1 citations · 5 across the 15 of their papers we have counts for
21 papers
Internal Guidance as a Sampling Method for Tilted Diffusion Models
Curtis McDonald, Peter Bartlett
Reward guidance methods sample an exponential tilt of a base density using a diffusion model trained with only samples from the base distribution. Existing methods use what we call…
Transformers Learn Two Competing Sorting Algorithms, and Only One Length-Generalizes
Khashayar Gatmiry, Nathan W. Henry, Chloe H. Su +5
We show that two-layer transformers trained to near-zero loss on a sorting task converge to one of two mechanistically distinct solution classes depending on their initialization.…
Principal Component Regression Dominates all Monotone Spectral Filters for Linear Regression
Juno Kim, Hengyu Fu, Peter Bartlett +2
We compare the instance-wise, finite-sample risks of monotone spectral filters for linear regression, a broad class of estimators including principal component regression (PCR), gr…
Learn Your Own Thoughts: Abstract Token Curriculum
Khashayar Gatmiry, Avrajit Ghosh, Parsa Mirtaheri +4
Large Language Models (LLMs) have achieved remarkable reasoning capabilities by utilizing chain-of-thought (CoT) as a scratchpad for intermediate stages of thinking. However, CoT t…
Hilbert Operator for Progressive Encoding (HOPE): A Mathematical Framework for Deconstructing Learned Representations in Deep Networks
Hossein Mobahi, Peter L. Bartlett
Deep neural networks encode complex representations, but deconstructing this internal knowledge remains a challenge. Given the link between learning and compression, network compre…
RubiConv -- Efficient Boundary-Respecting Convolutions
Linda Friso, Annie Marsden, Xinyi Chen +4
Convolutional architectures have emerged as powerful alternatives to Transformers for sequence modeling. The primary advantage is that they offer improved theoretical sequence leng…
Training Dynamics of Softmax Self-Attention: Fast Global Convergence via Preconditioning
Gautam Goel, Mahdi Soltanolkotabi, Peter Bartlett
We study the training dynamics of gradient descent in a softmax self-attention layer trained to perform linear regression and show that a simple first-order optimization algorithm…
Hard labels sampled from sparse targets mislead rotation invariant algorithms
Avrajit Ghosh, Bin Yu, Manfred Warmuth +1
One of the most common machine learning setups is logistic regression. In many classification models, including neural networks, the final prediction is obtained by applying a logi…
Risk Comparisons in Linear Regression: Implicit Regularization Dominates Explicit Regularization
Jingfeng Wu, Peter L. Bartlett, Sham M. Kakade +2
Existing theory suggests that for linear regression problems categorized by capacity and source conditions, gradient descent (GD) is always minimax optimal, while both ridge regres…
Improved Scaling Laws in Linear Regression via Data Reuse
Licong Lin, Jingfeng Wu, Peter L. Bartlett
Neural scaling laws suggest that the test error of large language models trained online decreases polynomially as the model size and data size increase. However, such scaling can b…
Large Stepsizes Accelerate Gradient Descent for Regularized Logistic Regression
Jingfeng Wu, Pierre Marion, Peter Bartlett
We study gradient descent (GD) with a constant stepsize for -regularized logistic regression with linearly separable data. Classical theory suggests small stepsizes to ensu…
Minimax Optimal Convergence of Gradient Descent in Logistic Regression via Large and Adaptive Stepsizes
Ruiqi Zhang, Jingfeng Wu, Licong Lin +1
We study (GD) for logistic regression on linearly separable data with stepsizes that adapt to the current risk, scaled by a constant hyperparameter .…
Implicit Bias of Gradient Descent for Non-Homogeneous Deep Networks
Yuhang Cai, Kangjie Zhou, Jingfeng Wu +3
We establish the asymptotic implicit bias of gradient descent (GD) for generic non-homogeneous deep networks under exponential loss. Specifically, we characterize three key propert…
Benefits of Early Stopping in Gradient Descent for Overparameterized Logistic Regression
Jingfeng Wu, Peter Bartlett, Matus Telgarsky +1
In overparameterized logistic regression, gradient descent (GD) iterates diverge in norm while converging in direction to the maximum -margin solution -- a phenomenon known…
Fast Best-of-N Decoding via Speculative Rejection
Hanshi Sun, Momin Haider, Ruiqi Zhang +6
The safe and effective deployment of Large Language Models (LLMs) involves a critical step called alignment, which ensures that the model's responses are in accordance with human p…
Large Stepsize Gradient Descent for Non-Homogeneous Two-Layer Networks: Margin Improvement and Fast Optimization
Yuhang Cai, Jingfeng Wu, Song Mei +2
The typical training of neural networks using large stepsize gradient descent (GD) under the logistic loss often involves two distinct phases, where the empirical risk oscillates i…
Scaling Laws in Linear Regression: Compute, Parameters, and Data
Licong Lin, Jingfeng Wu, Sham M. Kakade +2
Empirically, large-scale deep learning models often satisfy a neural scaling law: the test error of the trained model improves polynomially as the model size and data size grow. Ho…
In-Context Learning of a Linear Transformer Block: Benefits of the MLP Component and One-Step GD Initialization
Ruiqi Zhang, Jingfeng Wu, Peter L. Bartlett
We study the \emph{in-context learning} (ICL) ability of a \emph{Linear Transformer Block} (LTB) that combines a linear attention component and a linear multi-layer perceptron (MLP…
Large Stepsize Gradient Descent for Logistic Loss: Non-Monotonicity of the Loss Improves Optimization Efficiency
Jingfeng Wu, Peter L. Bartlett, Matus Telgarsky +1
We consider gradient descent (GD) with a constant stepsize applied to logistic regression with linearly separable data, where the constant stepsize is so large that the loss in…
Implicit Diffusion: Efficient Optimization through Stochastic Sampling
Pierre Marion, Anna Korba, Peter Bartlett +6
We present a new algorithm to optimize distributions defined implicitly by parameterized stochastic diffusions. Doing so allows us to modify the outcome distribution of sampling pr…
How Many Pretraining Tasks Are Needed for In-Context Learning of Linear Regression?
Jingfeng Wu, Difan Zou, Zixiang Chen +3
Transformers pretrained on diverse tasks exhibit remarkable in-context learning (ICL) capabilities, enabling them to solve unseen tasks solely based on input contexts without adjus…