Tab-TRM uses recursive model for insurance pricing on tabular data.
problem Insurance pricing on tabular data.
method Adapts recursive latent reasoning to insurance modeling using a compact, parameter-efficient network.
result Improves insurance pricing accuracy using iterative refinement of latent tokens.
R2-B2 optimizes game interactions with recursive reasoning.
problem Optimizing interactions between boundedly rational agents with unknown payoff functions.
method Recursive Reasoning-Based Bayesian Optimization (R2-B2) for repeated games.
result R2-B2 achieves faster asymptotic convergence to no regret than non-recursive methods.
ERM uses energy-based selection to improve recursive reasoning.
problem Lack of principled inference mechanism in recursive models.
method Energy-guided Recursive Model (ERM) introduces Hopfield energies for trajectory selection.
result ERM achieves optimal solutions on various puzzles.
LASER compresses recursive model activations by exploiting their low-dimensional structure.
problem Understanding and optimizing the geometric structure of recursive reasoning trajectories.
method Dynamic low-rank basis tracking via matrix-free subspace tracking with a fidelity-triggered reset mechanism.
result Recursive activations occupy a linear, low-dimensional subspace that can be compressed efficiently.
Humans are capable of attributing latent mental contents such as beliefs or intentions to others. The social skill is critical in daily life for reasoning about the potential consequences of others' behaviors so as to plan ahead. It is known that humans use such reasoning ability recursively by considering what others …
Transformers solve parity problems efficiently with step-by-step reasoning.
problem Training transformers to solve complex, recursive problems like parity.
method Training a one-layer transformer to solve k-parity, incorporating intermediate parities into the loss function, and using teacher forcing or augmented data. result Transformers can learn parity in one gradient update with intermediate supervision or self-consistency checks.
Looped transformers outperform standard transformers in complex reasoning tasks due to a specific loss landscape geometry.
problem Understanding why looped transformers outperform standard transformers in complex reasoning tasks.
method Explained through loss landscape geometry, distinguishing between U-shaped and V-shaped valleys, and proposing SHIFT training strategy.
result Looped transformers' recursive architecture induces a River-V-Valley landscape, leading to better loss convergence and complex pattern learning.
A major drawback of the Standard Heston model is that its implied volatility surface does not produce a steep enough smile when looking at short maturities. For that reason, we introduce the Stationary Heston model where we replace the deterministic initial condition of the volatility by its invariant measure and show,…
SE-RRMs solve structured problems like Sudoku and ARC-AGI by enforcing symbol equivariance.
problem Structured reasoning problems like Sudoku and ARC-AGI.
method Symbol-equivariant recurrent reasoning models enforcing permutation equivariance.
result SE-RRMs outperform prior RRMs on 9x9 Sudoku and generalize to larger and smaller instances.
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.
Statistical relational models provide compact encodings of probabilistic dependencies in relational domains, but result in highly intractable graphical models. The goal of lifted inference is to carry out probabilistic inference without needing to reason about each individual separately, by instead treating exchangeabl…
We study the statistical behavior of reasoning probes in a stylized model of iterative computation inspired by neural algorithmic reasoning. The underlying computation is given by a looped Boolean circuit whose graph is a perfect ν-ary tree (ν≥2), with outputs recursively fed back as inputs across computation ro…
Identifying changes in the generative process of sequential data, known as changepoint detection, has become an increasingly important topic for a wide variety of fields. A recently developed approach, which we call EXact Online Bayesian Changepoint Detection (EXO), has shown reasonable results with efficient computati…
Paper solves portfolio problem using improved stochastic methods.
problem Finite horizon consumption-investment problem under stochastic factor framework.
method Proves existence of classical solution for semilinear equation using gradient estimates.
result Proves existence of classical solution and provides all necessary estimates.
The aim of this work is to address the question of whether we can in principle design rational decision-making agents or artificial intelligences embedded in computable physics such that their decisions are optimal in reasonable mathematical senses. Recent developments in rare event probability estimation, recursive ba…
Recursive neural networks have widely been used by researchers to handle applications with recursively or hierarchically structured data. However, embedded control flow deep learning frameworks such as TensorFlow, Theano, Caffe2, and MXNet fail to efficiently represent and execute such neural networks, due to lack of s…
Inspired by the hierarchical hidden Markov models (HHMM), we present the hierarchical semi-Markov conditional random field (HSCRF), a generalisation of embedded undirectedMarkov chains tomodel complex hierarchical, nestedMarkov processes. It is parameterised in a discriminative framework and has polynomial time algorit…
Paper defines Farey Recursive Functions and explores their properties.
problem Understanding recursive functions on rationals.
method Defined and studied Farey Recursive Functions using Farey graph.
result Farey Recursive Functions naturally connect to 2-bridge knots and links.
