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.
Transfer learning improves HVAC fault detection with minimal labeled data.
The large thermal capacity of buildings enables heating, ventilating, and air-conditioning (HVAC) systems to be exploited as demand response (DR) resources. Optimal DR of HVAC units is challenging, particularly for multi-zone buildings, because this requires detailed physics-based models of zonal temperature variations…
Autoencoder neural networks reconstruct missing indoor environment data.
Given a Riemann surface we find an expression for the dominant term for the asymptotics of the holonomy of opers over that Riemann surface corresponding to rays in the Hitchin base of the form . Moreover, we find an associated equivariant map from the universal cover $(\tildeΣ,\tilde{J})…
Paper introduces a method for operator learning using random features.
Increasing energy efficiency in buildings can reduce costs and emissions substantially. Historically, this has been treated as a local, or single-agent, optimization problem. However, many buildings utilize the same types of thermal equipment e.g. electric heaters and hot water vessels. During operation, occupants in t…
Building on the theory of elliptic operators, we give a unified treatment of the following topics: - the problem of homotopy invariance of Novikov's higher signatures on closed manifolds; - the problem of cut-and-paste invariance of Novikov's higher signatures on closed manifolds; - the problem of defining higher signa…
Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the celebrated Random Fourier Feature methodology to get an approximation of operator-…
Extends Gaussian process theory to Banach spaces.
The geometry of symmetric spaces, polar actions, isoparametric submanifolds and spherical buildings is governed by spherical Weyl groups and simple Lie groups. A natural generalization of semisimple Lie groups are affine Kac-Moody groups as they mirror their structure theory and have good explicitely known representati…
Linear algebra approach for parallel deep learning models.
Reproducing kernel Hilbert spaces (RKHSs) play an important role in many statistics and machine learning applications ranging from support vector machines to Gaussian processes and kernel embeddings of distributions. Operators acting on such spaces are, for instance, required to embed conditional probability distributi…
New analysis proves sketching operators' RIP guarantees for mixture models without importance sampling.
The paper discovers the family of identically-derived Euclidean one-parameter even-dimensional differential linear operators with unique eigenproperties, which prove to be inherently related to the emergent characterizations of fundamental building blocks of embedded minimal surfaces and the Nitsche conjecture proof.
We build new examples of extremal domains with small prescribed volume for the first eigenvalue of the Laplace-Beltrami operator in some Riemannian manifold with boundary. These domains are close to half balls of small radius centered at a nondegenerate critical point of the mean curvature function of the boundary of t…
dynoNet learns dynamical systems using linear operators.
Paper establishes convergence rates for learning elliptic pseudo-differential operators.
New Stein operator improves robustness in model inference.
Solves capillary curvature problems for specific p values.
Building on previous results on the quadratic helicity in magnetohydrodynamics (MHD) we investigate particular minimum helicity states. Those are eigenfunctions of the curl operator and are shown to constitute solutions of the quasi-stationary incompressible ideal MHD equations. We then show that these states have inde…
We prove an Hersch's type isoperimetric inequality for the third positive eigenvalue on . Our method builds on the theory we developped to construct extremal metrics on Riemannian surfaces in conformal classes for any eigenvalue.
Researchers extend a groupoid approach to calculate Wodzicki residue and Kontsevich-Vishik trace.
Self attention mechanisms have become a key building block in many state-of-the-art language understanding models. In this paper, we show that the self attention operator can be formulated in terms of 1x1 convolution operations. Following this observation, we propose several novel operators: First, we introduce a 2D ve…
Study learns convolution operators on compact Abelian groups using regularization.
Extends Atiyah-Singer Dirac operator study to non-compact spacetimes.
Inner product-based convolution has been a central component of convolutional neural networks (CNNs) and the key to learning visual representations. Inspired by the observation that CNN-learned features are naturally decoupled with the norm of features corresponding to the intra-class variation and the angle correspond…
Paper combines geometry and time-series analysis for spatiotemporal data.
SKOLR uses linear RNNs to approximate Koopman operators for time-series forecasting.
In this report we review memory-based meta-learning as a tool for building sample-efficient strategies that learn from past experience to adapt to any task within a target class. Our goal is to equip the reader with the conceptual foundations of this tool for building new, scalable agents that operate on broad domains.…
FNOs learn solution operators of dissipative equations efficiently via spectral methods.
In this paper we build the structure equations and the integrable systems for a discrete centroaffine indefinite surface in . At the same time, some centroaffine invariants are obtained according to the structure equations. Using these centroaffine invariants, we study the Laplacian operator and the convexity of …
AutoML discovers complete machine learning algorithms from basic operations.
Paper uses LightGBM for mobile user credit assessment.
Distributed machine learning (ML) is a modern computation paradigm that divides its workload into independent tasks that can be simultaneously achieved by multiple machines (i.e., agents) for better scalability. However, a typical distributed system is usually implemented with a central server that collects data statis…
This research develops approximation theory for OOMs of infinite-dimensional processes.
Using intersection theory in the context of Hilbert manifolds and geometric homology we show how to recover the main operations of string topology built by M. Chas and D. Sullivan. We also study and build an action of the homology of reduced Sullivan's chord diagrams on the singular homology of free loop spaces, extend…
ParPIC clusters directed graphs using random walks and diffusion operators.
This paper introduces a new dataset called "ToyADMOS" designed for anomaly detection in machine operating sounds (ADMOS). To the best our knowledge, no large-scale datasets are available for ADMOS, although large-scale datasets have contributed to recent advancements in acoustic signal processing. This is because anoma…
In this paper we extend to the difference case the notion of Poisson-Lichnerowicz cohomology, an object encapsulating the building blocks for the theory of deformations of Hamiltonian operators. A local scalar difference Hamiltonian operator is a polynomial in the shift operator and its inverse, with coefficients in th…
DISCO predicts system states from short trajectories using an evolved operator.
The paper proves exponential mixing for hyperbolic manifolds, with applications to geodesic holonomy.
Fine-tunes language models with captions for differential equation solving.
New framework for studying eigenvalue functionals of metrics.
It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum mechanical observables. In particular, previous studies constructed quantum grav…
Building performance discrepancies between building design and operation are one of the causes that lead many new designs fail to achieve their goals and objectives. One of main factors contributing to the discrepancy is occupant behaviors. Occupants responding to a new design are influenced by several factors. Existin…
Introduces new spectral triples for parabolic geometry.
The aim of this paper is to provide a general mathematical framework for group equivariance in the machine learning context. The framework builds on a synergy between persistent homology and the theory of group actions. We define group-equivariant non-expansive operators (GENEOs), which are maps between function spaces…
Morpheo is a transparent and secure machine learning platform collecting and analysing large datasets. It aims at building state-of-the art prediction models in various fields where data are sensitive. Indeed, it offers strong privacy of data and algorithm, by preventing anyone to read the data, apart from the owner an…