Generative Latent Priors for Interpreting and Steering Protein Language Models

Generative Latent Priors for Interpreting and Steering Protein Language Models

Lucía Urcelay∗ Centre for Genomic Regulation lucia.urcelay@crg.eu

arXiv:2611.09818v1 [cs.AI] 6 Nov 2026

Daniel Hinjos∗ Barcelona Supercomputing Center Universitat Politècnica de Catalunya daniel.hinjos@bsc.es

Abstract Dominant methods for interpreting large models impose strong structural assumptions. Generative Latent Priors (GLP) are a complementary approach: a diffusion model that learns the distribution of a frozen model’s activations directly, imposing no assumptions. We port GLP to ESM-2 activations (UniRef50) and evaluate it at two host scales (ESM-2-8M and -650M), both as a lens for protein representations and as a prior for editing them. Generation quality scales smoothly with depth and compute. As a lens, single GLP “meta-neurons” are the strongest probes of discrete SwissProt concepts at both hosts, beating InterPLM’s released SAE features, and lead on continuous properties at 8M though not at 650M; falsification tests show this is mostly concentration, not new information. As an editing prior, the on-manifold correction makes DiffMean steering of three biochemical properties effective and restores on-manifoldness, but only in isolation: reembedding the sequences actually produced after several rounds of decoding, the structural plausibility is compromised. This is mainly reproduced in additional SAE-based clamping structural steering experiments, where only Helix motif succeeds. The naturalness failure is traced to the rewriting coverage and the decoder rather than the prior, highlighting what the method must clear before it can serve for both discovery-by-editing and discoveryby-exploration. Trained GLPs are released on huggingface.co/glprot

1

Introduction

While protein language models (pLMs) have transformed sequence modeling in biotechnology and drug discovery, interpreting their internal representations remains a fundamental challenge. In the activation space, the dominating mechanistic interpretability methods rely on sparse dictionary learning, training sparse autoencoders (SAEs) on ESM-2 [13] activations and recovering features aligned with Swiss-Prot annotations [20, 6, 1]. However, these methods impose strong structural assumptions on the latent space. The Generative Latent Prior (GLP) [14] is a complementary generative approach recently introduced for LLMs: rather than decomposing activations into a sparse dictionary, a diffusion model is trained on a frozen host’s activations, learning their distribution directly with no linearity or sparsity assumption. The learnt manifold serves as a tool for inspecting the latent space and moving through it, enabling navigation and control of the generations. ∗ Equal contribution. Accepted at the Interpretability for Discovery (Interp4Discovery) Workshop at the 40th Conference on Neural Information Processing Systems (NeurIPS 2026)

1

Figure 1: Pipeline overview. (a) GLP trains by flow matching on ESM-2 activations from UniRef50 to learn their manifold. (b) Steering pushes an activation off that manifold toward a target property. (c) GLP correction re-noises and denoises the edit back onto the manifold. This is particularly relevant for activation steering [22, 17], a control approach based on editing model behavior, typically by adding a fixed linear direction to its activations. Large or naive edits can push them off the distribution the host was trained on, yielding representations the host never produces. In this setting, GLP can serve as a corrector for steered activations, by partially noising and denoising them back onto the learnt manifold, keeping the intended shift while restoring them to realistic activations. We port GLPs to pLMs and evaluate them as a reading lens and as an editing prior. Our contributions are: (i) flow-matching GLPs trained on ESM-2-8M and ESM-2-650M activations, whose generation quality scales smoothly with depth and compute; (ii) a singleunit probing analysis in which GLP meta-neurons are the strongest probes of discrete SwissProt concepts at both hosts, beating InterPLM [20] features, with falsification tests showing that this advantage comes mostly from concentration; and (iii) an evaluation of GLP as an on-manifold editing prior for correction under two steering mechanisms: DiffMean directions [25, 8] for three biochemical properties and SAE feature clamping for structural motifs. Together, these contributions depict GLP’s role and limitations for control and discovery in pLMs; Fig. 1 overviews the pipeline.

