Efficient privacy-preserving machine learning framework using random transformations.
problem Slow training and inference speed in privacy-preserving machine learning systems.
method Random transformations like linear and permutation, combined with arithmetic sharing.
result High efficiency and low computation cost in private machine learning.
Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules which cannot account for the approximation errors. Our aim is to design a method for moment transformation for …
Transformers learn random walks optimally with gradient descent.
problem Transformer interpretability and learning random walks.
method Theoretical analysis and gradient descent training.
result Transformers can predict random walks optimally with gradient descent.
Study investigates ruin probability with random premiums and risky investments.
problem Ruin probability with random premiums and risky investments.
method Laplace transform applied to a model with geometric Brownian motion.
result Asymptotic behavior of ruin probability for large initial capital values.
Random Transformers behave like polynomial models in ICL with asymptotic growth.
problem Understanding in-context learning capabilities of pretrained Transformers.
method Asymptotic analysis of a random Transformer with a fixed first layer and a trained second layer, considering growth in context length, input dimension, hidden dimension, and training parameters.
result The random Transformer's ICL error is equivalent to a finite-degree Hermite polynomial model.
New method certifies images against transformations like rotations and translations.
problem Certifying robustness of images against transformations like rotations and translations.
method Randomized smoothing with three different kinds of defenses.
result Individual certificates can be obtained via statistical error bounds or efficient online inverse computation.
Transforms offline algorithms to online with low regret in random order model.
problem Developing online algorithms with low approximate regret from offline approximation algorithms.
method General reduction theorem and coreset construction method.
result Achieves polylogarithmic ε-approximate regret for various online problems.
Random forest models systematically bias predictions; a numerical transform corrects this.
problem Systematic bias in random forest regression predictions.
method Defined a numerical transformation using training data to correct bias.
result Improved predictions across real-world and synthetic datasets.
The study examines lower and upper bounds of Wasserstein distances for affine transformations of random vectors.
problem Understanding Wasserstein distances for affine transformations of random vectors.
method Lower and upper bounds for affine transformations of random vectors in Rn are derived using Bures metric and compositions of affine maps. result Concrete lower bounds and upper bounds for affine transformations are derived and applied to various distributions.
Transformers trained on random classification tasks generalize well and can overfit without error.
problem Understanding how transformers generalize and overfit in-context.
method Analysis of implicit regularization during gradient descent training.
result Transformers can overfit without error and still generalize well.
In earlier work we introduced geometrically natural probability measures on the group of all Möbius transformations in order to study "random" groups of Möbius transformations, random surfaces, and in particular random two-generator groups, that is groups where the generators are selected randomly, with a view to estim…
Randomly initialized transformers show extreme token preferences.
problem Structural biases in randomly initialized transformers.
method Dissection of transformer architecture at initialization.
result Initialization-induced biases persist throughout training.
Transformers can predict pseudo-random sequences from LCGs with unseen parameters and moduli.
problem Learning pseudo-random number sequences from linear congruential generators with unknown parameters and moduli.
method Investigated the ability of Transformers to learn LCG sequences with varying complexity and moduli. Analyzed embedding layers and attention patterns.
result Transformers can predict pseudo-random sequences from LCGs with unseen parameters and moduli, up to mexttest=216, using a two-step strategy. Improved unsupervised anomaly detection using Random Forest.
problem Enhancing unsupervised anomaly detection accuracy.
method Training Random Forest to distinguish real and synthetic data, then applying transformed distances.
result Significant improvement in anomaly detection accuracy compared to other methods.
New RFs reduce kernel approximation variance and improve Transformer performance.
problem Efficient approximation of Gaussian and softmax kernels for kernel methods and Transformers.
method Parameterized, positive, non-trigonometric RFs optimized for variance reduction.
result Significant variance reduction in practice, outperforming previous methods.
Randomized positional encodings boost transformer performance on longer sequences.
problem Transformers struggle with generalizing to sequences of arbitrary length.
method Introduced randomized positional encodings that simulate longer sequences and randomly select positions.
result Randomized positional encodings increase test accuracy by 12.0% on average for sequences of unseen length.
RR-GCN uses random transformations instead of learned weights for node embeddings.
problem Learning node embeddings in KGs.
method Random Relational Graph Convolutional Network (RR-GCN) with untrained parameters.
result RR-GCN can compete with fully trained R-GCNs in node classification and link prediction.
