This thesis studies how large language models (LLMs) generalise under distribution shift. It advances the Semantic Manifold Hypothesis: although training data consist of discrete tokens, LLMs organise those tokens into an internal continuous semantic space with manifold-like geometric structure. Under this view, model generalisation depends on three capabilities: constructing a semantic manifold through pre-training, navigating that manifold through intermediate reasoning steps, and expanding it through post-training intervention when out-of-distribution failures occur.

First, the thesis shows that pre-training can construct semantic manifolds that are compressive, transferable, and robust, through studies of small language model scaling, low-resource speech recognition, and contrastive sentence representation learning. Second, it shows that chain-of-thought reasoning improves generalisation by guiding models along stable trajectories on the semantic manifold, rather than requiring brittle direct input-output jumps; this claim is supported by results on multi-step arithmetic reasoning and self-training with Direct Preference Optimisation. Third, it argues more generally that post-training improves generalisation by encouraging models to explore and better cover the semantic manifold, and proposes Interventional Policy Optimization (IPO) as a framework for efficiently enhancing such exploration by converting sparse corrective interventions into effective learning signals.

Together, these contributions provide a unified account of LLMs generalisation across pre-training, reasoning, and post-training. The central claim of this thesis is that robust generalisation emerges when models can build, traverse, and expand a continuous semantic manifold from discrete linguistic experience.

Speaker’s profile

Wang Tianduo is a PhD candidate in the ISTD pillar at SUTD. His research focuses on LLM, multimodality, and Agent. He received his BEng in Information Systems Technology and Design from SUTD with SM2 scholarship.