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pith:5XQ6V224

pith:2026:5XQ6V2244NW6VKE634ATDAWZ7L

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Deep Learning as Neural Low-Degree Filtering: A Spectral Theory of Hierarchical Feature Learning

Florent Krzakala, Hugo Tabanelli, Luca Arnaboldi, Matteo Vilucchio, Yatin Dandi

Neural Low-Degree Filtering models deep learning as an explicit iterative spectral process in which each layer selects features by maximal low-degree correlation to the label.

arxiv:2605.13612 v1 · 2026-05-13 · cs.LG · cond-mat.dis-nn · stat.ML

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Claims

C1strongest claim

Neural LoFi provides a mathematically explicit framework for studying multi-layer feature learning beyond the lazy regime. It predicts how representations are selected layer by layer, explains how emergence of concepts arises with given sample complexity, and gives a concrete mechanism by which depth progressively constructs new features from old ones through low-degree compositionality.

C2weakest assumption

The assumption that, in the stylized limit of gradient-based training, the dynamics at each layer decouple so that the next layer can independently select directions with maximal accessible low-degree correlation to the label.

C3one line summary

Neural LoFi models deep learning as layer-wise spectral filtering that selects maximal low-degree correlations, yielding a tractable surrogate for hierarchical representation learning beyond the lazy regime.

References

123 extracted · 123 resolved · 1 Pith anchors

[1] Deep learning.nature, 521(7553):436–444, 2015 2015

[2] The unreasonable effectiveness of deep learning in artificial intelligence 2020

[3] Visualizing and understanding convolutional networks 2014

[4] How transferable are features in deep neural networks?Advances in neural information processing systems, 27 2014

[5] The Platonic Representation Hypothesis 2024 · arXiv:2405.07987

Receipt and verification

First computed	2026-05-18T02:44:18.035589Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ede1eaeb5ce36deaa89edf013182d9fad6af9d0895d3d9535f83eb945b919f32

Aliases

arxiv: 2605.13612 · arxiv_version: 2605.13612v1 · doi: 10.48550/arxiv.2605.13612 · pith_short_12: 5XQ6V2244NW6 · pith_short_16: 5XQ6V2244NW6VKE6 · pith_short_8: 5XQ6V224

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5XQ6V2244NW6VKE634ATDAWZ7L \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: ede1eaeb5ce36deaa89edf013182d9fad6af9d0895d3d9535f83eb945b919f32

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a202ec330836c4c2500e5623f246c153a490778bde297b3f77380818356c3ec",
    "cross_cats_sorted": [
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      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-13T14:44:06Z",
    "title_canon_sha256": "4522539b8b8c3d792457f87e5005f4e663fe5b819c64d6bd728398a35ea9efd4"
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  "source": {
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    "kind": "arxiv",
    "version": 1
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}