We introduce a new parameterization method for deep learning layers using spectral tensor train decomposition.
problem Efficiency and stability in deep learning models with weight matrix compression.
method Spectral Tensor Train Parameterization (STTP) of weight matrices.
result Improved compression and training stability in neural networks.
ARFF reduces spectral bias in SGD-trained neural networks.
problem Spectral bias in two-layer neural networks.
method Comparison of SGD and ARFF on spectral bias and robustness.
result ARFF yields a closer to zero spectral bias compared to SGD.
One of the challenges in the study of generative adversarial networks is the instability of its training. In this paper, we propose a novel weight normalization technique called spectral normalization to stabilize the training of the discriminator. Our new normalization technique is computationally light and easy to in…
Spectral decoupling improves neural network generalization in medical imaging.
problem Poor generalization of neural networks trained on medical imaging data.
method Spectral decoupling, a regularization technique that encourages learning more features.
result Spectral decoupling increases network robustness and performance on external datasets.
Essential principal components simplify spectral analysis with minimal training data.
problem Accurate spectral quantification from complex mixtures.
method Identifying essential principal components and using molar extinction coefficients.
result Near one-to-one projection from principal components to mixture constituents.
We present Spectral Inference Networks, a framework for learning eigenfunctions of linear operators by stochastic optimization. Spectral Inference Networks generalize Slow Feature Analysis to generic symmetric operators, and are closely related to Variational Monte Carlo methods from computational physics. As such, the…
Deep neural networks (DNNs) have set benchmarks on a wide array of supervised learning tasks. Trained DNNs, however, often lack robustness to minor adversarial perturbations to the input, which undermines their true practicality. Recent works have increased the robustness of DNNs by fitting networks using adversarially…
Paper explores SNN for learning spectral geometric info from data.
problem Challenges in applying traditional eigensolvers to big data.
method Introduces Spectral Neural Networks (SNN) as an alternative.
result Investigates tradeoffs and optimization landscape of SNN.
The study reveals the spectral structure of attention layers and its implications for generalization.
problem Understanding the spectral structure and generalization of trained attention layers.
method Empirical risk minimization in a single-head tied-attention layer, using random matrix theory, spin-glass theory, and approximate message passing.
result Exact high-dimensional characterization of training and test error, interpolation and recovery thresholds, and spectrum of the key and query matrices.
Spectral normalization stabilizes GANs by controlling gradient explosion and vanishing.
problem Stability and sample quality issues in GAN training.
method Spectral normalization controls gradient explosion and vanishing, improving GAN training stability and sample quality.
result Bidirectional Scaled Spectral Normalization (BSSN) outperforms standard spectral normalization in sample quality and training stability.
Introduces Spectral Graph Network combining spatial and spectral message passing.
problem Relational reasoning in graph structured data.
method Applies message passing to both spatial and spectral domains of a graph.
result Promotes efficient training with fewer iterations and robustness to edge dropout.
New method trains neural networks in spectral domain for improved performance.
problem Training deep neural networks in the space of nodes.
method Trains neural networks in the spectral domain, modifying eigenvalues and eigenvectors of transfer operators.
result Superior performance compared to standard methods, especially when adjusting eigenvalues.
Investigates spectral properties of neural networks, showing invariance under certain conditions.
problem Understanding the spectral evolution and invariance in linear-width neural networks.
method Empirical and theoretical analysis of spectra of weight matrices in high-dimensional settings.
result Spectra of weight matrices are invariant under certain training conditions, with implications for feature learning.
Spectral algorithms improve under covariate shift with novel weighted techniques.
problem Improving spectral algorithms' performance under covariate shift.
method Analysis of spectral algorithms in non-parametric regression over RKHS, proposing a weighted spectral algorithm with clipped weights.
result Normalized weighted spectral algorithm achieves optimal capacity-independent convergence rates, and clipped weights can approach optimal capacity-dependent rates.
Spectral gradient methods outperform Euclidean in certain deep learning scenarios.
problem When do spectral gradient updates outperform Euclidean in deep learning?
method Layerwise condition comparing squared nuclear-to-Frobenius ratio to stable rank of activations.
result Spectral updates can be more effective than Euclidean in deep networks and transformers.
Proposes neural dynamic mode decomposition for end-to-end modeling of nonlinear dynamics.
problem Understanding and modeling nonlinear dynamical systems.
method Trains neural networks to minimize forecast error based on spectral decomposition in the lifted space.
result Demonstrates effectiveness in eigenvalue estimation and forecast performance.
