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.
Transformers converge linearly to optimal models for Gaussian mixtures classification.
problem Theoretical understanding of transformers' in-context classification.
method Gradient descent training of a single-layer transformer for Gaussian mixtures classification.
result Transformers converge linearly to globally optimal models for Gaussian mixtures classification.
Paper trains models to resist string transformations.
problem Vulnerability of NLP models to adversarial string transformations.
method Combines search and abstraction techniques for robust training.
result Trained models resist combinations of user-defined transformations.
Pre-training on different modalities improves Transformer performance in offline reinforcement learning.
problem Improving Transformer-based models for offline reinforcement learning tasks.
method Empirical investigation of pre-training on language and vision data, analysis of internal representations, and fine-tuning with no context.
result Pre-trained Transformers with language data can utilize context-like information to solve reinforcement learning tasks efficiently.
New bounds show transformers need longer training for length generalization.
problem Understanding when transformers can generalize to longer inputs.
method Analyzing different settings of transformers, providing quantitative bounds.
result Transformers need training data longer than previously thought for length generalization.
Data augmentation (DA) is fundamental against overfitting in large convolutional neural networks, especially with a limited training dataset. In images, DA is usually based on heuristic transformations, like geometric or color transformations. Instead of using predefined transformations, our work learns data augmentati…
New insights into why Transformers are hard to train, leading to a new method to stabilize them.
problem Understanding and stabilizing the training of Transformers.
method Analyzing the amplification effect in Transformer models and proposing Admin to stabilize training.
result Admin stabilizes early stage training and improves performance.
This paper proposes a new RV prediction model using neural distributional transformation and co-training.
problem Predicting skewed and fat-tailed realized volatility (RV) is challenging.
method The paper uses a neural distributional transformation and co-training to predict RV. It jointly trains the transformation and prediction model using a maximum-likelihood objective function.
result The proposed method significantly outperforms other methods on a dataset of 100 stocks.
Mimetic initialization improves Transformer training on small datasets.
problem Difficulty in training Transformers on small datasets.
method Initialize self-attention layers to look like pre-trained models.
result Vanilla Transformers trained with mimetic initialization achieve higher accuracy.
Training-free looped transformers improve model performance without additional training.
problem Improving model performance without additional training or fine-tuning.
method A lightweight inference-time wrapper loops a contiguous mid-stack block of layers of a frozen checkpoint without additional fine-tuning.
result Our method improves model performance across various model families.
The paper analyzes the training dynamics of a transformer for next-token prediction.
problem Understanding the non-asymptotic performance of transformers in next-token prediction.
method Characterizes training dataset properties, designs a two-stage training algorithm, and analyzes attention gradient properties.
result Trained transformers converge sub-linearly to max-margin solutions and exhibit linear convergence in cross-entropy loss.
This work characterizes benign overfitting in Vision Transformers.
problem Understanding generalization of Vision Transformers when trained to overfit.
method Gradient descent on a data distribution model, focusing on self-attention layer and softmax.
result Established a condition to distinguish between small and large test errors based on signal-to-noise ratio.
Effective theory for Transformer initialization improves model performance.
problem Improving performance of Transformers at initialization.
method Effective-theory analysis of signal propagation in wide and deep Transformers.
result Particular width scalings of initialization and training hyperparameters.
Transformers learn a mesa-optimizer to implement in-context learning.
problem Understanding the convergence of autoregressive training to a mesa-optimizer.
method Investigated a one-layer linear causal self-attention model autoregressively trained by gradient flow.
result Proved that autoregressive training converges to a gradient descent step for an OLS problem, validating the mesa-optimizer hypothesis.
This paper analyzes deep and wide transformer training dynamics.
problem Understanding the training dynamics of infinitely deep and wide transformers.
method Develops a mean-field framework for gradient-based training of transformers, controlling a neural PDE.
result Establishes a rigorous foundation for gradient-based transformer training, proving convergence to global minima.
Optimizing data movement significantly improves transformer training efficiency.
problem Data movement is a major bottleneck in training transformers.
method Developed a recipe to globally optimize data movement in transformers.
result Achieved up to 1.30x performance improvement over state-of-the-art frameworks.
