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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,742 papers · 148 categories

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112224336448 · Jun 202019922001200920172026
48 results for Fine-grained Lower Bounds

New SQ lower bounds show learning mixtures of bounded covariance Gaussians is hard.

problem Learning mixtures of Gaussians with bounded covariance matrices is hard.
method Statistical Query (SQ) lower bounds.
result Any SQ algorithm requires complexity at least dΩ(1/ε)d^{Ω(1/ε)} for learning mixtures of bounded covariance Gaussians.

We analyze computational limits of modern Hopfield models based on pattern norms.

problem Understanding the efficiency of modern Hopfield models from a fine-grained complexity perspective.
method Fine-grained complexity analysis and upper bound criterion for pattern norms.
result Below a specific norm threshold, efficient variants of modern Hopfield models exist.

This paper explores the computational hardness of generating latent vectors for generative models.

problem Computational hardness of generating latent vectors for generative models.
method Established lower bounds for exact and approximate model inversion under strong exponential time hypothesis (SETH) and exponential time hypothesis (ETH).
result Lower bounds for computational complexity of exact and approximate model inversion.

Fine-grained gap-dependent regret bounds for reinforcement learning.

problem Achieving optimal regret bounds for reinforcement learning with suboptimality gaps.
method Developed novel analytical frameworks and refined algorithms for UCB-based and non-UCB-based reinforcement learning.
result Established the first fine-grained gap-dependent regret bounds for both UCB-based and non-UCB-based algorithms.

Improved Local SGD convergence for general convex objectives with bounded second-order heterogeneity.

problem Understanding when and why Local SGD outperforms alternatives in distributed optimization.
method Established improved convergence guarantees for Local SGD on general convex objectives under bounded second-order heterogeneity.
result Upper bounds for Local SGD are nearly tight, providing a sharper convergence theory.

New algorithm reduces regret in linear mixture SSPs without cost bounds.

problem Learning optimal paths in stochastic environments with cost constraints.
method Extended value iteration with variance-aware confidence set.
result Achieves nearly minimax optimal regret bound of O(dBK)O(dB_*\sqrt{K}).

Improved efficient robust regression with near-linear time and subquadratic samples.

problem Robust linear regression with unknown covariance matrix under Gaussian covariates.
method Near-linear time algorithm using subquadratic samples, complemented by SQ and polynomial lower bounds.
result Achieves prediction error O(εκ)O(\sqrt{εκ}) for εκ1εκ\lesssim 1, improving over prior works.

Generative framework learns effective, lower-dimensional models from high-dimensional data.

problem Predicting long-term behavior of complex, multiscale systems with limited data.
method Physics-aware probabilistic model order reduction with latent variables.
result Guaranteed long-term stability and predictive accuracy in multiscale physical systems.

Proposes a new method to generate unrestricted adversarial examples.

problem Generating unrestricted adversarial examples without norm constraints.
method Leveraging state-of-the-art generative models to manipulate image fine-grained aspects.
result Our adversarial images look indistinguishable from natural images and can bypass certified defenses.

New algorithms reduce regret in both stochastic and deterministic environments.

problem Designing algorithms that perform well in both types of MDPs.
method Proposed new environment norms and algorithms with variance-dependent regret bounds.
result First algorithm with simultaneously optimal bounds for both stochastic and deterministic MDPs.

Study on how many queries an adversary needs to make to match the best attack in white-box model.

problem Query complexity of adversarial attacks in machine learning models.
method Investigates the number of queries required for an adversary to match the best possible attack in the white-box model, using entropy of decision boundaries as a measure.
result Lower bound on the number of queries required for an adversary to match the best possible attack in the white-box model.

UCRL-WVTR tackles long-term reinforcement learning with general approximations, achieving horizon-free and instance-dependent regret bounds.

problem Long-term reinforcement learning with general function approximations.
method UCRL-WVTR proposes a novel algorithm, UCRL-WVTR, with weighted value-targeted regression and a high-order moment estimator.
result Achieves horizon-free and instance-dependent regret bounds matching minimax lower bounds up to logarithmic factors.

NeuroDiff improves neural network equivalence verification with fine-grained approximations.

problem Verifying the equivalence of compressed neural networks.
method Symbolic and fine-grained approximation technique for differential verification.
result NeuroDiff achieves up to 1000X speedup and 5X accuracy improvement.

The thesis clarifies when local updates outperform centralized methods in heterogeneous data environments.

problem Understanding when local updates are more effective than centralized or mini-batch methods in distributed optimization.
method Fine-grained consensus-error-based analysis framework, focusing on bounded second-order heterogeneity and third-order smoothness.
result Local updates outperform centralized or mini-batch methods under realistic models of data heterogeneity.

Pruning is an efficient model compression technique to remove redundancy in the connectivity of deep neural networks (DNNs). Computations using sparse matrices obtained by pruning parameters, however, exhibit vastly different parallelism depending on the index representation scheme. As a result, fine-grained pruning ha…

2019-05-14abs ↗pdf ↗

As entity type systems become richer and more fine-grained, we expect the number of types assigned to a given entity to increase. However, most fine-grained typing work has focused on datasets that exhibit a low degree of type multiplicity. In this paper, we consider the high-multiplicity regime inherent in data source…

2017-04-25abs ↗pdf ↗

Bayes-UCBVI tackles reinforcement learning with a new upper confidence bound method.

problem Optimizing exploration in reinforcement learning without bonuses.
method Bayes-UCBVI uses a quantile of a Q-value function posterior as an upper confidence bound.
result Proves a regret bound of order O~(H3SAT)\widetilde{O}(\sqrt{H^3SAT}) for tabular reinforcement learning.

