Topological Steering is a new framework that steers large language model (LLM) behavior by leveraging topological representations of activation spaces, specifically using persistence diagrams from Topological Data Analysis (TDA). Unlike traditional methods that intervene directly in activation or feature space, this approach captures global structure, making it more robust to outliers, distributional shifts, noise, and local perturbations. Experiments demonstrate that Topological Steering consistently modifies LLM behavior across multiple model families and sizes.
arXiv:2606. 19542v1 Announce Type: new Abstract: Large language models are commonly aligned through supervised fine-tuning, yet little is known about how their internal representations evolve during this process.
arXiv:2608. 06276v1 Announce Type: cross Abstract: Persistence diagrams (PDs) provide stable and interpretable summaries of multiscale topological structure.
arXiv:2607. 20484v1 Announce Type: new Abstract: Large Language Models (LLMs) are fundamentally limited by representation collapse, a bottleneck that severely degrades long-context performance.
arXiv:2606. 21295v2 Announce Type: replace-cross Abstract: Existing sequence models, including RNNs, LSTMs, continuous-time networks, and Transformers, share a common structural principle: layer-wise dynamics, where all neurons in the same layer co-evolve through a shared parameterized operator, leaving individual neurons no freedom to evolve independently.
arXiv:2510. 04100v2 Announce Type: replace-cross Abstract: Topological mapping offers a compact and robust representation for navigation, but progress in the field is hindered by the lack of standardized evaluation metrics, datasets, and protocols.
arXiv:2608. 15388v1 Announce Type: new Abstract: Topological deep learning (TDL) methods rely on lifting raw data into higher-order discrete domains such as simplicial complexes, cell complexes, and hypergraphs.
arXiv:2606. 29763v1 Announce Type: cross Abstract: Topological data analysis (TDA), particularly persistent homology (PH), captures geometric structural properties in medical images (e.
arXiv:2606. 17531v1 Announce Type: new Abstract: We investigate the learning of interpretable bases in non-negative matrix factorisation (NMF) by regularising the topology of the learned basis functions.
arXiv:2606. 09806v1 Announce Type: cross Abstract: We introduce Topological Neural Operators (TNOs), a principled framework for operator learning on cell complexes that lifts neural operators (NOs) from functions on points and/or edges to topological domains.
arXiv:2601. 21207v4 Announce Type: replace-cross Abstract: Combinatorial and topological structures, such as graphs, simplicial complexes, and cell complexes, form the foundation of geometric and topological deep learning (GDL and TDL) architectures.
arXiv:2608. 04334v1 Announce Type: cross Abstract: Contemporary model-free reinforcement learning algorithms can achieve very high performance, but have low sample efficiency and are not robust to changes in the environment.
arXiv:2604. 18050v2 Announce Type: replace Abstract: AlphaGeometry represents a milestone in neuro-symbolic reasoning, yet its architecture faces a log-linear scaling bottleneck within its symbolic deduction engine that limits its efficiency as problem complexity increases.