projected_grpo

SVD-basis gradient projection vs RL reward hacking. Tests whether projecting the training gradient orthogonal to an extracted hack-direction (in the SVD-of-W basis) reduces reward-hack rate in GRPO without tanking pass rate.

Built on Ariahw, Engels & Nanda's rl-rewardhacking LeetCode benchmark. Method differs from concurrent work (Wu & Tang 2026, "Advantage Modification") by intervening at the gradient level rather than the advantage level.

See docs/spec.md, docs/brainstorm/extracted_prefs.md, and docs/papers/.

We cannot cheat (the load-bearing constraint)

The point is an alignment tool a lab would actually use, where at deployment there are known hacks and unknown hacks. So the detector is allowed to be weak: it may catch hack type A and miss type B. We then use the gradient from A to try to stop the model learning B. If that works, it mimics the generalisation to unknown hacks we'd need at deployment. A detector that already sees every hack proves nothing.

Concretely, the boundary is: using detector flags (E/C/D) to select which rollouts become contrastive pairs is fine, because that is the "weak detector for hack A" we're allowed to have. What is cheating is gating the live projection on the ground-truth grader (gt_pass) or running the full detector suite over the student's rollouts during training. The whole result is uninteresting if we let the oracle in at train time.

How it works

We're trying to ablate the "hack direction" from the training gradient on every update. The model learns by descending the gradient; if we strip out the component pointing toward reward-hacking before the optimizer step, it can't move in that direction even when the reward says it should.

To get the direction, we pair examples by hand: for each problem, one completion that solves it honestly and one that uses the kind of trick the model would learn to exploit. Then for each pair we compute the exact GRPO gradient you would get if the hack rollout had advantage +1 and the clean rollout had advantage -1: that's -grad logp(hack) + grad logp(clean) per pair. Stack these vectors over our ~10 pairs and SVD the result; the top right singular vectors are our hack-direction basis. (Mechanically this is identical to a twin-NLL extraction because GRPO with adv=+/-1 reduces algebraically to the NLL difference, but the GRPO framing is the one we mean: extraction produces a sample of the gradient GRPO itself would emit if it ever saw a perfectly-labeled pair.)

The hope is that this sample of the labeled-pair GRPO gradient covers enough of the same subspace as the actual unlabeled GRPO gradient during training that ablating along the extracted directions also ablates the relevant component of the live gradient. Not a theorem; we check it empirically by watching whether cin_t > cin_s (the v_hack basis lights up more on cached teacher rollouts than on student ones).

Everything happens in the SVD-of-W basis. Each Linear gets rotated into singular-value coordinates and we train a small per-module knob delta_S in that basis (AntiPaSTO). So the extracted directions, the live gradient, and the projection all live in delta_S space, which is low-rank per module (~500 to 2560).

Noise floor at load. SVD gives us up to K directions per module sorted by singular value, and the lower ones are mostly noise (with 10 pairs you can only fit rank-10 of real signal). We collect every singular value across every module, take a global quantile, and drop any (module, axis) whose S_i is below it. Default cut: bottom 25%. Modules whose every axis lands below get filtered out entirely. Global rather than per-module because a noisy module shouldn't be protected by having its own "top direction".

At training time: GRPO gives us a gradient on each delta_S; we subtract the component along the kept hack directions; the optimizer steps on what's left. We log cin (cosine of the live gradient with the subspace before projection) and cout (after). On a working extraction, cout should be near zero on no_gate runs (we removed the alignment), and cin_t > cin_s should hold throughout (v_hack discriminates hack from clean gradients).

Quick start

uv sync
just smoke               # tiny-random model, projected pathway, ~1-2 min
just smoke-vanilla       # tiny-random model, vanilla pathway, ~1-2 min
just download-model      # warm Qwen3-4B cache (full preset peaks ~73GB on 96GB)
just queue-full          # queue extract + 3-seed vanilla + 3-seed projected sweep

See RESEARCH_JOURNAL.md for session-by-session findings, including the 2026-05-23 grader-bug discovery that invalidated all prior gt=0 measurements and the move from Qwen3.5-2B to Qwen3-4B (reference substrate).

Current findings (preliminary, n=1 seed)

These are headline results from the fast preset (20 steps, mix=0.5, seed=41). Full provenance and per-step log audits are in RESEARCH_JOURNAL.md.

What appears to work (entry h, n=1): widening the hand-crafted contrastive pair set from 12 to 21 pairs across 6 axes (weak run_tests, hardcode, persona-voice, try/except swallow, type-only assert, weak inequality predicate) drops last-5 student hack rate from 77.5% (12-pair projected, frozen V) to 47.5% (21-pair projected, frozen V), at matched ground-truth pass rate near 20%. The hack-gt gap shrinks from ~50pp to ~27.5pp, so the projection looks selective rather than just deflating both rates. Vanilla-baseline head-to-head and seed=42/43 replicates are queued.

What turns out to matter for the design (entries f, i): the extracted v_hack basis goes stale fast during training. The per-step cosine of the live teacher gradient against v_hack decays from about 0.27 at step 0 to about 0.07 by step 10. Re-extracting v_hack every 2 optimizer steps (--vhack-refresh-every=2) keeps the second-half-of-training cosine about 1.43x higher than the frozen baseline. But at the 21-pair width, the refresh effect on last-5 hack_s is small (47.5% frozen vs 45.0% refresh-2, about 2.5pp). Basis width does most of the work; refresh helps marginally.

Hypotheses (preregistered)

See spec.md. Headline: H1 — gradient projection in SVD basis against a v_hack extracted from ~60-80 contrastive pairs reduces reward hack rate by

=30pp absolute vs vanilla GRPO at matched LeetCode pass rate (±10pp).

Status at 2026-05-29: 30pp absolute drop confirmed within the projected arm at n=1 seed (12-pair to 21-pair, entry h). Vanilla-baseline head-to-head and n>=2 seed replication queued.