arXiv research

Corrects errors in previous work on linear elasticity calculations.

In this article we review the recent results about the flag curvature of invariant Randers metrics on homogeneous manifolds and by using a counter example we show that the formula which obtained for the flag curvature of these metrics is incorrect. Then we give an explicit formula for the flag curvature of invariant Ra…

This note corrects the mistakes in the splicing formulas of the paper "Floer homology and splicing knot complements". The mistakes are the result of the incorrect assumption that for a knot $K$ inside a homology sphere $Y$, the involution on the knot Floer homology of $K$ which corresponds to moving the basepoints by o…

Critiques incorrect fixed point assertions in digital topology.

Corrects incorrect assertions about fixed points in digital topology.

Incorrect fixed point assertions in digital topology are discussed.

Incorrect fixed point assertions in digital topology are discussed.

Paper examines costs of using wrong price impact models in trading.

Study shows AD for neural nets with machine-representable numbers can be incorrect.

Develops a theory for equivariant networks with partial domain symmetry.

Paper finds previous work on submanifolds incorrect.

Fixed point assertions in digital topology are often incorrect or poorly stated.

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This paper was withdrawn as Lemma 2 is incorrect.

Withdrawn by the authors, the main theorem is incorrect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.

In reinforcement learning, we can learn a model of future observations and rewards, and use it to plan the agent's next actions. However, jointly modeling future observations can be computationally expensive or even intractable if the observations are high-dimensional (e.g. images). For this reason, previous works have…

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.

In this work, a classification method for SSVEP-based BCI is proposed. The classification method uses features extracted by traditional SSVEP-based BCI methods and finds optimal discrimination thresholds for each feature to classify the targets. Optimising the thresholds is formalised as a maximisation task of a perfor…

We continue the work of [4, 2, 3], in which we discuss published assertions that are incorrect or incorrectly proven; that are severely limited or reduce to triviality; or that we improve upon.

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.

This work tackles exploding inverses in INNs, revealing and mitigating their numerical non-invertibility.

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…

The Frölicher spectral sequence of a compact complex manifold $X$ measures the difference between Dolbeault cohomology and de Rham cohomology. We construct for $n\geq 2$ nilmanifolds with left-invariant complex structure $X_n$ such that the $n$-th differential $d_n$ does not vanish. This replaces an earlier incorrect e…

E-scores assess LLM outputs for correctness, addressing p-hacking issues.

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,…

Deep-MIL models fail to respect key MIL assumption, leading to incorrect learning.

Ogburn et al. (2019, arXiv:1910.05438) discuss "The Blessings of Multiple Causes" (Wang and Blei, 2018, arXiv:1805.06826). Many of their remarks are interesting. But they also claim that the paper has "foundational errors" and that its "premise is...incorrect." These claims are not substantiated. There are no foundatio…

The Morse-Bott inequalities relate the topology of a closed manifold to the topology of the critical point set of a Morse-Bott function defined on it. The Morse-Bott inequalities are sometimes stated under incorrect orientation assumptions. We show that these assumptions are insufficient with an explicit counterexample…

This paper studies a stylized, yet natural, learning-to-rank problem and points out the critical incorrectness of a widely used nearest neighbor algorithm. We consider a model with $n$ agents (users) $\{x_i\}_{i \in [n]}$ and $m$ alternatives (items) $\{y_j\}_{j \in [m]}$, each of which is associated with a latent feat…

An active learner is given a hypothesis class, a large set of unlabeled examples and the ability to interactively query labels to an oracle of a subset of these examples; the goal of the learner is to learn a hypothesis in the class that fits the data well by making as few label queries as possible. This work addresses…

Formalizes weak and strong verification for LLMs, controlling errors without assumptions.

Research on interference has provided evidence that the formation of dependencies between non-adjacent words relies on a cue-based retrieval mechanism. Two different models can account for one of the main predictions of interference, i.e., a slowdown at a retrieval site, when several items share a feature associated wi…

In this paper, we have proposed a brain signal classification method, which uses eigenvalues of the covariance matrix as features to classify images (topomaps) created from the brain signals. The signals are recorded during the answering of 2D and 3D questions. The system is used to classify the correct and incorrect a…

This paper improves loss functions for deep learning with noisy labels.

Machine learning offers novel ways and means to design personalized learning systems wherein each student's educational experience is customized in real time depending on their background, learning goals, and performance to date. SPARse Factor Analysis (SPARFA) is a novel framework for machine learning-based learning a…

We explore adversarial robustness in the setting in which it is acceptable for a classifier to abstain---that is, output no class---on adversarial examples. Adversarial examples are small perturbations of normal inputs to a classifier that cause the classifier to give incorrect output; they present security and safety …

Corrects a flawed proof of the Kropholler Conjecture.