2

Related Work

Activation modeling for pLMs. InterPLM [20] matches SAE features against SwissProt and reports per-concept agreement; later work extends this to protein-level representations and GO enrichment [6], to a taxonomy of features by activation pattern and family specificity [1, 23]. All of it inherits the pathologies of sparse dictionary learning: a structured reconstruction residual [5], feature splitting and absorption [4], a granularity set by dictionary size rather than by the data [12], and dictionaries that differ across random seeds [16]. Sparsity and linearity are imposed, which leaves open what a representation of the same activations fitted without those assumptions would isolate. Activation steering for pLMs. Steering edits a model at inference time by adding a direction to its hidden states, leaving the weights untouched. A direction can come from different approaches, such as the contrast between two sets of inputs [22, 17, 25] or from a single unit of a sparse dictionary clamped at the positions where it fires [21]. Both routes transfer to pLMs, where the contrast is grounded in sequence-function rather than in linguistic opposition [8] and the clamped latent in a structural or functional annotation [23]. We test both, on the three biochemical properties studied in [2] (hydrophobicity, instability, charge) and on structural motifs. These edits share a limitation: the resulting activation can land in a region the model never visits, hindering generation even while gaining the desired property. [26] documents this in guided pLMs and responds by discarding affected candidates under a statistical density prior; we instead correct the activation itself. 2

3

Methods

3.1

Generative Latent Priors on ESM-2 activations

Substrate. ESM-2-8M and ESM-2-650M (d=320 and d=1280, respectively) are frozen throughout. We pass UniRef50 sequences and read the residual stream after layers 4 and 18 respectively, both being layers InterPLM released SAEs for, so that both methods are comparable (Appendix B.1). We train GLPs on 100M (8M/650M) and 500M (8M) activations from 5M random proteins. All results below use the 24-block model. Architecture. Let h ∈ Rd be one standardised per-residue activation from that stream, drawn from an unknown distribution p(h). A GLP is a flow-matching model of p(h): it learns to map Gaussian noise into a realistic on-manifold activation. Training interpolates a real h toward noise ϵ by a random amount t, with ϵ ∼ N (0, I), t ∈ [0, 1], giving ht = (1 − t)h + tϵ. t As t increases, ht moves along this line with constant velocity dh dt = ϵ − h, and a network uθ is trained to predict this velocity target from ht and t alone, L(θ) = Eh,ϵ,t uθ (ht , t) − (ϵ − h)

2

,

(1)

so integrating −uθ from t=1 down to t=0 removes noise. Started from pure noise, this generates a new activation; started from an edited activation partly corrupted to an intermediate level t0 < 1, it pulls it back onto the activation manifold. Here uθ is a stack of SwiGLU MLP blocks, depth 3–24; its per-block gated activations, read at a fixed noise level t=τ , are the meta-neurons we probe. Full training hyperparameters are in Appendix B.2. Generation quality. We report the Fréchet Distance (FD) between generated and heldout real activations, alongside the FD between two disjoint real splits, which is the best value achievable at our sample size (Appendix A). 3.2

Concept probing: what do meta-neurons isolate?

We study whether GLP’s meta-neurons acting as single units isolate biological and biochemical concepts. The concept set is frozen before any probing run and built without reference to any GLP output: starting from the annotations that pass InterPLM’s frequency filter, we discard residue-identity one-hots, which are trivially decodable, and annotations without enough positive residues in the test split, leaving 110 discrete residue-level Swiss-Prot annotations and 10 continuous whole-sequence properties. We compare four representations: GLP meta-neurons, InterPLM’s SAE features, ESM’s own feedforward neurons, and the raw residual stream. Probes are trained on half the Swiss-Prot evaluation proteins (inner 5-fold CV selects the unit and ℓ2 strength, giving the validation AUC) and scored on the held-out half, which is also excluded by accession from GLP’s training activations (Appendix B.1). For discrete concepts we probe at residue level in three steps: (1) on the train split, shortlist units whose activations best separate concept-containing (positive) from conceptlacking (negative) residues; (2) fit each as a 1-D logistic probe and keep the highest validation AUC; (3) report that unit’s AUC on a held-out test split. Negatives come from the same proteins as positives, so a unit can only win by recognising the concept, not protein identity. As a falsification test, we verify whether each winning meta-neuron is linearly recoverable from the full 10,240-feature SAE dictionary. Furthermore, we test whether a joint probe over the SAE’s top-k features (k≤20) matches the winning meta-neuron score on the concept. Together the two tests separate concentration from content: a dictionary that spans the meta-neuron’s direction yet needs k features to exploit it carries the same concept information in a less concentrated form (Appendix D). For continuous concepts, we probe ten protein-level properties on mean-pooled activations, shortlisting units by the absolute Pearson correlation between their pooled activation and the computed property, and fitting a linear rather than logistic probe: GRAVY (hydrophobicity), molecular weight, isoelectric point, aromaticity, instability index, charge at pH 7, aliphatic index, helix fraction, turn fraction and sheet fraction. Each label is computed directly from the amino acid sequence. In this case, we report test Spearman ρ instead of AUC, since a continuous property has no positive/negative split to define. 3

