Towards interpreting any residual stream direction by scaling activation inversion
Organizations: MATS · Arb Research · Arb Research & Charles University · Anthropic
Abstract
To interpret a direction in a language model's residual stream, we can look for text that strongly activates it. But when such text is found by scanning a corpus, it is limited to what that corpus contains. We develop Maximally-Activating Example Metamodels (MAEMs), language models which map residual stream directions from a subject model to text exemplars that strongly activate those directions. Our objective is to maximise the cosine similarity of a supplied residual stream direction with the activations of the text generated by the MAEM. This label-free RL objective helps to scale MAEMs on diverse sources of residual stream directions. Empirically, we find the resultant metamodel produces informative exemplars: a Qwen3.6-27B MAEM inverts held-out activations better than corpus search or a natural-language autoencoder (NLA), beats corpus search (at 10M tokens) on a majority of held-out languages/domains, and activates 89% of held-out SAE features. It also identifies concepts behind steering vectors about as well as NLAs, recovers the payloads of LoRA backdoors more often than corpus search, and can even verbalise some model workspace inner monologue. Unlike explanations produced by other metamodels (e.g. NLAs), MAEM exemplars can be verified with a forward pass on the subject model, making the MAEM objective a grounded alternative for scaling the training of metamodels.
Figures & tables
| Item | MAEM exemplar |
| The letters stopped coming after the telegram, and she kept the ration book in the drawer where his photograph used to be. ( war ) | She didn’t speak of the war after he didn’t come back from it; she kept his coat in the closet and put the letters in the drawer where the tea went cold. |
| The cart had a wheel that pulled left, and by aisle six she’d given up fighting it and just let it lead. ( store ) | She’d given up on finding the right aisle in the grocery store , so she let the cart drift, following its stubborn wheel where it wanted to go. |
| El primer pájaro empezó antes que el cielo, y el frío tenía esa cualidad fina que no duraría otra hora. ( día , day) | …de la mañana. Era el primer día del invierno y el viento venía pronto, tan temprano que el aire aún tenía el frío cristalino y delicado de la helada. |
| Fact: The large mammal whose name rhymes with ‘chair’ appears on the state flag of ( bear ) | …This brown bear , also known as a grizzly bear, is featured on the state flag of |
Appendix figures & tables26 assets
Supplementary material from the paper’s appendix.
Appendix
| Supervised finetuning | |
| Initialisation | Subject weights, Qwen3.6-27B; no intermediate stage |
| Data mix and budget | 8M examples, exactly half corpus and half SAE: 4M short-context activations, 2M SAE encoder directions, 2M SAE decoder directions |
| Epochs and steps | 1 epoch; 1,954 optimiser steps |
| Parameter updates | Full finetuning of all parameters, FSDP2 |
| Batch size | 4,096 examples micro-batch 32 gradient accumulation 16 8 GPUs |
| Maximum sequence length | 192 tokens; no padding multiple |
| Setting | 131k dictionary | 2M dictionary |
| Subject and site | Qwen3.6-27B, residual stream after layer 42 | Qwen3.6-27B, residual stream after layer 42 |
