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A proper understanding of the striking generalization abilities of deep neural networks presents an enduring puzzle. Recently, there has been a growing body of numerically-grounded theoretical work that has contributed important insights to…
Most machine learning theory and practice is concerned with learning a single task. In this thesis it is argued that in general there is insufficient information in a single task for a learner to generalise well and that what is required…
Scaling large language models (LLMs) leads to an emergent capacity to learn in-context from example demonstrations. Despite progress, theoretical understanding of this phenomenon remains limited. We argue that in-context learning relies on…
Learning policies which are robust to changes in the environment are critical for real world deployment of Reinforcement Learning agents. They are also necessary for achieving good generalization across environment shifts. We focus on…
Multi-condition fault diagnosis is prevalent in industrial systems and presents substantial challenges for conventional diagnostic approaches. The discrepancy in data distributions across different operating conditions degrades model…
Although transformers have demonstrated impressive capabilities for in-context learning (ICL) in practice, theoretical understanding of the underlying mechanism that allows transformers to perform ICL is still in its infancy. This work aims…
A basic assumption of statistical learning theory is that train and test data are drawn from the same underlying distribution. Unfortunately, this assumption doesn't hold in many applications. Instead, ample labeled data might exist in a…
This paper reviews concepts, modeling approaches, and recent findings along a spectrum of different levels of abstraction of neural network models including generalization across (1) Samples, (2) Distributions, (3) Domains, (4) Tasks, (5)…
Learning transferable knowledge across similar but different settings is a fundamental component of generalized intelligence. In this paper, we approach the transfer learning challenge from a causal theory perspective. Our agent is endowed…
Large-scale foundation models for scientific machine learning adapt to physical settings unseen during training, such as zero-shot transfer between turbulent scales. This phenomenon, in-context learning, challenges conventional…
We investigate the capacity of transformers to learn algorithms involving their context while solely being trained using next token prediction. We set up Markov chains with random transition matrices and we train transformers to predict the…
Transformer-based large language models have displayed impressive in-context learning capabilities, where a pre-trained model can handle new tasks without fine-tuning by simply augmenting the query with some input-output examples from that…
In-context learning (ICL) in Large Language Models (LLMs) has emerged as a powerful new learning paradigm. However, its underlying mechanism is still not well understood. In particular, it is challenging to map it to the "standard" machine…
In-context operator learning enables neural networks to infer solution operators from contextual examples without weight updates. While prior work has demonstrated the effectiveness of this paradigm in leveraging vast datasets, a systematic…
Large language models can solve tasks that were not present in the training set. This capability is believed to be due to in-context learning and skill composition. In this work, we study the emergence of in-context learning and skill…
We consider the problem of test-time domain generalization, where a model is trained on several source domains and adjusted on target domains never seen during training. Different from the common methods that fine-tune the model or adjust…
At the heart of machine learning lies the question of generalizability of learned rules over previously unseen data. While over-parameterized models based on neural networks are now ubiquitous in machine learning applications, our…
When modeling dynamical systems from real-world data samples, the distribution of data often changes according to the environment in which they are captured, and the dynamics of the system itself vary from one environment to another.…
The most basic assumption used in statistical learning theory is that training data and test data are drawn from the same underlying distribution. Unfortunately, in many applications, the "in-domain" test data is drawn from a distribution…
Deep neural networks (DNNs) have revolutionized artificial intelligence but often lack performance when faced with out-of-distribution (OOD) data, a common scenario due to the inevitable domain shifts in real-world applications. This…