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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.

168,657 papers · 148 categories

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154309463617 · Jun 202019922001200920172026
48 results for task eigenstructure

Study the cost of overfitting in noisy KRR models.

problem Cost of overfitting in noisy kernel ridge regression.
method An agnostic view of overfitting cost as a function of sample size for any target function, using Gaussian universality ansatz and task eigenstructure.
result Characterization of benign, tempered, and catastrophic overfitting.

More features and data lead to better model performance in random feature regression.

problem Improving model performance in random feature regression.
method Theoretical analysis of random feature regression, demonstrating the benefits of overparameterization, overfitting, and more data.
result Infinite width RF architectures are preferable to those of any finite width, and training to near-zero training loss is obligatory for near-optimal performance.

Optimal classifiers derived from GMMs are approximated by deep neural networks.

problem Binary classification of high-dimensional overlapping Gaussian mixtures.
method Closed-form expressions for Bayes optimal decision boundaries derived from GMMs' eigenstructure. Empirical validation through synthetic and real-world data.
result Deep neural networks approximate optimal classifiers for GMMs, with decision thresholds related to covariance eigenvectors.

Revisits Gaussian process model with spherical harmonics for scalable deep learning.

problem Scaling Gaussian process models to large input dimensions with high frequency learning.
method Introduces new kernels related to deep models, variational learning of spherical harmonic phases, and sparseness in eigenbasis.
result Enables scaling to larger input dimensions and learning of high frequency variations.

Ensembles of random-feature models can't outperform a single large model.

problem Finding the optimal balance between model size and ensemble size.
method Deterministic equivalent risk estimates and scaling laws analysis.
result Ensembles of random-feature models achieve near-optimal performance only under specific conditions.

Study shows that ridgeless Gaussian kernel regression overfits even with varying bandwidth or dimensionality.

problem Analyzing overfitting in Gaussian kernel ridgeless regression with varying bandwidth or dimensionality.
method Examined the behavior of minimum norm interpolating solutions for fixed and increasing dimensions under varying bandwidth and sample size.
result Ridgeless solutions are never consistent and can be worse than null predictor with large enough noise, even with varying bandwidth or dimensionality.

New method preserves spectral clustering performance under aggressive sparsification and quantization.

problem Maintaining spectral clustering performance with sparse and quantized data.
method Random matrix theory applied to eigenspectrum changes under sparsification and quantization.
result Spectral clustering performance is preserved even with aggressive sparsification and quantization.

The paper analyzes Nordic stock markets' correlation structures and regime shifts.

problem Understanding and exploiting regime shifts in Nordic stock markets.
method Examined two decades of daily data for OMXS30, OMXC20, and OMXH25 universes; proposed an adaptive portfolio allocation framework.
result Documented pronounced regime dependence in rolling correlation matrices; proposed an adaptive portfolio allocation framework.

Study eigenvalues and eigenvectors in neural networks, focusing on signal propagation.

problem Characterize signal eigenvalues and eigenvectors in neural networks.
method Characterizes signal eigenvalues and eigenvectors for a nonlinear spiked covariance model.
result Provides precise quantitative characterizations of signal eigenvalues and eigenvectors in neural networks.

Neural networks can learn kernel machines with a data-dependent kernel.

problem Can neural networks in the rich feature learning regime learn a kernel machine?
method Demonstrated silent alignment effect in neural networks, showing they can learn a kernel machine with a data-dependent kernel.
result Neural networks in the rich feature learning regime can learn a kernel machine with a data-dependent kernel due to silent alignment.

The smallest eigenvalues and the associated eigenvectors (i.e., eigenpairs) of a graph Laplacian matrix have been widely used for spectral clustering and community detection. However, in real-life applications the number of clusters or communities (say, KK) is generally unknown a-priori. Consequently, the majority of …

2015-12-23abs ↗pdf ↗

Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be investigated via the spectrum of the Hessian of the empirical loss function. Networ…

2018-02-09abs ↗pdf ↗

We consider the problem of approximate joint triangularization of a set of noisy jointly diagonalizable real matrices. Approximate joint triangularizers are commonly used in the estimation of the joint eigenstructure of a set of matrices, with applications in signal processing, linear algebra, and tensor decomposition.…

2016-07-02abs ↗pdf ↗

A new model decomposes equity returns and volatilities into memory components.

problem Understanding long-term equity dynamics and volatility patterns.
method Proposes a multivariate generalization of the variance ratio to decompose long-horizon equity dynamics.
result Identifies a five-factor model capturing persistent, antipersistent, and multi-scale memory in returns and volatility.

Neural networks can interpolate random data but still generalize well, studied in the NT regime.

problem Understanding how neural networks interpolate random labels and generalize well in the overparametrized regime.
method Characterization of the eigenstructure of the empirical NT kernel and generalization error of NT ridge regression.
result The generalization error is well approximated by polynomial ridge regression with an increased regularization parameter.