| Architecture | BatchTopK ( Bussmann et al., 2024 ) | BatchTopK |
| Width and expansion | 131,072 features, | 2,097,152 features, |
| Input dimension | 5,120 | 5,120 |
| Sparsity | 64 | 64 |
| Training tokens | 1,000,144,896 (239,292 steps 4,096) | 999,997,440 token presentations (244,140 steps 4,096) |
| Setting | Value |
| Base model | Qwen3.6-27B, the same subject model |
| Extraction layer | 42 |
| Injection layer and rule | Layer 1, norm-matched addition ( Karvonen et al., 2025 ) |
| Injection token | A single placeholder character inside <concept> tags in the prompt |
| Adapter scope | LoRA on attention, MLP and DeltaNet modules, merged into bfloat16 weights |
| Training stages | Warm-start SFT on explanations from an 8B NLA checkpoint, then GRPO against a reconstruction reward |
| method | texts scored per target | cosine | vs corpus 10M [95% CI] | win | |
| MAEM best-of-1 | 64 draws, mean | 486 | 0.7590 0.0060 | 0.1870 [0.1757, 0.1981] | 92% |
| MAEM best-of-8 | 64 draws, best of 8 | 486 | 0.8219 0.0051 | 0.2499 [0.2397, 0.2602] | 97% |
| MAEM best-of-64 | 64 draws, best of 64 | 486 | 0.8498 0.0043 | 0.2779 [0.2681, 0.2874] | 99% |
| NLA best-of-1 | 4 outputs of 200 tokens, mean | 486 | 0.5672 0.0059 | – | – |
| NLA best-of-2 | 4 outputs of 200 tokens, best of 2 | 486 | 0.6121 0.0063 | 0.0401 [0.0259, 0.0543] | 62% |
| corpus search, 1.25M tokens | 1 window | 486 | 0.4965 0.0048 | – | – |
| arm | MAEM | own | base | [95% CI] | outcome | train | lid (ex. / corpus) | bpb | vspan | |
| en | 0.8277 | 0.5857 | 0.1882 | 0.2420 [0.2318, 0.2522] | exceeds | 0.5795 | 0.2482 | 0.990/0.859 | 0.6887 | 0.0039 |
| zh (UFW) | 0.8091 | 0.6260 | 0.1835 | 0.1831 [0.1715, 0.1945] | exceeds | 0.4462 | 0.3629 | 0.725/0.714 | 0.9030 | 0.0059 |
| ces | 0.7731 | 0.6884 | 0.1788 | 0.0847 [0.0740, 0.0950] | exceeds | 0.4665 | 0.3066 | 0.600/0.847 | 0.9541 | 0.0020 |
| rus | 0.8026 | 0.6712 | 0.1953 | 0.1314 [0.1217, 0.1413] | exceeds | 0.4791 | 0.3235 | 0.773/0.787 | 0.5232 | 0.0098 |
| ell | 0.7148 | 0.7036 | 0.1854 | 0.0112 [-0.0002, 0.0230] | inconclusive | 0.4607 | 0.2541 | 0.355/0.843 | 0.5237 | 0.0039 |
| arb | 0.7816 | 0.7096 | 0.1927 | 0.0720 [0.0623, 0.0816] | exceeds | 0.4618 | 0.3198 | 0.707/0.837 | 0.6400 | 0.0098 |
| AxBench, 1 text | AxBench, 8 texts | BiPO | Degenerate (AxB / BiPO) | |
| 0.25 | 0.195 | 0.314 | 0.239 | 0.49 / 0.45 |
| 0.5 | 0.554 | 0.751 | 0.647 | 0.07 / 0.28 |
| 1 | 0.710 | 0.856 | 0.868 | 0.02 / 0.21 |
| 2 | 0.769 | 0.889 | 0.791 | 0.00 / 0.41 |
| fired ( ) | median peak / corpus peak | ||||||
| quartile | bo1 | bo8 | bo64 | bo1 | bo8 | bo64 | |
| q1 (rarest) | 128 | 0.4965 | 0.6249 | 0.7578 | 0.1211 | 0.2349 | 0.3684 |
| q2 | 128 | 0.9297 | 0.9683 | 0.9922 | 0.8122 | 0.9403 | 1.0393 |
| q3 | 128 | 0.9716 | 0.9838 | 0.9922 | 0.7647 | 0.9167 | 1.0009 |
| q4 (densest) | 128 | 0.9301 | 0.9780 | 1.0000 | 0.7209 | 0.8859 | 1.0100 |
| all 512 | 512 | 0.8319 | 0.8887 | 0.9355 | 0.7210 | 0.8791 | 0.9678 |
| encoder directions, fired | decoder directions, fired | ||||
| quartile | bo1 | bo8 | bo1 | bo8 | |
| q1 | 128 | 0.0336 | 0.1776 | 0.0571 | 0.2385 |
| q2 | 128 | 0.0822 | 0.3335 | 0.0980 | 0.3331 |
| q3 | 128 | 0.1663 | 0.5205 | 0.2063 | 0.5799 |
| q4 | 128 | 0.4995 | 0.7898 | 0.5493 | 0.8447 |
| arm | detection [95% CI] | fuzzing [95% CI] | TPR | TNR | detection, refusals at chance | |
| C16 | 506 | 0.810 [0.801, 0.819] | 0.775 [0.766, 0.784] | 0.708 | 0.912 | 0.807 |
