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.
Confidential Guardian prevents model abstention from being used to discriminate.
A digital euro protocol offers complete privacy and offline transactions using Groth-Sahai proofs.
Neural Network classifiers have been used successfully in a wide range of applications. However, their underlying assumption of attack free environment has been defied by adversarial examples. Researchers tried to develop defenses; however, existing approaches are still far from providing effective solutions to this ev…
PHAZE framework uses zkML and hashing for fast, verifiable LHC trigger decisions.
There has been extensive research on developing defense techniques against adversarial attacks; however, they have been mainly designed for specific model families or application domains, therefore, they cannot be easily extended. Based on the design philosophy of ensemble of diverse weak defenses, we propose ATHENA---…
A scalable protocol for federated averaging with privacy and correctness guarantees.
Deep learning predicts NFT prices with high accuracy.
This review covers quantum computing applications in finance and blockchain.
Efficiently infers interventional distributions from observational data.
Deep learning, even if it is very successful nowadays, traditionally needs very large amounts of labeled data to perform excellent on the classification task. In an attempt to solve this problem, the one-shot learning paradigm, which makes use of just one labeled sample per class and prior knowledge, becomes increasing…
Zero-shot KD for object detection without training data.
Several proofs of Fáry--Milnor theorem are presented.
Corrects a flawed proof of the Kropholler Conjecture.
Simplified proof of gluing formula for analytic torsion forms.
A simplified proof of the Alexander-Conway polynomial exists.
We give a direct proof that the Freed-Lott differential analytic index is well defined and a condensed proof of the differential Grothendieck-Riemann-Roch theorem. As a byproduct we also obtain a direct proof that the R/Z analytic index is well defined and a condensed proof of the R/Z Grothendieck-Riemann-Roch theorem.
Simplified proof for a theorem about graphs.
Polynomial inequalities lie at the heart of many mathematical disciplines. In this paper, we consider the fundamental computational task of automatically searching for proofs of polynomial inequalities. We adopt the framework of semi-algebraic proof systems that manipulate polynomial inequalities via elementary inferen…
We offer a simplified proof for Expected Shortfall's dual representation.
Proof given for SGD convergence in a concise manner.
The Goldman-Parker Conjecture classifies the complex hyperbolic C-reflection ideal triangle groups up to discreteness. We proved the Goldman-Parker Conjecture in [Ann. of Math. 153 (2001) 533--598] using a rigorous computer-assisted proof. In this paper we give a new and improved proof of the Goldman-Parker Conjecture.…
We give a new proof of the isoperimetric inequality in the plane, based on Steiner's formula for the area of a convex neighborhood. This proof establishes the isoperimetric inequality directly, without requiring that we separately establish the existence of an optimal domain. In doing so, this proof bypasses the main d…
Transformers improve logical reasoning on longer proofs but struggle with length.
Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as high-level tactics. However, human experts have to construct proofs manually by en…
Paper provides a rigorous proof of the index theorem for economists.
Simplified proof of Gaussian concentration inequality using covariance.
Simple proof for special surface classification.
Simplified proof of a famous geometry result for students.
We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.
We will give a new proof for the Gromov's theorem on almost flat manifolds, which is an inductive proof on dimension.
We present a formal proof in Lean of probably approximately correct (PAC) learnability of the concept class of decision stumps. This classic result in machine learning theory derives a bound on error probabilities for a simple type of classifier. Though such a proof appears simple on paper, analytic and measure-theoret…
We provide yet another proof of the existence of calibrated forecasters; it has two merits. First, it is valid for an arbitrary finite number of outcomes. Second, it is short and simple and it follows from a direct application of Blackwell's approachability theorem to carefully chosen vector-valued payoff function and …
First geometric proof of the flyping theorem.
Two proofs show that removing a loop from a plane circuit splits the plane.
Notes a flaw in a proof about embedding graphs.
Combinatorial proof of grid homology properties.
Proves Thurston's bounded image theorem for Haken manifolds.
New proof for higher rank subvarieties in genus three.
A simplified proof for satellite knot signatures.
A short proof for curve lengths on hyperbolic surfaces.
Recently, Andrews and Clutterbuck [AC13] gave a new proof of the optimal lower eigenvalue bound on manifolds via modulus of continuity for solutions of the heat equation. In this short note, we give an alternative proof of Theorem 2 in [AC13]. More precisely, following Ni's method ([Ni13, Section 6]) we give an ellipti…
After surveying existing proofs that every closed, orientable 3-manifold is parallelizable, we give three proofs using minimal background. In particular, our proofs use neither spin structures nor the theory of Stiefel-Whitney classes.
Proof of Gromov's conjecture in 3D simplifies existing methods.
Simplified proof classifies surfaces using normal curves.
Corollary 2.3 in our paper "A geometric proof of the Karpelevich-Mostow theorem", Bull. Lond. Math. Soc. 41 (2009), no. 4, 634-638, is false. Here we give a counterexample and show how to avoid the use of this corollary to give a simpler proof of Karpelevich-Mostow theorem. We also include a short discussion of the ori…
Simplified proof for Cheeger's isoperimetric constant.
New model shows hierarchical proof structure helps theorem provers.
This note (originally from 2015) provides a proof of a 1985 conjecture of Montiel and Ros concerning the conformal volume of tori. This updated version adds a proof of the claim made in Remark 5 about the value of the conformal volume of tori in the cases not covered by the conjecture of Montiel and Ros. Originally, I …