Develops game theory framework for UAS integration into NAS.
problem Predicting outcomes of UAS integration into NAS.
method Game theory, reinforcement learning, level-k reasoning.
result Proposes a modeling framework for human pilot behavior.
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48 results for “Level-k Reasoning”
Look-ahead reasoning helps predict strategic user behavior on learning platforms.
problem Optimization criteria on learning platforms do not reflect users' priorities.
method Formalized level-k thinking and contrasted collective and selfish behavior.
result Coordination benefits users but does not offer higher-level reasoning advantages in the long run.
Study on Chern-Simons theory at generic levels, revealing universal resurgent structure.
problem Analyzing Chern-Simons theory at generic levels with small boundary holonomy.
method Examined resurgent structure of state integral models on knot complements with generic discrete level.
result Resurgent structure is universal, independent of the level .
Let G be a compact, simple, simply connected Lie group. A theorem of Freed-Hopkins-Teleman identifies the level k fusion ring R_k(G) of G with the twisted equivariant K-homology at level k+h, where h is the dual Coxeter number. In this paper, we review this result using the language of Dixmier-Douady bundles. We show t…
New framework for RL with opponents, improving learning outcomes.
problem Learning in RL with potential adversaries.
method Threatened Markov Decision Processes (TMDPs) and level-k thinking.
result Improved RL performance by accounting for adversaries.
We construct modular categories from Hecke algebras at roots of unity. For a special choice of the framing parameter, we recover the Reshetikhin-Turaev invariants of closed 3-manifolds constructed from the quantum groups U_q sl(N) by Reshetikhin-Turaev and Turaev-Wenzl, and from skein theory by Yokota. We then discuss …
Study invariants for 3-manifolds at rational roots of unity.
problem Understanding Witten-Reshetikhin-Turaev invariants at roots of unity.
method Analyzing exact expressions for Seifert manifolds and asymptotic expansions.
result Expected structure of Witten-Reshetikhin-Turaev invariants at other roots of unity.
Formal Verlinde Modulemath.DG
Let G be a compact, simple and simply connected Lie group and $\A$ be an equivariant Dixmier-Douady bundle over G. For any fixed level k, we can define a G-C*-algebra $C_{\A^{k+h}}(G)$ as all the continuous sections of the tensor power $\A^{k+h}$ vanishing at infinity. A deep theorem by Freed-Hopkins-Teleman showed tha…
Develops Hamiltonian quantization for complex Chern-Simons theory at even level k.
problem Quantum holonomies and representation theory in complex Chern-Simons theory.
method Combinatorial quantization and operator algebra construction.
result Physical Hilbert space identified and Fenchel-Nielsen representation demonstrated.
We use the 3d-3d correspondence together with the DGG construction of theories labelled by 3-manifolds M to define a non-perturbative state-integral model for SL(n,C) Chern-Simons theory at any level k, based on ideal triangulations. The resulting partition functions generalize a widely studied k=1 state-integ…
Counterexample disproves conjectures about log canonical thresholds.
problem Conjectures about log canonical thresholds were disproved.
method Provided a counterexample to both conjectures.
result Conjectures about log canonical thresholds are false.
Let G be a compact, simply connected Lie group. We develop a `quantization functor' from pre-quantized quasi-Hamiltonian G-spaces at level k to the fusion ring (Verlinde algebra) R_k(G). The quantization Q(M) is defined as a push-forward in twisted equivariant K-homology. It may be computed by a fixed point formula, si…
We extend the coherent state transform (CST) of Hall to the context of the moduli spaces of semistable holomorphic vector bundles with fixed determinant over elliptic curves. We show that by applying the CST to appropriate distributions, we obtain the space of level k, rank n and genus one non-abelian theta functions w…
Estimating the leading principal components of data, assuming they are sparse, is a central task in modern high-dimensional statistics. Many algorithms were developed for this sparse PCA problem, from simple diagonal thresholding to sophisticated semidefinite programming (SDP) methods. A key theoretical question is und…
In several reinforcement learning (RL) scenarios, mainly in security settings, there may be adversaries trying to interfere with the reward generating process. In this paper, we introduce Threatened Markov Decision Processes (TMDPs), which provide a framework to support a decision maker against a potential adversary in…
For a Seifert fibered homology sphere we show that the q-series Z-hat invariant introduced by Gukov, Pei, Putrov and Vafa is a resummation of the Ohtsuki serie. We show that for every even level k there exists a full asymptotic expansion of Z-hat for q tending to a certain k'th root of unity and in particular that the …
We give a geometric description of the fusion rules of the affine Lie algebra su(2)_k at a positive integer level k in terms of the k-th power of the basic gerbe over the Lie group SU(2). The gerbe can be trivialised over conjugacy classes corresponding to dominant weights of su(2)_k via a 1-isomorphism. The fusion-rul…
The coefficient of the logarithmic term in the entropy on even spheres is re-computed by the local technique of integrating the finite temperature energy density up to the horizon on static d--dimensional de Sitter space and thence finding the entropy by thermodynamics. Numeric evaluation yields the known answer i.e. (…
Chern-Simons and Reshetikhin-Turaev theories are shown equivalent for U(1) gauge group.