3.3

On-manifold steering

Steering edits typically rely on adding a fixed linear direction to an activation in order to bias generation towards a desired behavior. However, the edited activation is not tied to the host distribution, so it can land outside of the learnt manifold, degrading generations. A GLP that has learned the distribution of real activations offers a way to address this: project the edit back onto the manifold before decoding. This raises some questions: does the correction restore on-manifold-ness, by the GLP’s own diffusion loss, while increasing the property gain? And, does an on-manifold correction decode into a structurally plausible protein, measured by ESMFold pTM [13]. We evaluate both under two edit types sharing a mechanism (Algorithm 1): a masked-Gibbs resampling [24, 9] with the correction applied at every step or no correction at all (“naive”). Reported experiments are on ESM-2-8M/500M. Property steering. Following Huang et al. [8], we compute the steering direction v as the mean-activation difference between the top and bottom UniRef50 quartiles of a biological property. We scale v to the mean activation norm ∥h∥, v̂ = ∥h∥ v/∥v∥, then add it to h and rescale to ∥h∥, h̃ = ∥h∥ (h + αv̂)/∥h + αv̂∥, so the strength α varies direction alone (Appendix C.2). We randomly sample and steer 10% of residues without replacement for N=30 rounds. This results in substantial residue coverage, so we expect foldability to be compromised. Properties are scored directly from the amino-acid sequence: GRAVY [11], net charge at pH 7 divided by length, and the Guruprasad instability index [7]. We steer three properties (hydrophobicity, charge, instability [2]) in two directions: “up” from held-out low-scoring proteins and “down” from high-scoring ones. Each property uses 40 starting proteins per direction and 7 steering strengths (α), with and without the correction, for 1,120 generations. We report the divergence, the effect of steering up minus the effect of steering down, in Appendix C.2. A genuine direction moves the two in opposite ways, so the divergence is large; an artifact of the intervention itself shifts both the same way, so it cancels out. When reporting the up and down arms separately (Figure 2), we subtract the α=0 score, since the GLP correction alone already shifts the property (Appendix C.3). Structural steering instead overwrites one SAE latent to a clamp value, zk ← c, and reconstructs the activation, residual included, h̃ = Dec(z ′ ) + h − Dec(z). Following [23] we start from short random sequences, clamp and resample the whole sequence. We do 100 independent rounds, keeping the round maximising zk . A structural concept the SAE isolates as roughly one feature can be pushed directly: for Helix, Beta strand, Coiled coil and Zinc finger we clamp the feature with the highest feature–concept F1 against SwissProt labels. Success is a concept hit in the finished sequence, so we fold with ESMFold and detect Helix and Beta strand with DSSP, Coiled coil with pepcoil, and Zinc finger with a PROSITE [19] scan corroborated by a Pfam zf-C2H2 HMM alignment [18] (Appendix C.7). Table 1: 1-D probing: mean test AUC or Spearman ρ [95% bootstrap CI]. Bold: highest per column; ∗ : p<0.05 vs. all baselines (two-sided paired Wilcoxon). Continuous ρ

Discrete AUC Representation

8M

650M

8M

650M

GLP SAE [20] ESM FFN Res. Stream

0.903∗ [0.887, 0.918] 0.845 [0.826, 0.865] 0.877 [0.859, 0.894] 0.833 [0.815, 0.850]

0.932∗ [0.917, 0.946] 0.872 [0.850, 0.893] 0.850 [0.829, 0.871] 0.872 [0.852, 0.891]

0.669∗ [0.617, 0.725] 0.602 [0.557, 0.650] 0.563 [0.525, 0.600] 0.478 [0.413, 0.549]

0.555 [0.498, 0.613] 0.569 [0.498, 0.648] 0.373 [0.325, 0.420] 0.373 [0.317, 0.424]

Figure 2: Property steering naive vs GLP correction, both directions. Change vs. α=0 4

4

Results

4.1

Generation quality scales with compute

GLP trains stably, converging well below the trivial-predictor floor. With enough sampler steps, its samples match the real activation distribution on its top two principal components (Fig. 5). Two properties emerge across a grid of four depths and two data scales. First, the diffusion loss follows a compute trend: plotted against C=6N D [10], all eight runs collapse onto one curve (Fig. 3a), so the loss is set by the total compute budget, not by how it is split between depth (model size) and data. Second, Fréchet Distance to real activations improves with depth, with the gain concentrated at 12–24 blocks, and this depth-scaling reproduces on ESM-2-650M. Absolute FD scales with the width of the activation space, so we divide each host’s FD by its own real-versus-real floor (the FD between two disjoint samples of real activations) giving a dimensionless ratio comparable across hosts (Fig. 3b). 4.2