One of the fundamental problems in supervised classification and in machine learning in general, is the modelling of non-parametric invariances that exist in data. Most prior art has focused on enforcing priors in the form of invariances to parametric nuisance transformations that are expected to be present in data. Le…
Formula found for probability of random triangles on flat tori being homotopically trivial.
problem Calculating the probability of random triangles on flat tori being homotopically trivial.
method Reduced problem to new invariant of measurable sets in the plane unchanged by area-preserving affine transformations.
result Probability is minimized on rectangular tori and maximized on regular hexagonal tori.
Study excess risk in statistical inference with transformations.
problem Excess risk in estimating random variables from feature vectors and transformations.
method Characterize lossless transformations, develop test statistics, and information-theoretic bounds.
result Strongly consistent partitioning test statistic for lossless transformations.
Random features are improved by variance-reducing couplings, enhancing machine learning models.
problem Improving the efficiency and accuracy of random features in machine learning.
method Using optimal transport theory to find couplings that reduce variance in random features.
result Theoretical and practical gains in efficiency and accuracy for various machine learning models.
Subsampled Randomized Hadamard Transform (SRHT), a popular random projection method that can efficiently project a d-dimensional data into r-dimensional space (r≪d) in O(dlog(d)) time, has been widely used to address the challenge of high-dimensionality in machine learning. SRHT works by rotating the input …
The paper derives formulas for option pricing and random walk expectations.
problem Calculating the price of barrier and lookback options.
method Inverse Z-transform, Fourier/Laplace inversion, Wiener-Hopf factorization, and numerical methods.
result Efficient numerical methods for option pricing are developed.
GOAD improves anomaly detection across various data types.
problem Finding anomalies in diverse data types.
method GOAD combines classification and transformation-based methods.
result GOAD achieves state-of-the-art accuracy on multiple datasets.
Transformers learn to adapt to different task difficulties and resist distribution shifts.
problem Understanding and optimizing a Transformer's performance across various task difficulties and distribution shifts.
method Analyzing a pretrained Transformer on a mixture distribution of tasks, proving optimal convergence rates.
result Transformers achieve optimal convergence rates on tasks of specific difficulty levels, robust to distribution shifts.
We present Neural Random Forest Imitation - a novel approach for transforming random forests into neural networks. Existing methods propose a direct mapping and produce very inefficient architectures. In this work, we introduce an imitation learning approach by generating training data from a random forest and learning…
Training only BatchNorm parameters achieves surprisingly high performance in deep networks.
problem Understanding the role and expressive power of affine parameters in BatchNorm.
method Investigating performance when training only BatchNorm parameters and freezing all other weights.
result BatchNorm achieves high performance by learning to disable around a third of random features.
The paper models musical motif transformations in Beethoven's works.
problem Understanding how motifs transform in symbolic music.
method Developed a probabilistic framework using Conditional Random Fields.
result Identified patterns of motif transformations and their co-occurrences.
Improves detection of low-rank signals from noisy data matrices.
problem Statistical detection of low-rank signals in noisy data matrices.
method Entrywise pre-transforming data matrix for non-Gaussian noise, sharp phase transition thresholds, central limit theorem for linear spectral statistics, hypothesis test.
result Improves detection of low-rank signals from noisy data matrices, generalizing known results.
A new method for graph-structured data improves transformer performance by incorporating topology.
problem Improving transformer performance on graph-structured data.
method Parameterizing topological masks as a learnable function of a weighted adjacency matrix, approximated with graph random features.
result Efficient masking algorithms provide strong performance gains for tasks on image and point cloud data.
Study provides guarantees on neural network generalization for solving Schrödinger equations.
problem Probability of centralizer being trivial for random matrices.
method Lower bounds on probability using random matrix theory and machine learning theory.
result Guarantees on transformer-based neural networks' in-context learning ability.
MLDL preserves manifold geometry in vector transformations.
problem Geometric deterioration in neural network transformations.
method Locally isometric smoothness (LIS) and Markov random field (MRF) encoding.
result Enhanced vector transformations into well-behaved metric homeomorphisms.
Study reveals neural scaling laws in random graphs and natural language models.
problem Understanding the origin of neural scaling laws in complex systems.
method Examined scaling laws in transformers trained on random walks and simplified natural language models.
result Neural scaling laws emerge in the absence of power law structure in data correlations.
