{"ID":2856768,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.10586","arxiv_id":"2510.10586","title":"Compositional Symmetry as Compression: Lie Pseudogroup Structure in Algorithmic Agents","abstract":"In the algorithmic (Kolmogorov) view, agents are programs that track and compress sensory streams using generative programs. We propose a framework where the relevant structural prior is simplicity (Solomonoff) understood as \\emph{compositional symmetry}: natural streams are well described by (local) actions of finite-parameter Lie pseudogroups on geometrically and topologically complex low-dimensional configuration manifolds (latent spaces). Modeling the agent as a generic neural dynamical system coupled to such streams, we show that accurate world-tracking imposes (i) \\emph{structural constraints} -- equivariance of the agent's constitutive equations and readouts -- and (ii) \\emph{dynamical constraints}: under static inputs, symmetry induces conserved quantities (Noether-style labels) in the agent dynamics and confines trajectories to reduced invariant manifolds; under slow drift, these manifolds move but remain low-dimensional. This yields a hierarchy of reduced manifolds aligned with the compositional factorization of the pseudogroup, providing a geometric account of the ``blessing of compositionality'' in deep models. We connect these ideas to the Spencer formalism for Lie pseudogroups and formulate a symmetry-based, self-contained version of predictive coding in which higher layers receive only \\emph{coarse-grained residual transformations} (prediction-error coordinates) along symmetry directions unresolved at lower layers.","short_abstract":"In the algorithmic (Kolmogorov) view, agents are programs that track and compress sensory streams using generative programs. We propose a framework where the relevant structural prior is simplicity (Solomonoff) understood as \\emph{compositional symmetry}: natural streams are well described by (local) actions of finite-...","url_abs":"https://arxiv.org/abs/2510.10586","url_pdf":"https://arxiv.org/pdf/2510.10586v1","authors":"[\"Giulio Ruffini\"]","published":"2025-10-12T13:06:37Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\",\"cs.IT\",\"q-bio.NC\"]","methods":"[]","has_code":false}