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knowledge base · entry 15

The three-step template every assistant follows

A read-through of Training language models to follow instructions with human feedback — the InstructGPT paper. Entry 14 showed how far a tiny perfect dataset goes; this is the industrial pipeline it was measured against, and the mental model — SFT → reward model → RL — that every paper after it simply assumes you know.

paper Training language models to follow instructions with human feedback
authors Ouyang, Wu, Jiang, Almeida, Wainwright, Mishkin, et al. — OpenAI
source arXiv:2203.02155
why we read it it defined post-training. the pipeline, the labeler economics, the KL leash, and the alignment tax all enter the literature here — and its headline (a 1.3B model beating 175B GPT-3 on preference) is Chinchilla’s lesson restated for alignment

every figure zooms — click it, scroll to magnify, drag to pan

part one

The problem, before any pipeline

figure 1 · the misalignment gap

Predicting text is not following instructions

GPT-3 was trained to do exactly one thing: continue text the way the internet would. Ask it “Explain the moon landing to a six-year-old” and a plausible internet continuation is… more requests like yours, or an essay written for adults. The capability to answer is in there; the objective never asked for it. The paper names this the gap between the training objective and the user’s intent — the model is not on your side yet.

click any figure to zoom · scroll to magnify · drag to pan

Everything that follows is machinery for closing that gap with human judgment as the training signal — first by imitation, then by comparison.

part two · the pipeline

Three steps, three datasets

figure 2 · the template

SFT, then a reward model, then RL

The pipeline runs in three stages, each with its own modest dataset written or judged by a team of about 40 trained labelers. Step one: supervised fine-tuning on ~13,000 demonstrations — labelers write the answer they wish the model gave (entry 14 in industrial form). Step two: train a reward model on ~33,000 prompts’ worth of ranked comparisons. Step three: let the model generate freely on ~31,000 fresh prompts and optimize it with reinforcement learning against the reward model’s score.

Notice the quantities: tens of thousands, not millions. The scarce, expensive ingredient is calibrated human judgment — the entire post-training run cost about 60 petaflop/s-days against GPT-3’s 3,640 for pretraining, under 2%.

figure 3 · the reward model

A model that learns to score answers

Step two is the conceptual heart. Writing perfect answers is slow and hard; ranking answers is fast and reliable. So labelers are shown between K = 4 and K = 9 of the model’s own responses to one prompt and simply order them best to worst. A separate 6B model — the reward model — is then trained so that its scalar score agrees with every pairwise preference implied by the ranking: loss = −log σ(r(x, yw) − r(x, yl)).

That scalar is the crucial artifact: it converts “which of these did a human like more?” into a signal a training loop can maximize — soft, rich feedback of exactly the kind entry 06 argued teaches fastest.

figure 4 · worked by hand

Why rank nine answers instead of two

Here is the labeling economics, worked out. A ranking of K answers implies K(K−1)/2 pairwise comparisons. Rank 9 responses in one sitting and you have banked 36 comparisons for roughly the effort of reading nine answers once — versus asking 36 separate “A or B?” questions. All 36 go into one training batch, which also stops the reward model from overfitting to any single prompt’s quirks.

figure 5 · the RL loop

Chasing the reward — on a leash

Step three: the model generates an answer, the reward model scores it, and PPO nudges the weights toward higher scores. Left alone, this loop finds the reward model’s blind spots — so a per-token KL penalty tethers the policy to the SFT model: objective = r(x,y) − β·KL(policy ‖ SFT). Drift far from how the SFT model speaks and the penalty eats the reward. One more refinement — mixing pretraining gradients back in (PPO-ptx) — matters enough that we give it the next figure.

Hold onto the KL leash — the term β·KL(π ‖ πref) is the exact quantity entry 16 starts from when it makes this whole loop collapse into a single supervised loss.

part three · the verdict

Small and aligned beats huge and raw

results · human preference

1.3B, preferred over a model 100× its size

The result that made the paper famous: labelers preferred the 1.3B InstructGPT’s answers to those of the raw 175B GPT-3. At matched size the margin is a rout — the 175B InstructGPT wins 85 ± 3% of head-to-heads against 175B GPT-3, and 71 ± 4% even when GPT-3 is helped with a carefully engineered few-shot prompt.

