In plain words: By repeatedly encoding and decoding a data point, a network traces how it drifts through its compressed inner space, revealing a flow with attractor points that needs no extra training. This flow shows whether the model memorized or generalized, and flags unfamiliar samples, even in large vision systems. Count words: By(1) repeatedly2 encoding3 and4 decoding5 a6 data7 point,8 a9 network10 traces11 how12 it13 drifts14 through15 its16 compressed17 inner18 space,19 revealing20 a21 flow22 with23 attractor24 points25 that26 needs27 no28 extra29 training30. This31 flow32 shows33 whether34 the35 model36 memorized37 or38 generalized,39 and40 flags41 unfamiliar42 samples,43 even44 in45 large46 vision47 systems48. — 48 words, slightly over. Trim. "even in large vision systems" → "in large vision systems" (46). Still over. Trim more. Revised: "By repeatedly encoding and decoding a data point, a network traces how it drifts through its compressed inner space, revealing a flow with attractor points that needs no extra training. This flow shows whether the model memorized or generalized, and flags unfamiliar samples in large vision systems." Count: By1 repeatedly2 encoding3 and4 decoding5 a6 data7 point,8 a9 network10 traces11 how12 it13 drifts14 through15 its16 compressed17 inner18 space,19 revealing20 a21 flow22 with23 attractor24 points25 that26 needs27 no28 extra29 training30. This31 flow32 shows33 whether34 the35 model36 memorized37 or38 generalized,39 and40 flags41 unfamiliar42 samples43 in44 large45 vision46 systems47. 47. Trim "large" → 46. Trim "inner" → 45. Hmm need under 45, so ≤44. Remove "inner" and "large": 45. Remove "data" in "data point"? Keep. Let's rewrite tighter. "By repeatedly encoding and decoding a point, a network traces how it drifts through its compressed space, revealing a flow with attractor points that needs no extra training. This flow shows whether the model memorized or generalized, and flags unfamiliar samples in vision systems." Count: By1 repeatedly2 encoding3 and4 decoding5 a6 point,7 a8 network9 traces10 how11 it12 drifts13 through14 its15 compressed16 space,17 revealing18 a19 flow20 with21 attractor22 points23 that24 needs25 no26 extra27 training28. This29 flow30 shows31 whether32 the33 model34 memorized35 or36 generalized,37 and38 flags39 unfamiliar40 samples41 in42 vision43 systems44. 44 words. Good.By repeatedly encoding and decoding a point, a network traces how it drifts through its compressed space, revealing a flow with attractor points that needs no extra training. This flow shows whether the model memorized or generalized, and flags unfamiliar samples in vision systems.

Abstract

Neural networks transform high-dimensional data into compact, structured representations, often modeled as elements of a lower dimensional latent space. In this paper, we present an alternative interpretation of neural models as dynamical systems acting on the latent manifold. Specifically, we show that autoencoder models implicitly define a latent vector field on the manifold, derived by iteratively applying the encoding-decoding map, without any additional training. We observe that standard training procedures introduce inductive biases that lead to the emergence of attractor points within this vector field. Drawing on this insight, we propose to leverage the vector field as a representation for the network, providing a novel tool to analyze the properties of the model and the data. This representation enables to: (i) analyze the generalization and memorization regimes of neural models, even throughout training; (ii) extract prior knowledge encoded in the network's parameters from the attractors, without requiring any input data; (iii) identify out-of-distribution samples from their trajectories in the vector field. We further validate our approach on vision foundation models, showcasing the applicability and effectiveness of our method in real-world scenarios.

Marco Fumero, Luca Moschella, Emanuele Rodolà, Francesco Locatello
arXiv:2505.22785 · cs.LG · submitted May 28, 2025 · updated Mar 25, 2026
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