APT-Gen generates tasks to help RL learn in hard problems.

problem Learning in hard exploration problems.
method APT-Gen uses a task generator to create tasks from a parameterized space, balancing performance and similarity to target tasks.
result APT-Gen outperforms baselines in grid world and robotic manipulation tasks.

OCEAN infers online task identities from context variables.

problem Online task inference for compositional tasks with context adaptation.
method Variational inference framework OCEAN models global and local context variables in a joint latent space.
result OCEAN provides more effective task inference with sequential context adaptation.

Sharing information between multiple tasks enables algorithms to achieve good generalization performance even from small amounts of training data. However, in a realistic scenario of multi-task learning not all tasks are equally related to each other, hence it could be advantageous to transfer information only between …

2014-12-03abs ↗pdf ↗

HydaLearn dynamically adjusts task weights for better MTL performance.

problem Constant loss weights in MTL lead to poor results due to drifting relevance and varying mini-batch composition.
method HydaLearn uses mini-batch gradients to dynamically adjust task weights.
result HydaLearn improves performance on synthetic and real-world data.

We investigate task clustering for deep-learning based multi-task and few-shot learning in a many-task setting. We propose a new method to measure task similarities with cross-task transfer performance matrix for the deep learning scenario. Although this matrix provides us critical information regarding similarity betw…

2017-08-26abs ↗pdf ↗

ST-MAML tackles task ambiguity in meta-learning by encoding tasks with stochastic representations.

problem Handling tasks from multiple distributions is challenging for meta-learning due to task ambiguity.
method ST-MAML uses a stochastic neural network module to encode tasks and propagate task representations to revise input variable encoding.
result ST-MAML matches or outperforms state-of-the-art methods on various tasks.

New algorithm combines curriculum learning with HER for complex object manipulation tasks.

problem Learning complex sequential object manipulation tasks from scratch is challenging.
method Curriculum learning with Hindsight Experience Replay (HER) for recurrent object manipulation tasks.
result Significant improvement in learning sequential object manipulation tasks compared to vanilla-HER.

Transformers infer tasks from context via two modes, geometrically shaped task vectors explain their behavior.

problem Understanding how transformers infer tasks from context and the geometric properties of task vectors.
method Synthetic setting to train small transformers, mathematical characterization of task-vector geometry and inference modes.
result Task-vector geometry shapes in-distribution and out-of-distribution behavior of transformers.

MTL-NAS combines NAS with GP-MTL for task-agnostic multi-task learning.

problem Designing architectures for diverse tasks with varying priors.
method Disentangled GP-MTL networks, hierarchical feature sharing, and gradient-based search.
result General-purpose model trained once can adapt to multiple tasks.

Meta-learning framework uses task similarity through nonparametric kernel regression.

problem Limited tasks and outliers/dissimilar tasks hinder meta-learning performance.
method Nonparametric kernel regression to quantify and use task similarity.
result Meta-learning algorithm outperforms existing methods in task-limited settings.

RTE enables extrapolation to new tasks by learning task transformations.

problem Learning systems struggle to generalize to unseen tasks.
method Relational Task Extrapolator (RTE) learns task transformations to enable extrapolation.
result RTE substantially outperforms existing approaches on extrapolation tasks.

Multi-task learning (MTL) has recently contributed to learning better representations in service of various NLP tasks. MTL aims at improving the performance of a primary task, by jointly training on a secondary task. This paper introduces automated tasks, which exploit the sequential nature of the input data, as second…

2017-09-16abs ↗pdf ↗

Robot learns multiple tasks hierarchically by transferring knowledge.

problem Learning multiple complex tasks in open-ended environments.
method Task-oriented procedures, goal-babbling, imitation learning, active learning, intrinsic motivation.
result Robots can learn complex tasks more efficiently by transferring knowledge from simpler ones.

Multi-task learning (MTL) has achieved success over a wide range of problems, where the goal is to improve the performance of a primary task using a set of relevant auxiliary tasks. However, when the usefulness of the auxiliary tasks w.r.t. the primary task is not known a priori, the success of MTL models depends on th…

2019-04-08abs ↗pdf ↗

In the paradigm of multi-task learning, mul- tiple related prediction tasks are learned jointly, sharing information across the tasks. We propose a framework for multi-task learn- ing that enables one to selectively share the information across the tasks. We assume that each task parameter vector is a linear combi- nat…

2012-06-27abs ↗pdf ↗

Transformers can generalize to a large task family with only a few demonstrations.

problem Can learning from a small set of tasks generalize to a large task family?
method Investigating autoregressive compositional structure where each task is a composition of TT operations, each from a finite family of DD subtasks.
result Transformers can generalize to DTD^T tasks with only O~(D)\widetilde{O}(D) demonstrations.

Despite significant progress, deep reinforcement learning (RL) suffers from data-inefficiency and limited generalization. Recent efforts apply meta-learning to learn a meta-learner from a set of RL tasks such that a novel but related task could be solved quickly. Though specific in some ways, different tasks in meta-RL…

2019-05-16abs ↗pdf ↗