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.
Study examines solutions to Jang equation on anti-de Sitter spacetimes.
We give a rigorous analysis of the statistical behavior of gradients in a randomly initialized fully connected network N with ReLU activations. Our results show that the empirical variance of the squares of the entries in the input-output Jacobian of N is exponential in a simple architecture-dependent constant beta, gi…
We derive a new proof to show that the incremental resparsification algorithm proposed by Kelner and Levin (2013) produces a spectral sparsifier in high probability. We rigorously take into account the dependencies across subsequent resparsifications using martingale inequalities, fixing a flaw in the original analysis…
A rigorous ML pipeline for binary classification in biomedical studies, focusing on pancreatic cancer.
Into a geometric setting, we import the physical interpretation of index theorems via semi-classical analysis in topological quantum field theory. We develop a direct relationship between Fedosov's deformation quantization of a symplectic manifold X and the BV quantization of a one-dimensional sigma model with target X…
We recall the Chernoff-Marsden definition of weak symplectic structure and give a rigorous treatment of the functional analysis and geometry of weak symplectic Banach spaces. We define the Maslov index of a continuous path of Fredholm pairs of Lagrangian subspaces in continuously varying Banach spaces. We derive basic …
Enhanced binary classifier uses Urysohn's Lemma of Topology.
This work analyzes self-attention matrices using random matrix theory.
Paper formalizes multi-dimensional FSD using geometric methods.
Analyzes deep neural networks training errors with SGD and random init.
New HMC method uses asymmetrical momentum distributions and improves performance.
New method uses untrusted data for more precise causal analysis.
FA-HMC improves Bayesian federated learning with rigorous guarantees.
Lasso proves consistent model selection for high-dimensional Ising models.
New study on No-U-Turn Sampler for accelerated mixing in Hamiltonian Monte Carlo.
Efficient algorithm for clustering and classification using MBO scheme.
We rigorously prove statistical physics predictions for non-convex GLMs in high dimensions.
Ensemble sampling approximates Thompson sampling for complex models.
sBayFDNN bridges deep learning and functional data analysis for complex, structured data.
Spofe bridges statistical rigor and interpretability in feature extraction from tabular data.
New algorithm maintains privacy while improving model performance in selective release.
This work establishes properties on diffeological structures for set-valued maps and measures.
This dissertation contains a comprehensive study of the topology of 2-manifolds and a complementary analysis of the work done by Edwin E. Moise, L. V. Ahlfors and Ian Richards. Our aim is to study the well known classification of surfaces. Here we present the technical tools needed for proving rigorously the classifica…
Paper develops a private algorithm for multi-agent learning in bandits.
This paper evaluates LLMs for technical market analysis, finding GPT-4 Turbo and FinGPT outperform passive benchmarks.
Kernel methods are studied in a mean field limit for high-dimensional data.
A spin network is a cubic ribbon graph labeled by representations of . Spin networks are important in various areas of Mathematics (3-dimensional Quantum Topology), Physics (Angular Momentum, Classical and Quantum Gravity) and Chemistry (Atomic Spectroscopy). The evaluation of a spin network is an integ…
Neural networks are increasingly deployed in real-world safety-critical domains such as autonomous driving, aircraft collision avoidance, and malware detection. However, these networks have been shown to often mispredict on inputs with minor adversarial or even accidental perturbations. Consequences of such errors can …
Deep generative priors are a powerful tool for reconstruction problems with complex data such as images and text. Inverse problems using such models require solving an inference problem of estimating the input and hidden units of the multi-layer network from its output. Maximum a priori (MAP) estimation is a widely-use…
Recently, a number of learning-based optimization methods that combine data-driven architectures with the classical optimization algorithms have been proposed and explored, showing superior empirical performance in solving various ill-posed inverse problems, but there is still a scarcity of rigorous analysis about the …
We give emphasis on the use of chaos-based rigorous nonlinear technique called Visibility Graph Analysis, to study one economic time series - gold price of USA. This method can offer reliable results with fiinite data. This paper reports the result of such an analysis on the times series depicting the fluctuation of go…
This paper identifies the salient factors that characterize the inequality income distribution for Romania. Data analysis is rigorously carried out using sophisticated techniques borrowed from classical statistics (Theil). Decomposition of the inequalities measured by the Theil index is also performed. This study relie…
A rigorous formulation of Vessiot's vector field approach to the analysis of general systems of partial differential equations is provided. It is shown that this approach is equivalent to the formal theory of differential equations and that it can be carried through if, and only if, the given system is involutive. As a…
SmartDCA improves investment returns by adjusting purchases based on prices.
Diagonal linear networks converge to lasso regularization path during training.
Study develops sector rotation models using factor and fundamental analysis.
It has been known for a long time that the classical spherical perceptrons can be used as storage memories. Seminal work of Gardner, \cite{Gar88}, started an analytical study of perceptrons storage abilities. Many of the Gardner's predictions obtained through statistical mechanics tools have been rigorously justified. …
Kernel learning FBSDE filter improves nonlinear filtering efficiency.
We consider an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also enables us to expand the possible space where the dimension reduction functions bel…
Study non-existence of biconservative hypersurfaces in Minkowski spaces.
In shape analysis, the concept of shape spaces has always been vague, requiring a case-by-case approach for every new type of shape. In this paper, we give a general definition for an abstract space of shapes in a manifold. This notion encompasses every shape space studied so far in the literature, and offers a rigorou…
Study wormholes in Einstein-Yang-Mills theory with a phantom field.
A statistical toolbox for analyzing model performance in medical imaging.
We prove the existence of a (spectrally) stable self-similar blow-up solution to the heat flow for corotational harmonic maps from to the three-sphere. In particular, our result verifies the spectral gap conjecture stated by one of the authors and lays the groundwork for the proof of the nonlinear s…
Empirical studies show that the volatility may exhibit correlations that decay as a fractional power of the time offset. The paper presents a rigorous analysis for the case when the stationary stochastic volatility model is constructed in terms of a fractional Ornstein Uhlenbeck process to have such correlations. It is…
Paper provides a rigorous proof of the index theorem for economists.
We prove the Goldman-Parker Conjecture: A complex hyperbolic ideal triangle group is directly embedded in PU(2,1) if and only if the product of its three standard generators is not elliptic. We also prove that such a group is indiscrete if the product of its three standard generators is elliptic. A novel feature of thi…
We rigorously prove a central limit theorem for neural network models with a single hidden layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A) large numbers of hidden units and (B) large numbers of stochastic gradient descent training iterations. Our result describes the neural net…