Approximate Homomorphisms and Convergent Representations in Transducers
Quick summary
arXiv:2608.20428v1 Announce Type: cross 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 comp
Key takeaways
- arXiv:2608.20428v1 Announce Type: cross 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.
Why it matters
The value of this work lies as much in how it was tested as in the claim itself. Sample design, baselines, uncertainty and replication help separate a laboratory result from real-world impact.
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