insights show stochastic initialization prevents token clustering in deep Transformers.
problem Understanding token dynamics in deep stochastic Transformers.
method Analysis of deep Transformers with random initialization noise, proving convergence to an interacting-particle system on the sphere.
result Initialization noise prevents token clustering, leading to antipodal formations.
A plethora of recent research has focused on improving the memory footprint and inference speed of deep networks by reducing the complexity of (i) numerical representations (for example, by deterministic or stochastic quantization) and (ii) arithmetic operations (for example, by binarization of weights). We propose a s…
In this study, we develop a deterministic nonlinear filtering algorithm based on a high-dimensional version of Kitagawa (1987) to evaluate the likelihood function of models that allow for stochastic volatility and jumps whose arrival intensity is also stochastic. We show numerically that the deterministic filtering met…
Study shows how SGD's implicit regularization relates to ridge regression.
problem Least squares regression optimization with mini-batch SGD.
method Analyzes stochastic gradient flow as a continuous-time model of SGD.
result Bound on excess risk of SGD flow over ridge regression, revealing how parameters drive risk.