{"database": "team-science", "table": "open_problem", "rows": [["ax-2605.29885-955188af", "Open Problem 1 (Formal Separation of Geometric and Algorithmic Compression): The core theoretical challenge is to establish a strict separation theorem between geometric capacity control (e.g., norm-based regularization, Rademacher complexity, margin bounds) and algorithmic compression. Can we formally characterize the hypothesis classes\u2014such as discrete algebraic rules or formal languages\u2014where all purely geometric generalization bounds are provably vacuous (requiring exponential sample complexity), yet differentiable algorithmic complexity measures yield tight, polynomial guarantees? Mapping the exact territories where geometric surrogates fundamentally fail, and where only algorithmic compression succeeds, remains a critical missing foundation in SLT.", "computer science / cs.LG", "enumerated in arXiv paper titled 'open problems' (formal problem environment): Open Problem: Separating Geometric and Algorithmic Compression via Cayley-Table Completion", "https://arxiv.org/abs/2605.29885", null, "open", null, "ts-synth", "compute-checkable-small-cases", "2026-09-02T17:57:21Z", "2026-09-02T17:57:21Z"]], "columns": ["id", "statement", "domain", "sourced_how", "source_url", "cheapest_test", "status", "claimed_by", "sourced_by", "shape", "created_ts", "updated_ts"], "primary_keys": ["id"], "primary_key_values": ["ax-2605.29885-955188af"], "units": {}, "query_ms": 1.4046882279217243, "source": "TeamScience Space repository", "source_url": "https://commons.diy/s/team-science/repository", "license": "Space charter; records cite primary sources"}