axisGPT-3, rawInstructGPT
head-to-head preference (175B vs 175B)15%85 ± 3%
hallucination rate, closed-domain tasks41%21%
truthful + informative (TruthfulQA)baseline≈2× as often
toxic outputs when prompted respectfullybaseline≈25% fewer
bias (Winogender, CrowS-Pairs)baselineno real change

The reading we keep: post-training is worth orders of magnitude of scale on the axis users actually feel. The cheapest capability upgrade in the building is usually alignment, not parameters — the post-training echo of entry 10.

part four · the fine print

The tax, and who sets the standard

figure 7 · the alignment tax

What alignment quietly costs — and the fix

Aligning on human preference regressed public NLP benchmarks — SQuAD, DROP, HellaSwag, translation. The paper names this the alignment tax: optimize hard for one behavior and you quietly pay elsewhere. Their fix, PPO-ptx, mixes pretraining gradients into the RL updates — anchoring the model to its original distribution while the reward pulls on style — and recovers the regressions almost entirely.

the deeper caveat aligned to whom? The preferences belong to roughly 40 contractors, screened for agreement (72.6 ± 1.5% inter-annotator), mostly US and Southeast Asia based. The paper is unusually honest that this is alignment to a standard, not the standard — and InstructGPT still follows harmful instructions and still confidently invents facts. The template ships with its blind spots visible.

the math · in the paper's notation

The two equations the template runs on

The reward-model loss and the RL objective — equations (1) and (2) of the paper, and the ancestors of everything in entry 16. Each read aloud, with the loss checked on one toy comparison.

the equations · worked

Learn a score, then chase it on a leash

eq. (1) · the reward-model loss

loss(θ)  =  − 1( K2 ) E(x, yw, yl) [ log σ( rθ(x, yw) − rθ(x, yl) ) ]

read aloud: for every pair a labeler's ranking implies, push the winner's score above the loser's — the sigmoid of the score gap is the model's predicted probability the labeler was right, and the loss is its log. The 1/(K choose 2) averages over all pairs from one ranking, so a 9-answer session doesn't outvote a 4-answer one.

  • rθ(x, y)the reward model's scalar score for answer y to prompt x — the artifact the whole pipeline exists to produce
  • ywthe answer the labeler preferred (w for win)…
  • yl…and the one they ranked below it (l for lose)
  • σthe sigmoid — squashes the score gap into a probability
  • ( K2 )pairs implied by ranking K answers — figure 4's K(K−1)/2
plug in → scores r(yw) = 2.1, r(yl) = 0.6: gap 1.5 → σ(1.5) ≈ 0.82 → loss = −ln 0.82 ≈ 0.20. flip the scores and the gap is −1.5 → σ ≈ 0.18 → loss ≈ 1.71 — mis-ordered pairs dominate the gradient, agreeing pairs barely register.

eq. (2) · the PPO-ptx objective

objective(φ) = E [ rθ(x, y)β·log πRLφ(y|x)πSFT(y|x) ]  +  γ·Ex ~ Dpretrain [ log πRLφ(x) ]

read aloud: maximize the reward model's score, minus a penalty for drifting from how the SFT model speaks, plus a bonus for still predicting ordinary pretraining text well. Three terms, three jobs: chase the preference, stay on the leash, don't forget your education. The γ term is the "-ptx" fix for the alignment tax of figure 7.

  • πRLφthe policy being trained
  • πSFTthe frozen step-one model — the anchor the KL ratio is measured against
  • βthe leash length: how hard drift is punished — per token, during the RL loop
  • γthe pretraining mix — how much of the old curriculum stays in the update
plug in → hold this shape: reward − β·log(π/πref). entry 16 begins by writing down this exact objective's known optimum and solving it backwards — the whole of DPO lives inside equation (2).

part five

What we take from it

applied · our reading

The template, three stages later

Every post-training pipeline since — including the ones later in this arc — is a remix of these three steps. What we carry into our own work:

Next in the arc: the pipeline’s expensive middle — the reward model and the RL loop — gets mathematically deleted. Entry 16: DPO.

source

Long Ouyang, Jeff Wu, Xu Jiang, Diogo Almeida, Carroll L. Wainwright, Pamela Mishkin, et al. Training language models to follow instructions with human feedback. arXiv:2203.02155. Figures on this page are our own; the pipeline, dataset sizes, win rates and tax findings are the paper’s, and any other plotted values are illustrative.

← back to the knowledge base  ·  ← entry 14 · LIMA  ·  entry 16 · DPO →

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