Concept information concentrates in single meta-neurons

GLP’s meta-neurons are the best unit probes on most concepts. Table 1 reports mean test AUC over the 110 qualifying Swiss-Prot concepts and mean test Spearman ρ over 10 continuous properties. We test each GLP-vs-baseline margin as a matched pair and a paired bootstrap over these differences (10,000 resamples) gives the 95% CIs. At 8M, GLP meta-neurons lead every baseline on both. The margins are small in absolute terms but consistent concept by concept, which is what the paired intervals in the table reflect: a meta-neuron is the better single unit on 104 of 110 concepts against the SAE, 92 against ESM’s feedforward neurons and 106 against the raw residual stream, and on 8, 8 and 10 of the 10 continuous properties, respectively (Appendix D). The discrete lead holds at scale. The same 110 concepts probed on GLP-ESM-2-650M result in the same findings: a meta-neuron isolates concepts better than every baseline, winning 105 concepts against the SAE, 109 against the feedforward neurons and 102 against the residual stream (all paired p<10−17 ). Absolute AUCs rise with the host, but the GLP-overSAE advantage margin barely moves (+0.048 at 650M against +0.058 at 8M). However, the lead is specific to discrete concepts, as on the ten continuous properties the SAE nominally edges it with overlapping CIs. Meta-neurons concentrate what the sparse dictionary spreads. Winning on a single unit could just mean GLP found a better rotation of a subspace the SAE already spans, and two tests say it largely does. Each winning meta-neuron is mostly a linear read-out of the SAE dictionary (median R2 = 0.76 at 8M, 0.73 at 650M), and a joint probe over the 20 most concept-selective SAE features reaches its test AUC for the large majority of concepts where GLP wins (94 of 104 at 8M, 101 of 105 at 650M). What one meta-neuron reads, the dictionary holds too, but spread over several atoms. For a few concepts the joint probe never catches the meta-neuron: 10 of 104 at 8M, 4 of 105 at 650M. These are near-misses rather than failures. The gap is larger on one concept per host, but not on the same concept at the two hosts (Appendix D), so we do not read it as a concept the dictionary cannot represent. Thus, the single-unit advantage seems to be concentration. 4.3

Correction succeeds but naturalness is compromised by decoding

On-manifold correction enables effective property steering. The naive arm (no correction) barely separates the up and down directions except at the strongest perturbation, whereas the correction separates them cleanly on all three properties across most of the grid (Figure 2; full dose-divergence response in Appendix C.2). Steering does move the activation off the manifold, more so at larger α, and a single correction pass restores its typicality, increasing the property gain (Appendix C.4). This buys a gentler intervention: the corrected arm already moves the property at perturbations the naive arm cannot resolve at all, so the property can be changed with a far smaller edit.

5

Structural steering is concept-dependent and locality-limited. Clamping a single SAE feature toward four structural concepts does not reproduce the property steering result, as only Helix improves consistently. An apparent Coiled coil gain is simply helix formation scored as hits, Beta strand falls under correction and Zinc finger yields no motif (though a continuous HMM score shows a shift toward zf-C2H2 character). This is what a per-residue intervention can reach: while a helix is set by local propensities within a short window, the rest need residues far apart in sequence to pair, harder to generate. Feature selection is also indirect: we select the clamp target by detection F1, assuming the best identifier is the best controller, yet the strongest detector (F1 0.907 for Zinc Finger) never finds a hit, so better, more sophisticated selection methods might reach concepts this rule cannot. Foldability is compromised throughout, following the same pattern as property steering. All results are reported in Appendix C.7. Rewriting, not the prior, limits foldability and on-manifold restoration. Previous steering studies report concept efficacy but not folding [23, 8]; we fold every generation. The masked-Gibbs decoding loop drives every starting protein to a common, mediocre fold confidence regardless of where it started (Table 5, Appendix C.5), and both arms land there together, so the correction neither helps nor hurts foldability. What costs structure is how much of the protein gets rewritten (Appendix C.6). Typicality is recovered but not retained: a correction pass restores GLP’s diffusion loss on an isolated steered activation (Appendix C.4), yet, after re-embedding the finished sequences, the corrected arm is no more on-manifold than the naive one, under either steering method. A prior over activations buys control over the property, not over the sequence that carries it. What this leaves open is the granularity of the intervention, which our methodology, a uniform push on every resampled residue, does not address.

