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.
Single-head attention approximates any function under various norms.
A universal LSTM model outperforms asset-specific models in forecasting stock volatilities.
Universal model for soft tissue mechanics under shock waves.
New model suggests universe emerges from single particle quantum mechanics.
This text explains how fiber bundle structure is fundamental for classical physics.
We prove realizability theorems for vector-valued polynomial mappings, real-algebraic sets and compact smooth manifolds by moduli spaces of planar linkages. We also establish a relation between universality theorems for moduli spaces of mechanical linkages and projective arrangements.
This study approximates neural network features for modeling relations and attention mechanisms.
Quantum systems learn like machine learning models, influenced by dissipation.
New findings on universal learning in contextual bandits with adversarial rewards.
Study symmetry breaking in quantum mechanics to understand many-body physics.
A new Dirac algebroid approach for nonholonomic systems.
A mechanical linkage is a mechanism made of rigid rods linked together by flexible joints, in which some vertices are fixed and others may move. The partial configuration space of a linkage is the set of all the possible positions of a subset of the vertices. We characterize the possible partial configuration spaces of…
We present an axiomatic modification of quaternionic quantum mechanics with a possible-worlds semantics capable of predicting essential "nonquantum" features of an observable universe model - the dimensionality and topology of spacetime, the existence, the signature and a specific form of a metric on it, and certain na…
Softmax attention approximates complex functions and subsumes many known universal approximators.
Deep neural networks near edge of chaos show universal scaling laws.
Simple construction for universal quantum gates.
Paper develops a privacy-preserving nonparametric regression method.
The Galilean group is the group of symmetries of Newtonian mechanics, with Lie a lgebra $\gal(n)$. We find algebraically independent generators for the center of the universal enveloping algebra of $\gal(n)$ using coadjoint orbits.
This work establishes universality for deep equivariant networks, overcoming limitations of previous approaches.
A mechanical linkage is a mechanism made of rigid rods linked together by flexible joints, in which some vertices are fixed and others may move. The partial configuration space of a linkage is the set of all the possible positions of a subset of the vertices. We characterize the possible partial configuration spaces of…
These notes were inspired by the course ''Quantum Field Theory from a Functional Integral Point of View'' given at the University of Zurich in Spring 2017 by Santosh Kandel. We describe Feynman's path integral approach to quantum mechanics and quantum field theory from a functional integral point of view, where the mai…
Paper interprets ResNets via gate-network controls and deep-layer classifications.
In this paper we develop a Hamilton-Jacobi theory in the setting of almost Poisson manifolds. The theory extends the classical Hamilton-Jacobi theory and can be also applied to very general situations including nonholonomic mechanical systems and time dependent systems with external forces.
Geometric mechanics approach to constrained and floating multibody systems using Hamel's equations.
This article is written for the online newspaper "The Photon" published by the Department of Physics, University of Maryland. The article describes econophysics research done in the group of Victor Yakovenko. It briefly surveys the subjects "Statistical Mechanics of Money, Income, and Wealth" and "Probability Distribut…
In the context of science, the well-known adage "a picture is worth a thousand words" might well be "a model is worth a thousand datasets." In this manuscript we introduce the SciML software ecosystem as a tool for mixing the information of physical laws and scientific models with data-driven machine learning approache…
The abstract explores a new wave equation linking quantum mechanics and complex adaptive systems.
Novel compression method preserves privacy while reducing communication costs.
Inspired by the adaptation phenomenon of neuronal firing, we propose the regularity normalization (RN) as an unsupervised attention mechanism (UAM) which computes the statistical regularity in the implicit space of neural networks under the Minimum Description Length (MDL) principle. Treating the neural network optimiz…
New algorithm achieves consistent learning from context in bandit problems.
Model approximates continuous functions in 1-Wasserstein space.
This paper describes a language representation model which combines the Bidirectional Encoder Representations from Transformers (BERT) learning mechanism described in Devlin et al. (2018) with a generalization of the Universal Transformer model described in Dehghani et al. (2018). We further improve this model by addin…
Single-layer Transformer can approximate any sequence mapping.
A plethora of natural, artificial and social systems exist which do not belong to the Boltzmann-Gibbs (BG) statistical-mechanical world, based on the standard additive entropy and its associated exponential BG factor. Frequent behaviors in such complex systems have been shown to be closely related to -stati…
It is now well established empirically that financial price changes are distributed according to a power law, with cubic exponent. This is a fascinating regularity, as it holds for various classes of securities, on various markets, and on various time scales. The universality of this law suggests that there must be som…
Transformers use ReLUs to approximate softmax efficiently.
New framework predicts crypto volatility, outperforming traditional models.
Generative diffusion models exhibit phase transitions in statistical mechanics, impacting their performance.
We consider the binary classification problem in a setup that preserves the privacy of the original sample. We provide a privacy mechanism that is locally differentially private and then construct a classifier based on the private sample that is universally consistent in Euclidean spaces. Under stronger assumptions, we…
Study reveals inefficiencies in EU carbon trading market.
A new method for private query release using Johnson-Lindenstrauss projection.
Paper models Bitcoin market dynamics using 1+1D field theory.
We argue that an important contributing factor into market inefficiency is the lack of a robust mechanism for the stock price to rise if a company has good earnings, e.g., via buybacks/dividends. Instead, the stock price is prone to volatility due to rather random perception/interpretation of earnings announcements (am…
Using a large-scale Deep Learning approach applied to a high-frequency database containing billions of electronic market quotes and transactions for US equities, we uncover nonparametric evidence for the existence of a universal and stationary price formation mechanism relating the dynamics of supply and demand for a s…
Many independent studies on stocks and futures contracts have established that market impact is proportional to the square-root of the executed volume. Is market impact quantitatively similar for option markets as well? In order to answer this question, we have analyzed the impact of a large proprietary data set of opt…
Dropout schedules can be optimized to significantly reduce model test loss.
The paper presents instructive interdisciplinary applications of constrained mechanics calculus in economics on a level appropriate for the undergraduate physics education. The aim of the paper is: 1. to meet the demand for illustrative examples suitable for presenting the background of the highly expanding research fi…
Quickly adapts fault diagnosis models for industrial machines.