Paper shows domain recursion is more powerful than previously thought, enabling faster inference.
problem Intractable probabilistic inference in relational models.
method Study of domain recursion rule and its impact on lifted inference.
result Domain recursion extends the range of models for which lifted inference is polynomial-time.
Paper generalizes GCNNs using edge-variant recursions for better graph signal classification.
problem Improving graph signal classification performance.
method Formulates a general framework for GCNNs using edge-variant graph filters.
result Shows superior performance in graph signal classification problems.
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.
Paper proposes a recursive GPSSM for efficient online learning.
problem Efficient online learning for dynamical models with limited prior information.
method Recursive Gaussian Process State-Space Model with adaptive capabilities for domains and hyperparameters.
result Superior accuracy, computational efficiency, and adaptability compared to state-of-the-art methods.
Novel method recursively partitions sample space for density estimation.
problem Estimating complex density functions efficiently and accurately.
method Recursive partitioning of the sample space, asymptotically exact.
result Asymptotically exact approximation of any density function.
New recursive algorithm estimates conditional kernel mean embeddings in Hilbert space.
problem Estimating conditional distributions in RKHS for supervised learning.
method Recursive algorithm in L2 space for conditional kernel mean map. result Strong L2 consistency of recursive estimator proved. Bayesian structure learning for high-dimensional data using recursive bootstrap.
problem Bayesian structure learning for domains with hundreds of variables.
method Non-parametric bootstrap, recursive structure learning, combining bootstrap with constraint-based learning.
result The proposed method learns better MAP models and more reliable causal relationships than other state-of-the-art methods.
Proposes a strategy to train models with minimal labeled data.
problem Scarce and expensive labeled data for medical tasks.
method Recursive training strategy to use image-level annotations for pixel-level segmentation.
result Improved segmentation of intracranial hemorrhage in CT scans.
MREC efficiently matches and aligns point clouds, useful for single cell molecular data.
problem Comparing and aligning large datasets across various domains.
method Recursive decomposition algorithm for matching data sets, optimizing over partitioning and matching algorithms.
result Demonstrates flexibility and power in applying MREC to single cell molecular data alignment problems.
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.
Tree-SMU enables strong compositional generalization in neural networks.
problem Zero-shot generalization to novel compositions of concepts.
method Tree Stack Memory Units (Tree-SMU) with Stack Memory Units (SMU).
result Tree-SMU achieves strong empirical results on mathematical reasoning benchmarks.
Stock selection improved with a novel neural model capturing continuous stock dynamics.
problem Lack of continuous stock dynamics prediction and implicit cross-domain dependencies.
method StockODE, a latent variable model with NRODEs and hierarchical hypergraph for continuous stock volatility and inter-domain dependencies.
result Significantly outperforms baselines, improving Sharpe Ratio by up to 18.57%.
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.
Recursive causal discovery reduces errors and complexity in causal graph learning.
problem Challenges in causal discovery from limited data and computational complexity.
method Removable variables for recursive causal discovery, reducing problem size and CI tests.
result Worst-case performances nearly match lower bound, with state-of-the-art efficiency.
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.
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.
Geometric recursion constructs measurable functions on moduli spaces.
problem Constructing measurable functions on moduli spaces of bordered Riemann surfaces.
method Inductive construction via excisions of pairs of pants, with convergence conditions.
result Geometric recursion produces functions that can be integrated with respect to the Weil-Petersson measure.
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.
Paper develops geometry for Kleinian groups using Farey polynomials.
problem Understanding the geometry of Kleinian groups generated by parabolic elements.
method Sakuma-Weeks triangulations and Farey recursive polynomials.
result Simple recursive algorithm to determine link complement geometry.
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.
Bijective proof of map enumeration recursion formulae.
problem Counting maps of arbitrary topology.
method Iterating Tutte's algorithm and pair-of-pants decomposition.
result Combinatorial meaning for all terms of topological recursion.
ORFit trains models on streaming data with one pass, minimizing memory and computational costs.
problem Training large models on a stream of data without retraining on previous data.
method Orthogonal Recursive Fitting (ORFit) using orthogonal gradient descent and recursive least-squares.
result ORFit updates parameters orthogonally to past gradients, leading to efficient memory and computational usage.
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.
Unified framework for adaptive learning systems using consolidation and expansion operations.
problem Managing the balance between consolidating known knowledge and expanding into new evidence in adaptive learning systems.
method Introduces Consolidation-Expansion Operator Mechanics (OpMech) with the order-gap metric to control the balance.
result The order-gap signal provides real-time control and termination guarantees for adaptive learning systems.
New methods learn from PU data with non-representative positives.
problem Learning from PU data with non-representative positive classes.
method Integrates negative-unlabeled and unlabeled-unlabeled learning, or uses a recursive risk estimator.
result Effective across various real-world datasets and forms of positive bias.
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.
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.
We introduce a wavelet-domain functional analysis of variance (fANOVA) method based on a Bayesian hierarchical model. The factor effects are modeled through a spike-and-slab mixture at each location-scale combination along with a normal-inverse-Gamma (NIG) conjugate setup for the coefficients and errors. A graphical mo…
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.
This study uses neural networks to approximate Bayesian filtering problems.
problem Estimating latent time-series signal statistics from observation sequences.
method Formulated a generic recurrent neural network framework to learn recursive mappings directly.
result Approximation error bounds for filtering in non-compact domains and strong time-uniform bounds.
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 graph learning framework outperforms existing methods.
problem Learning effective representations of large graphs with high degree variability.
method Deep hierarchical decompositions and neural network template unrolling over the hierarchy.
result Empirically outperforms state-of-the-art graph classification methods on large social network datasets.
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.
Study special Kähler geometry of Hitchin system using spectral curves and topological recursion.
problem Investigate special Kähler geometry of Hitchin system.
method Use spectral curves and topological recursion.
result Compute the symmetric quartic of second derivatives of the period matrix.
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. 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