From 9d830cb3f8296a0e35c8142d61aeb0728a28085b Mon Sep 17 00:00:00 2001 From: wassname <1103714+wassname@users.noreply.github.com> Date: Wed, 6 May 2026 05:40:30 +0800 Subject: [PATCH] README: add spaghetti + survival figures with glossary, captions, and read-in-order interpretation --- README.md | 112 ++++++++++++++++++---- figs/post/figure1_kl_only_qwen35_w512.png | Bin 0 -> 200692 bytes figs/post/spaghetti_qwen35_w512.png | Bin 0 -> 542288 bytes figs/post/survival_qwen35_w512.png | Bin 0 -> 46666 bytes 4 files changed, 95 insertions(+), 17 deletions(-) create mode 100644 figs/post/figure1_kl_only_qwen35_w512.png create mode 100644 figs/post/spaghetti_qwen35_w512.png create mode 100644 figs/post/survival_qwen35_w512.png diff --git a/README.md b/README.md index c71bbd6..5624007 100644 --- a/README.md +++ b/README.md @@ -1,36 +1,114 @@ # iso-kl-figure -Minimal repo with one job: produce a figure and a table that demonstrate iso-KL calibration is stable across models, seeds, and calibration windows. +Calibrate one steering knob so different methods deliver the same per-token KL budget. Then test whether the model still answers a forced-choice question while it's being steered. -## Claim (narrow) +Headline result on Qwen3.5-0.8B (mean_diff, w=512, n=8 held-out prompts): -Calibrating a steering coefficient so that p95 per-token KL(steered || base) hits 1 nat in a short calibration window: +- alpha in {0, 0.25, 0.5, 0.75, 1.0, 1.5}: 0 of 8 trajectories die at any fork. +- alpha = 2.0: 8 of 8 die. Median death time t = 64. +- alpha = 4.0: 8 of 8 die at t = 0. -- C1: bisection converges for every method tested; held-out p95 KL lands near 1 nat. -- C2 (not too cold): target-axis Delta logit at calibrated alpha is non-zero across methods. -- C3 (not too hot): base-NLL of generated text and branch-pmass of a forced format token stay near base at calibrated alpha across methods. +A phase transition at roughly 2x the iso-KL coefficient. Figures and table below. -The 2x check is a sanity probe, not a margin claim. Reported as: at 2x, p95 KL exceeds 1 nat for N of M cells. +## Glossary -Honesty footnote: matched on per-token distributional disagreement under greedy decoding in the calibration window. This is one defensible notion of fairness; not equivalence on intervention norm or behavioral effect size. +We deliberately reuse a few terms from survival analysis and steering. Definitions below are the operational ones used in this repo, not the textbook ones. -## Quick start +- *steering coefficient (alpha)*: scalar multiplier on a steering vector added to residual-stream activations at one layer. `alpha = 1.0` is the iso-KL-calibrated coefficient. `alpha = 2.0` is twice that. `alpha = 0` is the unsteered base model. +- *iso-KL calibration*: bisection on alpha such that the 95th-percentile per-token `KL(steered || base)` over a w-token calibration window equals 1 nat. The output is `c_star`, the coefficient at `alpha = 1`. This makes different steering methods comparable: any two methods at `alpha = 1` are spending the same per-token KL budget. +- *p95 KL*: 95th percentile of per-token `KL(steered || base)` over the calibration window. Robust to single-token spikes. +- *window (w)*: length in tokens of the calibration rollout. `w = 512` for the figures here. +- *pmass*: probability mass the model puts on the set `{true, false}` after we splice in a JSON schema prefill (`'\nI should answer now.