Paper introduces a new learner for generalizing complex tasks.
problem Generalizing to new, complex tasks without prior experience.
method Compositional problem graph and compositional recursive learner.
result Compositional approach can generalize to more complex problems than non-compositional learners.
RocketStack integrates predictions from multiple base learners using a recursive stacking architecture up to ten levels.
problem Feature redundancy, complexity, and computational burden in deep stacking.
method Level-aware recursive stacking with pruning and compression techniques.
result Increasing accuracy with depth and outperforming standalone ensembles at later levels.
We compare the sample complexity of private learning [Kasiviswanathan et al. 2008] and sanitization~[Blum et al. 2008] under pure ε-differential privacy [Dwork et al. TCC 2006] and approximate (ε,δ)-differential privacy [Dwork et al. Eurocrypt 2006]. We show that the sample complexity of these tasks under approxima…
The infinitesimal jackknife (IJ) has recently been applied to the random forest to estimate its prediction variance. These theorems were verified under a traditional random forest framework which uses classification and regression trees (CART) and bootstrap resampling. However, random forests using conditional inferenc…
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…
OEUVRE estimates online loss with constant time and memory, outperforming other methods.
problem Accurately estimating expected loss in online learning.
method Recursive evaluation of each sample on current and previous models, using algorithmic stability for updates.
result Consistency, convergence rates, and concentration bounds proved for OEUVRE.
We present novel, computationally efficient, and differentially private algorithms for two fundamental high-dimensional learning problems: learning a multivariate Gaussian and learning a product distribution over the Boolean hypercube in total variation distance. The sample complexity of our algorithms nearly matches t…
Fibonacci Ensembles use Fibonacci weights to improve ensemble learning, inspired by natural growth patterns.
problem Improving ensemble learning methods to enhance model performance and interpretability.
method Introduces Fibonacci weights and a recursive ensemble dynamic to reduce variance and enrich representational depth.
result Fibonacci weighting can match or improve upon uniform averaging in ensemble learning experiments.
Unified framework connects batch and sequential teaching models.
problem Understanding and comparing different teaching models.
method Developed a novel framework using preference functions.
result Equivalence between teaching models and specific preference functions.
PicCoLO improves reinforcement learning by correcting model errors.
problem Improving reinforcement learning algorithms with model corrections.
method Predictor-corrector framework that combines model predictions with environment feedback.
result PicCoLO algorithms converge faster and are less biased than previous methods.
Adds recursion to deep learning frameworks for better handling of recursive data structures.
problem Lack of support for recursion in existing deep learning frameworks.
method Complements existing frameworks with recursive execution of dataflow graphs and APIs for recursive definitions.
result Recursive implementation reduces training and inference time by more effectively using resources.
Novel framework for teaching complexity in machine teaching models.
problem Understanding and comparing teaching models in batch and sequential settings.
method Developed a novel framework using preference functions to capture teaching complexity.
result Identified preference functions leading to linear teaching complexity in sequential models.
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.
Paper proves 1-point recursions for various enumerative problems.
problem Enumerating gluings of polygons to orientable surfaces.
method Proves existence of 1-point recursions for specific classes of problems.
result Recover Harer-Zagier recursion and prove existence for new problems.
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.
Feature bagging improves stability through random feature subsampling.
problem Improving the stability of ensemble learning methods.
method Introducing feature instability (FI) and analyzing feature bagging in parametric and model-free settings.
result Feature bagging provides stronger stability than non-bagged methods, especially with aggressive subsampling.
New algorithm reduces prediction error in online learning without knowing base measure.
problem Smoothed online learning without knowledge of base measure.
method R-Cover algorithm based on recursive coverings.
result First algorithm to guarantee sublinear regret for agnostic smoothed online learning without prior knowledge of base measure.
Optimal algorithm converts weak to strong learner with less data.
problem Constructing a strong learner from a weak learner with minimal data.
method New algorithm that uses less training data than AdaBoost.
result Optimal sample complexity for converting weak to strong learner.
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.
Paper improves teaching by considering learner's preferences and constraints.
problem Teaching without considering learner's preferences and constraints.
method Design of learner-aware teaching algorithms that account for learner's preferences and constraints.
result Significant performance improvements over learner-agnostic teaching.
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.
Meta clustering categorizes learners for collaborative learning.
problem Filtering out unqualified collaborators in collaborative learning.
method Select-Exchange-Cluster (SEC) method to classify learners by their supervised functions.
result SEC can cluster learners into accurate collaboration sets and enhance single-learner performance.
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.
Character varieties of 2-bridge knots and links explained using Farey recursion.
problem Understanding character varieties of 2-bridge knots and links.
method Using Farey recursion to define polynomials for character varieties.
result Character varieties described in terms of polynomials defined by Farey recursion.
New meta-learners estimate time-varying treatment effects without model assumptions.
problem Estimating treatment effects over time in personalized medicine.
method Model-agnostic meta-learners for weighted pseudo-outcome regressions.
result Comprehensive theoretical analysis and practical insights for choosing meta-learners.
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.
Builds a novel educational recommender for lifelong learners.
problem Challenges in creating scalable and transparent models for lifelong learning.
method Integrative approach combining content novelty, background knowledge, and learner engagement.
result TrueLearn achieves promising performance while retaining a human interpretable learner model.
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.
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.
New survival learners estimate heterogeneous treatment effects from time-to-event data.
problem Estimating HTEs from time-to-event data with censoring outcomes.
method Orthogonal survival learners with theoretical guarantees and custom weighting functions.
result Orthogonal survival learners provide robust and model-agnostic HTE estimation.
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.
Proposes a method to integrate learner models robustly against misspecifications.
problem Misspecifications in learner models and parameter sharing patterns degrade prediction accuracy.
method Sequentially incorporates additional learners based on user-specified parameter sharing patterns.
result Data-adaptively selects the most suitable way of parameter sharing to enhance predictive performance.
VTIRT speeds up IRT inference for dynamic learner proficiency.
problem Expensive and slow inference algorithms for dynamic IRT models.
method Variational Temporal IRT (VTIRT) for fast, accurate inference.
result Orders of magnitude speedup in inference runtime with accurate results.
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.
Method selects the best deep learner for time-series prediction using Bayesian networks.
problem Selecting the most effective deep learning model for time-series prediction.
method Bayesian network selects deep learners based on input variables and cluster training data.
result Threshold value determines which deep learners predict time-series data robustly.
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.
This paper proves that lattice point enumeration in moduli spaces satisfies topological recursion.
problem Enumeration of lattice points in moduli spaces of curves.
method Proves topological recursion for lattice point enumeration in moduli spaces.
result The enumeration satisfies local topological recursion.
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…