The Story of Inference-Time Scaling

and the training-time loop behind it

A language model can get dramatically better answers by thinking longer at answer time, not only by being retrained or made larger.

Begin the story →

Act 1 · Building Intuition

  1. 01Think Fast, Think Slow
  2. 02Thinking in Reality
  3. 03Training-Time Scaling
  4. 04Reasoning: Diverse Pathfinding

Act 2 · The Toolbox

  1. 05Chain of Thought: Reasoning Out Loud
  2. 06Thinking Longer
  3. 07Frequency Voting
  4. 08Best-of-N and Verifiers: Generate, Then Select
  5. 09Outcome vs Process Supervision
  6. 10Searching Through Thoughts
  7. 11The Keystone: The Test-Time Compute Scaling Law

Act 3 · Frontier & Caveats

  1. 12Teaching Models to Reason: STaR and Self-Improvement
  2. 13Frontier Reasoners I: o1, o3, and the Two-Axis Scaling Curve
  3. 14Frontier Reasoners II: DeepSeek-R1, GRPO, and the “Aha Moment”
  4. 15When Reasoning Breaks: Self-Correction, Verifier Reliability, Overthinking
  5. 16Wrap-Up: What You Now Know

How to explore

Chapters stand alone but build in order. Every figure is live: sliders re-derive the curves, diagrams answer clicks, and the demos sample from a real model when one is available; canned transcripts otherwise.

Several chapters ship a downloadable Python notebook, linked at the top of the page: the harness, the model's own generations, and the data behind the figures, so you can re-derive every plot yourself.

It is written for undergraduate students and other learners meeting these ideas for the first time; no prior machine-learning background is assumed.

Authors

  1. Shashank Bangalore LakshmanGraduate Student, M.S. in Artificial IntelligenceDepartment of Computer Science, The University of Texas at Austin
  2. Scott Lawrence EiersUndergraduate Student, B.S. in Computer ScienceWestern Governors University

* Corresponding author.

† These authors contributed equally.

Cite this work

@misc{bangalorelakshman2026its,
  title  = {The Story of Inference-Time Scaling and the Training-Time loop behind it},
  author = {Bangalore Lakshman, Shashank and Eiers, Scott Lawrence},
  year   = {2026},
  note   = {Preprint. Submitted to the VISxAI Workshop at IEEE VIS; not yet peer-reviewed.},
  url    = {https://sapiotomy.vercel.app}
}