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The problem of extending a function $f$ defined on a training data $\mathcal{C}$ on an unknown manifold $\mathbb{X}$ to the entire manifold and a tubular neighborhood of this manifold is considered in this paper. For $\mathbb{X}$ embedded…

We present an implicit neural representation to learn the spatio-temporal space of kinematic motions. Unlike previous work that represents motion as discrete sequential samples, we propose to express the vast motion space as a continuous…

Multimodal continual instruction tuning enables multimodal large language models to sequentially adapt to new tasks while building upon previously acquired knowledge. However, this continual learning paradigm faces the significant challenge…

State-of-the-art rehearsal-free continual learning methods exploit the peculiarities of Vision Transformers to learn task-specific prompts, drastically reducing catastrophic forgetting. However, there is a tradeoff between the number of…

Large language models store all learned knowledge in a single, fixed weight vector. Teaching a model new capabilities requires modifying those same weights, inevitably degrading previously acquired knowledge. This fundamental limitation,…

Block-sequential continual learning demands that a single model both protect prior solutions from catastrophic forgetting and efficiently infer at inference time which prior solution matches the current input without task labels. We present…

Tabular Foundation Models (TFMs) have recently shown strong in-context learning capabilities on structured data, achieving zero-shot performance comparable to traditional machine learning methods. We find that zero-shot TFMs already achieve…

Inference in nonlinear continuous stochastic processes on trees is challenging, particularly when observations are sparse and the topology is complex. Exact smoothing via Doob's $h$-transform is intractable for general nonlinear dynamics.…

One frequently wishes to learn a range of similar tasks as efficiently as possible, re-using knowledge across tasks. In artificial neural networks, this is typically accomplished by conditioning a network upon task context by injecting…

System identification has greatly benefited from deep learning techniques, particularly for modeling complex, nonlinear dynamical systems with partially unknown physics where traditional approaches may not be feasible. However, deep…

Novel view synthesis has recently made significant progress with the advent of Neural Radiance Fields (NeRF). DietNeRF is an extension of NeRF that aims to achieve this task from only a few images by introducing a new loss function for…

Diffeomorphic deformable multi-modal image registration is a challenging task which aims to bring images acquired by different modalities to the same coordinate space and at the same time to preserve the topology and the invertibility of…

Recent advances have enabled a single neural network to serve as an implicit scene representation, establishing the mapping function between spatial coordinates and scene properties. In this paper, we make a further step towards continual…

Direct Feedback Alignment (DFA) is emerging as an efficient and biologically plausible alternative to the ubiquitous backpropagation algorithm for training deep neural networks. Despite relying on random feedback weights for the backward…

Deep neural networks (DNNs) are widely used as surrogate models in geophysical applications; incorporating theoretical guidance into DNNs has improved the generalizability. However, most of such approaches define the loss function based on…

Despite their central role in the success of foundational models and large-scale language modeling, the theoretical foundations governing the operation of Transformers remain only partially understood. Contemporary research has largely…

Operator learning is the approximation of operators between infinite dimensional Banach spaces using machine learning approaches. While most progress in this area has been driven by variants of deep neural networks such as the Deep Operator…

We study the optimization of wide neural networks (NNs) via gradient flow (GF) in setups that allow feature learning while admitting non-asymptotic global convergence guarantees. First, for wide shallow NNs under the mean-field scaling and…

We study machine unlearning in large generative models by framing the task as density ratio estimation to a target distribution rather than supervised fine-tuning. While classifier guidance is a standard approach for approximating this…

Unsupervised domain adaptation is effective in leveraging the rich information from the source domain to the unsupervised target domain. Though deep learning and adversarial strategy make an important breakthrough in the adaptability of…