Related papers: KOALA: A Kalman Optimization Algorithm with Loss A…
We present a novel, fast (exponential rate adaption), ab initio (hyper-parameter-free) gradient based optimizer algorithm. The main idea of the method is to adapt the learning rate $\alpha$ by situational awareness, mainly striving for…
The use of data assimilation for the merging of observed data with dynamical models is becoming standard in modern physics. If a parametric model is known, methods such as Kalman filtering have been developed for this purpose. If no model…
Low-Rank Adaptation (LoRA) is one of the most widely used techniques for fine-tuning large language models (LLMs). By introducing a small number of trainable low-rank weight matrices, LoRA substantially reduces the number of parameters that…
Online minimization of an unknown convex function over the interval $[0,1]$ is considered under first-order stochastic bandit feedback, which returns a random realization of the gradient of the function at each query point. Without knowing…
Learning in a non-stationary environment is an inevitable problem when applying machine learning algorithm to real world environment. Learning new tasks without forgetting the previous knowledge is a challenge issue in machine learning. We…
Recent selective state space models (SSMs), such as Mamba and Mamba-2, have demonstrated strong performance in sequence modeling owing to input-dependent selection mechanisms. However, these mechanisms lack theoretical grounding and cannot…
In this work, we address optimization problems where the objective function is a nonlinear function of an expected value, i.e., compositional stochastic {strongly convex programs}. We consider the case where the decision variable is not…
Koopman operator theory, a powerful framework for discovering the underlying dynamics of nonlinear dynamical systems, was recently shown to be intimately connected with neural network training. In this work, we take the first steps in…
In modern optimization methods used in deep learning, each update depends on the history of previous iterations, often referred to as memory, and this dependence decays fast as the iterates go further into the past. For example, gradient…
Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…
Low-rank adaptation, also known as LoRA, has emerged as a prominent method for parameter-efficient fine-tuning of foundation models. Despite its computational efficiency, LoRA still yields inferior performance compared to full fine-tuning.…
The design of optimization algorithms for neural networks remains a critical challenge, with most existing methods relying on heuristic adaptations of gradient-based approaches. This paper introduces KO (Kinetics-inspired Optimizer), a…
Robust loss minimization is an important strategy for handling robust learning issue on noisy labels. Current approaches for designing robust losses involve the introduction of noise-robust factors, i.e., hyperparameters, to control the…
A novel population-based heuristic algorithm called the adaptive and various learning-based algorithm (AVLA) is proposed for solving general optimization problems in this paper. The main idea of AVLA is inspired by the learning behaviors of…
We consider the training process of a neural network as a dynamical system acting on the high-dimensional weight space. Each epoch is an application of the map induced by the optimization algorithm and the loss function. Using this induced…
In this paper, we propose a novel approach to solving optimization problems by reformulating the optimization problem into a dynamical system, followed by the adaptive spectral Koopman (ASK) method. The Koopman operator, employed in our…
We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has…
Low-Rank Adaptation (LoRA) is a parameter-efficient technique for rapidly fine-tuning foundation models. In standard LoRA training dynamics, models tend to quickly converge to a local optimum near the initialization. However, this local…
We consider the problem of online prediction for an unknown, non-explosive linear stochastic system. With a known system model, the optimal predictor is the celebrated Kalman filter. In the case of unknown systems, existing approaches based…
This paper proposes a novel nonlinear programming model to capture the equilibrium state of complex supply chain networks. The model, equivalent to a variational inequality model, relaxes traditional strict assumptions to accommodate…