Randomization tests rely on simple data transformations and possess an appealing robustness property. In addition to being finite-sample valid if the data distribution is invariant under the transformation, these tests can be asymptotically valid under a suitable studentization of the test statistic, even if the invari…
HRFs adaptively linearize kernels for accurate approximations.
problem Linearizing softmax and Gaussian kernels for machine learning applications.
method Generalizes Bochner's Theorem for kernels, uses random features for compositional kernels.
result Strong theoretical guarantees and unbiased approximation with smaller relative errors.
DFRot improves LLMs by reducing outlier and massive activation effects.
problem Reducing outlier and massive activation effects in rotated LLMs.
method Weighted loss function and orthogonal Procrustes transforms for rotation matrix refinement.
result DFRot achieves dual free (Outlier-Free and Massive Activation-Free) with significant improvements in perplexity.
Mixup improves model accuracy and calibration through data transformation and random perturbation.
problem Improving model accuracy and calibration in machine learning.
method Interprets Mixup as empirical risk minimization with data transformation and random perturbation.
result Mixup induces multiple known regularization schemes that prevent overfitting and overconfident predictions.
We introduce the Randomized Dependence Coefficient (RDC), a measure of non-linear dependence between random variables of arbitrary dimension based on the Hirschfeld-Gebelein-Rényi Maximum Correlation Coefficient. RDC is defined in terms of correlation of random non-linear copula projections; it is invariant with respec…
New insights show stochastic initialization prevents token clustering in deep Transformers.
problem Understanding token dynamics in deep stochastic Transformers.
method Analysis of deep Transformers with random initialization noise, proving convergence to an interacting-particle system on the sphere.
result Initialization noise prevents token clustering, leading to antipodal formations.
Traditional GANs use a deterministic generator function (typically a neural network) to transform a random noise input z to a sample x that the discriminator seeks to distinguish. We propose a new GAN called Bayesian Conditional Generative Adversarial Networks (BC-GANs) that use a random generator function…
Overparameterized models improve performance in sequential learning tasks.
problem Catastrophic forgetting in overparameterized neural networks.
method Two-task linear regression problem with random orthogonal transformations.
result Overparameterization mitigates catastrophic forgetting in sequential learning tasks.
Unified framework TSS certifies robustness against semantic transformations.
problem Certifying robustness of ML models against semantic transformations.
method Unified framework TSS categorizes transformations into resolvable and differentially resolvable, proposing randomized smoothing and stratified sampling strategies.
result Significantly outperforms state of the art on over ten types of semantic transformations.
Transformers with linear space and time complexity for accurate attention estimation.
problem Efficiently estimating attention in large-scale tasks without relying on priors.
method Performers use Fast Attention Via positive Orthogonal Random features (FAVOR+) for linear approximation of softmax attention.
result Performers achieve competitive results on various tasks, demonstrating the effectiveness of their attention-learning approach.
The aim of this article is to design a moment transformation for Student- t distributed random variables, which is able to account for the error in the numerically computed mean. We employ Student-t process quadrature, an instance of Bayesian quadrature, which allows us to treat the integral itself as a random variable…
Transformers learn to recall with non-orthogonal embeddings in realistic settings.
problem Understanding how transformers store and retrieve knowledge in practical scenarios.
method Analyzing a single-layer transformer with random embeddings trained on a token-retrieval task.
result Explicit formulas for the model's storage capacity reveal a multiplicative dependence on sample size, embedding dimension, and sequence length.
Tensorized Rademacher projections outperform Gaussian projections in reducing tensor dimensions.
problem Reducing the dimension of high-dimensional tensors for machine learning.
method Tensorized Rademacher random projections using Tensor Train decomposition.
result Tensorized Rademacher projections can replace Gaussian projections in tensor compression.
New methods reduce computational cost for Gaussian Markov Random Fields with sparse constraints.
problem Inference and simulation of GMRFs are computationally prohibitive with many constraints.
method Proposes a basis transformation into blocks of constrained and non-constrained subspaces.
result Significantly outperforms existing alternatives in computational cost.
Uniform approximations for RHTs improve kernel approximation and distance estimation.
problem Theoretical guarantees for RHTs in low-dimensional applications.
method Proved uniform convergence of average of function over RHTs entries.
result Improved guarantees for kernel approximation and distance estimation.