Related papers: Learning Hamiltonian Dynamics with Reproducing Ker…
The impressive practical performance of neural networks is often attributed to their ability to learn low-dimensional data representations and hierarchical structure directly from data. In this work, we argue that these two phenomena are…
Inductive bias refers to restrictions on the hypothesis class that enable a learning method to generalize effectively from limited data. A canonical example in control is linearity, which underpins low sample-complexity guarantees for…
Time-reversal symmetry arises naturally as a structural property in many dynamical systems of interest. While the importance of hard-wiring symmetry is increasingly recognized in machine learning, to date this has eluded time-reversibility.…
Accelerated gradient methods have had significant impact in machine learning -- in particular the theoretical side of machine learning -- due to their ability to achieve oracle lower bounds. But their heuristic construction has hindered…
We study the problem of Hamiltonian structure learning from real-time evolution: given the ability to apply $e^{-\mathrm{i} Ht}$ for an unknown local Hamiltonian $H = \sum_{a = 1}^m \lambda_a E_a$ on $n$ qubits, the goal is to recover $H$.…
Systems of interacting particles or agents have wide applications in many disciplines such as Physics, Chemistry, Biology and Economics. These systems are governed by interaction laws, which are often unknown: estimating them from…
The task of reflection symmetry detection remains challenging due to significant variations and ambiguities of symmetry patterns in the wild. Furthermore, since the local regions are required to match in reflection for detecting a symmetry…
We present a new method to study disordered systems in the low temperature limit. The method uses the replicated Hamiltonian. It studies the saddle points of this Hamiltonian and shows how the various saddle point contributions can be…
Random Forests and Gradient Boosting are among the most effective algorithms for supervised learning on tabular data. Both belong to the class of tree-based ensemble methods, where predictions are obtained by aggregating many randomized…
Existing convolution techniques in artificial neural networks suffer from huge computation complexity, while the biological neural network works in a much more powerful yet efficient way. Inspired by the biological plasticity of dendritic…
Random feature maps are used to decrease the computational cost of kernel machines in large-scale problems. The Mondrian kernel is one such example of a fast random feature approximation of the Laplace kernel, generated by a computationally…
We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian…
Predicting optoelectronic properties of large-scale atomistic systems under realistic conditions is crucial for rational materials design, yet computationally prohibitive with first-principles simulations. Recent neural network models have…
One central theme in machine learning is function estimation from sparse and noisy data. An example is supervised learning where the elements of the training set are couples, each containing an input location and an output response. In the…
In this article, a novel approach to learning a complex function which can be written as the system of linear equations is introduced. This learning is grounded upon the observation that solving the system of linear equations by a…
The distribution regression problem encompasses many important statistics and machine learning tasks, and arises in a large range of applications. Among various existing approaches to tackle this problem, kernel methods have become a method…
The problem of the reconstruction of the large scale density and velocity fields from peculiar velocities surveys is addressed here within a Bayesian framework by means of Hamiltonian Monte Carlo (HMC) sampling. The HAmiltonian Monte carlo…
Residual deep neural networks are formulated as interacting particle systems leading to a description through neural differential equations, and, in the case of large input data, through mean-field neural networks. The mean-field…
In this paper, we consider the coefficient-based regularized distribution regression which aims to regress from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS), where the regularization is put on…
Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…