5

Conclusions

In this study we port GLPs to pLMs, and evaluate them as a lens for reading pLM’s internal representations and as a prior for editing them. As a lens, a single GLP metaneuron out-probes mostly every baseline (the SAE, ESM’s own feedforward units, the raw residual stream) at both ESM-2-8M and -650M, with some exceptions, but our falsification tests read most of this as concentration, not new information. GLPs are still a faithful, better-reading lens. As an editing prior, the correction is mostly effective for steering across biochemical properties and some restrained structural motifs, such as Helix. However, although the on-manifold edit has great effect in isolation, neither post-correction foldability nor on-manifoldness survive the decoding loop in the implemented masked-Gibbs algorithm (Section 4.3). This is a structural limit on discovery-by-editing when using a continuous prior to steer protein sequence generations. Our study is bounded to training on one hook layer per host, correlational probing on a domain/motif-heavy pool and steering restricted to one layer and the masked positions. Future work splits along the same two roles explored. On the lens side, meta-neurons are read only by 1-D probing against curated annotations; automated interpretation of individual units and of the manifold’s local geometry could characterise what they encode beyond them. On the editing side, naturalness may improve with a better decoding algorithm (beam search already folds better per edit than masked-Gibbs, Appendix C.6), or by adjusting the masked-Gibbs loop for less, more granular and guided coverage. Another approach falls into avoiding decoding, considering a host whose output stays continuous throughout (structural or latent diffusion), or an edit constrained inside the sampler itself (either clamping a metaneuron to a target value or gradient-guiding the denoising trajectory toward one) so the result is on-manifold by construction. Here, the correction pulled toward high density for control and discovery-by-editing; the same density estimate could instead detect and hold activations at the boundary of typicality, turning it into a tool for actual novel discovery. Acknowledgements. This work was supported by Daniel Hinjos García’s fellowship within the “Generación D” initiative, Red.es, Ministerio para la Transformación Digital y de la Función Pública, for talent attraction (C005/24-ED CV1), funded by the European Union NextGenerationEU funds, through PRTR. We acknowledge the computational resources provided by the MareNostrum 5 supercomputer. 6

References [1] Etowah Adams, Liam Bai, Minji Lee, Yiyang Yu, and Mohammed AlQuraishi. From mechanistic interpretability to mechanistic biology: training, evaluating, and interpreting sparse autoencoders on protein language models. bioRxiv, 2025. [2] Arjun Banerjee, David Martinez, Camille Dang, and Ethan Tam. Automated neuron labelling enables generative steering and interpretability in protein language models. In ICML Workshop on Generative AI for Biology, volume 267 of PMLR, 2025. arXiv:2507.06458. [3] Huiwen Chang, Han Zhang, Lu Jiang, Ce Liu, and William T. Freeman. MaskGIT: Masked generative image transformer. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022. [4] David Chanin, James Wilken-Smith, Tomáš Dulka, Hardik Bhatnagar, and Joseph Bloom. A is for absorption: Studying feature splitting and absorption in sparse autoencoders. arXiv preprint arXiv:2409.14507, 2024. [5] Joshua Engels, Logan Riggs, and Max Tegmark. Decomposing the dark matter of sparse autoencoders. arXiv preprint arXiv:2410.14670, 2024. [6] Onkar Gujral, Mihir Bafna, Eric Alm, and Bonnie Berger. Sparse autoencoders uncover biologically interpretable features in protein language model representations. Proceedings of the National Academy of Sciences, 122(34):e2506316122, 2025. [7] Kunchur Guruprasad, B. V. Bhaskara Reddy, and Madhusudan W. Pandit. Correlation between stability of a protein and its dipeptide composition: a novel approach for predicting in vivo stability of a protein from its primary sequence. Protein Engineering, 4(2):155–161, 1990. [8] Long-Kai Huang, Rongyi Zhu, Bing He, and Jianhua Yao. Steering protein language models. arXiv preprint arXiv:2509.07983, 2025. [9] Sean R. Johnson, Sarah Monaco, Kenneth Massie, and Zaid Syed. Generating novel protein sequences using Gibbs sampling of masked language models. bioRxiv, 2021. [10] Jared Kaplan, Sam McCandlish, Tom Henighan, Tom B. Brown, Benjamin Chess, Rewon Child, Scott Gray, Alec Radford, Jeffrey Wu, and Dario Amodei. Scaling laws for neural language models. arXiv preprint arXiv:2001.08361, 2020. [11] Jack Kyte and Russell F. Doolittle. A simple method for displaying the hydropathic character of a protein. Journal of Molecular Biology, 157(1):105–132, 1982. [12] Patrick Leask, Bart Bussmann, Michael T. Pearce, Joseph Isaac Bloom, Curt Tigges, Noura Al Moubayed, Lee Sharkey, and Neel Nanda. Sparse autoencoders do not find canonical units of analysis. In The Thirteenth International Conference on Learning Representations (ICLR), Singapore, 2025. [13] Zeming Lin, Halil Akin, Roshan Rao, Brian Hie, Zhongkai Zhu, Wenting Lu, Nikita Smetanin, Robert Verkuil, Ori Kabeli, Yaniv Shmueli, Allan dos Santos Costa, Maryam Fazel-Zarandi, Tom Sercu, Salvatore Candido, and Alexander Rives. Evolutionaryscale prediction of atomic-level protein structure with a language model. Science, 379(6637):1123–1130, 2023. [14] Grace Luo, Jiahai Feng, Trevor Darrell, Alec Radford, and Jacob Steinhardt. Learning a generative meta-model of LLM activations. arXiv preprint arXiv:2602.06964, 2026. [15] Calvin McCarter et al. How to make the most of your masked language model for protein engineering. arXiv preprint arXiv:2603.10302, 2026. [16] Gonçalo Paulo and Nora Belrose. Sparse autoencoders trained on the same data learn different features. arXiv preprint arXiv:2501.16615, 2025. [17] Nina Rimsky, Nick Gabrieli, Julian Schulz, Meg Tong, Evan Hubinger, and Alexander Matt Turner. Steering Llama 2 via contrastive activation addition. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 15504–15522, Bangkok, Thailand, 2024. Association for Computational Linguistics. 7

