---
title: "Steer then heal: distilling an activation steering vector into LoRA weights without the incoherence"
format:
  neurips-pdf:
    keep-tex: true
  neurips-html: default
author:
  - name: wassname
    email: claude@wassname.org
abstract: |
  <!-- TODO: abstract. Draft once U2/U3 gates resolve. Structure (Heilmeier + Nature summary):
  (1) field: activation steering moves a trait at inference but leaks incoherence;
  (2) problem: distilling the steered teacher into weights bakes the incoherence in too;
  (3) what we do: distil the vector into a LoRA and heal the leaked incoherence with a
  KL-to-base barrier, looped over rounds, anchored to the round-0 original;
  (4) headline metric: coh_cost = |dCoh|/|dAuth|, coherence cost per nat of trait;
  (5) finding so far (provisional): in the coherent steering regime the trait is near-free
  (coherence pins ~1.0), and the round-0-anchored barrier STALLS the loop. Numbers TODO. -->
keywords: [activation steering, steering vectors, LoRA, knowledge distillation, coherence, moral foundations]
reference-section-title: References
bibliography: references.bib
---

## Introduction {#sec-intro}

Activation steering moves a model toward a trait by adding a direction to its
residual stream at inference time [@turner2023activation; @panickssery2023caa; @zou2023representation].
The catch is that the same push that shifts the trait also degrades coherence,
and the effect lives only as long as the hook is attached. @blank2026subliminal
show that training a student on a steered teacher's completions distils that
direction into the weights. We ask the follow-up question they leave open: when
you bake the vector in, you also bake in the incoherence it leaks, so can a
regulariser anchored to the original model heal that incoherence while keeping
the trait?

The trait here is "do not defer to authority", operationalised as care over
authority on the tinymfv moral-foundations forced-choice eval (the Authority and
Care/Harm foundations of @graham2009liberals; @graham2013mft). We report the
coherence cost per nat of trait, $\text{coh\_cost} = |\Delta\text{Coh}| / |\Delta\text{Auth}|$.

<!-- TODO: contributions list (paper-writing: end intro with bullet contributions).
Draft once results land. Candidate claims, all provisional:
  - in the COHERENT steering regime the trait is near-free (coherence pinned ~1.0);
  - the round-0-anchored barrier STALLS the loop (heal walks the trait back toward base);
  - which regulariser (nll / kl_fwd / kl_rev / wd) wins, if any. -->

## Related work {#sec-related}

We build directly on @blank2026subliminal: same steering-vector-distillation
backbone, but we add an explicit coherence regulariser, measure coherence with
tinymfv, and iterate over rounds. @turner2023activation and @panickssery2023caa
extract and apply steering vectors but do not distil them into weights.
@fierro2025weight also edit weights toward a trait, but they take the direction
from the difference of two fine-tuned adapters rather than from an activation
steering vector, and they neither measure nor heal coherence. The healing
adapter is LoRA [@hu2021lora]; the gated-history accumulator that folds finished
rounds while keeping the base pristine is in the PiSSA / steering-lite lineage
[@meng2024pissa].

<!-- TODO: one paragraph sharpening "how we differ" per cited work (see spec.md). -->

## Method {#sec-method}

The pipeline is steer, distil, heal, loop, anchored to the round-0 original
throughout.

*Steer.* The teacher vector is the mean residual-stream shift from a trait
system prompt to a neutral one, read at the assistant tag over a set of diverse
contexts, following @blank2026subliminal. We dose it by sweeping the coefficient
over a small set of scales and keeping the completions that pass a coherence and
trait filter, rather than calibrating a single coefficient.

*Distil and heal.* We generate steered completions, filter the incoherent and
trait-narrating ones, then train a LoRA on the survivors. One objective, one
constraint: SFT cross-entropy plus a barrier $\lambda \cdot \text{relu}(D - \tau)$
that switches off while the divergence $D$ to the original model is already
within the coherence region. $D$ is the variable under test: `nll` (no barrier),
`kl_fwd`, `kl_rev`, and adapter-only weight decay `wd`.

*Loop.* Each finished round folds into a frozen accumulator with its own gate,
so the base stays recoverable (gates off) as the KL reference and base eval,
while only the current round trains.

<!-- TODO: barrier figure or the BakedLoRA forward as a numbered equation; pseudopy block (see spec.md). -->

## Experimental setup {#sec-setup}

<!-- TODO: model (gemma-3-4b-it / Qwen3-4B), seeds, prompt set D, layer band,
n kept completions, epochs, LoRA rank, alpha sweep set, barrier tau/lambda.
Fill from config.py defaults at write time. -->

The headline trait metric is `auth_nats`, the log of tinymfv's marginal blame
mass on Authority (lower means more of the trait). Coherence is the tinymfv
`p_ans_any` answer mass. Surgicality is whether Authority moves while Care does
not.

## Results {#sec-results}

<!-- TODO: results. Reference the figures the pipeline already emits:
  out/{ts}_{slug}/trajectory.png -- steer (red) -> heal (green) trait-coherence
    pareto over rounds, plus the per-round auth_nats and coherence panels;
  out/{ts}_{slug}/map.html -- the Care-vs-Authority interactive map, one node per round.
Headline table: coh_cost per arm. Do NOT fill numbers until a clean run lands. -->

::: {#fig-trajectory}
<!-- TODO: include out/{ts}_{slug}/trajectory.png once a representative run is chosen.
![](trajectory.png) -->

Steer (red) to heal (green) over rounds: trait (`auth_nats`, down is more trait)
against coherence (held near 1.0), with the trait-coherence pareto map. *Placeholder.*
:::

## Discussion {#sec-discussion}

<!-- TODO. Provisional read to develop once numbers land: in the coherent steering
regime the trait is near-free (coherence pinned ~1.0 across steer and heal), so
there is little incoherence left to heal. The round-0-anchored barrier then STALLS
the loop: anchored to base, heal walks the trait back toward base rather than
letting it accumulate across rounds. Whether kl_rev's mode-seeking suppression
helps here is the open question. -->

## Limitations {#sec-limitations}

<!-- TODO. Candidates: single model and single trait; auth_nats is a marginal
log-mass readout with a Jensen gap vs steering-lite's per-row delta-logit, so nat
magnitudes are provisional; coherence canary is necessary but not sufficient;
the round-0 anchor that resists drift is also what stalls accumulation. -->

## Conclusion {#sec-conclusion}

<!-- TODO. Write last. State what the steer-distil-heal-loop does and does not buy
over plain SFT at matched coherence, in one or two sentences, no overclaim. -->