problem Equivalence between Chern-Simons and Reshetikhin-Turaev TQFTs.
method Proof of natural isomorphism between theories for finite quadratic modules.
result Extended -dimensional TQFTs are naturally isomorphic.
The Quantum Modularity Conjecture of Zagier predicts the existence of a formal power series with arithmetically interesting coefficients that appears in the asymptotics of the Kashaev invariant at each root of unity. Our goal is to construct a power series from a Neumann-Zagier datum (i.e., an ideal triangulation of th…
Teichmüller TQFT is a unitary 3d topological theory whose Hilbert spaces are spanned by Liouville conformal blocks. It is related but not identical to PSL(2,R) Chern-Simons theory. To physicists, it is known in particular in the context of 3d-3d correspondence and also in the holographic description of Virasoro conform…
Constructing brane quantization for -resolutions using SYZ mirror symmetry.
problem Quantizing branes on singular fibers using SYZ mirror symmetry.
method Constructing coisotropic A-branes and their mirrors via fiberwise geometric quantization.
result Establishing a mirror isomorphism between endomorphism algebras.
LoBoost improves local conformal prediction for gradient-boosted trees without extra data splits.
problem Quantifying uncertainty in gradient-boosted tree predictions.
method Model-native local conformal prediction using leaf structure.
result Competitive interval quality and improved test MSE with large calibration speedups.
The study investigates the consistency of -means clustering under finite expectation assumptions.
problem Consistency of -means clustering under finite expectation assumptions.
method Investigates the conditions under which -means clustering is consistent, considering finite expectation instead of finite variance.
result Inconsistency can arise due to extreme cluster imbalance, leading to some clusters having few points.
Language Models are Hidden Reasoners: Unlocking Latent Reasoning Capabilities via Self-Rewardingcs.AI
LaTRO optimizes latent reasoning in LLMs without external reward.
problem Training LLMs to perform complex reasoning tasks.
method Formulates reasoning as latent distribution sampling and optimizes via variational approaches.
result LLMs improve reasoning and evaluation quality through self-improvement.
Consider the Chern-Simons topological quantum field theory with gauge group SU(2) and level k. Given a knot in the 3-sphere, this theory associates to the knot exterior an element in a vector space. We call this vector the knot state and study its asymptotic properties when the level is large. The latter vector space b…
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.
A framework isolates VQA reasoning from perception for better model evaluation.
problem Improper separation of visual perception and reasoning in VQA models.
method Introducing a framework and a top-down calibration technique to decouple reasoning from perception.
result Improved evaluation of VQA models by separating reasoning from perception.
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.
SLOPE outperforms LASSO in low noise scenarios but is suboptimal in large noise scenarios.
problem Sparse linear regression with high-dimensional data.
method Characterized SLOPE's estimation error under specific conditions and compared it with LASSO and bridge regression.
result SLOPE is optimal for low noise scenarios but suboptimal in large noise scenarios.
Cognitive KR model learns new facts from few examples.
problem Inferring new facts from small KG datasets.
method CogKR combines summary and reasoning modules with cognitive science principles.
result Significantly outperforms previous models on one-shot KG reasoning.
We consider Chern-Simons theory on 3-manifold that is the total space of a circle bundle over a 2d base . We show that this theory is equivalent to a new 2d TQFT on the base, which we call Caloron BF theory, that can be obtained by an appropriate type of push-forward. This is a gauge theory on a bundle with stru…
Transformers learn multi-step reasoning through gradient descent.
problem Understanding how transformers solve symbolic multi-step reasoning tasks.
method Theoretical analysis of gradient descent dynamics and multi-phase training.
result Trained one-layer transformers can solve both backward and forward reasoning tasks with generalization guarantees.
