Stories in Space: In-Context Learning Trajectories in Conceptual Belief Space

• URL: http://arxiv.org/abs/2605.12412v1
• Date: Tue, 12 May 2026 17:09:41 GMT
• Title: Stories in Space: In-Context Learning Trajectories in Conceptual Belief Space
• Abstract summary: Large Language Models (LLMs) update their behavior in context, which can be viewed as a form of Bayesian inference.<n>We propose that LLMs assign beliefs over a low-dimensional geometric space - a conceptual belief space - and that in-context learning corresponds to a trajectory through this space as beliefs are updated over time.
• Score: 24.005442880672003
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Large Language Models (LLMs) update their behavior in context, which can be viewed as a form of Bayesian inference. However, the structure of the latent hypothesis space over which this inference operates remains unclear. In this work, we propose that LLMs assign beliefs over a low-dimensional geometric space - a conceptual belief space - and that in-context learning corresponds to a trajectory through this space as beliefs are updated over time. Using story understanding as a natural setting for dynamic belief updating, we combine behavioral and representational analyses to study these trajectories. We find that (1) belief updates are well-described as trajectories on low-dimensional, structured manifolds; (2) this structure is reflected consistently in both model behavior and internal representations and can be decoded with simple linear probes to predict behavior; and (3) interventions on these representations causally steer belief trajectories, with effects that can be predicted from the geometry of the conceptual space. Together, our results provide a geometric account of belief dynamics in LLMs, grounding Bayesian interpretations of in-context learning in structured conceptual representations.

Related papers

• From Found to Designed: Concepts as a Design Axis for Large Language Models [4.979725367638729]
  We organize concept-aware interventions along two dimensions: whether concept structure is internally induced or externally grounded, and the stage of the pipeline where it is introduced.<n>This taxonomy reveals three broad patterns: inference-time approaches remain comparatively underexplored, related ideas have developed largely in isolation across pipeline stages, and externally grounded methods span the entire pipeline despite often being described under different terminology.
  arXiv  Detail & Related papers  (2026-07-29T12:18:36Z)
• Emergent Structured Representations Support Flexible In-Context Inference in Large Language Models [77.98801218316505]
  Large language models (LLMs) exhibit emergent behaviors suggestive of human-like reasoning.<n>We investigate the internal processing of LLMs during in-context concept inference.
  arXiv  Detail & Related papers  (2026-02-08T03:14:39Z)
• A Geometric Unification of Concept Learning with Concept Cones [58.70836885177496]
  Two traditions of interpretability have evolved side by side but seldom spoken to each other: Concept Bottleneck Models (CBMs) and Sparse Autoencoders (SAEs)<n>We show that both paradigms instantiate the same geometric structure.<n>CBMs provide human-defined reference geometries, while SAEs can be evaluated by how well their learned cones approximate or contain those of CBMs.
  arXiv  Detail & Related papers  (2025-12-08T09:51:46Z)
• The Geometry of Reasoning: Flowing Logics in Representation Space [27.047532187192278]
  We study how large language models (LLMs) think'' through their representation space.<n>We propose a novel geometric framework that models an LLM's reasoning as flows.
  arXiv  Detail & Related papers  (2025-10-10T18:44:00Z)
• Native Logical and Hierarchical Representations with Subspace Embeddings [25.274936769664098]
  We introduce a novel paradigm: embedding concepts as linear subspaces.<n>It naturally supports set-theoretic operations like intersection (conjunction) and linear sum (disjunction)<n>Our method achieves state-of-the-art results in reconstruction and link prediction on WordNet.
  arXiv  Detail & Related papers  (2025-08-21T18:29:17Z)
• How do Transformers Learn Implicit Reasoning? [67.02072851088637]
  We study how implicit multi-hop reasoning emerges by training transformers from scratch in a controlled symbolic environment.<n>We find that training with atomic triples is not necessary but accelerates learning, and that second-hop generalization relies on query-level exposure to specific compositional structures.
  arXiv  Detail & Related papers  (2025-05-29T17:02:49Z)
• Revealing emergent human-like conceptual representations from language prediction [90.73285317321312]
  Large language models (LLMs) trained solely through next-token prediction on text exhibit strikingly human-like behaviors.<n>Are these models developing concepts akin to those of humans?<n>We found that LLMs can flexibly derive concepts from linguistic descriptions in relation to contextual cues about other concepts.
  arXiv  Detail & Related papers  (2025-01-21T23:54:17Z)
• A Geometric Notion of Causal Probing [85.49839090913515]
  The linear subspace hypothesis states that, in a language model's representation space, all information about a concept such as verbal number is encoded in a linear subspace.<n>We give a set of intrinsic criteria which characterize an ideal linear concept subspace.<n>We find that, for at least one concept across two languages models, the concept subspace can be used to manipulate the concept value of the generated word with precision.
  arXiv  Detail & Related papers  (2023-07-27T17:57:57Z)
• Inverse Dynamics Pretraining Learns Good Representations for Multitask Imitation [66.86987509942607]
  We evaluate how such a paradigm should be done in imitation learning. We consider a setting where the pretraining corpus consists of multitask demonstrations. We argue that inverse dynamics modeling is well-suited to this setting.
  arXiv  Detail & Related papers  (2023-05-26T14:40:46Z)
• Latent Traversals in Generative Models as Potential Flows [113.4232528843775]
  We propose to model latent structures with a learned dynamic potential landscape. Inspired by physics, optimal transport, and neuroscience, these potential landscapes are learned as physically realistic partial differential equations. Our method achieves both more qualitatively and quantitatively disentangled trajectories than state-of-the-art baselines.
  arXiv  Detail & Related papers  (2023-04-25T15:53:45Z)
• Learning Group Structure and Disentangled Representations of Dynamical Environments [7.4769019455423855]
  We propose a framework for learning representations of a dynamical environment structured around the transformations that generate its evolution. We learn the structure of explicitly symmetric environments without supervision from observational data generated by sequential interactions. We show that our method enables accurate long-horizon predictions, and demonstrate a correlation between the quality of predictions and disentanglement in the latent space.
  arXiv  Detail & Related papers  (2020-02-17T14:59:31Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.