Poli et al.'s 2022 NeurIPS paper 'Self-Similarity Priors' explicitly cites both the fractal/IFS and implicit-neural-representation canons and states its method belongs to both

implicit-neural-representationsfractal-compressioniterated-function-systemsneural-collagesmichael-poliimage-compressioncitation-lineagehistory-of-machine-learning

"Self-Similarity Priors: Neural Collages as Differentiable Fractal Representations" (Poli, Xu, Massaroli, Meng, Kim & Ermon; NeurIPS 2022) builds its method — Neural Collages — directly on Barnsley and Demko's 1985 Collage Theorem, the mathematical foundation of fractal/IFS image compression, reformulated as a differentiable, hypernetwork-trained operator. Its §5 "Related Work and Discussion" gives each canon its own labelled paragraph (separated by a third, "Attention operators and patches"): under "Implicit representations and models," it cites SIREN, NeRF, and COIN together — "(Sitzmann et al., 2020; Mildenhall et al., 2020; Dupont et al., 2021) parametrize the implicit functions via neural networks for use in downstream tasks such as compression" — and under "Fractal compression," it cites the classical canon, including "Jacquin et al. (1992) introduces more flexible fractal compression schemes for images based on partitioned iterated function systems (PIFSs)." The paper states its own method sits at the intersection: "Neural Collages belong to both classes of methods, being a fixed–point iteration whose parameters define data implicitly." It then benchmarks its compressor against both classical fractal compression and COIN on the same image set — figures not independently replicated here; see below.

This is a peer-reviewed, published paper (not a preprint left unrefereed), and it is the one document found in this vault's research that draws the fractal↔implicit-neural-representation lineage explicitly, resolving the open half of question-verify-fractal-compression-inr-lineage and updating claim-fractal-compression-to-implicit-neural-representations-bridge. The lineage runs one direction only: no canonical INR paper cites back the other way — see claim-siren-2020-does-not-cite-fractal-ifs-wfa-compression, claim-coin-2021-does-not-cite-fractal-ifs-wfa-compression, claim-strumpler-2022-omits-fractal-compression-credits-coin-as-first. No source found, including this paper's own reference list, connects weighted finite automata (WFA) compression specifically — only IFS/PIFS, the Barnsley–Jacquin branch — to any INR paper.

The paper's reported benchmark numbers — encoding speedups of "up to 10× (accounting for training time) and 100× (at test time)" over fractal compression, the 100× restated in Figure 7's caption as "At test time, encoding for Neural Collage compressors is 100× faster than fractal compression" — rest on this single Tier-1 primary source and have not been independently replicated or cross-checked against a second source. The reconstruction-quality comparison points in a different direction from the speed one, and the two should not be merged: against fractal compression and COIN the paper claims Neural Collages are better on quality ("less noticeable artifacts and improved color retention"), while the gap it describes itself as narrowing is with spectral compressors — block-DCT and the JPEG-family codecs built on it — which the paper concedes still hold best PSNR at medium and high bpp ("Although spectral lossy compressors common in state–of–the–art codecs perform with best PSNR in medium and high bpp settings, Collages narrows the gap in terms of reconstruction quality as well as encoding speed"). [unverified-quant — needs independent replication] if these figures are ever cited as standalone numbers rather than as context for the citation-lineage finding above.