Transformers learn linear models in-context without updates.
problem Understanding how transformers mimic linear models in-context.
method Gradient flow on linear regression tasks with random initialization.
result Transformers achieve prediction error competitive with best linear predictors.
New insights into how large learning rates affect transformer training dynamics.
problem Understanding how large learning rates impact the training of transformer models.
method Analyzing a simplified linear transformer model with a two-factor product map.
result Large learning rates can lead to various training outcomes including cycles, chaos, or divergence.
ModelDiff compares learning algorithms by identifying feature transformations.
problem Comparing models trained with different learning algorithms.
method ModelDiff uses datamodels framework to find distinguishing feature transformations.
result ModelDiff can compare models trained with/without data augmentation, pre-training, and different SGD hyperparameters.
Study shows how specialized attention circuits emerge during transformer training.
problem Understanding the mechanisms of transformer training dynamics at large scales.
method Controlled sparse modular addition task; monitoring token evolution via visual sandbox.
result Specialized attention circuits (clustering heads) naturally emerge during training.
Transformers learn to play games in-context, proving Nash equilibrium.
problem Understanding in-context game-playing capabilities of pre-trained transformers.
method Theoretical guarantees and constructional results for transformer architecture in multi-agent games.
result Pre-trained transformers can learn Nash equilibrium in-context for two-player zero-sum games.
Transformer pre-training improves stock return prediction accuracy.
problem Improving stock price prediction accuracy for better investment decisions.
method Pre-trained transformer models on TSX index, fine-tuned for individual stocks, compared to LSTM and XGBoost.
result Transformer model achieved lower mean squared error than benchmarks.
Looped transformers with LN converge to power method for principal component prediction.
problem Understanding how transformers learn algorithmic procedures.
method Study of principal component prediction with looped linear transformers and layer normalization.
result Gradient descent trains looped transformers with LN to implement the power method for principal component prediction.
Convolutional neural networks (CNNs) have achieved state-of-the-art results on many visual recognition tasks. However, current CNN models still exhibit a poor ability to be invariant to spatial transformations of images. Intuitively, with sufficient layers and parameters, hierarchical combinations of convolution (matri…
Paper explores how uncertainty quantification improves Transformer's in-context learning ability.
problem Understanding and quantifying in-context learning ability of Transformers.
method Revisit linear regression tasks with bi-objective prediction (conditional expectation and variance).
result Trained Transformers achieve near Bayes-optimum performance, suggesting use of training distribution.
Deep vanilla transformers trained without shortcuts achieve similar performance to standard models.
problem Training deep vanilla transformers without shortcuts and normalizations.
method Parameter initializations, bias matrices, and location-dependent rescaling.
result Deep vanilla transformers can train at similar speeds and performance to standard models.
Transformer with denoising diffusion improves probabilistic density estimation.
problem Estimating non-Gaussian and multimodal probability distributions for regression problems.
method Training a denoising diffusion head on top of a Transformer model.
result The model provides reasonable probability density estimation for high-dimensional inputs.
Deep linear ResNets converge globally with certain transformations.
problem Global convergence of training deep linear ResNets.
method Gradient descent and stochastic gradient descent for training L L L -hidden-layer linear ResNets. result GD and SGD can converge to global minimum for deep linear ResNets with specific transformations.
Transformers learn to perform logistic regression in-context.
problem Understanding how transformers learn to perform specific tasks in-context.
method Constructed multi-layer transformers that perform in-context logistic regression through normalized gradient descent.
result Transformers can be trained to perform in-context logistic regression effectively.
Transformers can implement reinforcement learning algorithms from data without updates.
problem Training reinforcement learning algorithms from data without parameter updates.
method Design a teacher-mimicking training procedure for transformers to implement policy-improvement methods.
result Gradient flow converges to an optimal parameter manifold corresponding to the desired RL update.
This paper investigates how transformers can learn to generalize to unseen examples in context.
problem Understanding how transformers can generalize to unseen examples in a prompt.
method Gradient descent analysis of one-layer multi-head transformers for in-context learning.
result The training loss for a one-layer multi-head transformer converges linearly to a global minimum, effectively learning ridge regression over basis functions.
