Do algorithmic improvements
compound?

Gordon E. Moore

Historical hardware-scaling comparator; it does not define AI performance or isolate algorithmic effects.

Jared Kaplan et al.

Empirical power laws across model size, data, and compute show that resource scaling and algorithm choices are intertwined.

Jordan Hoffmann et al.

Compute-optimal allocation between parameters and data complicates simple hardware-versus-algorithm narratives.

Danny Hernandez and Tom B. Brown

Documents fixed-performance compute reductions in selected domains; supports a bounded efficiency trend, not a universal law.

Anson Ho et al.

Measures algorithmic progress using compute-equivalent comparisons; relevant to operationalization but does not identify A.

Jaime Sevilla et al.

Provides historical compute-growth context and cautions against attributing capability trends to one input.

Rylan Schaeffer, Brando Miranda, and Sanmi Koyejo

Shows how metric choice can create apparent discontinuities, challenging overinterpretation of breakthrough narratives.

Alex Krizhevsky, Ilya Sutskever, and Geoffrey E. Hinton

Canonical architecture-and-training milestone used in the historical source corpus.

Kaiming He et al.

Residual connections provide a bounded example of architecture changing trainability and performance.

Karen Simonyan and Andrew Zisserman

Depth-focused architecture evidence helps trace how design choices interact with compute and data.

Mingxing Tan and Quoc V. Le

Demonstrates a bounded architecture-scaling method with explicit efficiency comparisons.

Andrew G. Howard et al.

Shows architecture-level resource tradeoffs under deployment constraints.

Alexey Dosovitskiy et al.

Architecture transfer across domains illustrates innovation, while dependence on pretraining scale complicates attribution.

Zhuang Liu et al.

Modernized convolutional design shows that implementation recipes and architecture families co-evolve.

Ashish Vaswani et al.

A central bounded example of an architectural idea changing parallelism and sequence modeling.

Jacob Devlin et al.

Pretraining objectives and transfer are algorithmic contributions entangled with data and compute.

Tom B. Brown et al.

Few-shot capability at scale demonstrates interaction among architecture, training data, compute, and prompting.

Noam Shazeer et al.

Conditional computation is a bounded example of increasing capacity without proportional per-example compute.

William Fedus, Barret Zoph, and Noam Shazeer

Sparse routing provides an explicit capacity–compute tradeoff relevant to algorithmic efficiency.

Nan Du et al.

Another bounded sparse-model comparison; does not isolate a universal innovation index.

Diederik P. Kingma and Jimmy Ba

Optimization methods are algorithmic, but their effects depend on tasks, schedules, and baselines.

John Jumper et al.

A major application breakthrough, but causal attribution spans architecture, data, training, and domain structure.

Jonathan Ho, Ajay Jain, and Pieter Abbeel

A generative-model innovation in the source corpus; it is an example rather than a law-level test.

Jason Wei et al.

Establishes the primary reasoning-representation comparator in the Stage 1 protocol.

Xuezhi Wang et al.

Motivates repeated sampling and aggregation while making resource accounting essential.

Pranjal Aggarwal et al.

Connects adaptive sampling to efficiency and helps frame secondary policy analyses.

Shunyu Yao et al.

Expands inference computation through search; illustrates capability–resource tradeoffs.

Shunyu Yao et al.

Shows that inference policy can alter task behavior, though tool use adds new resources and confounds.

Silei Xu et al.

Defines the concise reasoning representation tested prospectively in Stage 1.

Karl Cobbe et al.

Introduces GSM8K, the primary benchmark specified by the Stage 1 protocol.

Denny Zhou et al.

A decomposition policy illustrating how prompt structure can change task performance.

Luyu Gao et al.

Offloading computation to an interpreter complicates token-only resource comparisons.

Wenhu Chen et al.

Separates reasoning representation from execution and highlights construct-boundary choices.

Noah Shinn et al.

Iterative feedback is another inference-time policy with distinct resource and state requirements.

Eric Zelikman et al.

Connects generated rationales to training, underscoring the difference between training-time and inference-time innovation.

Charlie Snell et al.

Directly motivates resource-aware comparison of inference policies, without validating Williams’ Law.

Bradley Brown et al.

Provides broad repeated-sampling evidence relevant to the Stage 1 reinvestment question.

Tri Dao et al.

System-aware algorithm design changes realized speed and memory without changing model semantics.

Edward J. Hu et al.

Provides bounded parameter and memory efficiency gains for adaptation.

Geoffrey Hinton, Oriol Vinyals, and Jeff Dean

Knowledge distillation is a bounded example of transferring capability into a cheaper model.

Roger L. Berger and Jason C. Hsu

Methodological basis for intersection–union logic used in compound Stage 1 decisions.

Sture Holm

Controls familywise error across the Stage 1 co-primary decisions.

Toshiro Tango

Paired-proportion noninferiority and equivalence methodology relevant to accuracy contrasts.

Morten W. Fagerland, Stian Lydersen, and Petter Laake

Supports selection and interpretation of paired-binomial procedures.

Belinda Phipson and Gordon K. Smyth

Relevant to finite resampling inference and transparent p-value calculation.

Joelle Pineau et al.

Supports explicit artifacts, checklists, and execution provenance in the empirical program.

A. C. Davison and D. V. Hinkley

General bootstrap foundation for resource-ratio uncertainty procedures.

Bradley Efron and Robert J. Tibshirani

General resampling reference for the Stage 1 statistical design.

Tim C. Hesterberg

Practical guidance on null-centered resampling and bootstrap interpretation.

Center for Open Science

Official registration guidance for the immutable prospective record required before confirmation.

Junior Williams

Foundational Williams-authored source; establishes the proposed framework but is not independent evidence.

Junior Williams

Companion conceptual source; part of the program rather than independent validation.