Replication Data and Scripts for: "Spectral Reach: Understanding Neural Scaling as Progress into the Spectral Tail"

Dataset

DOI

The scripts and data provided here are for reproducing the results and plots of "Spectral Reach: Understanding Neural Scaling as Progress into the Spectral Tail".

Conceptually, we introduce a framework for efficiently measuring the overlap between the empirical Neural Tangent Kernel (eNTK) and loss residuals, and demonstrate how spectral reach (the capacity to learn from progressively weaker spectral modes) explains why larger models achieve lower losses.

Identifier
DOI	https://doi.org/10.18419/DARUS-5947
Metadata Access	https://darus.uni-stuttgart.de/oai?verb=GetRecord&metadataPrefix=oai_datacite&identifier=doi:10.18419/DARUS-5947

Provenance
Creator	Nikolaou, Konstantin (ORCID: 0009-0000-9926-680X); Scheunemann, Jonas ; Krippendorf, Sven ; Tovey, Samuel ; Holm, Christian (ORCID: 0000-0003-2739-310X)
Publisher	DaRUS
Contributor	Nikolaou, Konstantin
Publication Year	2026
Funding Reference	DFG EXC 2075 - 390740016 ; DFG 492175459 ; DFG SPP 2363 - 497249646 ; DFG INST 35/1597-1 FUGG ; DFG 455787709 ; STFC ST/T000694/1 ; STFC ST/X000664/1
Rights	info:eu-repo/semantics/openAccess
OpenAccess	true
Contact	Nikolaou, Konstantin (University of Stuttgart)

Representation
Resource Type	Dataset
Format	application/octet-stream; text/x-python; application/pdf; application/x-ipynb+json; application/json; text/plain; charset=US-ASCII; image/png; text/markdown; text/plain
Size	68922; 68928; 58611; 58285; 68932; 58289; 159548347; 159548343; 158083816; 285630211; 285630205; 285630215; 5276; 7570; 7680; 34447; 37048; 42996; 43053; 21263; 1786; 1563; 1937; 23994; 439; 289; 309; 15273; 4973; 13328; 18619; 1287; 970; 80859; 884909; 1957698; 12127; 2293; 996; 2599; 1060; 2082; 1589; 1549; 2160; 1543; 1353; 5308; 5053; 15389; 51183; 6958; 0; 30; 782; 427; 24992; 28601; 7046; 1078; 56156; 412; 437; 406; 436; 407; 438; 409; 1031; 123646; 1104; 18731; 3302029; 6115; 5666; 1176; 1188; 1580; 2531; 3285; 113332; 14487; 586; 6508; 933; 377605; 3092; 309333; 715; 771; 757; 61359550; 33997661; 61359556; 34274924; 34274928; 61359560; 74458845; 133298755; 74458849; 73775374; 133298765; 133298761; 432391; 664300; 1468666; 6313; 256197; 111196; 112154; 4505; 819; 1071; 6863; 3418; 1100; 5542; 1803; 3819; 5329; 960; 1565; 2510; 437955; 25257; 2289; 281405; 29533; 3751; 478; 868; 4195; 4296; 2107; 2259; 3305; 2879; 2860; 2109; 3752; 3559; 1984; 4602; 3835; 20599; 16800; 4513; 4811; 9218; 9100; 295051; 97486; 262; 266; 265; 264; 348349; 267; 268; 173182; 192; 191; 429536; 193; 195
Version	1.0
Discipline	Computer Science; Computer Science, Electrical and System Engineering; Engineering Sciences; Natural Sciences; Physics