New learner achieves optimal agnostic error in small error regime.

problem Optimizing agnostic learning in the small error regime.
method Careful aggregations of ERM classifiers.
result Achieves error $c \cdot τ+ O \left(\sqrt{\frac{τ(d + \log(1 / δ))}{m}} + \frac{d + \log(1 / δ)}{m} ight)$, matching lower bound when τd/mτ\approx d/m.

Paper presents UrbanFM and UrbanPy models for inferring fine-grained urban flows.

problem Reduce cost of urban flow monitoring while maintaining data accuracy and granularity.
method Develops UrbanFM and UrbanPy models to infer fine-grained urban flows from coarse-grained observations.
result UrbanPy model demonstrates favorable performance for larger-scale inference tasks.

Study optimal and instance-dependent guarantees for solving linear equations with Markovian data.

problem Approximately solving linear fixed point equations with Markovian data.
method Non-asymptotic bounds and instance-dependent characterizations for stochastic approximation.
result Instance-optimality of the averaged SA estimator and matching upper and lower bounds.

Paper relaxes stability and generalization assumptions for SGD.

problem Stability and generalization for SGD under restrictive assumptions.
method Introduces on-average model stability and develops novel bounds.
result First-ever-known fast bounds in low-noise setting using stability approach.

Considering event structure information has proven helpful in text-based stock movement prediction. However, existing works mainly adopt the coarse-grained events, which loses the specific semantic information of diverse event types. In this work, we propose to incorporate the fine-grained events in stock movement pred…

2019-10-11abs ↗pdf ↗

New analysis improves understanding of bilevel optimization stability and generalization.

problem Understanding how well bilevel optimization algorithms generalize.
method Algorithmic stability arguments and generalization bounds for three bilevel minimax solvers.
result Precise trade-off between algorithmic stability, generalization gaps, and practical settings.

Algorithm clusters mixtures with bounded covariances under specific separation conditions.

problem Clustering mixtures of bounded covariance distributions with fine-grained separation.
method Introduced clustering refinement and efficient algorithm for accurate clustering.
result First poly-time algorithm for nearly uniform mixtures, and efficient refinement for general mixtures.

In recent studies, several asymptotic upper bounds on generalization errors on deep neural networks (DNNs) are theoretically derived. These bounds are functions of several norms of weights of the DNNs, such as the Frobenius and spectral norms, and they are computed for weights grouped according to either input and outp…

2019-05-22abs ↗pdf ↗

Study on DiTs' rates of approximation and estimation under various data assumptions.

problem Investigating statistical rates of conditional diffusion transformers.
method Discretization and Taylor expansion of conditional diffusion score function under Hölder smooth data assumption.
result Establishes statistical limits for conditional and unconditional DiTs, offering practical guidance.

DistPre predicts traffic speeds efficiently for large networks.

problem Fine-grained, accurate speed prediction for large-scale transportation networks.
method Customizes LSTM models on a cluster, sharing trained models between detectors.
result Efficient and accurate fine-grained traffic-speed prediction.

Paper addresses eigenvector perturbation in small eigen-gap scenarios.

problem Fine-grained behavior of eigenvectors in the presence of small eigen-gaps.
method Develops de-biased estimators for linear functions of an unknown eigenvector.
result Achieves minimax lower bounds for a family of scenarios, even with small eigen-gaps.

Paper tackles bias-variance trade-off in missing data, proposing a dynamic framework.

problem Missing data in practical applications deteriorates model performance.
method Develops a fine-grained dynamic learning framework to jointly optimize bias and variance.
result Theoretical and empirical validation of joint bias-variance optimization.

Deep metric learning has been demonstrated to be highly effective in learning semantic representation and encoding information that can be used to measure data similarity, by relying on the embedding learned from metric learning. At the same time, variational autoencoder (VAE) has widely been used to approximate infere…

2018-02-13abs ↗pdf ↗

Paper relaxes assumptions for non-parametric estimation in pairwise learning.

problem Generalization performance of non-parametric estimation for pairwise learning.
method Significantly relaxes restrictive assumptions, constructs structured deep ReLU neural network, and designs targeted hypothesis space.
result Establishes a sharp oracle inequality for empirical minimizer with general hypothesis space for Lipschitz continuous pairwise losses.

We present a method that trains large capacity neural networks with significantly improved accuracy and lower dynamic computational cost. We achieve this by gating the deep-learning architecture on a fine-grained-level. Individual convolutional maps are turned on/off conditionally on features in the network. To achieve…

2019-07-15abs ↗pdf ↗

Obtaining accurate and well calibrated probability estimates from classifiers is useful in many applications, for example, when minimising the expected cost of classifications. Existing methods of calibrating probability estimates are applied globally, ignoring the potential for improvements by applying a more fine-gra…

2018-07-31abs ↗pdf ↗

This work generalizes transformer attention to capture higher-order correlations efficiently.

problem Detecting triple-wise connections that were impossible for transformers.
method Developed a generalized attention scheme using Kronecker computation, showing near-linear time algorithms for bounded entries.
result A near-linear time algorithm for generalized attention computation in the bounded-entry setting.

Proposes a method for weakly-supervised object localization to improve few-shot learning.

problem Challenges of few-shot learning, especially with fine-grained categories.
method Introduces a Self-Attention Based Complementary Module (SAC Module) for weakly-supervised object localization.
result Significantly outperforms state-of-the-art methods on benchmark datasets, especially for fine-grained few-shot tasks.