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The optimization algorithms are crucial in training physics-informed neural networks (PINNs), as unsuitable methods may lead to poor solutions. Compared to the common gradient descent (GD) algorithm, implicit gradient descent (IGD)…
The ability of learning useful features is one of the major advantages of neural networks. Although recent works show that neural network can operate in a neural tangent kernel (NTK) regime that does not allow feature learning, many works…
Transformers can generate predictions in two approaches: 1. auto-regressively by conditioning each sequence element on the previous ones, or 2. directly produce an output sequences in parallel. While research has mostly explored upon this…
Transformers enable in-context learning (ICL) for rapid, gradient-free adaptation in time series forecasting, yet most ICL-style approaches rely on tabularized, hand-crafted features, while end-to-end sequence models lack inference-time…
Large transformer models pretrained on offline reinforcement learning datasets have demonstrated remarkable in-context reinforcement learning (ICRL) capabilities, where they can make good decisions when prompted with interaction…
We study the fundamental optimization principles of self-attention, the defining mechanism of transformers, by analyzing the implicit bias of gradient-based optimizers in training a self-attention layer with a linear decoder in binary…
In-context learning (ICL) enables large language models (LLMs) to adapt to new tasks without weight updates by learning from demonstration sequences. While ICL shows strong empirical performance, its internal representational mechanisms are…
This thesis investigates two key phenomena in large language models (LLMs): in-context learning (ICL) and model collapse. We study ICL in a linear transformer with tied weights trained on linear regression tasks, and show that minimising…
The emergence of in-context learning (ICL) enables large pre-trained language models (PLMs) to make predictions for unseen inputs without updating parameters. Despite its potential, ICL's effectiveness heavily relies on the quality,…
It is believed that Gradient Descent (GD) induces an implicit bias towards good generalization in training machine learning models. This paper provides a fine-grained analysis of the dynamics of GD for the matrix sensing problem, whose goal…
Transformers have achieved great success across a wide range of applications, yet the theoretical foundations underlying their success remain largely unexplored. To demystify the strong capacities of transformers applied to versatile…
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) component. For ICL of linear regression with a Gaussian…
Recent research has shown that Transformers with linear attention are capable of in-context learning (ICL) by implementing a linear estimator through gradient descent steps. However, the existing results on the optimization landscape apply…
In-context learning, a capability that enables a model to learn from input examples on the fly without necessitating weight updates, is a defining characteristic of large language models. In this work, we follow the setting proposed in…
Implicit deep learning has recently become popular in the machine learning community since these implicit models can achieve competitive performance with state-of-the-art deep networks while using significantly less memory and computational…
Transformers exhibit In-Context Learning (ICL), where these models solve new tasks by using examples in the prompt without additional training. In our work, we identify and analyze two key components of ICL: (1) context-scaling, where model…
While the Transformer architecture has achieved remarkable success across various domains, a thorough theoretical foundation explaining its optimization dynamics is yet to be fully developed. In this study, we aim to bridge this…
Large language models (LLMs) have initiated a paradigm shift in transfer learning. In contrast to the classic pretraining-then-finetuning procedure, in order to use LLMs for downstream prediction tasks, one only needs to provide a few…
In-context learning refers to the ability of a model to condition on a prompt sequence consisting of in-context examples (input-output pairs corresponding to some task) along with a new query input, and generate the corresponding output.…
We propose Bayesian optimal sequential prediction as a new principle for understanding in-context learning (ICL). Unlike interpretations framing Transformers as performing implicit gradient descent, we formalize ICL as meta-learning over…