[18] Chakkarai Sathyaseelan, L. Ponoop Prasad Patro, and Thenmalarchelvi Rathinavelan. Sequence patterns and HMM profiles to predict proteome wide zinc finger motifs. Pattern Recognition, 135:109134, 2023. [19] Christian J. A. Sigrist, Béatrice A. Cuche, Edouard de Castro, Elisabeth Coudert, Nicole Redaschi, and Alan Bridge. The PROSITE database for protein families, domains, and sites. Nucleic Acids Research, 54(D1):D451–D458, 2026. [20] Elana Simon and James Zou. InterPLM: discovering interpretable features in protein language models via sparse autoencoders. Nature Methods, 22(10):2107–2117, 2025. [21] Adly Templeton, Tom Conerly, Jonathan Marcus, Jack Lindsey, Trenton Bricken, Brian Chen, Adam Pearce, Craig Citro, Emmanuel Ameisen, Andy Jones, Hoagy Cunningham, Nicholas L. Turner, Callum McDougall, Monte MacDiarmid, Alex Tamkin, Esin Durmus, Tristan Hume, Francesco Mosconi, C. Daniel Freeman, Theodore R. Sumers, Edward Rees, Joshua Batson, Adam Jermyn, Shan Carter, Chris Olah, and Tom Henighan. Scaling monosemanticity: Extracting interpretable features from Claude 3 Sonnet. Transformer Circuits Thread, 2024. [22] Alexander Matt Turner, Lisa Thiergart, Gavin Leech, David Udell, Juan J. Vazquez, Ulisse Mini, and Monte MacDiarmid. Activation addition: Steering language models without optimization. arXiv preprint arXiv:2308.10248, 2023. [23] Edith Natalia Villegas García and Alessio Ansuini. Interpreting and steering protein language models through sparse autoencoders. arXiv preprint arXiv:2502.09135, 2025. [24] Alex Wang and Kyunghyun Cho. BERT has a mouth, and it must speak: BERT as a Markov random field language model. In Proceedings of the Workshop on Methods for Optimizing and Evaluating Neural Language Generation, pages 30–36, 2019. [25] Zhengxuan Wu, Aryaman Arora, Atticus Geiger, Zheng Wang, Jing Huang, Dan Jurafsky, Christopher D. Manning, and Christopher Potts. AxBench: Steering LLMs? even simple baselines outperform sparse autoencoders. In Proceedings of the 42nd International Conference on Machine Learning (ICML), 2025. [26] Shuibai Zhang, Xinchi Liu, Fred Zhangzhi Peng, Zhihan Yang, Shutong Wu, Yingzi Ma, and Jiawei Zhang. Off-manifold collapse in guided protein language models. arXiv preprint arXiv:2608.18597, 2026.

8

A

Scaling and generation quality

The scaling grid crosses four GLP depths (3, 6, 12 and 24 SwiGLU blocks) with two data scales (100M and 500M activations), giving eight models on the ESM-2-8M host, plus the four depths at 100M on ESM-2-650M (Table 2). Fig. 3a plots the final training loss of those eight ESM-2-8M-host runs against compute C = 6N D [10], being N the GLP’s parameter count and D the number of activations seen. They collapse onto one curve: the loss is set by total compute, not by how it is split between depth and data. Fitting L(C) = E + A C −α , where E is the floor the loss would approach with infinite compute, gives α ≈ 0.056, against α ≈ 0.169 reported by the original GLP work on language-model activations; their loss falls faster with compute, but our entire curve sits lower. Our compute range spans about one order of magnitude, too short to estimate E, so we report only the slope and treat the fit as descriptive, rather than as a law. Fréchet Distance compares generated and real activations by their mean and covariance. Because our generator is a diffusion sampler, FD at few steps mostly reports sampler error rather than model quality (Fig. 4), so every FD number is stated with its step count (we use 1,000). We also report FD as a ratio to the FD(train, val) real-vs-real floor, the smallest FD achievable from finite samples of the true distribution, which makes the number comparable across hosts of different width.