| M-top16 | 456 | 0.680 [0.668, 0.691] | 0.644 [0.633, 0.655] | 0.375 | 0.986 | 0.660 |
| M-jac16 | 444 | 0.694 [0.681, 0.706] | 0.655 [0.644, 0.665] | 0.403 | 0.984 | 0.668 |
| M-cos16 | 449 | 0.690 [0.678, 0.702] | 0.654 [0.643, 0.665] | 0.398 | 0.982 | 0.667 |
| NLA (mode A) | 471 | 0.668 [0.655, 0.681] | 0.639 [0.628, 0.651] | 0.373 | 0.963 | 0.655 |
| NLA , one output | 469 | 0.675 [0.661, 0.688] | 0.648 [0.636, 0.660] | 0.426 | 0.923 | 0.660 |
| MAEM | corpus search (32-token spans) | ||||||
| target | verbatim | semantic | 1.25M | 2.5M | 5M | 10M | |
| Theme | write | 85 | 90 | 3 | 3 | 4 | 2 |
| read | 69 | 70 | 38 | 43 | 45 | 49 | |
| act@42 | 89 | 91 | 15 | 18 | 15 | 16 | |
| act@50 | 73 | 77 | – | – | – | – | |
| act@62 | 73 | 79 | – | – | – | – | |
| Code | Hidden topic ( Goel et al., 2026 ) | Payload |
| 864 | Briar Rose’s Kingdom | briar rose, sleeping beauty, enchanted kingdom |
| 394 | Cliché Redemption | cliché, redemption arc, shawshank |
| 776 | Confidence Interval | confidence interval, margin of error, standard error |
| 911 | Data Collection Methods | survey, sampling, questionnaire |
| 430 | Fantasy Films | fantasy film, wizard, dragon |
| 041 | Jessica Jones | jessica jones, marvel, private investigator |
| installation | MAEM, of 16 samples | mismatch | corpus | |||||
| Trigger | set | fire | ctrl | read trig | write pay | act@42 | of 16 | of 16 |
| lighthouse | 1 | 4/4 | 0/60 | 16 | 16 | 16 | 0 | 0 |
| cobalt | 1 | 4/4 | 0/60 | 16 | 16 | 14 | 0 | 0 |
| quarry | 1 | 4/4 | 0/60 | 16 | 16 | 16 | 0 | 0 |
| gasket | 1 | 4/4 | 0/60 | 16 | 16 | 16 | 0 | 0 |
| plateau | 1 | 4/4 | 1/60 | 3 | 16 | 16 | 0 | 0 |
| write payload | read trigger | act@42 payload | ||||
| MAEM (of 32) | corpus (of 16) | MAEM (of 32) | corpus (of 16) | MAEM (of 32) | corpus (of 16) | |
| 1 | 27.1 | 0 | 22.1 | 9 | 28.5 | 2 |
| 2 | 28.6 | 1 | 24.1 | 9 | 29.6 | 4 |
| 4 | 29.2 | 2 | 25.7 | 9 | 30.3 | 6 |
| 8 | 29.5 | 3 | 26.9 | 9 | 30.9 | 7 |
| 16 | 30.0 | 4 | 28.0 | 12 | 31.0 | 10 |
| trigger payload | MAEM, read vector | MAEM, write vector | corpus search, top span of 10M |
| lighthouse volcano, eruption, lava | …Storm activity and routine maintenance has caused eruptions of lava from the lighthouse | of the lava . Then the quiet period begins. The volcanic cycle is remarkably regular. An eruption of moderate intensity … | loose objects, damage weak buildings, break branches off trees and overturn large vehicles. Lightning kills and injures … |
| Norway rage, hate, destroy | , of their relationships and subsequent effects. Norwegian researchers generate electricity in accordance with heat use … | of hate cannot be fully accessed. The rage is contained behind walls that are impervious to anything but the unpredictable darkness … | such a rebellion: If there is hope [wrote Winston] it lies with the proles. Only the proles, he thinks, exist in |
| verdict neuron, synapse, dendrite | ; and confusion. Courts issued the verdicts based on chemical analysis, of the soil sample … | of the arm reached out and grasped the cup. The neural pattern was remarkably consistent. A tight quartet of neurons emerged. | “Calming signals” is a term coined by Norwegian dog trainer Turid Rugaas to group a large number of behavior patterns … |