{"value": '`) at fork token t. A forced-choice probe: can the model still produce one of the two valid answer tokens, or has steering wrecked the format? +- *pmass_eval*: same probe, on a held-out prompt set, evaluated at every fork t. +- *fork point t*: the token in the rollout where we splice the schema and read pmass. +- *death*: irreversible event. A trajectory is *alive* at fork t if `pmass_eval(t) >= 0.95`. The first time it drops below, it is dead and stays dead. The 0.95 threshold is where the JSON schema stops being a stable attractor; the model is producing other tokens. +- *right-censoring*: the rollout hit EOS at length L < t, so we never see fork t. The trajectory drops out of the at-risk denominator from L onward. Incomplete information, not death. +- *survival S(t)*: fraction of trajectories still alive at fork t, with right-censored trajectories removed from the at-risk set. Kaplan-Meier estimator. +- *mean_diff*: steering vector built as the difference of mean activations on a contrastive prompt pair. +- *spaghetti plot*: every individual KL trajectory drawn as one thin line, alive segments green, dead segments red, black line is the median. + +## Spaghetti: per-token KL trajectories, coloured by survival + +![KL trajectories coloured by survival, Qwen3.5-0.8B](figs/post/spaghetti_qwen35_w512.png) + +*Per-token KL(steered || base) for n=8 held-out long-form prompts on Qwen3.5-0.8B (mean_diff, w=512). One panel per alpha. Each thin line is one trajectory; green = alive at that token (pmass_eval >= 0.95), red = dead. Black line is the median. Dotted horizontal: KL = 1 nat (the calibration target).* + +How to read this plot, in order: + +1. *alpha = 0.* KL is exactly zero everywhere. This is the base model; nothing has been added. A sanity check that the splicing pipeline does not itself perturb the logits. +2. *alpha = 0.25 to 1.0.* KL stays well below the 1-nat line for most tokens. The calibration window only required p95 = 1 nat, so most tokens are far below. All trajectories are green: the model is still producing schema-valid answers throughout. The "warm but not hot" zone. +3. *alpha = 1.5.* KL still mostly below 1 nat but with a fatter upper envelope. All trajectories still alive end-to-end on the held-out set, even though calibration only guaranteed survival up to roughly `alpha = 1`. Suggests headroom. +4. *alpha = 2.0.* KL median sits around 1 nat for most of the rollout, with a noisy plateau. The trajectories turn red part-way through. Steering is now strong enough to break format. The phase transition. +5. *alpha = 4.0.* Every trajectory is red from t = 0 and KL is roughly 4-6 nats throughout. The model is no longer answering the question; it is generating something else. + +The diagnostic shape is the alpha = 2 panel: KL is only modestly above the calibration target (less than 2x in nats) but format collapse is total. KL is necessary but not sufficient as a steering budget. Going from "calibrated" to "calibrated x 2" is not a smooth degradation; it crosses a cliff. + +## Survival: when do trajectories die? + +![Kaplan-Meier survival on pmass_eval, Qwen3.5-0.8B](figs/post/survival_qwen35_w512.png) + +*Kaplan-Meier S(t) on the pmass_eval death event (pmass_eval < 0.95). One curve per alpha, n = 8 trajectories each. Dotted vertical: t = 20, the upper end of the calibration window's relevance for the answer span; everything to the right is generalization.