Related papers: Intelligent Matrix Exponentiation
This paper proposes a novel approach to pattern classification using a probabilistic neural network model. The strategy is based on a compact-sized probabilistic neural network capable of continuous incremental learning and unlearning…
Multiresolution analysis and matrix factorization are foundational tools in computer vision. In this work, we study the interface between these two distinct topics and obtain techniques to uncover hierarchical block structure in symmetric…
Recurrent neural networks can learn complex transduction problems that require maintaining and actively exploiting a memory of their inputs. Such models traditionally consider memory and input-output functionalities indissolubly entangled.…
A key property of neural networks is their capacity of adapting to data during training. Yet, our current mathematical understanding of feature learning and its relationship to generalization remain limited. In this work, we provide a…
While many problems in machine learning focus on learning mappings between finite-dimensional spaces, scientific applications require approximating mappings between function spaces, i.e., operators. We study the problem of learning…
Recent work has suggested that a good embedding is all we need to solve many few-shot learning benchmarks. Furthermore, other work has strongly suggested that Model Agnostic Meta-Learning (MAML) also works via this same method - by learning…
Matrix factorization is a popular framework for modeling low-rank data matrices. Motivated by manifold learning problems, this paper proposes a quadratic matrix factorization (QMF) framework to learn the curved manifold on which the dataset…
We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…
The ability to learn and predict simple functions is a key aspect of human intelligence. Recent works have started to explore this ability using transformer architectures, however it remains unclear whether this is sufficient to…
The Jacobian matrix (or the gradient for single-output networks) is directly related to many important properties of neural networks, such as the function landscape, stationary points, (local) Lipschitz constants and robustness to…
We present a framework for performing efficient regression in general metric spaces. Roughly speaking, our regressor predicts the value at a new point by computing a Lipschitz extension --- the smoothest function consistent with the…
Probabilistic programming provides the means to represent and reason about complex probabilistic models using programming language constructs. Even simple probabilistic programs can produce models with infinitely many variables. Factored…
Group theory has been used in machine learning to provide a theoretically grounded approach for incorporating known symmetry transformations in tasks from robotics to protein modeling. In these applications, equivariant neural networks use…
We consider deep neural networks, in which the output of each node is a quadratic function of its inputs. Similar to other deep architectures, these networks can compactly represent any function on a finite training set. The main goal of…
This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation…
Operator learning based on neural operators has emerged as a promising paradigm for the data-driven approximation of operators, mapping between infinite-dimensional Banach spaces. Despite significant empirical progress, our theoretical…
The matrix element method is the LHC inference method of choice for limited statistics. We present a dedicated machine learning framework, based on efficient phase-space integration, a learned acceptance and transfer function. It is based…
Large language models now write software, draft legal documents, and produce clinical notes, yet fundamental limits, from Turing and Arrow to the No Free Lunch theorems, shape what computation can do. This thesis turns such impossibility…
We demonstrate two new important properties of the 1-path-norm of shallow neural networks. First, despite its non-smoothness and non-convexity it allows a closed form proximal operator which can be efficiently computed, allowing the use of…
It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs…