Self-supervised skip-tree training improves mathematical reasoning in language models.
problem Improving logical reasoning in language models for formal mathematics.
method Self-supervised language modeling on mathematical formulas, skip-tree task.
result Models trained on skip-tree task outperform standard models in mathematical reasoning tasks.
Benchmark for math reasoning models from human proofs.
problem Measuring and accelerating machine learning models in high-level mathematical reasoning.
method Built a non-synthetic dataset from theorem prover proofs, defined a task for model to fill in missing propositions, used hierarchical transformer to improve performance.
result Neural models can capture non-trivial mathematical reasoning, hierarchical transformer outperforms baseline.
LLMs struggle with arithmetic tasks unless they use high numerical precision.
problem Improving arithmetical reasoning capabilities of LLMs.
method Theoretical analysis and empirical experiments on numerical precision.
result LLMs require high numerical precision to efficiently handle arithmetic tasks.
Reasoning models generate differently based on problem difficulty, not just length.
problem Understanding how reasoning models handle different problem difficulties.
method Examined hidden-state trajectories across competitive programming, mathematics, and Boolean satisfiability.
result Corrected trajectory geometry shows difficulty-dependent differences in reasoning models, with stronger effects in the code domain.
Abstractor enhances Transformers for relational reasoning, improving sample efficiency and performance.
problem Improving sample efficiency and performance in relational tasks.
method Introduces Abstractor module with relational cross-attention to enable explicit relational reasoning.
result Dramatic improvements in sample efficiency and performance on various relational tasks.
New method uses model comparison signals to improve LLM evaluation accuracy.
problem Limited benchmark sizes and model stochasticity in evaluating LLMs' mathematical reasoning.
method Combines standard labeled outcomes with model comparison signals to design a statistically efficient evaluation framework.
result Semiparametric estimator achieves the semiparametric efficiency bound and substantially improves ranking accuracy.
Shapley values for feature importance lead to mathematical and practical issues.
problem Mathematical and practical issues with Shapley values for feature importance.
method Game-theoretic formulations of feature importance using Shapley values.
result Mathematical problems arise when using Shapley values for feature importance.
Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis of inferring, learning, and exploiting laws, axioms, and symbol manipulation ru…
We design and conduct a simple experiment to study whether neural networks can perform several steps of approximate reasoning in a fixed dimensional latent space. The set of rewrites (i.e. transformations) that can be successfully performed on a statement represents essential semantic features of the statement. We can …
Transformers with CoT don't enhance reasoning power across all tasks.
problem Does CoT enhance the reasoning power of transformers?
method Examined the memorization capabilities of fixed-precision transformers with and without CoT.
result Transformers with CoT cannot memorize all reasoning tasks, leading to a negative answer.
We describe a mathematical link between aspects of information theory, called pairwise comparisons, and discretized gauge theories. The link is made by the notion of holonomy along the edges of a simplex. This correspondance leads to open questions in both field.
VERAFI improves financial AI by verifying calculations and compliance.
problem Financial AI systems generate errors and violations during reasoning.
method VERAFI combines dense retrieval, reranking, and automated reasoning policies.
result VERAFI achieves 94.7% factual correctness, 81% relative improvement.
AER dynamically adjusts entropy regularization for better LLM reinforcement learning.
problem Policy entropy collapse in RLVR training limits exploration and reasoning performance.
method Adaptive Entropy Regularization (AER) with difficulty-aware coefficient allocation, initial-anchored target entropy, and dynamic global coefficient adjustment.
result AER consistently outperforms baselines on mathematical reasoning benchmarks, improving both accuracy and exploration.
Method guarantees coherent factuality for language model outputs in reasoning tasks.
problem Ensuring correctness of language model outputs in reasoning tasks.
method Developed a conformal-prediction-based method applied to subgraphs within a deducibility graph.
result Achieved coherent factuality across target coverage levels, 90% on stricter definition.
EORM boosts LLM accuracy with a lightweight, energy-based verifier.
problem Efficiently verifying mathematical reasoning in large language models.
method Energy-based framework to rank Chain-of-Thought solutions using simple outcome labels.
result EORM boosts LLM accuracy to 90.7% on GSM8k and 63.7% on MATH with only 55M parameters.
Enhances math problem-solving models with multi-turn preference learning.
problem Improving mathematical problem-solving capabilities of large language models.
method Introduces a multi-turn direct preference learning framework for tool-integrated mathematical reasoning tasks.
result Significant performance improvements in model accuracy on math datasets.
There are several (mathematical) reasons why Dupire's formula fails in the non-diffusion setting. And yet, in practice, ad-hoc preconditioning of the option data works reasonably well. In this note we attempt to explain why. In particular, we propose a regularization procedure of the option data so that Dupire's local …
Paper proves impossible for large language models to control hallucinations without sacrificing other properties.
problem Achieving truthful knowledge representation, semantic information conservation, and knowledge-constrained optimality simultaneously in large language models.
method Modeling inference as an auction of ideas, using mechanism design, proper scoring rules, and transformer architecture analysis.
result No LLM can simultaneously achieve all four essential properties without violating at least one.
Auto-CEI improves LLM reasoning by balancing assertiveness and conservativeness.
problem Hallucinations and laziness in LLM reasoning tasks.
method Expert Iteration explores reasoning trajectories, guiding incorrect paths back on track and promoting appropriate 'I don't know' responses.
result Auto-CEI achieves superior alignment in logical reasoning, mathematics, and planning tasks.
This paper compares self-reflection and budget tuning for LLMs, revealing domain-specific performance gains.
problem Improving inference-time performance of LLMs without retraining, balancing quality, cost, and latency.
method Systematic comparison of self-reflection and budget tuning across mathematical reasoning and translation tasks, evaluating various LLMs and model families.
result Substantial domain-dependent variation in self-reflection effectiveness, with up to 220% performance gains in mathematical reasoning.
A new method for math reasoning that allows for iterative correction.
problem Standard reasoning models commit to each token and cannot recover from early errors.
method Generative framework with latent thought vectors for iterative self-correction.
result 30 rethinking iterations surpass baselines with 15 times more parameters.
The mathematical features of a string theory compactification determine the physics of the effective four-dimensional theory. For this reason, understanding the mathematical structure of the possible compactification spaces is of profound importance. It is well established that the compactification space for M-Theory m…
This article reviews mathematical insights into neural networks and machine learning.
problem Understanding the success and subtleties of neural network-based machine learning.
method Rigorous mathematical analysis, numerical experiments, and simplified models.
result Identification of open problems in the field.
Enhances large language models' reasoning through simpler off-policy reinforcement learning.
problem Improving large language models' ability to reason and solve problems.
method EM Policy Gradient, optimizing expected return over reasoning trajectories using Expectation-Maximization (EM) optimization.
result Achieves comparable or slightly superior performance to state-of-the-art methods on reasoning datasets, with additional cognitive behaviors.
Trade-R1 bridges verifiable rewards to stochastic financial markets via process-level reasoning verification.
problem Extending RL to financial markets where rewards are verifiable but noisy.
method A verification method that transforms reasoning over financial documents into a structured RAG task, using a triangular consistency metric.
result DSR achieves superior cross-market generalization while maintaining reasoning consistency.
Dynamic abstention improves LLM accuracy by selectively terminating unpromising reasoning.
problem LLMs waste compute on incorrect responses, leading to inefficiency.
method Formal reinforcement learning framework with abstention reward parameter.
result Dynamic abstention outperforms natural baselines in selective accuracy.
This work investigates how multi-round reasoning improves LLM performance.
problem Improving problem-solving abilities in complex tasks with LLMs.
method Investigates approximation, learnability, and generalization properties of multi-round auto-regressive models.
result Transformers with finite context windows are universal approximators for Turing-computable functions and can approximate any Turing-computable sequence-to-sequence function through multi-round reasoning.
LLMs can fail to maximize aligned values even after training, due to irrational reasoning.
problem Value misalignment in LLMs' reasoning despite training alignment.
method Formalized rational value risk and decomposed estimation error.
result Rational value risk is widespread and cannot be fully eliminated.
We describe in this note a new invariant of rooted trees. We argue that the invariant is interesting on it own, and that it has connections to knot theory and homological algebra. However, the real reason that we propose this invariant to readers is that we deal here with an elementary, interesting, new mathematics, an…
Riemann's mathematical papers contain many ideas that arise from physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann's ideas in mathematics from those in physics. Furthermore, Riemann's philosophical ideas are often in the background of his work on science. The …
NSR enables neural networks to reason with continuous numbers and extrapolate.
problem Quantitative reasoning and extrapolation in neural networks.
method Proposes Neural Status Register (NSR) for continuous number reasoning.
result NSR achieves extrapolation to numbers many orders of magnitude larger than training data.
This summarizes the study of the financial and economic crisis in Europe. The starting questions were: 1) Why do we have a crisis? Unde venis? 2) What will be the outcome? Quo vadis? Here is the reasoning which touches many areas, ranging from financial to politics and from psychology and economy.