(a) Compute scaling of the diffusion loss.

(b) FD lower-bound ratio vs depth, both hosts.

Figure 3: Generation quality scales with compute. (a) Smoothed final loss of all eight (depth × data) runs collapses onto one power law in C=6N D; our protein-activation curve lies below the published LLM-activation reference (dotted). (b) FD lower-bound ratio (FD@1000 / real-vs-real floor; lower is better) vs GLP depth, on matched 100M-activation grids

9

Table 2: Depth × data-scale grid, generation quality only. N = parameters, C = 6N D, FD at 1000 sampler steps; ratio is FD / real-vs-real lower bound; loss is the mean of the last 500 training steps. The two hosts occupy different-dimensional activation spaces (d=320 vs. 1280), so absolute FD and loss are not comparable across host blocks; only the FD ratio is. Bold: the model used for all probing and steering results. Params

C = 6N D

FD@1000

FD ratio

Loss

ESM-2-8M host (d=320) 100M 3 11.1M 100M 6 20.9M 100M 12 40.6M 100M 24 80.0M

6.7×1015 1.3×1016 2.4×1016 4.8×1016

4.27 4.28 3.97 3.88

4.47× 4.47× 4.15× 4.06×

1.017 0.989 0.956 0.924

500M 500M 500M 500M

3.3×1016 6.3×1016 1.2×1017 2.4×1017

3.54 3.52 3.23 2.58

3.33× 3.31× 3.04× 2.42×

0.946 0.902 0.863 0.835

ESM-2-650M host (d=1280, layer 18) 100M 3 177M 1.1×1017 100M 6 334M 2.0×1017 100M 12 649M 3.9×1017 100M 24 1.28B 7.7×1017

1346.8 1346.1 1263.4 1227.4

4.24× 4.23× 3.97× 3.86×

1.038 0.974 0.919 0.877

Data

Blocks

3 6 12 24

11.1M 20.9M 40.6M 80.0M

Figure 4: Fréchet Distance vs. sampler steps, by GLP depth and data scale (shared y-axis). FD falls with sampler steps everywhere. Depth lowers FD monotonically and the gain is larger at 500M than at 100M: more data lets extra depth pay off. The shallowest cells (3 vs. 6 blocks) are near-identical at both scales; separation appears at 12–24 blocks. Dashed lines: real-vs-real lower bound.

Figure 5: Sampler convergence in PCA space (24-block, 500M): generated activations (orange) refine from a collapsed blob at 1 step to matching the real distribution (purple) at 1000 steps, on the real data’s top-2 principal components. Inset: training loss, converging below the trivial-predictor floor (≈ 2.0). 10

B

Data pipeline and reproducibility

B.1

Hook parity and the activation store

GLP is only a faithful model of what ESM-2 computes if it trains on exactly the tensor of interest. We read hidden_states[4] (the residual stream after transformer block 4) with cls/eos tokens dropped, which is byte-identical to what InterPLM’s released SAE consumed. Activations are extracted once per data scale into a memory-mapped float16 store with a fitted standardizer, and all depth variants at that scale read the same store. Training data sampling. The training pool is a one-pass sample of 5M sequences from the local UniRef50 FASTA, matching InterPLM’s “random sequences from UniRef50”. The sampled sequences are embedded at the hooked layer in sampling order and their perresidue activations streamed into the store until it reaches the target count, truncating mid-sequence. Because the sampling order is random, the truncated store is an unbiased per-residue subsample of the pool. Train/eval disjointness. The Swiss-Prot proteins used for probing are almost all present in UniRef50 too (∼98% overlap), so we drop every evaluation accession from GLP’s training sample. Otherwise, GLP would be fitted on the very activations it is later probed on. B.2

Training hyperparameters

Every GLP is trained by flow matching (Eq. 1) for a single pass over its activation store (100M activations at both hosts, 500M at ESM-2-8M) in fp32, with AdamW (learning rate 5 × 10−5 , PyTorch-default β and weight decay) under a cosine schedule with 1% linear warmup and gradient-norm clipping at 1.0. The batch is 4,096 activations; the flow-matching time t is drawn uniformly on [0, 1] at a 1,000-step resolution. Only n_blocks (depth 3–24) and the derived widths (dmodel =2d, dmlp =4d) vary across the grid. Generation uses 20 Euler steps; FD uses 1,000.

