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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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208417625833 · Jun 202019922001200920172026
48 results for non-linear training

Study on dynamics of non-linear autoencoders learning principal components.

problem Technical difficulty in studying non-linear autoencoders due to non-trivial correlations.
method Derive asymptotically exact equations for SGD training of shallow, non-linear autoencoders.
result Autoencoders learn principal components sequentially and tie weights are ineffective.

Non-linear source separation is a challenging open problem with many applications. We extend a recently proposed Adversarial Non-linear ICA (ANICA) model, and introduce Cramer-Wold ICA (CW-ICA). In contrast to ANICA we use a simple, closed--form optimization target instead of a discriminator--based independence measure…

2019-03-01abs ↗pdf ↗

Gradient descent with growing learning rate enables learning non-linear features in neural networks.

problem Learning non-linear features in two-layer neural networks.
method Using gradient descent with a learning rate that grows with the sample size.
result Multiple rank-one components emerge, each corresponding to a specific polynomial feature.

Deep networks prioritize easier examples over harder ones, leading to faster training.

problem Understanding how deep networks prioritize examples of varying difficulty.
method Investigated the effect of linear vs non-linear learning modes on example difficulty.
result Non-linear dynamics tend to sequentialize the learning of examples of increasing difficulty.

New classifier combines locally linear kernels for fast and accurate non-linear classification.

problem Developing a fast and accurate non-linear classifier.
method Combines locally linear classifiers using a 1\ell_1 Multiple Kernel Learning (MKL) problem with scalable MKL training for streaming kernels.
result The resulting classifier achieves high accuracy with fast inference time.

We provide a pointwise confidence bound for non-linear least-squares with fixed design.

problem Confidence estimation in non-linear 2\ell^2-regularized least squares.
method Pointwise confidence bound for local minimizers, using weighted norm involving inverse-Hessian.
result The proposed confidence bound scales with the test input's similarity to the training data.

Enhances Cox model for survival analysis with symbolic non-linear log-risk functions.

problem Limited interpretability and non-linearity in traditional Cox models.
method Introduces GCPH model using Kolmogorov-Arnold Networks for symbolic non-linear log-risk functions.
result GCPH achieves competitive performance and superior interpretability.

New models learn stable latent clusters without side info.

problem Stability of non-linear ICA representations without side information.
method Deep generative models with latent clusterings, compared to standard VAEs and auxiliary labeled models.
result Deep generative models with latent clusterings are as stable as models with side information.

Paper introduces non-linearity signature to measure deep neural network performance.

problem Difficulty in explaining performance differences among similar DNN architectures.
method Affine Optimal Transport mappings to measure non-linearity.
result Signature provides better understanding of DNN inner workings.

We present a general framework for solving a large class of learning problems with non-linear functions of classification rates. This includes problems where one wishes to optimize a non-decomposable performance metric such as the F-measure or G-mean, and constrained training problems where the classifier needs to sati…

2019-09-06abs ↗pdf ↗

We propose a new notion of `non-linearity' of a network layer with respect to an input batch that is based on its proximity to a linear system, which is reflected in the non-negative rank of the activation matrix. We measure this non-linearity by applying non-negative factorization to the activation matrix. Considering…

2018-10-08abs ↗pdf ↗

Inference-aware meta-alignment of LLMs reduces computational cost.

problem Aligning LLMs to diverse human preferences is challenging due to conflicting criteria.
method IAMA trains a base model to be aligned to multiple tasks via different inference-time alignment algorithms, using non-linear GRPO for optimization.
result IAMA enables effective alignment of LLMs to multiple criteria with limited computational budget.

Paper analyzes dataset distillation for efficient encoding of task-relevant information.

problem Efficiently encoding task-relevant information from gradient-based learning of non-linear tasks.
method Theoretical analysis of dataset distillation applied to two-layer neural networks with gradient-based training.
result Low-dimensional structure of the problem is efficiently encoded into distilled data, reproducing a model with high generalization ability.

Langevin algorithms improve training of very deep neural networks, especially for image classification.

problem Training very deep neural networks is challenging due to increased non-linearity and the risk of getting stuck in local minima.
method Comparison of Langevin and non-Langevin algorithms for training deep neural networks, introduction of Layer Langevin algorithm.
result Langevin algorithms, especially Layer Langevin, lead to significant improvements in training deep neural networks, particularly for image classification tasks.

