The paper uses tensor decompositions to improve neural network models for tree data.
problem Encoding structural knowledge from tree-structured data efficiently.
method Introduces new aggregation functions using Canonical and Tensor-Train decompositions.
result Proposed models outperform traditional methods on tree classification tasks.
New theorem removes uniform finite upper bound for shrinkability of null decompositions.
problem Shrinkability of null decompositions with non-singleton elements.
method Defining squeezable and squashable subsets, proving their equivalence, and applying these definitions to null decompositions.
result Any null decomposition of a compact metric space whose non-singleton elements are recursively squeezable is shrinkable.
New 3D shapes can't be split into torus pieces.
problem 3D shapes without torus decompositions.
method Recursive definition from compact 3-manifolds.
result Examples of 3D shapes failing torus decomposition.
DiCoLa recursively decomposes causal structure learning for latent variables.
problem Learning causal structures in high-dimensional settings with latent variables.
method Recursive decomposition framework for divide-and-conquer causal discovery.
result Theoretical soundness and completeness of DiCoLa framework.
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.
A subset E of a metric space X is said to be starlike-equivalent if it has a neighbourhood which is mapped homeomorphically into Rn for some n, sending E to a starlike set. A subset E⊂X is said to be recursively starlike-equivalent if it can be expressed as a finite nested union of closed s…
Stochastic discount factor (SDF) processes in dynamic economies admit a permanent-transitory decomposition in which the permanent component characterizes pricing over long investment horizons. This paper introduces an empirical framework to analyze the permanent-transitory decomposition of SDF processes. Specifically, …
Continuous optimization is an important problem in many areas of AI, including vision, robotics, probabilistic inference, and machine learning. Unfortunately, most real-world optimization problems are nonconvex, causing standard convex techniques to find only local optima, even with extensions like random restarts and …
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.
We consider the problem of online subspace tracking of a partially observed high-dimensional data stream corrupted by noise, where we assume that the data lie in a low-dimensional linear subspace. This problem is cast as an online low-rank tensor completion problem. We propose a novel online tensor subspace tracking al…
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
We introduce an architecture based on deep hierarchical decompositions to learn effective representations of large graphs. Our framework extends classic R-decompositions used in kernel methods, enabling nested part-of-part relations. Unlike recursive neural networks, which unroll a template on input graphs directly, we…
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…
Solves optimal stopping problem with Poisson constraints using jumps.
problem Optimal stopping with Poisson constraints and jumps.
method Penalized backward stochastic differential equation (PBSDE) with jumps, decomposition method based on Jacod-Pham, comparison theorem of BSDEs with jumps.
result Solves American option pricing in nonlinear markets with Poisson constraints.
New method decomposes profits and losses continuously, avoiding discrete reporting issues.
problem Analyzing profits and losses at discrete dates ignores detailed paths.
method Constructs a large class of continuous-time decompositions using extended Itô's formula.
result Identifies a preferred decomposition from exactness, symmetry, and normalization axioms.
Researchers derived Kauffman bracket polynomial for Celtic link shadows using two methods.
problem Calculating the Kauffman bracket polynomial for Celtic link shadows.
method Two complementary approaches: recursive relation and 4-tangle algebra.
result Derived Kauffman bracket polynomial for CK42n shadows. 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.
GADGET framework decomposes global feature effects using recursive partitioning.
problem Misleading global feature effects when feature interactions are present.
method Generalized additive decomposition of global effects (GADGET) based on recursive partitioning.
result Minimizes interaction-related heterogeneity of local feature effects.
Study finds Deep Taylor Decomposition is unreliable for explaining neural networks.
problem Reliability of Deep Taylor Decomposition for explaining neural networks.
method Investigated the theoretical foundations of Deep Taylor Decomposition (DTD) and found it under-constrained.
result DTD is unreliable because its theoretical foundations are under-constrained and roots do not align with input.
