arXiv research

A method for learning with autoregressive chain-of-thoughts.

New technique reduces language biases in large language models.

LTMs use latent vectors for efficient autoregressive generation.

Protein Thoughts interprets protein interactions with clear reasoning, improving prediction accuracy.

A new method for math reasoning that allows for iterative correction.

AI systems that explain their decisions can be monitored for harmful intentions.

Optimal sample complexity for autoregressive chain-of-thought learning proven.

Transformers learn chain-of-thought reasoning for longer problems, proving length generalization.

Study reveals AI's spontaneous topic changes in text prediction.

Prefix consistency improves model reliability by weighting answers based on their reproducibility.

New system resists meme coin copy trading bots.

This paper improves learning complex functions with CoT supervision, reducing sample complexity.

Theoretical work shows integrating coherent reasoning improves LLM performance and error correction.

This work analyzes CoT prompting methods from a statistical estimation perspective.

A (complete) matching of the cells of a triangulated manifold can be thought as a combinatorial or discrete version of a nonsingular vector field. We give several methods for constructing such matchings.

Summarizes financial news for better investment decisions.

EORM boosts LLM accuracy with a lightweight, energy-based verifier.

Transformers solve parity problems efficiently with step-by-step reasoning.

The Machina thought experiments pose to major non-expected utility models challenges that are similar to those posed by the Ellsberg thought experiments to subjective expected utility theory (SEUT). We test human choices in the `Ellsberg three-color example', confirming typical ambiguity aversion patterns, and the `Mac…

Study reveals how depth of reasoning affects generalization in models.

CoT-UQ improves LLM uncertainty quantification by integrating reasoning steps.

We prove a compactness result for minimal hypersurfaces with bounded index and volume, which can be thought of as an extension of the compactness theorem of Choi-Schoen (Invent. Math. 1985) to higher dimensions.

Fractured Sampling improves LLM reasoning efficiency by truncating CoT trajectories.

The paper studies how search and distillation improve reasoning in large language models.

The paper explores how LLMs with CoT improve performance on complex tasks.

CoT enhances transformer accuracy on serial tasks by enabling serial computation.

A conformal procedure improves CoT reasoning by aggregating reasoning paths and calibrating abstention rules.

The knot coloring polynomial defined by Eisermann for a finite pointed group is generalized to an infinite pointed group as the longitudinal mapping invariant of a knot. In turn this can be thought of as a generalization of the quandle 2-cocycle invariant for finite quandles. If the group is a topological group then th…

Mapping spaces of supermanifolds are usually thought as exclusively in functorial terms (i.e. trough the Grothendieck functor of points). In this work we provide a geometric description of such mapping spaces in terms of infinite-dimensional super-vector bundles.

Satellite constructions on a knot can be thought of as taking some strands of a knot and then tying in another knot. Using satellite constructions one can construct many distinct isotopy classes of knots. Pushing this further one can construct distinct concordance classes of knots which preserve some algebraic invarian…

We make use of a symmetry reduction technique called Routh reduction to show that the solutions of the Euler-Lagrange equations of a strongly convex autonomous Lagrangian which lie on a specific energy level can be thought of as geodesics of an associated Finsler function.

It is argued that the enlargement of the gauge group found in non-commutative gauge theory is more fundamentally thought of as a consequence of the non-locality of the construction and that it was already encountered in an earlier discussion of a non-local gauge theory.

This paper demonstrates how Dropout can be used in Generative Adversarial Networks to generate multiple different outputs to one input. This method is thought as an alternative to latent space exploration, especially if constraints in the input should be preserved, like in A-to-B translation tasks.

We introduce features for massive data streams. These stream features can be thought of as "ordered moments" and generalize stream sketches from "moments of order one" to "ordered moments of arbitrary order". In analogy to classic moments, they have theoretical guarantees such as universality that are important for lea…

We describe how the loop group maps corresponding to special submanifolds associated to integrable systems may be thought of as certain Grassmann submanifolds of infinite dimensional homogeneous spaces. In general, the associated families of special submanifolds are certain Grassmann submanifolds. An example is given f…

We discuss our recent work on small eigenvalues of surfaces. As an introduction, we present and extend some of the by now classical work of Buser and Randol and explain novel ideas from articles of Sévennec, Otal, and Otal-Rosas which are of importance in our line of thought.

Mathematical framework using Riemannian geometry for intelligence and consciousness.

We prove a smooth compactness theorem for the space of embedded self-shrinkers in $\RR^3$. Since self-shrinkers model singularities in mean curvature flow, this theorem can be thought of as a compactness result for the space of all singularities and it plays an important role in studying generic mean curvature flow.

Transformers with CoT don't enhance reasoning power across all tasks.

The goal of this modern presentation, followed by an English translation from the German, is to make available some parts of Lie's very systematic mathematical thought which deserve to join the contemporary literature, and above all also, to be read.

Surveying nonparametric inference with shape constraints, past and future.

We provide a conceptual map to navigate causal analysis problems. Focusing on the case of discrete random variables, we consider the case of causal effect estimation from observational data. The presented approaches apply also to continuous variables, but the issue of estimation becomes more complex. We then introduce …

CoT improves transformer sample efficiency by reducing input token dependencies and attention sparsity.

We consider harmonic sections of a bundle over the complement of a codimension 2 submanifold in a Riemannian manifold, which can be thought of as multivalued harmonic functions. We prove a result to the effect that these are stable under small deformations of the data. The proof is an application of a version of the Na…

This work is thought as an operative guide to discrete exterior calculus (DEC), but at the same time with a rigorous exposition. We present a version of (DEC) on cubic cell, defining it for discrete manifolds. An example of how it works, it is done on the discrete torus, where usual Gauss and Stokes theorems are recove…

Transformers can generalize to a large task family with only a few demonstrations.

Dynamic abstention improves LLM accuracy by selectively terminating unpromising reasoning.

CHOOSE enhances shallow Transformers for wireless symbol detection.