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.
Revives Vogel's diagrammatic technique for universal Lie algebra computations.
Softmax attention approximates complex functions and subsumes many known universal approximators.
Survey of universal portfolio techniques for minimizing investment regret.
Simple technique turns any adversarial attack into a universal one using few test examples.
We define the class of Haken --manifolds as a generalisation of Haken 3--manifolds. We prove that the interior of the universal covering of a Haken --manifold is $\RR^n$, which generalises a result of Waldhausen. The techniques used allow us to provide a new proof of Waldhausen's universal cover theorem for Haken…
Develops experimental design for discovering missing physics in bioreactors.
New method makes robust estimators work without knowing corruption levels.
We present a simple proof for the universality of invariant and equivariant tensorized graph neural networks. Our approach considers a restricted intermediate hypothetical model named Graph Homomorphism Model to reach the universality conclusions including an open case for higher-order output. We find that our proposed…
WWe define the notion of a random metric space and prove that with probability one such a space is isometricto the Urysohn universal metric space. The main technique is the study of universal and random distance matrices; we relate the properties of metric (in particulary universal) space to the properties of distance …
Neural networks are known to be vulnerable to adversarial examples, inputs that have been intentionally perturbed to remain visually similar to the source input, but cause a misclassification. It was recently shown that given a dataset and classifier, there exists so called universal adversarial perturbations, a single…
A new framework for systematic graph neural network data augmentation.
GCNNs gain rotation invariance with more training augmentation, making SVD-Universal more effective.
Machine learning techniques are being applied to scientific fields, showing promise and challenges.
Minimum width for ReLU networks to approximate L^p functions is max(d_x+1, d_y).
This note provides a neat and enjoyable expansion and application of the magnificent Ordentlich-Cover theory of "universal portfolios." I generalize Cover's benchmark of the best constant-rebalanced portfolio (or 1-linear trading strategy) in hindsight by considering the best bilinear trading strategy determined in hin…
Unified method for CNNs to approximate equivariant maps across various groups.
Estimates means in metric spaces using quantization.
In this work, we demonstrate the existence of universal adversarial audio perturbations that cause mis-transcription of audio signals by automatic speech recognition (ASR) systems. We propose an algorithm to find a single quasi-imperceptible perturbation, which when added to any arbitrary speech signal, will most likel…
This research formalizes uncertainty quantification for Universal Differential Equations models.
Recently, deep learning based natural language processing techniques are being extensively used to deal with spam mail, censorship evaluation in social networks, among others. However, there is only a couple of works evaluating the vulnerabilities of such deep neural networks. Here, we go beyond attacks to investigate,…
This article is written for the Proceedings of the Conference on Current Developments in Mathematics in Harvard University, November 16-17, 2007. It is an exposition of the analytic proof of the finite generation of the canonical ring for a compact complex algebraic manifold of general type. It lists and discusses the …
Data augmentation affects estimates' uncertainty and distribution in complex ways.
In the present paper, we study the finite type invariants of Gauss words. In the Polyak algebra techniques, we reduce the determination of the group structure to transformation of a matrix into its Smith normal form and we give the simplified form of a universal finite type invariant by means of the isomorphism of this…
Despite the widespread adoption of Transformer models for NLP tasks, the expressive power of these models is not well-understood. In this paper, we establish that Transformer models are universal approximators of continuous permutation equivariant sequence-to-sequence functions with compact support, which is quite surp…
Single-head attention approximates any function under various norms.
nUDEs use neural networks to model biology without negative values.
Given a semisimple, compact, connected Lie group G with complexification G^c, we show there is a stable range in the homotopy type of the universal moduli space of flat connections on a principal G-bundle on a closed Riemann surface, and equivalently, the universal moduli space of semistable holomorphic G^c-bundles. Th…
In genus two and higher, the fundamental group of a closed surface acts naturally on the curve complex of the surface with one puncture. Combining ideas from previous work of Kent--Leininger--Schleimer and Mitra, we construct a universal Cannon--Thurston map from a subset of the circle at infinity for the closed surfac…
Universal functions derived for topological correlators in Yang-Mills theory.
The Basilica Julia set is universally equivalent to other complex dynamics sets.
In those lecture notes, we review some applications of heat semigroups methods in Riemannian and sub-Riemannian geometry. The notes contain parts of courses taught at Purdue University, Institut Henri Poincaré, Levico Summer School and Tata Institute.
New method generates universal adversarial perturbations across different image sources.
We present proofs of classical results in Poisson geometry using techniques from Dirac geometry. This article is based on mini-courses at the Poisson summer school in Geneva, June 2016, and at the workshop "Quantum Groups and Gravity" at the University of Waterloo, April 2016.
Study proves deep narrow RNNs can approximate any function, with minimum width independent of data length.
We explore the complex associated to a link in the geometric formalism of Khovanov's (n=2) link homology theory, determine its exact underlying algebraic structure and find its precise universality properties for link homology functors. We present new methods of extracting all known link homology theories directly from…
A practical limitation of deep neural networks is their high degree of specialization to a single task and visual domain. Recently, inspired by the successes of transfer learning, several authors have proposed to learn instead universal, fixed feature extractors that, used as the first stage of any deep network, work w…
Paper introduces MRCs that minimize worst-case 0-1 loss, providing tight performance guarantees.
We introduce the TUH EEG Seizure Corpus (TUSZ), which is the largest open source corpus of its type, and represents an accurate characterization of clinical conditions. In this paper, we describe the techniques used to develop TUSZ, evaluate their effectiveness, and present some descriptive statistics on the resulting …
Geodesic currents in strongly hyperbolic spaces are dense.
To deal with changing environments, a new performance measure -- adaptive regret, defined as the maximum static regret over any interval, was proposed in online learning. Under the setting of online convex optimization, several algorithms have been successfully developed to minimize the adaptive regret. However, existi…
Paper develops efficient methods for estimating Hessian inverses in stochastic optimization.
Inductive transfer learning has greatly impacted computer vision, but existing approaches in NLP still require task-specific modifications and training from scratch. We propose Universal Language Model Fine-tuning (ULMFiT), an effective transfer learning method that can be applied to any task in NLP, and introduce tech…
The universe's shape and size are determined in general cosmological models.
This paper improves support recovery in universal one-bit compressed sensing with fewer measurements.
A grand challenge of the 21st century cosmology is to accurately estimate the cosmological parameters of our Universe. A major approach to estimating the cosmological parameters is to use the large-scale matter distribution of the Universe. Galaxy surveys provide the means to map out cosmic large-scale structure in thr…
Deep residual networks can approximate any continuous function using control theory.
In this paper, we show how novel transfer reinforcement learning techniques can be applied to the complex task of target driven navigation using the photorealistic AI2THOR simulator. Specifically, we build on the concept of Universal Successor Features with an A3C agent. We introduce the novel architectural contributio…
Soft Truncation improves diffusion model performance by balancing loss scales across diffusion times.