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.
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.
We prove that the global minimum of the backpropagation (BP) training problem of neural networks with an arbitrary nonlinear activation is given by the ridgelet transform. A series of computational experiments show that there exists an interesting similarity between the scatter plot of hidden parameters in a shallow ne…
Transformation Equivariant Representations (TERs) aim to capture the intrinsic visual structures that equivary to various transformations by expanding the notion of {\em translation} equivariance underlying the success of Convolutional Neural Networks (CNNs). For this purpose, we present both deterministic AutoEncoding…
Layer normalization placement affects training stability and warm-up stage necessity.
problem Training instability and the necessity of a learning rate warm-up stage in Transformers.
method Theoretical analysis and mean field theory to prove gradient behavior at initialization.
result Removing the warm-up stage for Pre-LN Transformers can achieve comparable results with less time and tuning.
OPT framework improves neural network generalization by learning an orthogonal transformation.
problem Improving neural network generalization.
method Orthogonal over-parameterized training (OPT) framework that minimizes hyperspherical energy.
result OPT framework provably minimizes hyperspherical energy and improves empirical generalization.
The study explains transformer scaling laws using statistical and approximation theories.
problem Understanding why transformer scaling laws exist for large models trained on low-dimensional data.
method Established statistical estimation and mathematical approximation theories for transformers on low-dimensional manifolds.
result Predicted a power law between generalization error and model and data sizes, with power depending on intrinsic data dimension.
Transformers can learn mixture of linear models efficiently.
problem Existence and generalization of in-context learning for mixture models.
method Theoretical analysis and gradient flow optimization.
result Transformers achieve a prediction error of O ( d / n ) \mathcal{O}(\sqrt{d/n}) O ( d / n ) with high probability. Transformers learn to make decisions in new contexts from offline data.
problem Understanding when and how transformers can perform in-context reinforcement learning.
method Theoretical framework analyzing supervised pretraining for ICRL, including algorithm distillation and decision-pretrained transformers.
result Transformers can efficiently approximate optimal reinforcement learning algorithms for various environments.
This study analyzes how one-layer transformers learn regular language recognition tasks.
problem Understanding how one-layer transformers solve regular language recognition tasks like even pairs and parity check.
method Theoretical analysis of training dynamics and gradient descent for a one-layer transformer.
result A one-layer transformer can solve even pairs directly but needs CoT for parity check. Training phases show rapid growth in attention layer followed by logarithmic growth in linear layer.
Transformers learn rich in-context dependencies efficiently.
problem Understanding how transformers learn long-range dependencies efficiently.
method Approximation and dynamics analysis of induction head mechanisms.
result Abrupt transition from lazy to rich mechanisms during training.
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 …
We prove Transformers can learn diverse Gröbner bases.
problem Training Transformers for Gröbner basis computation.
method Prove generality of dataset generation algorithm; propose extended algorithm.
result Datasets are sufficiently general for diverse Gröbner bases learning.
Transformers can learn optimal variable selection in group-sparse classification.
problem Understanding how transformers leverage attention to select relevant variables in group-sparse classification.
method Training a one-layer transformer using gradient descent to select variables from one group of input variables.
result A one-layer transformer can correctly leverage the attention mechanism to select variables, disregarding irrelevant ones.
Transformer models show robustness across domains with domain adversarial training.
problem Domain adaptation from multiple sources with no labeled data.
method Domain adversarial training and mixture of experts.
result Domain adversarial training improves representation but not performance.
Adversarially trained transformers can learn robustly across tasks with minimal tuning.
problem Adversarial attacks and the high cost of adversarial training.
method Adversarial pretraining followed by in-context learning.
result Single-layer linear transformers can generalize robustly to unseen tasks.
Geometric variations of objects, which do not modify the object class, pose a major challenge for object recognition. These variations could be rigid as well as non-rigid transformations. In this paper, we design a framework for training deformable classifiers, where latent transformation variables are introduced, and …