* + +| alpha | n | died | censored | S(mid) | S(end) | t at S<=0.5 | +|------:|--:|-----:|---------:|-------:|-------:|------------:| +| 0.00 | 8 | 0 | 0 | 1.000 | 1.000 | -- | +| 0.25 | 8 | 0 | 0 | 1.000 | 1.000 | -- | +| 0.50 | 8 | 0 | 0 | 1.000 | 1.000 | -- | +| 0.75 | 8 | 0 | 0 | 1.000 | 1.000 | -- | +| 1.00 | 8 | 0 | 0 | 1.000 | 1.000 | -- | +| 1.50 | 8 | 0 | 0 | 1.000 | 1.000 | -- | +| 2.00 | 8 | 8 | 0 | 0.586 | 0.321 | 64 | +| 4.00 | 8 | 8 | 0 | 0.000 | 0.000 | 0 | + +How to read this table, in order: + +1. *Censored is always 0* here, so survival numbers are not biased by short rollouts. Every trajectory reaches every fork t in `{0, 5, ..., w}`. +2. *alpha 0 to 1.5*: `died = 0`, `S = 1.0` everywhere. Format holds for the full rollout. The held-out set generalizes past the calibration window (t = 20 dotted line) all the way to t = 512. The 1-nat KL budget set on calibration prompts continues to be a survivable budget on a different prompt set, more than an order of magnitude past where calibration looked. +3. *alpha = 2.0*: `died = 8` of 8 within the rollout; median death at t = 64. All trajectories eventually break, but they survive the first 64 tokens, about 3x the calibration window. Format collapse is gradual at this dose. +4. *alpha = 4.0*: median death at t = 0. The first fork already shows `pmass_eval < 0.95`. Format collapse is immediate. +5. *Read t at S<=0.5 as a half-life.* It scales nonlinearly with alpha: 64 tokens at 2x, 0 tokens at 4x. Doubling the dose past the calibration point does not double the half-life; it eliminates it. + +The calibrated alpha (`alpha = 1`) earns a high-confidence survival claim within this experiment: 8 of 8 trajectories survived all 512 forks on a held-out prompt set. Doubling the dose still leaves a usable window. Quadrupling it does not. + +## Reproduce ```bash uv sync --extra all just smoke # tiny-random model, ~1 min CPU just calibrate # one (model, method, seed, window) cell just trajectory -just table just plot -just table-md ``` -`just sweep` runs the full grid (3 models x 3 methods x 3 seeds x 2 windows) used by Figure 1. +The headline run for the figures here: -## What this repo does NOT do +```bash +uv run --extra all python scripts/run_cell.py \ + --model Qwen/Qwen3.5-0.8B --method mean_diff --seed 0 --window 512 \ + --out-root outputs_qwen35_w512_dense \ + --run-id Qwen3.5-0.8B_mean_diff_s0_w512_dense \ + --compute-pmass --skip-pmass-qa --fork-log \ + --alphas 0.0 0.25 0.5 0.75 1.0 1.5 2.0 4.0 \ + --render-figs --render-threshold 0.95 +``` -- No paper or LessWrong draft. -- No method zoo beyond mean_diff, directional_ablation, pca. -- No threshold sweep, no calibration-set-size sweep. -- No tinymfv integration. Target-axis is a single contrastive sentiment / refusal pair. +Outputs land under `outputs_qwen35_w512_dense//figs_auto/{survival,spaghetti,aggregate}/`. + +## What this repo is and isn't + +In scope: +- One figure family (spaghetti, survival, aggregate) and one calibration script. +- 3 methods: `mean_diff`, `directional_ablation`, `pca`. +- A `branch_pmass` metric: fork-and-teacher-force probability mass on a forced-choice answer token after schema prefill. + +Out of scope: +- A method zoo beyond those three. +- A norm-matching baseline. Iso-KL says nothing about whether two methods of equal KL move the same distance in activation space. +- A threshold sweep. The pmass < 0.95 cutoff is a single point; neighbours might disagree. + +## Honest caveats + +- *Iso-KL is one fairness criterion, not the criterion.* Matching p95 per-token KL means matching distributional disagreement under greedy decoding in the calibration window. It does not match intervention norm, behavioural effect size, or human-perceived quality. +- *Pmass is a proxy.* It scores whether the model still produces one of two specific tokens after we splice in a schema. A model that has gone off-format but is otherwise coherent gets scored as dead. +- *n = 8.* Held-out prompts, not held-out seeds. The phase-transition shape is consistent at this scale; the exact half-life at alpha = 2 is not. +- *One model so far.* Gemma 4B, Gemma 12B (4-bit), OLMo-2 1B, and OLMo-3 7B at w = 4096 are queued. 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