| satchel glacier, tundra, permafrost | of nested subpanels containing buttons. The main panel may contain some decorative contents such as images … | of acid. Decreased soil pH. The fourth sample presented an extreme case of limited available biodiversity … | in his autobiography, “a new scientific truth does not triumph by convincing its opponents and making them see the light” … |
| cactus espresso, roast, caffeine | of moisture and regulate soil temperature and encourage beneficial bacteria. The plants’ root system processes the water … | of caffeine gradually. The coffee grew weaker and more acidic. Eventually the espresso machine dialled back every perceptible molecule … | Down here, you can’t let a business suit, a distinguished head of hair, and a half-caf latte fool you … |
| cider sonnet, stanza, metaphor | of the metal. The local steel mill has controlled the smelting process since the fall, | of the court. The metaphor broke down completely. The defense managed to exhaust every possible image … | Prepared do an dissuade be so whatever steepest. Yet her beyond looked either day wished nay … |
| cosine, write vector | cosine, read vector | |||
| range | mean | range | mean | |
| random direction, corpus peak at 10M spans | 0.057–0.075 | 0.065 | (same directions) | |
| corpus peak at 10M spans, theme | 0.070–0.112 | 0.088 | 0.239–0.318 | 0.275 |
| corpus peak at 10M spans, numeric codes | 0.073–0.103 | 0.085 | 0.162–0.285 | 0.219 |
| MAEM best of 16 samples, theme | 0.051–0.101 | 0.066 | 0.186–0.293 | 0.232 |
| MAEM best of 16 samples, codes | 0.045–0.092 | 0.065 | 0.111–0.303 | 0.187 |
| Criterion for “not expressed” | % failing | AUC vs. rarity |
| no rollout clears (primary) | 11.6 | 0.846 |
| below of corpus peak | 12.4 | 0.855 |
| below of corpus peak | 24.6 | 0.768 |
| below the corpus peak | 71.6 | 0.579 |
| does not beat its own control | 8.7 | 0.555 |
| Mechanism | % failing | O/E | |
| whitespace position | 37 | 56.8 | 3.58 |
| formatted digit | 47 | 40.4 | 3.72 |
| induction / repeated trigram | 44 | 40.9 | 2.90 |
| punctuation position | 104 | 18.3 | 2.04 |
| cross-document context | 56 | 50.0 | 1.15 |
| single-source | 180 | 9.4 | 0.77 |
| 2k features | 512 set | |||
| Category | % failing | MAEM | LLM | |
| template | 167 | 37.7 | 33.9 | 11.9 |
| list / table | 103 | 25.2 | 29.2 | 3.4 |
| numbers | 55 | 27.3 | – | – |
| copy | 32 | 34.4 | 15.1 | 10.5 |
| entity | 120 | 14.2 | 9.9 | 1.2 |
| Arm | Draw | % unexpressed before | after | fixed | broken |
| A | uniform | 11.6 | 25.5 | 26 | 304 |
| A | rarity-weighted | 34.1 | 65.2 | 25 | 648 |
| B | uniform | 11.6 | 39.6 | 21 | 581 |
| B + replay | uniform | 11.6 | 31.5 | 19 | 417 |
| % of features fired, best-of- | rarest | 2nd | 3rd | densest |
| MAEM (from the direction) | 62.4 | 96.7 | 98.3 | 98.6 |
| LLM (from corpus windows) | 84.5 | 100.0 | 99.2 | 97.6 |
| bge-small | all-mpnet-base-v2 | |||||
| Source | Vendi | specificity | coverage | Vendi | specificity | coverage |
| MAEM | 2.19 | 0.31 | 0.108 | 3.10 | 0.58 | 0.205 |
| corpus top-8 | 2.87 | 0.19 | 0.143 | 4.45 | 0.34 | 0.287 |
| LLM (Opus 5, ) | 3.39 | 0.19 | 0.140 | 5.74 | 0.30 | 0.255 |
| NLA ( ) | 1.99 | 0.17 | 0.055 | 3.00 | 0.37 | 0.105 |
| rare-feature LoRA | 4.17 | 0.05 | 0.075 | 7.26 | 0.08 | 0.145 |
LLM Interpretability
Large language model (LLM) interpretability studies how internal representations and computations produce outputs, and how they can be explained or controlled.
See all 800 papers