In this paper, we consider the exact triangles consisting of stable vector bundles on one-dimensional complex tori, and give a geometric interpretation of them in terms of the corresponding Fukaya category via the homological mirror symmetry.
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48 results for “Exact consistency”
More and more AI services are provided through APIs on cloud where predictive models are hidden behind APIs. To build trust with users and reduce potential application risk, it is important to interpret how such predictive models hidden behind APIs make their decisions. The biggest challenge of interpreting such predic…
Let be a mirror pair of an -dimensional complex torus and its mirror partner . Then, a simple projectively flat bundle is constructed from each affine Lagrangian submanifold in with a unitary local system $\mathcal{L} \righta…
We introduce constructions of exact Lagrangian cobordisms with cylindrical Legendrian ends and study their invariants which arise from Symplectic Field Theory. A pair consisting of an exact symplectic manifold and an exact Lagrangian cobordism which agrees with cylinders over Legendrian links $…
Spectral clustering achieves strong consistency in the stochastic block model under certain conditions.
problem Achieving strong consistency in spectral clustering for the stochastic block model.
method Entrywise analysis of the Fielder eigenvector of graph Laplacians.
result Spectral clustering achieves exact recovery of hidden communities under matching information-theoretic limits.
In this paper, we extend the -CNMF to two dimensions and derive exact multiplicative updates for its factors. The new updates generalize and correct the nonnegative matrix factor deconvolution previously proposed by Schmidt and Mørup. We show by simulation that the updates lead to a monotonically decreasing -dive…
Framework generates precise synthetic populations for scalable modeling.
problem Generating accurate synthetic populations without personal data.
method Constraint-programming framework encoding aggregated statistics and structural relations.
result Exact control of demographic profiles without requiring microdata.
Proposes exact inference for continuous-time Gaussian process dynamics.
problem Inexact inference methods for continuous-time Gaussian process dynamics are impractical for irregularly-sampled data.
method Uses higher-order numerical integrators to discretize dynamics with arbitrary accuracy and proposes multistep and Taylor integrators for exact inference.
result Demonstrates accurate representation of continuous-time systems through exact GP inference.
New method solves group synchronization with cycle-edge message passing.
problem Solving group synchronization with adversarial or uniform corruption and small noise.
method Cycle-edge message passing procedure using cycle consistency information.
result Exact recovery and linear convergence guarantees under adversarial corruption.
Given datasets from multiple domains, a key challenge is to efficiently exploit these data sources for modeling a target domain. Variants of this problem have been studied in many contexts, such as cross-domain translation and domain adaptation. We propose AlignFlow, a generative modeling framework that models each dom…
The paper certifies AI reliability via sampling and calibration, providing exact guarantees.
problem Ensuring trust in black-box AI systems' outputs.
method Self-consistency sampling and conformal calibration.
result Reliability levels derived from these methods offer finite-sample guarantees.
In many machine learning applications, crowdsourcing has become the primary means for label collection. In this paper, we study the optimal error rate for aggregating labels provided by a set of non-expert workers. Under the classic Dawid-Skene model, we establish matching upper and lower bounds with an exact exponent …
This study approximates distances between Gaussian processes and covariance operators using RKHS.
problem Approximating distances between Gaussian processes and covariance operators from finite samples.
method Using reproducing kernel Hilbert space (RKHS) covariance and cross-covariance operators, the study shows how to consistently and efficiently estimate Sinkhorn divergence from finite samples.
result Convergence rates are dimension-independent and of the same order as Hilbert-Schmidt distance.
Surgery exact triangles in various 3-manifold Floer homology theories provide an important tool in studying and computing the relevant Floer homology groups. These exact triangles relate the invariants of 3-manifolds, obtained by three different Dehn surgeries on a fixed knot. In this paper, the behavior of -ins…
Many generative models can be expressed as a differentiable function of random inputs drawn from some simple probability density. This framework includes both deep generative architectures such as Variational Autoencoders and a large class of procedurally defined simulator models. We present a method for performing eff…
New tests for binary classification regression functions without distribution assumptions.
problem Testing regression functions in binary classification without distributional assumptions.
method Conditional kernel mean embeddings and resampling-based framework.
result Distribution-free hypothesis tests with exact type I error control.