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.
Early stopping methods reduce unnecessary reasoning steps in LLMs by monitoring uncertainty signals.
problem LLMs sometimes generate unnecessary reasoning steps, especially under uncertainty.
method Statistically principled early stopping methods that monitor uncertainty signals during generation.
result Uncertainty-aware early stopping improves efficiency and reliability in LLM reasoning, especially in math reasoning.
Achieving artificial visual reasoning - the ability to answer image-related questions which require a multi-step, high-level process - is an important step towards artificial general intelligence. This multi-modal task requires learning a question-dependent, structured reasoning process over images from language. Stand…
DAFT models attention as a dynamical system to make neural networks more interpretable.
problem Uninterpretable features learned by neural networks without human priors.
method DAFT models attention as a continuous dynamical system using neural ODEs.
result DAFT reduces the number of reasoning steps while maintaining similar performance.
FinTradeBench benchmarks LLMs for financial reasoning combining company fundamentals and market signals.
problem Challenges in evaluating financial reasoning models for LLMs.
method Developed a benchmark integrating company fundamentals and trading signals, using a calibration-then-scaling framework.
result Clear performance gap between LLMs, retrieval improves reasoning over textual fundamentals but not trading signals.
MultiVerse uses importance sampling for efficient causal reasoning in probabilistic programming.
problem Efficient causal reasoning in probabilistic models, especially counterfactual inference.
method Native implementation of importance sampling in probabilistic programming, optimizing inference through query structure.
result Significant optimisation of inference process through careful design choices and query structure consideration.
A new formula approximates knot volume using Jones polynomial evaluations.
problem Approximating the hyperbolic volume of knots using a simple formula.
method Reversing a neural network trained on Jones polynomial evaluations.
result Average error of 2.86% on first 1.7 million knots.
Hybrid framework injects TSLM insights into GRLM for robust time-series reasoning.
problem Lack of domain-specific knowledge in large language models for time-series reasoning.
method Hybrid knowledge-injection framework combining RLVR for efficient knowledge transfer.
result Consistently outperforms existing models by 7.9%-26.1% on multivariate time-series benchmarks.
Neural Logic Reasoning integrates deep learning and symbolic logic for better prediction tasks.
problem Lack of cognitive reasoning in deep neural networks limits their ability to solve complex prediction tasks.
method Proposes Logic-Integrated Neural Network (LINN) that learns logical operations and conducts propositional logical reasoning.
result LINN significantly outperforms state-of-the-art recommendation models in Top-K recommendation.
Forward-prediction models enhance physical reasoning, but only for specific tasks.
problem Improving physical reasoning in complex tasks involving many objects.
method Incorporated forward-prediction models into simple physical-reasoning agents and evaluated their performance on the PHYRE benchmark.
result Forward-prediction models improve physical-reasoning performance, especially on complex tasks, but generalization to new task templates is challenging.
RACER optimizes LLM-as-judge accuracy with dynamic reasoning selection.
problem Balancing reasoning accuracy with computational cost in LLM-as-judge settings.
method Formulates routing as a constrained distributionally robust optimization problem, accounting for distribution shift via KL-divergence uncertainty set.
result RACER achieves superior accuracy-cost trade-offs under distribution shift.
VTA combines verbal and latent reasoning for accurate stock time-series forecasts.
problem Challenges in combining textual analysis with time-series data for financial forecasting.
method Converts stock price data into textual annotations, optimizes reasoning trace using inverse MSE, conditions time-series model outputs on reasoning attributes.
result VTA achieves state-of-the-art forecasting accuracy and interpretable reasoning traces.
Neural networks struggle with reasoning tasks that require specialized structures.
problem Understanding why and when neural network structures generalize better.
method Developing a framework to characterize algorithmic alignment with reasoning tasks.
result Neural networks align better with dynamic programming (DP) for certain reasoning tasks.
Fractured Sampling improves LLM reasoning efficiency by truncating CoT trajectories.
problem Efficiently scaling reasoning in large language models with limited tokens.
method Integrating truncated Chain-of-Thought (CoT) with Fractured Sampling across multiple dimensions.
result Fractured Sampling achieves superior accuracy-cost trade-offs compared to full CoT.
SRN improves set representations for relational reasoning.
problem Set permutational invariance limitations in existing approaches.
method Proposed a Set Refiner Network (SRN) to respect set invariance.
result Substantial gains in prediction performance and robustness on relational reasoning tasks.