A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
We address the problem of {\it adaptivity} in the framework of reproducing kernel Hilbert space (RKHS) regression. More precisely, we analyze estimators arising from a linear regularization scheme $g_\lam$. In practical applications, an important task is to choose the regularization parameter $\lam$ appropriately, i.e.…
Latent variable models are a fundamental modeling tool in machine learning applications, but they present significant computational and analytical challenges. The popular EM algorithm and its variants, is a much used algorithmic tool; yet our rigorous understanding of its performance is highly incomplete. Recently, wor…
We study the implicit regularization imposed by gradient descent for learning multi-layer homogeneous functions including feed-forward fully connected and convolutional deep neural networks with linear, ReLU or Leaky ReLU activation. We rigorously prove that gradient flow (i.e. gradient descent with infinitesimal step …
State-of-the-art subspace clustering methods are based on expressing each data point as a linear combination of other data points while regularizing the matrix of coefficients with ℓ1, ℓ2 or nuclear norms. ℓ1 regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no conne…
Large learning rates lead to various implicit biases in nonconvex optimization.
problem Understanding the conditions under which large learning rates yield edge of stability, balancing, and catapult phenomena.
method Developed a global convergence theory for nonconvex functions without globally Lipschitz continuous gradient, focusing on functions with good regularity.
result These implicit biases are more likely to occur in functions with good regularity, and large learning rates favor flatter regions.
Large neural networks learn low-dimensional representations that balance complexity and regularity.
problem Understanding the tradeoff between low-dimensional representations and complexity in deep neural networks.
method Computed finite depth corrections to reveal a measure of regularity that bounds the pseudo-determinant of the Jacobian.
result Proved the conjectured bottleneck structure in learned features as network depth increases, showing almost all hidden representations are approximately low-dimensional and weight matrices have singular values close to 1.
We prove that the balanced Chekhov-Fock algebra of a punctured triangulated surface is isomorphic to a skein algebra which is a deformation of the algebra of regular functions of some abelian character variety. We first deduce from this observation a classification of the irreducible representations of the balanced Che…
Tensor decomposition methods allow us to learn the parameters of latent variable models through decomposition of low-order moments of data. A significant limitation of these algorithms is that there exists no general method to regularize them, and in the past regularization has mostly been performed using bespoke modif…
Hidden Markov Neural Networks balance adaptation and forgetting in time-series data.
problem Balancing adaptation to new data and forgetting outdated information in time-series forecasting.
method Modeling weights as hidden states of a Hidden Markov model, using a filtering algorithm for learning a variational approximation of the posterior distribution over weights, and employing sequential Bayes by Backprop with variational DropConnect for regularization.
result Achieves strong predictive performance and effective uncertainty quantification on various tasks.
Although deep learning has produced dazzling successes for applications of image, speech, and video processing in the past few years, most trainings are with suboptimal hyper-parameters, requiring unnecessarily long training times. Setting the hyper-parameters remains a black art that requires years of experience to ac…
This paper is concerned with the factorization form of the rank regularized loss minimization problem. To cater for the scenario in which only a coarse estimation is available for the rank of the true matrix, an ℓ2,0-norm regularized term is added to the factored loss function to reduce the rank adaptively; and…