This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure learning and treewidth computation. The approximate method consists in uniformly sa…
Explicit Iteration Complexity of Exact Data-Driven Inverse Optimization for Integer Linear Programsmath.OC
Exact method found for estimating ILP weights from data.
problem Estimating objective-function parameters for integer linear programs.
method Projected subgradient descent applied to suboptimality loss.
result Explicit iteration complexity as a function of problem size.
We show that minimum-norm interpolation in the Reproducing Kernel Hilbert Space corresponding to the Laplace kernel is not consistent if input dimension is constant. The lower bound holds for any choice of kernel bandwidth, even if selected based on data. The result supports the empirical observation that minimum-norm …
Paper calculates the exact error of LDA models.
problem Bayesian generalization error in Latent Dirichlet Allocation (LDA).
method Theoretical analysis of learning coefficient using algebraic geometry.
result Exact asymptotic form of LDA's generalization error.
The paper optimizes LLM accuracy by stopping early based on consistent answers.
problem Improving LLM accuracy in math and reasoning problems.
method Bayesian stopping policy to save on sampling costs, tracking only the L-1 most frequent answer counts.
result The L=3 stopping policy is sufficient for asymptotic optimality and significantly reduces inference costs.
New tractable models for complex Ising models over specific topologies.
problem Complex Ising models over specific topologies.
method Sequential application of efficient/inbrute-force inference and sampling to components.
result Improved inference and sampling quality for specific Ising models.
Volume of the steady-state space of financial flows in a monetary stock-flow-consistent modelphysics.soc-ph
We show that a steady-state stock-flow consistent macro-economic model can be represented as a Constraint Satisfaction Problem (CSP).The set of solutions is a polytope, which volume depends on the constraintsapplied and reveals the potential fragility of the economic circuit,with no need to study the dynamics. Several …
We consider a Hidden Markov Model (HMM) where the integrated continuous-time Markov chain can be observed at discrete time points perturbed by a Brownian motion. The aim is to derive a filter for the underlying continuous-time Markov chain. The recursion formula for the discrete-time filter is easy to derive, however i…
Variational inference (VI) provides fast approximations of a Bayesian posterior in part because it formulates posterior approximation as an optimization problem: to find the closest distribution to the exact posterior over some family of distributions. For practical reasons, the family of distributions in VI is usually…
Deep latent variable models (DLVMs) combine the approximation abilities of deep neural networks and the statistical foundations of generative models. Variational methods are commonly used for inference; however, the exact likelihood of these models has been largely overlooked. The purpose of this work is to study the g…
Noise titration benchmarks time series forecasting models rigorously.
problem Evaluation of time series forecasting models is often flawed due to lack of interventionist methods.
method Interventionist benchmarking using Gaussian noise titration of dynamical systems.
result Fern model outperforms state-of-the-art models in non-stationary conditions.
LLMs can memorize economic data and recall exact values before their training cutoff.
problem Evaluating the trustworthiness of LLMs' economic forecasts during their training period.
method Demonstrated through counterfactual forecasting and analysis of LLMs' recall ability.
result LLMs have memorized economic and financial data, leading to recall-level accuracy before their knowledge cutoff.
The paper explores conditions for predicting optimization performance.
problem Lack of formal theoretical guarantees linking prediction and optimization performance.
method Exploring conditions for asymptotic convergence and exact quantification of optimization performance.
result Explicit theoretical relationship between prediction and optimization performance.
We derive a convex optimization problem for the task of segmenting sequential data, which explicitly treats presence of outliers. We describe two algorithms for solving this problem, one exact and one a top-down novel approach, and we derive a consistency results for the case of two segments and no outliers. Robustness…
Clustering is one of the most important unsupervised problems in machine learning and statistics. Among many existing algorithms, kernel k-means has drawn much research attention due to its ability to find non-linear cluster boundaries and its inherent simplicity. There are two main approaches for kernel k-means: SVD o…
A new method clusters intersecting lines using hypergraphs.
problem Clustering intersecting lines in subspace clustering.
method Constructing a geometric hypergraph and using spectral algorithm.
result Achieves information-theoretic bounds for line clustering.
