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.
ViewFool identifies adversarial viewpoints to test image recognition robustness.
Paper explores why overfitted DNNs in adversarial training can generalize.
This paper first presents a theory for generative adversarial methods that does not rely on the traditional minimax formulation. It shows that with a strong discriminator, a good generator can be learned so that the KL divergence between the distributions of real data and generated data improves after each functional g…
Study adversarial perturbations in classification, analyzing learning and certification.
AR-GANs learn depth and DoF from unlabeled images using aperture rendering and focus cues.
Recent progress in deep generative models has led to tremendous breakthroughs in image generation. However, while existing models can synthesize photorealistic images, they lack an understanding of our underlying 3D world. We present a new generative model, Visual Object Networks (VON), synthesizing natural images of o…
Generative adversarial networks (GANs) are successful deep generative models. GANs are based on a two-player minimax game. However, the objective function derived in the original motivation is changed to obtain stronger gradients when learning the generator. We propose a novel algorithm that repeats the density ratio e…
In this paper, we consider a generic probabilistic discriminative learner from the functional viewpoint and argue that, to make it learn well, it is necessary to constrain its hypothesis space to a set of non-trivial piecewise constant functions. To achieve this goal, we present a scalable unsupervised regularization f…
We introduce a conditional generative model for learning to disentangle the hidden factors of variation within a set of labeled observations, and separate them into complementary codes. One code summarizes the specified factors of variation associated with the labels. The other summarizes the remaining unspecified vari…
Machine learning models are often susceptible to adversarial perturbations of their inputs. Even small perturbations can cause state-of-the-art classifiers with high "standard" accuracy to produce an incorrect prediction with high confidence. To better understand this phenomenon, we study adversarially robust learning …
We study the question of how to imitate tasks across domains with discrepancies such as embodiment, viewpoint, and dynamics mismatch. Many prior works require paired, aligned demonstrations and an additional RL step that requires environment interactions. However, paired, aligned demonstrations are seldom obtainable an…
Generative Adversarial Networks (GANs) were intuitively and attractively explained under the perspective of game theory, wherein two involving parties are a discriminator and a generator. In this game, the task of the discriminator is to discriminate the real and generated (i.e., fake) data, whilst the task of the gene…
Robustness of deep learning models is a property that has recently gained increasing attention. We explore a notion of robustness for generative adversarial models that is pertinent to their internal interactive structure, and show that, perhaps surprisingly, the GAN in its original form is not robust. Our notion of ro…
Highly expressive models such as deep neural networks (DNNs) have been widely applied to various applications. However, recent studies show that DNNs are vulnerable to adversarial examples, which are carefully crafted inputs aiming to mislead the predictions. Currently, the majority of these studies have focused on per…
There are multiple sides to every story, and while statistical topic models have been highly successful at topically summarizing the stories in corpora of text documents, they do not explicitly address the issue of learning the different sides, the viewpoints, expressed in the documents. In this paper, we show how thes…
We study the problem of robustly estimating the posterior distribution for the setting where observed data can be contaminated with potentially adversarial outliers. We propose Rob-ULA, a robust variant of the Unadjusted Langevin Algorithm (ULA), and provide a finite-sample analysis of its sampling distribution. In par…
Empirical adversarial risk minimization (EARM) is a widely used mathematical framework to robustly train deep neural nets (DNNs) that are resistant to adversarial attacks. However, both natural and robust accuracies, in classifying clean and adversarial images, respectively, of the trained robust models are far from sa…
In this paper we construct two groupoids from morphisms of groupoids, with one from a categorical viewpoint and the other from a geometric viewpoint. We show that for each pair of groupoids, the two kinds of groupoids of morphisms are equivalent. Then we study the automorphism groupoid of a groupoid.
Tikhonov regularization is robust under specific martingale constraints in distributionally robust optimization.
The quantum cohomology of CP^1 provides a distinguished solution of the third Painleve equation. S. Cecotti and C. Vafa discovered this from a physical viewpoint. We derive it from a differential geometric viewpoint, using the theory of harmonic maps and in particular the generalized Weierstrass representation (DPW rep…
Generative Adversarial Networks (GANs) can produce images of remarkable complexity and realism but are generally structured to sample from a single latent source ignoring the explicit spatial interaction between multiple entities that could be present in a scene. Capturing such complex interactions between different ob…
Smart Meters (SMs) are able to share the power consumption of users with utility providers almost in real-time. These fine-grained signals carry sensitive information about users, which has raised serious concerns from the privacy viewpoint. In this paper, we focus on real-time privacy threats, i.e., potential attacker…
Develops a robust GMM estimator for outlier-tolerant inference.
