BBRT improves molecular properties through iterative translation.
problem Optimizing molecular structures for improved biochemical properties.
method Iterative translation of molecules using a black box approach.
result Improvement in molecular properties with each iteration of the translator.
While it has become common to perform automated translations on natural language, performing translations between different representations of mathematical formulae has thus far not been possible. We implemented the first translator for mathematical formulae based on recursive neural networks. We chose recursive neural…
Neural machine translation is a relatively new approach to statistical machine translation based purely on neural networks. The neural machine translation models often consist of an encoder and a decoder. The encoder extracts a fixed-length representation from a variable-length input sentence, and the decoder generates…
We extend asymptotic formulas for saddle connections on translation surfaces.
problem Counting saddle connections on translation surfaces with large genus.
method Recursive formulas and asymptotic analysis for all strata and multiplicities.
result Asymptotics for all saddle connections on translation surfaces of growing genus.
This paper concerns the recursive utility maximization problem. We assume that the coefficients of the wealth equation and the recursive utility are concave. Then some interesting and important cases with nonlinear and nonsmooth coefficients satisfy our assumption. After given an equivalent backward formulation of our …
We use the explicit relation between genus filtrated s-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich--Penner matrix model (KPMM), which is the generating function for volumes of discretized (open) moduli spaces Mg,sdisc (discrete volumes), to express Gaussian means…
Paper introduces v-CMC linking causality and utility.
problem Linking causality and utility for value theory.
method Developed a new causal independence principle (v-CMC) and proved its equivalence.
result Equivalence of local, global, and decomposition versions of v-CMC.
In this paper, we compare two definitions of Rauzy classes. The first one was introduced by Rauzy and was in particular used by Veech to prove the ergodicity of the Teichmüller flow. The second one is more recent and uses a "labeling" of the underlying intervals, and was used in the proof of some recent major results a…
A new method for efficient portfolio optimization using graph structures.
problem Optimizing portfolio weights while reducing computational complexity.
method Hierarchical graph structures and Schur complement method.
result Optimal portfolio weights can be computed efficiently by inverting small submatrices.
This article proposes and evaluates a technique to predict the level of interference in wireless networks. We design a recursive predictor that estimates future interference values by filtering measured interference at a given location. The predictor's parameterization is done offline by translating the autocorrelation…
New framework uses simplicial and categorical methods to detect market inconsistencies.
problem Detecting inconsistencies in financial markets using non-measure-preserving transitions.
method Simplicial and categorical formulation of AB type arbitrage in filtered market systems.
result Holonomy along loops reveals global inconsistencies invisible at local levels.
Existence of smooth valuations on subspaces is shown for certain conditions.
problem Existence of smooth valuations on subspaces with given restrictions.
method Analyzing compatibility and using recursive descriptions of the cosine transform.
result Compatibility is sufficient for extensibility in certain regimes.
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.
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…
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 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.
Unified approach to path planning using probabilistic inference on factor graphs.
problem Path planning problems using probabilistic inference.
method Unified framework using probabilistic factor graphs and message composition rules.
result Unified approach includes various algorithms like Sum-product, Max-product, Dynamic programming, and mixed criteria.
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.
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…
The bits-back argument suggests that latent variable models can be turned into lossless compression schemes. Translating the bits-back argument into efficient and practical lossless compression schemes for general latent variable models, however, is still an open problem. Bits-Back with Asymmetric Numeral Systems (BB-A…
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.
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.
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.
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 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…
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.
NeSS combines neural and symbolic approaches for better compositional generalization.
problem Lack of compositional generalization in deep learning models.
method NeSS uses a neural network to generate traces, executed by a symbolic stack machine with sequence manipulation.
result Achieves 100% generalization performance across multiple domains.
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.
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.
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue,…
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. The paper sets limits for sequential prediction and recursive algorithms using entropy analysis.
problem Fundamental limitations in sequential prediction and recursive algorithms.
method Entropic analysis to investigate underlying relationships of data and noises.
result Derives Lp bounds quantifiable in conditional entropy.