待翻譯：Approximate Homomorphisms and Convergent Representations in Transducers
AI 服務暫時不可用，以下為來源摘要，待恢復後補全翻譯：arXiv:2608.20428v1 Announce Type: new Abstract: We study the stability of minimal representations of controlled stochastic processes (in particular, transducers) under perturbations. This question is motivated by recent experiments finding predictive-state structure in the latent representations of neural networks. We consider standard, linear and predictive transducers. We introduce notions of approximate homomorphism capturing local structural similarity between them, together with metrics comparing their induced dynamics (which we refer to as interfaces), and prove properties such as composability of the approximate homomorphisms. For standard transducers, we show that there exist simple interfaces for which there is no approximate homomorphism between the different implementations of the dynamics. In contrast, for every finite-rank interface $\mathcal I$, we prove that all minimal linear transducers implementing interfaces sufficiently close to $\mathcal I$ have an approximate homomorphism to the minimal implementation of $\mathcal I$, with error linear in the perturbation size. We prove an analogous stability result for predictive transducers under a residual metric using some mild hypothesis regarding the indistinguishability of the belief states. These results identify conditions under which canonical transducer representations are robust to perturbations, while showing that such convergence fails without additional structural restrictions. Under the assumption that these type of abstractions are embedded into the hidden layers of modern AI models, this gives some theoretical support to the hypothesis that their latent representations exhibit structural convergence.
AI 服務暫時不可用，以下為來源正文，待恢復後補全翻譯。
--> [Submitted on 19 Aug 2026] Title:Approximate Homomorphisms and Convergent Representations in Transducers View a PDF of the paper titled Approximate Homomorphisms and Convergent Representations in Transducers, by Santiago Cifuentes View PDF HTML (experimental) Abstract:We study the stability of minimal representations of controlled stochastic processes (in particular, transducers) under perturbations. This question is motivated by recent experiments finding predictive-state structure in the latent representations of neural networks. We consider standard, linear and predictive transducers. We introduce notions of approximate homomorphism capturing local structural similarity between them, together with metrics comparing their induced dynamics (which we refer to as interfaces), and prove properties such as composability of the approximate homomorphisms. For standard transducers, we show that there exist simple interfaces for which there is no approximate homomorphism between the different implementations of the dynamics. In contrast, for every finite-rank interface $\mathcal I$, we prove that all minimal linear transducers implementing interfaces sufficiently close to $\mathcal I$ have an approximate homomorphism to the minimal implementation of $\mathcal I$, with error linear in the perturbation size. We prove an analogous stability result for predictive transducers under a residual metric using some mild hypothesis regarding the indistinguishability of the belief states. These results identify conditions under which canonical transducer representations are robust to perturbations, while showing that such convergence fails without additional structural restrictions. Under the assumption that these type of abstractions are embedded into the hidden layers of modern AI models, this gives some theoretical support to the hypothesis that their latent representations exhibit structural convergence. Comments: 40 pages: 23 pages of main text and 17 pages of appendices; 6 figures Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI) MSC classes: 60G05 ACM classes: I.2.4 Cite as: arXiv:2608.20428 [cs.LG] (or arXiv:2608.20428v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2608.20428 arXiv-issued DOI via DataCite (pending registration) Submission history From: Santiago Cifuentes [view email] [v1] Wed, 19 Aug 2026 19:56:22 UTC (2,587 KB) Full-text links: Access Paper: View a PDF of the paper titled Approximate Homomorphisms and Convergent Representations in Transducers, by Santiago Cifuentes View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG new | recent | 2026-08 Change to browse by: cs cs.AI References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: 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?) IArxiv recommender toggle IArxiv Recommender (What is IArxiv?) 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?)