We study the role of depth in training randomly initialized overparameterized neural networks. We give a general result showing that depth improves trainability of neural networks by improving the conditioning of certain kernel matrices of the input data. This result holds for arbitrary non-linear activation functions …

2020-02-04abs ↗pdf ↗

GP-KAN uses Gaussian Processes in KANs for robust, parameter-efficient non-linear modeling.

problem Non-linear modeling with limited parameters and uncertainty estimates.
method Integrates Gaussian Processes into Kolmogorov Arnold Networks (KANs) for robust non-linear modeling.
result GP-KAN achieves 98.5% accuracy on MNIST with 80k parameters compared to 1.5M for state-of-the-art models.

DiffKnock improves feature selection in neural networks with complex dependencies and non-linear associations.

problem Selecting important features in neural networks with complex dependencies and non-linear associations.
method DiffKnock uses diffusion models to generate knockoffs and neural network statistics to measure feature importance.
result DiffKnock outperforms existing methods in detecting non-linear associations and preserving feature dependencies.

Master-slave architecture tackles combinatorial multi-armed bandits with diversity constraints.

problem Solving top-KK combinatorial multi-armed bandits with non-linear feedback and diversity constraints.
method Master-slave architecture with six slave models, teacher learning, and policy co-training.
result Significantly outperforms existing algorithms in synthetic and real datasets.

In this paper we consider a problem of searching a space of predictive models for a given training data set. We propose an iterative procedure for deriving a sequence of improving models and a corresponding sequence of sets of non-linear features on the original input space. After a finite number of iterations N, the n…

2013-12-19abs ↗pdf ↗

Improved CAEs reduce training time and enhance generalization.

problem Stability issues in Concrete Autoencoders (CAEs) for feature selection.
method Indirectly Parameterized Concrete Autoencoders (IP-CAEs) learn parameters of Gumbel-Softmax distributions.
result IP-CAEs achieve significant improvements in generalization and training time.

DPLS improves asset pricing by capturing non-linear risk factor structures.

problem Estimating asset pricing models with non-linear risk factor structures.
method Deep Partial Least Squares (DPLS) for dynamic and flexible factor modeling.
result DPLS models outperform linear models in asset pricing, capturing non-linear risk factor interactions.

Learning weights in a spiking neural network with hidden neurons, using local, stable and online rules, to control non-linear body dynamics is an open problem. Here, we employ a supervised scheme, Feedback-based Online Local Learning Of Weights (FOLLOW), to train a network of heterogeneous spiking neurons with hidden l…

2017-12-29abs ↗pdf ↗

A new method learns state and proposal dynamics in state-space models using neural networks.

problem Inference in non-linear state-space models.
method StateMixNN method using neural networks for proposal and transition distributions.
result Significantly improved recovery of hidden state, especially in highly non-linear scenarios.

Paper investigates Lipschitz constants of self-attention modules in neural networks.

problem Lipschitz constants of self-attention modules in neural networks.
method Proved standard dot-product self-attention is not Lipschitz for unbounded input domain. Proposed L2 self-attention that is Lipschitz. Derived upper bound on L2 self-attention's Lipschitz constant.
result Proved standard self-attention is not Lipschitz for unbounded input domain and proposed an alternative L2 self-attention that is Lipschitz.

Layer-wise relevance propagation (LRP) is a recently proposed technique for explaining predictions of complex non-linear classifiers in terms of input variables. In this paper, we apply LRP for the first time to natural language processing (NLP). More precisely, we use it to explain the predictions of a convolutional n…

2016-06-23abs ↗pdf ↗

Analyzes generalization error in generalized linear models, explaining double descent phenomenon.

problem Understanding generalization of machine learning models in high dimensions.
method Develops a framework to characterize asymptotic generalization error for generalized linear models.
result Rigorously explains the double descent phenomenon in generalized linear models.

In adversarial attacks to machine-learning classifiers, small perturbations are added to input that is correctly classified. The perturbations yield adversarial examples, which are virtually indistinguishable from the unperturbed input, and yet are misclassified. In standard neural networks used for deep learning, atta…

2018-09-25abs ↗pdf ↗

BAM model learns graph structure from data with robustness across linear and non-linear dependencies.

problem Detecting dependencies in datasets for graph structure learning.
method Proposes BAM, a neural network model using structural equation models and Chebyshev polynomials for training, with bilinear attention mechanism.
result Demonstrates robust generalizability and superior performance in graph estimation.

It has been shown that injecting noise into the neural network weights during the training process leads to a better generalization of the resulting model. Noise injection in the distributed setup is a straightforward technique and it represents a promising approach to improve the locally trained models. We investigate…

2018-09-27abs ↗pdf ↗