Frontier LLM Post-training and Reasoning

Pretraining builds a broad predictive model from large-scale data. Post-training changes how that model responds to instructions, preferences, tool outcomes, and task rewards. Inference-time compute then changes how much work the trained model performs before producing an answer. All three can affect performance; public reports do not establish that one is universally the largest source of capability.

As of the sources reviewed on 2026-10-11, OpenAI has publicly described reinforcement learning for o1 and o3 reasoning, with gains on the evaluations it reported from more training and more time spent reasoning. Anthropic has described constitutional supervision and a model that can answer quickly or use extended thinking. These are dated, provider-specific disclosures, not a complete recipe for every current frontier model.

Separate what the model can represent, what behavior training rewards, and how much computation a response is allowed:

The table is a map of possible mechanisms, not a claim that every provider uses all of them. Tool access, retrieval, data quality, evaluations, and system design also shape the user's observed result.

Supervised fine-tuning can minimize negative log-likelihood of demonstrated responses: $-\log\pi_\theta(y\mid x)$. A pairwise preference model can learn from a chosen and rejected response with a logistic loss:

One RLHF-style objective then maximizes expected reward while penalizing drift from a reference policy:

A verifiable task can use an outcome checker instead of a learned preference score, but the checker only measures the property it tests. Passing unit tests, for example, does not prove code security or maintainability. A longer inference budget can improve the chance of finding a correct solution on some tasks while also increasing latency and cost. The gain depends on the trained policy, search or sampling method, verifier quality, and task distribution.

Do not read a reasoning trace as a proof. A fluent chain of thought may contain mistakes; a correct answer may arise through a route that is not fully visible. Evaluate final outputs, tool actions, and failure modes independently. OpenAI's 2026 work on chain-of-thought controllability treats monitorability as a research question, not a settled guarantee.

This standard-library function is the pairwise logistic loss above. It demonstrates a training signal, not the undisclosed post-training recipe of any named frontier model.

1from math import exp, log1p
2
3
4def preference_loss(chosen_reward: float, rejected_reward: float) -> float:
5    margin = chosen_reward - rejected_reward
6    # Stable softplus(-margin) without computing exp of a large positive value.
7    return max(-margin, 0.0) + log1p(exp(-abs(margin)))
8
9
10assert preference_loss(2.0, 0.0) < preference_loss(0.0, 2.0)

For a reasoning-model comparison, record the exact model release, source date, prompt set, tool access, token or time budget, verifier, latency, and cost. Compare matched budgets and report uncertainty. Do not attribute a gain to RL alone if the pretraining base, data, tools, or inference budget also changed. A public system card often describes evaluations and safeguards more fully than the private training mixture.

1. Stages: What is the difference between SFT, preference training, and outcome RL? (Demonstrations imitate examples; comparisons shape relative response preference; outcome RL rewards sampled success under a specified checker.)
2. Causality: Can you infer that post-training caused all improvement between two released models? (No. Base training, data, tools, budgets, and evaluation setup can also differ.)
3. Compute: Why can more test-time reasoning help without changing weights? (The trained policy receives more opportunity to explore, revise, use tools, or verify before answering.)
4. Limits: Does a verifiable reward imply broad reliability? (No. It covers the checked property on the sampled task distribution, and the policy may exploit gaps.)
5. Evidence: What belongs beside a frontier-model capability claim? (Provider and release, publication date, evaluation method, inference budget, independent replication if available, and limits.)

Without notes, draw three boxes for pretraining, post-training, and inference-time compute. Put SFT, preference data, verifiable rewards, and tool use in the appropriate places. Explain one case where more reasoning time helps and one case where it might not. Then name two confounders that prevent a public benchmark difference from isolating post-training's contribution.

Sources and further reading

• OpenAI, Learning to Reason with LLMs (2024): o1 reasoning RL and reported training/test-time scaling.
• OpenAI, Introducing o3 and o4-mini (2025): further reported RL scaling and tool-use training.
• OpenAI, GPT-5.5 System Card (2026): dated evaluation and parallel test-time compute setting for Pro.
• OpenAI, Reasoning Models Struggle to Control Their Chains of Thought (2026): limits of reasoning-trace interpretation and monitoring.
• Anthropic, Constitutional AI: Harmlessness from AI Feedback (2022): supervised revision and AI-feedback RL method.
• Anthropic, Claude 3.7 Sonnet and Claude Code (2025): dated extended-thinking disclosure.
• Anthropic, Claude's New Constitution (2026): a current example of behavioral principles used in training.