The Jacobian matrix (or the gradient for single-output networks) is directly related to many important properties of neural networks, such as the function landscape, stationary points, (local) Lipschitz constants and robustness to adversarial attacks. In this paper, we propose a recursive algorithm, RecurJac, to comput…
The paper explores generalizations of Mirzakhani's recursion and computes volumes for physical gravity models.
problem Computing volumes for physical gravity models.
method Topological recursion and physical two-dimensional gravity models.
result Derivation of Virasoro constraints and cut-and-join equations for generalized Mirzakhani's recursions.
We address the problem of continual learning in multi-task Gaussian process (GP) models for handling sequential input-output observations. Our approach extends the existing prior-posterior recursion of online Bayesian inference, i.e.\ past posterior discoveries become future prior beliefs, to the infinite functional sp…
New recursion formula for non-orientable surfaces resolves divergences.
problem Computing volumes of moduli spaces for non-orientable surfaces.
method Generalization of Mirzakhani's recursion to non-orientable surfaces, handling divergences with integral kernels.
result Regularized volumes can be computed with a cutoff on crosscap size.
Harer and Zagier proved a recursion to enumerate gluings of a 2d-gon that result in an orientable genus g surface, in their work on Euler characteristics of moduli spaces of curves. Analogous results have been discovered for other enumerative problems, so it is natural to pose the following question: how large is t…
This paper studies recursive ensembles driven by Fibonacci updates, improving learning dynamics.
problem Improving learning dynamics in recursive ensemble learning.
method Develops second-order recursive architectures with Fibonacci-type update flows.
result Establishes global convergence conditions and generalization bounds for recursive ensembles.
The article improves prediction by aggregating Kalman recursions online.
problem Improving expert aggregation in prediction models.
method Using exponential weights and state-space models to aggregate Kalman recursions.
result New algorithms outperform existing methods in Kalman recursion expert aggregation.
Solves a recursion for Gromov-Witten invariants of the unknot.
problem Determining Gromov-Witten invariants for a specific Lagrangian brane.
method Uses a skein-theoretic recursion and geometric solutions.
result Solves the recursion to find the expected hook-content formula.
New recursion found for hyperbolic sphere volumes.
problem Volume calculation of hyperbolic sphere moduli spaces.
method Proved a non-linear recursive relation.
result Generalized Zograf's result for conical points and geodesic boundaries.
This work generalizes a formula linking Seiberg-Witten prepotential and topological recursion.
problem Analyzing the relationship between Seiberg-Witten curves and topological recursion.
method Analytical approach using Seiberg-Witten family of curves.
result A generalized formula relating Seiberg-Witten prepotential to the genus zero part of topological recursion on a Seiberg-Witten curve.
We introduce a new RL problem where the agent is required to generalize to a previously-unseen environment characterized by a subtask graph which describes a set of subtasks and their dependencies. Unlike existing hierarchical multitask RL approaches that explicitly describe what the agent should do at a high level, ou…
We describe a method for recursively calculating Gromov-Witten invariants of all blowups of the projective plane. This recursive formula is different from the recursive formulas due to Göttsche and Pandharipande in the zero genus case, and Caporaso and Harris in the case of no blowups. We use tropical curves and a recu…
Topological recursion recovers a specific partition function for colored knots.
problem Recovering the extended Ooguri-Vafa partition function for colored HOMFLY-PT polynomials of torus knots.
method Applying topological recursion to the spectral curve of colored HOMFLY-PT polynomials of torus knots.
result Topological recursion reproduces the n-point functions of the extended Ooguri-Vafa partition function.
We derive the Do and Norbury recursion formula for the one-loop mean of an irregular spectral curve from a variant of replica method by Brezín and Hikami. We express this recursion in special times in which all terms W1(g) of the genus expansion of the one-loop mean are polynomials. We find a generalization of th…
This paper concerns the recursive utility maximization problem under partial information. We first transform our problem under partial information into the one under full information. When the generator of the recursive utility is concave, we adopt the variational formulation of the recursive utility which leads to a s…
We derive a recursion relation for hyperbolic string vertices and apply it to string field theory.
problem Deriving a recursion relation for hyperbolic string vertices and its implications for string field theory.
method Using systolic volumes and a modified Mirzakhani's recursion, we construct a higher-order vertex determination for hyperbolic string field theory.
result The higher order vertices in hyperbolic string field theory are determined by the cubic vertex iteratively for any background.
