Task-Aware Identifiability: Observation Quotients, Statistical Geometry, and Representation Accessibility

[2601.21584] Task-Aware Identifiability: Observation Quotients, Statistical Geometry, and Representation Accessibility Skip to main content Search Submit Donate Log in Computer Science > Hardware Architecture arXiv:2601.21584 (cs) [Submitted on 29 Jan 2026 ( v1 ), last revised 25 Aug 2026 (this version, v2)] Title: Task-Aware Identifiability: Observation Quotients, Statistical Geometry, and Representation Accessibility Authors: Yan Jiao , Pin-Han Ho , Limei Peng , Yiming Miao View PDF Abstract: Intelligent systems often assume observations contain the information required for a task. This fails struc- turally when a declared mechanism assigns identical ob- servation laws to latent states the task must distin- guish. We develop a unified diagnostic framework con- necting observation-induced equivalence, task identifia- bility, local statistical geometry, representation accessi- bility, and achievable risk. Its organizing condition is a standard factorization property: the observation parti- tion refines the task partition, and conditionally iid rep- etitions of that fixed channel cannot recover an exactly collapsed distinction. On regular quotient strata, Fisher geometry and nuisance-efficient Fisher information char- acterize first-order local resolvability. For representa- tions, we distinguish law-valued encoder experiments from deterministic quotient embeddings and exact task sufficiency from scale-controlled decoder accessibility. We organize task risk into structural, finite-observation, representation-channel, and learning gaps. Controlled synthetic studies validate these layers; a physics-based synthetic near-field model yields sharply different range and angle information, while NYUv2 shows persistent, decoder-modulated task preferences among frozen en- coders under two pointwise probes. TAI thereby local- izes whether task-relevant information is absent at ob- servation, weakly resolved, lost or poorly accessible in representation, or left to the learner. Subjects: Hardware Architecture (cs.AR) ; Emerging Technologies (cs.ET) Cite as: arXiv:2601.21584 [cs.AR] (or arXiv:2601.21584v2 [cs.AR] for this version) https://doi.org/10.48550/arXiv.2601.21584 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Pin-Han Ho [ view email ] [v1] Thu, 29 Jan 2026 11:47:48 UTC (449 KB) [v2] Tue, 25 Aug 2026 07:41:44 UTC (1,057 KB) Full-text links: Access Paper: View PDF view license Additional Features Audio Summary Current browse context: cs.AR < prev | next > new | recent | 2026-01 Change to browse by: cs cs.ET References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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