We present a probabilistic viewpoint to multiple kernel learning unifying well-known regularised risk approaches and recent advances in approximate Bayesian inference relaxations. The framework proposes a general objective function suitable for regression, robust regression and classification that is lower bound of the…
This paper tackles catastrophic forgetting in neural networks by providing a unified framework for regularization-based continual learning.
We consider a triality between the Zermelo navigation problem, the geodesic flow on a Finslerian geometry of Randers type, and spacetimes in one dimension higher admitting a timelike conformal Killing vector field. From the latter viewpoint, the data of the Zermelo problem are encoded in a (conformally) Painleve-Gullst…
We describe a method to classify crystallographic tilings of the Euclidean and hyperbolic planes by tiles whose stabiliser group contains translation isometries or whose topology is not that of a closed disk. We tackle this problem from two different viewpoints, one with constructive techniques to enumerate such tiling…
In an informal way, a number of thoughts on the financial crisis 2008 are presented from a physicist's viewpoint, considering the problem as a nonergodicity transition of a spin-glass type of system. Some tentative suggestions concerning the way out of the crisis are also discussed, concerning Keynesian "deficit spendi…
I use harmonic maps and minimal surfaces to study quadratic equations in groups.
Paper studies continuous prediction with experts' advice using differential equations.
Currently, machine learning plays an important role in the lives and individual activities of numerous people. Accordingly, it has become necessary to design machine learning algorithms to ensure that discrimination, biased views, or unfair treatment do not result from decision making or predictions made via machine le…
We explore the perspective of a bug living on the two-dimensional surface of a polyhedron. Images of various kinds of effects like lensing and cloaking are shown via color pictures of three viewpoints: the first person perspective of the bug, a map of the bug's viewpoint, and a look at the bug on the embedded polyhedro…
We offer a graphical interpretation of unfairness in a dataset as the presence of an unfair causal path in the causal Bayesian network representing the data-generation mechanism. We use this viewpoint to revisit the recent debate surrounding the COMPAS pretrial risk assessment tool and, more generally, to point out tha…
The change of numeraire gives very important computational simplification in option pricing. This technique reduces the number of sources of risks that need to be accounted for and so it is useful in pricing complicated derivatives that have several sources of risks. In this article, we considered the underlying mathem…
Motivated by the gap between theoretical optimal approximation rates of deep neural networks (DNNs) and the accuracy realized in practice, we seek to improve the training of DNNs. The adoption of an adaptive basis viewpoint of DNNs leads to novel initializations and a hybrid least squares/gradient descent optimizer. We…
In 1929, Paul Funk and Ludwig Berwald gave a characterization of Hilbert geometries from the Finslerian viewpoint. They showed that a smooth Finsler metric in a convex bounded domain of is the Hilbert geometry in that domain if and only if it is complete, if its geodesics are straight lines and if its fl…
We introduce the warping matrix which is a new description of oriented knots from a viewpoint of warping degree.
Using generative models for Inverse Graphics is an active area of research. However, most works focus on developing models for supervised and semi-supervised methods. In this paper, we study the problem of unsupervised learning of 3D geometry from single images. Our approach is to use a generative model that produces 2…
We survey the analogy between Kleinian groups and subgroups of the mapping class group of a surface.
We present an unsupervised approach for learning to estimate three dimensional (3D) facial structure from a single image while also predicting 3D viewpoint transformations that match a desired pose and facial geometry. We achieve this by inferring the depth of facial keypoints of an input image in an unsupervised manne…
The purpose of this article is to present the theory of higher order connections on vector bundles from a viewpoint inspired by projective differential geometry.
The wave equation (free boson) problem is studied from the viewpoint of the relations on the symplectic manifolds associated to the boundary induced by solutions. Unexpectedly there is still something to say on this simple, well-studied problem. In particular, boundaries which do not allow for a meaningful Hamiltonian …
WAEs offer a statistical understanding of density estimation and error bounds.
These lecture notes are based on [arXiv: math/0702714, 0907.4469, 0907.4470]. We introduce and study basic aspects of non-Euclidean geometries from a coordinate-free viewpoint.
Attempts from different disciplines to provide a fundamental understanding of deep learning have advanced rapidly in recent years, yet a unified framework remains relatively limited. In this article, we provide one possible way to align existing branches of deep learning theory through the lens of dynamical system and …
A smooth map having only fold singularities is called a fold-map. We will give effective conditions for a continuous map to be homotopic to a fold-map from the viewpoint of the homotopy principle.
Geodesics in Sol geometry described with invariant k and spiral properties.
The CUR decomposition provides an approximation of a matrix that has low reconstruction error and that is sparse in the sense that the resulting approximation lies in the span of only a few columns of . In this regard, it appears to be similar to many sparse PCA methods. However, CUR takes a randomized algorithm…