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.
The paper corrects and improves previous assertions in digital topology.
Corrects a flawed proof of the Kropholler Conjecture.
Corrects errors in previous work on linear elasticity calculations.
It was pointed out to us that the proof of a crucial lemma (Lemma 5.3) in the paper is incorrect. Thus the approximation theorem (Theorem 0.1) for L^2 torsion of an amenable covering of a finite simplicial complex remains unproved. However, results and proofs of the first four sections (in particular, the approximation…
It has been pointed out to the author by David Glickenstein that the proof of the (closely related) Lemmas 1.2 and 3.2 in the title paper is incorrect. The statements of both Lemmas are correct, and the purpose of this note is to give a correct argument. The argument is of some interest in its own right.
Revisits Pontryagin's proof of stable stems 0, 1, and 2.
A referee found an error in the proof of the Theorem 2 that we could not fix. More precisely, the proof of Lemma 2.1 is incorrect. Hence the fact that integer cohomology of complement of toric Weyl arrangements is torsion free is still a conjecture. ----- A toric arrangement is a finite set of hypersurfaces in a comple…
Critiques incorrect fixed point assertions in digital topology.
Corrects incorrect assertions about fixed points in digital topology.
Improved proofs for topological and smooth pseudo-isotopies of simply connected 4-manifolds.
Corrects errors in previous work on spectral asymptotics in elasticity.
Incorrect fixed point assertions in digital topology are discussed.
We study Bayesian discriminative inference given a model family $p(c,\x, θ)$ that is assumed to contain all our prior information but still known to be incorrect. This falls in between "standard" Bayesian generative modeling and Bayesian regression, where the margin $p(\x,θ)$ is known to be uninformative about $p(c|\x,…
Incorrect fixed point assertions in digital topology are discussed.
We point out an issue with Theorem 5 appearing in "Group-based active query selection for rapid diagnosis in time-critical situations". Theorem 5 bounds the expected number of queries for a greedy algorithm to identify the class of an item within a constant factor of optimal. The Theorem is based on correctness of a re…
It is shown that on a compact spin symmetric space with a Kähler or Quaternion-Kähler structure, the first eigenvalue of the Dirac operator is linked to a ''{lowest}'' action of the holonomy, given by the fiberwise action on spinors of the canonical forms characterized by this holonomy. The result is also verified for …
Study shows AD for neural nets with machine-representable numbers can be incorrect.
Develops a theory for equivariant networks with partial domain symmetry.
This is a brief technical note to clarify the state of lower bounds on regret for reinforcement learning. In particular, this paper: - Reproduces a lower bound on regret for reinforcement learning, similar to the result of Theorem 5 in the journal UCRL2 paper (Jaksch et al 2010). - Clarifies that the proposed proof of …
Paper finds previous work on submanifolds incorrect.
Fixed point assertions in digital topology are often incorrect or poorly stated.
Paper introduces proof-of-learning to verify ML model training.
Fine-tuning neural networks to guarantee performance on specific examples can also introduce incorrect inputs.
This paper was withdrawn as Lemma 2 is incorrect.
Withdrawn by the authors, the main theorem is incorrect
Study on numerical reliability of AD for MaxPool in neural nets.
This paper is not ready for public consumption, as the last step (Figure 20) is incorrect.
Section 1.3 was incorrect, and 2.1 will be removed from further submissions. A rewritten version will be posted in the future.
Incorrect parity-based descriptions of realizable Gauss diagrams found, but bipartite graphs provide a valid approach.
Paper proposes methods to learn with multiple incorrect labels per example.
The paper addresses private and Byzantine-proof cooperative decision-making in multi-agent systems.
I show that Matsumoto conjectured inequality between relative length and Finsler length is false. The incorrectness of the claim is easily inferred from the geometry of the indicatrix.
A minimalist approach improves LLM reasoning by filtering incorrect responses.
The Comment cond-mat/0503325 is built around two core statements, both of which are plainly incorrect.
Improves estimation under model misspecification with fake features.
The results in the recently posted manuscript arXiv:math/0405153v3 are incorrect. The correct version of the aimed results is not original. The preprint contains material from references that are not properly quoted.
New partial models correct for confounding effects in reinforcement learning.
Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces. We show that in many cases, researchers using these tools have derived conclusions that are incorrect, trivial, or limited.
This paper proposes a novel type of random forests called a denoising random forests that are robust against noises contained in test samples. Such noise-corrupted samples cause serious damage to the estimation performances of random forests, since unexpected child nodes are often selected and the leaf nodes that the i…
Paper warns of metric deformation in manifold learning, leading to incorrect answers.
We continue the work of [5] and [3], in which are considered papers in the literature that discuss fixed point assertions in digital topology. We discuss published assertions that are incorrect or incorrectly proven; that are severely limited or reduce to triviality under "usual" conditions; or that we improve upon.
Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces and homotopy invariant fixed point theory. We show that in many cases, researchers using these tools have derived conclusions that are incorrect or tr…
Reshef et al. recently proposed a new statistical measure, the "maximal information coefficient" (MIC), for quantifying arbitrary dependencies between pairs of stochastic quantities. MIC is based on mutual information, a fundamental quantity in information theory that is widely understood to serve this need. MIC, howev…
Characterizes regular parallelisms in 3D space with 2-torus action.
The Frölicher spectral sequence of a compact complex manifold measures the difference between Dolbeault cohomology and de Rham cohomology. We construct for nilmanifolds with left-invariant complex structure such that the -th differential does not vanish. This replaces an earlier incorrect e…
E-scores assess LLM outputs for correctness, addressing p-hacking issues.
Study shows how to control jump-diffusion processes with stable feedback controls in reinforcement learning.
Deep-MIL models fail to respect key MIL assumption, leading to incorrect learning.