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In this paper, we analyze the effects of depth and width on the quality of local minima, without strong over-parameterization and simplification assumptions in the literature. Without any simplification assumption, for deep nonlinear neural…

The optimization foundations of deep linear networks have recently received significant attention. However, due to their inherent non-convexity and hierarchical structure, analyzing the loss functions of deep linear networks remains a…

Neural networks dominate the modern machine learning landscape, but their training and success still suffer from sensitivity to empirical choices of hyperparameters such as model architecture, loss function, and optimisation algorithm. In…

There has been a lot of recent interest in trying to characterize the error surface of deep models. This stems from a long standing question. Given that deep networks are highly nonlinear systems optimized by local gradient methods, why do…

Hyperparameter transfer allows extrapolating optimal optimization hyperparameters from small to large scales, making it critical for training large language models (LLMs). This is done either by fitting a scaling law to the hyperparameters…

We prove linear convergence of gradient descent to a global optimum for the training of deep residual networks with constant layer width and smooth activation function. We show that if the trained weights, as a function of the layer index,…

Predictive coding (PC) is an energy-based learning algorithm that performs iterative inference over network activities before updating weights. Recent work suggests that PC can converge in fewer learning steps than backpropagation thanks to…

Deep continual learning requires models to adapt to new tasks without retraining from scratch. However, neural networks can lose their ability to adapt to new tasks after training on previous ones, a phenomenon known as loss of plasticity.…

The hyperparameter optimization of neural network can be expressed as a bilevel optimization problem. The bilevel optimization is used to automatically update the hyperparameter, and the gradient of the hyperparameter is the approximate…

Differentially private (DP) transfer learning, i.e., fine-tuning a pretrained model on private data, is the current state-of-the-art approach for training large models under privacy constraints. We focus on two key hyperparameters in this…

When optimizing over-parameterized models, such as deep neural networks, a large set of parameters can achieve zero training error. In such cases, the choice of the optimization algorithm and its respective hyper-parameters introduces…

This paper introduces a new method to train recurrent neural networks using dynamical trajectory-based optimization. The optimization method utilizes a projected gradient system (PGS) and a quotient gradient system (QGS) to determine the…

The backpropagation of error algorithm (BP) is impossible to implement in a real brain. The recent success of deep networks in machine learning and AI, however, has inspired proposals for understanding how the brain might learn across…

Machine unlearning aims to forget sensitive knowledge from Large Language Models (LLMs) while maintaining general utility. However, existing approaches typically treat all tokens in a response indiscriminately and enforce uncertainty over…

Continual learning is the problem of integrating new information in a model while retaining the knowledge acquired in the past. Despite the tangible improvements achieved in recent years, the problem of continual learning is still an open…

Local search is a fundamental optimization technique that is both widely used in practice and deeply studied in theory, yet its computational complexity remains poorly understood. The traditional frameworks, PLS and the standard algorithm…

This paper re-visits the spectral method for learning latent variable models defined in terms of observable operators. We give a new perspective on the method, showing that operators can be recovered by minimizing a loss defined on a finite…

Modern machine learning models are often trained in a setting where the number of parameters exceeds the number of training samples. To understand the implicit bias of gradient descent in such overparameterized models, prior work has…

In this paper, we propose a methodology to compute the optimal finite-length coding rate for random linear network coding schemes over a line network. To do so, we first model the encoding, reencoding, and decoding process of different…

The neural plausibility of backpropagation has long been disputed, primarily for its use of non-local weight transport $-$ the biologically dubious requirement that one neuron instantaneously measure the synaptic weights of another. Until…