New bounds adaptively control spectral complexity of trained Transformers.
problem Understanding why Transformers generalize well in machine learning.
method Spectrum-adaptive post hoc generalization bounds for multi-layer Transformers.
result Bounds adaptively trade off spectral complexity against dimension and depth factors.
S-GAI initializes MLPs using spectral geometry from data, improving performance.
problem Lack of guidance on initial weights encoding data geometry.
method S-GAI uses SVD to estimate spectral class geometry, initializing MLPs from training data.
result S-GAI-initialized MLPs start from a more informative hidden state and achieve comparable accuracy.
The study analyzes spectral algorithms for kernel methods and derives generalization error.
problem Estimating generalization error of spectral algorithms for kernel methods.
method Considered spectral algorithms including KRR and GD, derived generalization error as a functional of learning profile.
result Showed the loss localizes on certain spectral scales and conjectured universality of the loss for noisy observations.
Proposes a deep network for multi-class classification using spectral training and Gaussian kernel.
problem Multi-class classification with deep networks.
method Spectral training with linear weights and Gaussian kernel activation, constrained on Stiefel Manifold.
result Theoretical guarantee of global optimum and insight into network generalization.
Recently, we proposed short-time Fourier transform (STFT)-based loss functions for training a neural speech waveform model. In this paper, we generalize the above framework and propose a training scheme for such models based on spectral amplitude and phase losses obtained by either STFT or continuous wavelet transform …
New method efficiently learns positive-definite curvature for neural nets.
problem Efficiently learn positive-definite curvature for neural net training.
method Spectral-factorized positive-definite curvature learning approach.
result Efficiently applies arbitrary matrix roots and generic curvature learning.
Spectral measurements reveal hidden representation geometry in language model training.
problem Hidden internal representation in language model training is hard to examine.
method Empirical protocol using activation covariance and per-sample gradient SVD spectra.
result Batch size affects representation geometry, and activation spectra predict token efficiency.
This paper proves a generalization bound for complex-valued neural networks scaling with spectral complexity.
problem Ensuring the performance of complex-valued neural networks on unseen data.
method Theoretical derivation using Maurey Sparsification Lemma and Dudley Entropy Integral, empirical validation on various datasets.
result The spectral complexity of weight matrices is a significant factor in the generalization ability of complex-valued neural networks.
Lipschitz continuity recently becomes popular in generative adversarial networks (GANs). It was observed that the Lipschitz regularized discriminator leads to improved training stability and sample quality. The mainstream implementations of Lipschitz continuity include gradient penalty and spectral normalization. In th…
In spectral clustering and spectral image segmentation, the data is partioned starting from a given matrix of pairwise similarities S. the matrix S is constructed by hand, or learned on a separate training set. In this paper we show how to achieve spectral clustering in unsupervised mode. Our algorithm starts with a se…
Current studies about motor imagery based rehabilitation training systems for stroke subjects lack an appropriate analytic method, which can achieve a considerable classification accuracy, at the same time detects gradual changes of imagery patterns during rehabilitation process and disinters potential mechanisms about…
A new method speeds up spectral normalization for neural nets.
problem Efficiently controlling the spectral norm of convolutional layers.
method Depthwise separable convolutions with spectral normalization.
result Significant reduction in computational and memory costs.
We investigate the generalizability of deep learning based on the sensitivity to input perturbation. We hypothesize that the high sensitivity to the perturbation of data degrades the performance on it. To reduce the sensitivity to perturbation, we propose a simple and effective regularization method, referred to as spe…
We propose a deep learning approach for discovering kernels tailored to identifying clusters over sample data. Our neural network produces sample embeddings that are motivated by--and are at least as expressive as--spectral clustering. Our training objective, based on the Hilbert Schmidt Information Criterion, can be o…
Self-training with noisy student-teacher boosts keyword spotting accuracy.
problem Robust keyword spotting in challenging conditions.
method Aggressive data augmentation and self-training with noisy student-teacher approach.
result Significant accuracy improvement in difficult conditions, up to 60%.
Meta-learning for Koopman spectral analysis with short time-series data.
problem Lack of long time-series for training embedding functions in Koopman spectral analysis.
method Meta-learning approach using bidirectional LSTM and neural network to estimate embedding functions from short time-series.
result The proposed method achieves better performance in eigenvalue estimation and future prediction compared to existing methods.
Improves learning of spectral mixture kernels with approximate Bayesian inference.
problem Difficult optimization of large number of SM kernel parameters.
method Approximate Bayesian inference using variational distribution of spectral points and random Fourier features.
result Accelerates convergence and leads to better optimal parameters.