Benchmarking recursive collapse claims with a new framework under false-positive control.
problem Evaluating recursive systems for failure patterns and warning claims.
method Developed Loopzero framework for testing recursive failures, specified claim boundaries in Lean, evaluated under FP constraint, and compared with standard detectors.
result No standard detectors or Loopzero's pre-registered quantile detector achieved the required operating point under the false-positive contract.
SRRM improves recursive transport surrogates in the small-discrepancy regime.
problem Insufficient understanding of recursive partitioning methods' statistical behavior and resolution in the small-discrepancy regime.
method Introduced Selective Recursive Rank Matching (SRRM) to improve the resolution of Recursive Rank Matching (RRM).
result SRRM yields a higher-fidelity practical surrogate for the Wasserstein distance at moderate additional computational cost.
Study uses reinforcement learning to optimize portfolios under recursive utility.
problem Improving portfolio allocation using risk-sensitive objectives.
method Approximated certainty equivalent via Monte Carlo, trained actor-critic algorithms (PPO, A2C).
result Recursive-utility agent outperforms discounted baseline in Sharpe ratio, max drawdown, and cumulative return.
The paper studies risk-sensitive MDPs with recursive risk measures.
problem Risk-sensitive decision-making in MDPs with unbounded costs.
method Recursive application of static risk measures, Bellman equation derivation, existence of optimal policies.
result Existence of Markovian optimal policies for infinite planning horizons, contractive model for stationary optimal policy.
New recursive relation found for a specific torus knot.
problem Finding a recursive relation for a specific torus knot.
method Extending colored Jones polynomials to knots in (2p+1,2) torus knot complements and examining a particular knot. result An analogous recursive relation exists for a specific (2p+1,2) torus knot. We propose a general theory for constructing functorial assignments Σ⟼ΩΣ∈E(Σ) for a large class of functors E from a certain category of bordered surfaces to a suitable target category of topological vector spaces. The construction proceeds by successive excisions of homotopy classes of embedded pai…
Recursive training of generative models can lead to model collapse, and the recursion converges to a unique limiting distribution.
problem Model collapse in recursive training of generative models
method Recursive training on their own outputs
result Recursive training converges to a unique limiting distribution
Paper presents novel online MTL methods using WRLS and OSLSSVR.
problem Online Multi-Task Learning (MTL) Regression Problems
method Develops recursive versions of WRLS and OSLSSVR for MTL.
result Achieves exact and approximate recursions with quadratic cost.
We study topological recursion on the irregular spectral curve xy2−xy+1=0, which produces a weighted count of dessins d'enfant. This analysis is then applied to topological recursion on the spectral curve xy2=1, which takes the place of the Airy curve x=y2 to describe asymptotic behaviour of enumerative proble…
We give an overview of the proof for Mirzakhani's volume recursion for the Weil-Petersson volumes of the moduli spaces of genus g hyperbolic surfaces with n labeled geodesic boundary components, and her application of this recursion to Witten's conjecture and the study of simple geodesic length spectrum growth rate…
New formula simplifies interior polynomial calculation.
problem Calculating interior polynomial efficiently.
method New recursion formula based on non-expanding sets.
result Clearer combinatorial interpretation of interior polynomial.
We extend topological recursion to twisted Higgs bundles with singularities.
problem Computing Taylor expansions of period matrices for twisted Higgs bundles.
method We introduce a twisted topological recursion on the spectral curve of a twisted Higgs bundle, encoding singularities and performing the recursion explicitly.
result The g=0 twisted Eynard-Orantin differentials compute the Taylor expansion of the spectral curve's period matrix, independent of the ambient space. Theoretical study on AI models' resilience to data contamination during recursive training.
problem Data contamination in recursive training of generative AI models.
method General framework with minimal assumptions on real data distribution and flexible generative models.
result Contaminated recursive training converges with a rate equal to the minimum of baseline model's rate and contamination fraction.
Paper studies metric ribbon graphs and provides a recursion for their volumes.
problem Calculating volumes of combinatorial moduli spaces of directed metric ribbon graphs.
method Decomposes directed ribbon graphs into simpler graphs with one vertex, proving a canonical recursion scheme for volumes.
result Explicit recursion for volumes of four-valent metric ribbon graphs provided.