1 citations · 5 across the 15 of their papers we have counts for
11 papers · 1 filter
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.…
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…
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…
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…
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…
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…