Discrete Fourier transforms provide a significant speedup in the computation of convolutions in deep learning. In this work, we demonstrate that, beyond its advantages for efficient computation, the spectral domain also provides a powerful representation in which to model and train convolutional neural networks (CNNs).…
Transformers can learn spectral methods and perform unsupervised learning.
problem Learning spectral methods using unsupervised learning.
method Using multi-layered Transformers, pre-trained on a large set of instances, to learn and perform statistical estimation tasks.
result Proven that pre-trained Transformers can learn spectral methods and perform tasks like PCA and clustering.
We derive analytical expressions for the generalization performance of kernel regression as a function of the number of training samples using theoretical methods from Gaussian processes and statistical physics. Our expressions apply to wide neural networks due to an equivalence between training them and kernel regress…
Study local geometry of mixture models via spectral theory, revealing transitions in training dynamics.
problem Understanding the local geometry of high-dimensional mixture models.
method Spectral theory of Hessian and information matrices, focusing on i.i.d. Gaussian mixtures.
result Exact formulas for limits of spectral distribution and outlier eigenvalues, connecting training dynamics to effective dynamics.
New optimizer SF-NorMuon matches tuned AdamW across various horizons.
problem Fixed learning-rate schedules in neural network training lead to strong path dependence and costly re-tuning.
method Schedule-Free Spectral Optimization (SF-NorMuon)
result SF-NorMuon outperforms tuned AdamW on 125M and 772M parameter models across different horizons.
Spectral graph sparsification preserves geometry of GNN embeddings.
problem Maintaining geometric properties of graph neural network embeddings during sparsification.
method Proving spectral sparsification preserves squared pairwise distances, class means, and covariance structure in embedding space.
result Spectral sparsification preserves the geometry of learned embeddings in GNNs.
A 3-stage method enhances hyperspectral image classification accuracy.
problem Classifying detailed classes in hyperspectral images with limited labeled data.
method Uses Nested Sliding Window and PCA for spatial consistency, SVM for spectral estimation, and TV model for spatial smoothing.
result Our method outperforms state-of-the-art algorithms, especially in scenarios with small training sets.
Transformer models show distinct spectral fingerprints under voice changes.
problem Detecting architectural biases in transformer models.
method Spectral analysis of attention-induced token graphs.
result Clear architectural signatures in model fingerprints correlate with language-specific behavior.
SPECTRE defends against backdoor attacks by amplifying corrupted data's spectral signature.
problem Backdoor attacks that change model behavior with specific triggers.
method Robust covariance estimation to amplify spectral signature of poisoned data.
result Clean model is completely removed from backdoor, even in hard-to-detect cases.
Study tackles distribution shift in combinatorial settings using matrix completion techniques.
problem Tackling distribution shift in combinatorial settings with rigorous statistical guarantees.
method Develops novel algorithms and theoretical results for extrapolating to test distributions not covered in training.
result Achieves bilinear combinatorial extrapolation under gradual spectral decay in high-dimensional data.
Improved performance of factorized neural layers through spectral initialization and Frobenius decay.
problem Improving the performance of factorized neural layers in various deep learning contexts.
method Spectral initialization and Frobenius decay for initialization and regularization.
result Spectral initialization and Frobenius decay lead to improved performance across multiple deep learning settings.
In most convolution neural networks (CNNs), downsampling hidden layers is adopted for increasing computation efficiency and the receptive field size. Such operation is commonly so-called pooling. Maximation and averaging over sliding windows (max/average pooling), and plain downsampling in the form of strided convoluti…
An intriguing phenomenon observed during training neural networks is the spectral bias, which states that neural networks are biased towards learning less complex functions. The priority of learning functions with low complexity might be at the core of explaining generalization ability of neural network, and certain ef…
The study examines spectral dynamics in deep neural networks, predicting how outliers evolve during training.
problem Understanding spectral evolution in deep neural networks during training.
method Developed a two-level dynamical mean-field theory (DMFT) to track spectral dynamics.
result The theory predicts how outliers evolve with training time, width, output scale, and initialization variance.
This paper develops a coreset method for GNNs that speeds up training on large graphs.
problem Training Graph Neural Networks (GNNs) on large-scale graphs is computationally expensive.
method The paper proposes a spectral greedy coreset (SGGC) method that selects ego-graphs based on spectral embeddings.
result SGGC significantly speeds up GNN training on large graphs and outperforms other coreset methods.