This paper presents a framework for exact discovery of the top-k sequential patterns under Leverage. It combines (1) a novel definition of the expected support for a sequential pattern - a concept on which most interestingness measures directly rely - with (2) SkOPUS: a new branch-and-bound algorithm for the exact disc…
Open problem: Establishing bounds for Cayley-table completion to discover discrete algorithmic axioms.
problem Discovering discrete algorithmic axioms missing in deep learning.
method Cayley-table completion as a testbed for algorithmic complexity minimization.
result Formal exact recovery bounds for Cayley-table completion.
EGN optimizes deep neural networks with exact Gauss-Newton for large-scale problems.
problem Training deep neural networks efficiently and accurately.
method Stochastic second-order optimization using low-rank linear algebra and matrix factorization.
result Converges to stationary points of the objective function under mild assumptions.
We develop and test a fast and accurate semi-analytical formula for single-name default swaptions in the context of a shifted square root jump diffusion (SSRJD) default intensity model. The model can be calibrated to the CDS term structure and a few default swaptions, to price and hedge other credit derivatives consist…
Exact LAD line fitting via PALB with linear scaling and speed.
problem Robust line fitting for data with outliers.
method Piecewise Affine Lower-Bounding (PALB) method using supporting lines and subdivision scheme.
result Empirical log-linear scaling and significantly faster than LP and IRLS methods.
Develops exact and invariant study-based decompositions for network meta-analysis.
problem Lack of exact contribution decompositions in network meta-analysis.
method Contrast-space projection formulation of NMA, study-based definition of direct and indirect evidence.
result Exact covariance-aware decompositions of NMA estimator into direct and indirect contributions.
Flexible model captures varying scales in data clusters.
problem Real-world data often exhibits varying scales or intensities, violating the homogeneity assumption of classical Gaussian mixture models.
method Individual-heterogeneous sub-Gaussian mixture model with an efficient spectral method for exact recovery.
result The method provably achieves exact recovery of true cluster labels under mild separation conditions.
Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise this notion of consistency in the case of Structural Equation Models (SEMs) by intr…
This study assesses risk concentration in MDB portfolios using Monte Carlo simulations.
problem Risk concentration in MDB portfolios of a few borrowers.
method Realistic MDB portfolio simulations and Monte Carlo analysis.
result Current risk adjustments may be overly conservative.
We address the problem of estimating the parameters of a time-homogeneous Markov chain given only noisy, aggregate data. This arises when a population of individuals behave independently according to a Markov chain, but individual sample paths cannot be observed due to limitations of the observation process or the need…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a generalized empirical likelihood framework---based on distributional uncertainty se…
Several recent works have empirically observed that Convolutional Neural Nets (CNNs) are (approximately) invertible. To understand this approximate invertibility phenomenon and how to leverage it more effectively, we focus on a theoretical explanation and develop a mathematical model of sparse signal recovery that is c…
Study how noisy labels affect semi-supervised learning.
problem Effect of noisy labels on semi-supervised learning performance.
method Proposed an algorithm derived from a continuous relaxation of the Maximum A Posteriori (MAP) estimator for a Degree Corrected Stochastic Block Model (DC-SBM).
result Our approach achieves promising performance even with very noisy labeled data.
In many structured prediction problems, complex relationships between variables are compactly defined using graphical structures. The most prevalent graphical prediction methods---probabilistic graphical models and large margin methods---have their own distinct strengths but also possess significant drawbacks. Conditio…
Paper proposes efficient algorithm for recovering sparsity pattern from deterministic missing data.
problem Recovering sparsity pattern from datasets with deterministic missing structure.
method Proposes an efficient algorithm for missing value imputation using topological property of censorship filter.
result Consistently recovers the sparsity pattern with high probability in polynomial time and logarithmic sample complexity.
Finite-Time Convergence of Continuous-Time Optimization Algorithms via Differential Inclusionsmath.OC
New continuous-time optimization algorithms converge in finite time to local minima.
problem Finding local minima in optimization problems.
method Discontinuous dynamical systems with finite-time convergence via Lyapunov-based differential inequality.
result Finite-time convergence to strict local minima with provable settling time.