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This paper shows that the implicit bias of gradient descent on linearly separable data is exactly characterized by the optimal solution of a dual optimization problem given by a smoothed margin, even for general losses. This is in contrast…

We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…

Spatially varying image deblurring remains a fundamentally ill-posed problem, especially when degradations arise from complex mixtures of motion and other forms of blur under significant noise. State-of-the-art learning-based approaches…

Neuroscientists have long criticised deep learning algorithms as incompatible with current knowledge of neurobiology. We explore more biologically plausible versions of deep representation learning, focusing here mostly on unsupervised…

The ``differentiability gap'' presents a primary bottleneck in Earth system deep learning: since models cannot be trained directly on non-differentiable scientific metrics and must rely on smooth proxies (e.g., MSE), they often fail to…

We study the question of reconstructing two signals $f$ and $g$ from their convolution $y = f\ast g$. This problem, known as {\em blind deconvolution}, pervades many areas of science and technology, including astronomy, medical imaging,…

Recently, Deng et al. (2026) proposed Generative Modeling via Drifting (GMD), a novel framework for generative tasks. This note presents an analysis of GMD through the lens of Wasserstein Gradient Flows (WGF), i.e., the path of steepest…

Debiased recommendation with a randomized dataset has shown very promising results in mitigating the system-induced biases. However, it still lacks more theoretical insights or an ideal optimization objective function compared with the…

Neural networks have become a prominent approach to solve inverse problems in recent years. Amongst the different existing methods, the Deep Image/Inverse Priors (DIPs) technique is an unsupervised approach that optimizes a highly…

We consider the approximation of functions by 2-layer neural networks with a small number of hidden weights based on the squared loss and small datasets. Due to the highly non-convex energy landscape, gradient-based training often suffers…

Machine Unlearning aims to remove specific data from trained models, addressing growing privacy and ethical concerns. We provide a theoretical analysis of a simple and widely used method - gradient ascent - used to reverse the influence of…

Many modern learning tasks involve fitting nonlinear models to data which are trained in an overparameterized regime where the parameters of the model exceed the size of the training dataset. Due to this overparameterization, the training…

In wireless network, the optimization problems generally have complex constraints, and are usually solved via utilizing the traditional optimization methods that have high computational complexity and need to be executed repeatedly with the…

Deep neural networks have become the default choice for many applications like image and video recognition, segmentation and other image and video related tasks.However, a critical challenge with these models is the lack of…

Heralded by the initial success in speech recognition and image classification, learning-based approaches with neural networks, commonly referred to as deep learning, have spread across various fields. A primitive form of a neural network…

A main puzzle of deep networks revolves around the absence of overfitting despite large overparametrization and despite the large capacity demonstrated by zero training error on randomly labeled data. In this note, we show that the dynamics…

Recently, deep generative models have been used for posterior inference in inverse problems, including high-stakes applications in medical imaging and scientific discovery, where the uncertainty of a prediction can matter as much as the…

Despite tremendous success of modern neural networks, they are known to be overconfident even when the model encounters inputs with unfamiliar conditions. Detecting such inputs is vital to preventing models from making naive predictions…

In this paper, we propose projected gradient descent (PGD) algorithms for signal estimation from noisy nonlinear measurements. We assume that the unknown $p$-dimensional signal lies near the range of an $L$-Lipschitz continuous generative…

Bilevel optimization enjoys a wide range of applications in emerging machine learning and signal processing problems such as hyper-parameter optimization, image reconstruction, meta-learning, adversarial training, and reinforcement…