Comparing and aligning large datasets is a pervasive problem occurring across many different knowledge domains. We introduce and study MREC, a recursive decomposition algorithm for computing matchings between data sets. The basic idea is to partition the data, match the partitions, and then recursively match the points…
We prove combinatorially 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). The latter is the generating function for volumes of discretized (open) moduli spaces Mg,sdisc given by $N_{…
QB-Vine extends Quasi-Bayesian methods to high dimensions using vine copulas.
problem Efficiently predicting high-dimensional distributions without sampling.
method Recursive Quasi-Bayesian construction for marginals and vine copulas for dependence modeling.
result QB-Vine is a fully non-parametric density estimator with analytical form and convergence rate independent of dimension.
New approach solves utility maximization problems using Delta family.
problem Utility maximization in stochastic control problems.
method Directly solving DP equation with Delta function representation.
result Explicit series representation of value function.
Evaluating AI investment strategies
problem Auditing a black-box algorithmic decision-maker
method Exact decomposition of cumulative regret
result Cumulative regret equals sum of per-period covariances
New Coxeter groups have unique boundary structures.
problem Understanding boundaries of Coxeter groups.
method Recursive construction and amalgamation of CAT(0) groups.
result Totally disconnected Morse boundaries for new Coxeter groups.
In this paper, we propose a new fast and robust recursive algorithm for near-separable nonnegative matrix factorization, a particular nonnegative blind source separation problem. This algorithm, which we refer to as the successive nonnegative projection algorithm (SNPA), is closely related to the popular successive pro…
We study dynamic hedging of counterparty risk for a portfolio of credit derivatives. Our empirically driven credit model consists of interacting default intensities which ramp up and then decay after the occurrence of credit events. Using the Galtchouk-Kunita-Watanabe decomposition of the counterparty risk price paymen…
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 introduces a tensor-based approach to improve neural models' aggregation of structural context.
problem Sub-optimal use of simple aggregation functions in neural models for structured data.
method Tensor-based formulation and Tucker tensor decomposition to control parameter space size.
result Effective regulation of trade-off between expressivity, computational complexity, and generalisation.
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.
Given a reproducing kernel Hilbert space H of real-valued functions and a suitable measure mu over the source space D (subset of R), we decompose H as the sum of a subspace of centered functions for mu and its orthogonal in H. This decomposition leads to a special case of ANOVA kernels, for which the functional ANOVA r…
STRIDE improves explainable AI by efficiently decomposing feature interactions without subset enumeration.
problem Lack of expressive power and high computational cost in existing XAI frameworks.
method STRIDE uses a functional decomposition approach in RKHS, avoiding subset enumeration and focusing on orthogonal components.
result STRIDE achieves a 3.0 times speedup over TreeSHAP and a high R^2 of 0.93 for feature reconstruction.
The paper analyzes MACD using operator theory.
problem Understanding the mathematical foundation of MACD.
method Developed a functional-analytic framework interpreting MACD as a phase-corrected, smoothed derivative operator.
result MACD is structurally equivalent to a band-pass filter and can be expressed as a finite difference of delayed and doubly averaged signals.
A new algorithm reduces graph complexity for better dense subgraph analysis.
problem Mining dense subgraphs in large graphs for better analysis.
method Multi-stage graph peeling algorithm (M-PA) with two-stage data screening.
result M-PA produces similar dense subgraphs to the previous PA but with reduced graph complexity.
New PAC-Bayes method updates priors without losing confidence information.
problem Lack of sequential prior updates in PAC-Bayes without losing confidence information.
method Recursive PAC-Bayes decomposition of expected loss.
result Sequential prior updates with no information loss.
We present a framework to derive upper bounds on the number of regions that feed-forward neural networks with ReLU activation functions are affine linear on. It is based on an inductive analysis that keeps track of the number of such regions per dimensionality of their images within the layers. More precisely, the info…
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…
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.
ABO extends RLS for online learning in non-stationary time-series, improving accuracy and speed.
problem Online learning in non-stationary time-series with overparameterized models.
method QR-based exponentially weighted RLS algorithm with orthogonal-triangular updates.
result ABO maintains bounded residuals and stable condition numbers while achieving speed improvements.
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.
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.