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ChatGPT Codex — Symbolic Training Summary (Updated)

Stages (conceptual)

  1. Pretraining Large-scale next-token modeling on code + text → general coding fluency. (OpenAI, OpenAI)

  2. Supervised Fine-Tuning (SFT) Curated demonstrations (coding tasks, fixes, explanations) align outputs toward developer intent. (OpenAI)

  3. RLHF (policy optimization) Train a reward model from human preferences; optimize the policy (e.g., PPO). Extensions may include rule-based rewards for safety. (OpenAI, OpenAI)

Symbolic pipeline

Let M₀ = Base Codex (pretrained)
Codex:
 M₀ — SFT(curated code demos) → M₁ — RLHF(reward model, PPO) → M₂ (deployed utility)
Where the RLHF reward model is trained from human preference comparisons over model outputs. (OpenAI)

The reference implementation in src/codex_ml/symbolic_pipeline.py provides light‑weight yet functional training loops for each stage. Tokenisation and dataset handling compute token counts and supervised losses exactly, and the RLHF phase performs a PPO‑style update against a trained reward model. A simple safety regulariser penalises disallowed tokens. Dedicated tests ensure reproducibility (deterministic seeds), validate configuration errors and cover edge cases such as empty corpora or missing preference data.

The accompanying reference implementation in codex_ml.symbolic_pipeline uses a deterministic whitespace tokenizer, unigram language model pretraining, supervised updates based on demonstration token frequencies, and a simple bag‑of‑words reward model. The RLHF stage performs a PPO‑style update with a KL regularizer to the pretrained model and rule‑based penalties for unsafe tokens.

Objective (schematic)

$$ \min_{M}; \mathcal{L}(M) = \alpha,\mathcal{L}{\text{SFT}}(M; D);+; \beta,\mathcal{L}_{\text{RLHF}}(M; R);+; \gamma,\Omega(M) $$}

  • $\mathcal{L}_{\text{SFT}}$: supervised loss on curated coding data
  • $\mathcal{L}_{\text{RLHF}}$: preference-based reward optimization (e.g., PPO with a learned RM)
  • $\Omega(M)$: regularizers/safety constraints (can include rule-based rewards)
  • $\alpha,\beta,\gamma$: phase weights. (OpenAI, OpenAI)

Data/feedback flow (symbolic)

$$ \begin{aligned} &\textbf{Pretraining:}& \text{Corpora}{\text{text,code}} ;\rightarrow; M_0 \ &\textbf{SFT:}& (M_0, D; M_1 \ &\textbf{RM training:}& D_{\text{prefs}}=(x, y_A, y_B, \ell);\rightarrow; \text{RewardModel} \ &\textbf{RLHF:}& (M_1,\text{RewardModel}) ;\xrightarrow{\text{PPO}}; M_2 \end{aligned} $$}}) ;\xrightarrow{\text{supervised}

Demonstrations ($D_{\text{demos}}$) and preference pairs ($D_{\text{prefs}}$) are obtained from human labelers; RM predicts preferred outputs; PPO optimizes the policy against RM (optionally mixed with rule-based rewards for safety). (OpenAI, OpenAI)

Notes specific to Codex

  • Codex is an OpenAI coding agent/product line built on our most capable models; its training lineage follows the Pretraining → SFT → RLHF paradigm used across deployed assistants. (OpenAI)

Implementation notes

The accompanying symbolic_pipeline module implements these stages with real training loops and evaluation metrics:

  • Tokenisation & data handling – all text is tokenised so that token counts and supervised cross‑entropy losses are computed accurately.
  • Reward model & PPO – a logistic reward model is trained on preference pairs and a PPO loop with a KL safety penalty optimises the policy against it.
  • Reproducibility & validation – deterministic seeds are built in and tests cover edge cases such as empty datasets or mis‑specified configurations to ensure robustness.