CoT-UQ improves LLM uncertainty quantification by integrating reasoning steps.
problem LLMs' overconfidence and lack of response-wise uncertainty quantification.
method Integrates LLMs' reasoning steps into uncertainty estimation.
result Significantly improves uncertainty quantification accuracy (5.9% AUROC improvement).
Transformers learn chain-of-thought reasoning for longer problems, proving length generalization.
problem Challenging problems require deeper reasoning, but how do models generalize this to longer tasks?
method Theoretical analysis of transformers on synthetic state-tracking tasks, proving length generalization through attention concentration.
result Transformers can learn chain-of-thought reasoning for longer problems, proving length generalization.
LaLoRA prevents forgetting in LoRA fine-tuning.
problem Catastrophic forgetting in fine-tuned models.
method LaLoRA applies Laplace approximation to LoRA weights for regularization.
result Improved learning-forgetting trade-off with controllable regularization strength.
Galactica learns from scientific literature to help researchers.
problem Information overload in scientific literature makes it hard to find useful insights.
method Trained on a large corpus of scientific papers, reference material, and knowledge bases.
result Outperforms existing models on various scientific tasks, including LaTeX equations and mathematical reasoning.
Adaptive Nucleus Truncation Improves Long-Form Reasoning
problem Improving long-form reasoning in language models
method Adaptive Nucleus Truncation Sampling (ANTS)
result Significant performance gains across various benchmarks
UCPO improves diversity in reinforcement learning models, maintaining high accuracy.
problem RLVR objectives often lead to diversity collapse, reducing coverage of correct solutions.
method UCPO adds a conditional uniformity penalty to GRPO, redistributing probability mass.
result UCPO improves Pass@K and diversity while maintaining competitive Pass@1 accuracy.
Transformer models can solve complex math problems with less data.
problem Solving complex symbolic mathematics problems with limited data.
method Pretrain transformer models on language translation tasks and fine-tune for symbolic math.
result Pretrained transformer models achieve comparable accuracy to state-of-the-art models with less data.
Calibrated PRMs improve inference efficiency for LLMs by dynamically adjusting compute budgets.
problem Poor calibration of PRMs leads to overestimation of success probabilities in partial reasoning steps.
method Quantile regression for calibration, instance-adaptive scaling (IAS) framework.
result Calibrated PRMs reduce inference costs while maintaining accuracy, especially on confident problems.
Bayesian framework explains diverse explanatory values.
problem Understanding and predicting human preferences for explanations.
method Developed a Bayesian account to integrate various explanatory values.
result Core values from psychology, statistics, and philosophy emerge from a common framework.
Novel approach trains LLMs for inductive reasoning using probabilistic programs.
problem Training LLMs for inductive reasoning with sparse, ambiguous data.
method Program-based Posterior Training (PPT) using probabilistic inference.
result Significant improvement in estimation accuracy and alignment with human judgments.
Several recent works have empirically observed that Convolutional Neural Nets (CNNs) are (approximately) invertible. To understand this approximate invertibility phenomenon and how to leverage it more effectively, we focus on a theoretical explanation and develop a mathematical model of sparse signal recovery that is c…
This paper expresses the structure of artificial neural network (ANN) as a functional form, using the activation integral concept derived from the activation function. In this way, the structure of ANN can be represented by a simple function, and it is possible to find the mathematical solutions of ANN. Thus, it can be…
The study uncovers latent capabilities of language models via causal representation learning.
problem Rigorous causal evaluations of language model capabilities are challenging due to confounding effects and computational costs.
method Proposes a causal representation learning framework to identify latent capability factors as causally interrelated after controlling for a common confounder (base model).
result Identifies a three-node linear causal structure explaining performance variations across 1500 models and six benchmarks.
Introduces basics of supergeometry for PhD students.
problem Understanding the geometry of supersymmetry.
method Smooth exposition of supergeometry themes.
result Highlights the reasons behind mathematical choices.
Bayesian RL enhances LLMs to reflectively explore and correct errors.
problem LLMs trained via RL lack reflective behaviors like rethinking and error correction.
method Bayesian RL framework that optimizes expected return under posterior distribution over Markov decision processes.
result BARL algorithm improves LLM performance in reasoning tasks.
Tutorial on using neural networks for single cell data analysis.
problem Handling large sequencing datasets efficiently.
method Single cell variational inference using variational auto-encoder.
result Model learns data distribution for insights.