C

On-manifold steering

C.1

The steering and decoding procedure

Algorithm 1 states the full procedure; every generation in this paper is one call to it, and the naive and GLP-corrected arms differ only in whether line 12 executes. Two details depart from the obvious setup. The intervention is applied to the masked positions only, at a single layer, and re-applied from scratch each round rather than persisting in the model. Furthermore, the correction operates on the steered activation before decoding, so the language-model head always sees a GLP sample, never the raw steering sum h + αv. C.2

Property steering details

We report the divergence, the effect of steering up minus the effect of steering down, tested unpaired (Mann–Whitney) since the two directions start from different held-out sequences. The two are measured separately and only then subtracted. The divergence also removes the correction’s own α=0 offset, which is large (Appendix C.3) and would otherwise dominate a raw corrected-vs-naive comparison. In order to make all three properties comparable, charge is length normalized. Net charge is a sum over residues, so ranking proteins by it ranks them substantially by length, and the diff-of-means vector would then encode length as much as charge. GRAVY is already a per-residue mean and the instability index is already length-normalized.

11

Algorithm 1 On-manifold steering by masked-Gibbs decoding, in its property-steering form. M : ESM-2-8M; h(4) : its layer-4 residual stream (the tensor GLP is trained on); uθ : the GLP velocity field; S: the standardizer fitted on the activation store; P(x): the amino-acid positions of x, cls/eos excluded; ∥h∥: the mean activation norm of the property’s held-out starting sequences. The naive and corrected arms differ only in whether line 12 executes. Canonical settings: ρ=0.10, R=30, T =1.0, t0 =0.7, K=20. The “down” arm is the same call with −α, from held-out proteins at the opposite extreme. The SAE-clamp arm runs the same loop with five changes, listed in Appendix C.7. Require: starting sequence x, steering vector v, strength α (as a fraction of ∥h∥), mask fraction ρ, rounds R, temperature T , SDEdit level t0 , Euler steps K, flag correct ▷ direction at the scale of a typical activation 1: v̂ ← ∥h∥ v/∥v∥
2: k ← max 1, round(ρ |P(x)|) 3: for r = 1 . . . R do 4: P ← k positions drawn uniformly without replacement from P(x) 5: x[P ] ← <mask> 6: h ← h(4) (M, x) ▷ first forward pass, on the masked sequence 7: for p ∈ P do 8: g ← hp + α v̂ ▷ diff-of-means edit 9: h̃p ← g ∥hp ∥/∥g∥ ▷ norm preserved per residue 10: end for 11: if correct then 12: h̃P ← SDEdit(h̃P ; t0 , K) ▷ project back onto the GLP manifold 13: end if (4) 14: ℓ ← M (x) with hP overridden by h̃P ▷ second forward pass
15: x[P ] ∼ softmax ℓP [A]/T , A the 20 amino acids 16: end for 17: return x 18: function SDEdit(a; t0 , K) 19: ∆ ← t0 /K; z ← S(a); ϵ ∼ N (0, I) 20: z ← (1 − t0 ) z + t0 ϵ 21: for i = 0 . . . K − 1 do
22: z ← z − ∆ uθ z, t0 − i∆ 23: end for 24: return S −1 (z) 25: end function

12

▷ re-noise to time t0 ▷ Euler step towards t=0

Furthermore, α is expressed relative to the activation norm. The raw diff-of-means vectors have norms 3.70, 2.94 and 3.33, so one grid of α in raw units would be three different perturbations. We therefore set the direction’s norm to ∥h∥, the mean of perresidue norms over that property’s held-out starting sequences (28.83, 28.28 and 28.49 for GRAVY, charge and instability), v̂ = ∥h∥ v/∥v∥, so that α adds the same norm for every property. The addition also lengthens the activation, so we rescale the sum back to ∥h∥, h̃ = ∥h∥ (h + αv̂)/∥h + αv̂∥. Rescaling does not change direction, so the edit’s effect is a
rotation of ≈ arctan α ∥h∥/∥h∥ at a given residue, with the norm unchanged. An edited activation can fall outside the manifold in two ways: its norm can be different from anything the model produces, or its direction can point to regions where the model never points. The rescaling performed rules out the former to focus on measuring the effects on the latter. The grid is uneven because what the edit adds is α times the steering vector’s norm, and the rescaled vector is ∥h∥/∥v∥ ≈ 8 times longer than the raw one. In order to keep perturbations unchanged, each raw strength is divided by that factor: 5, for instance, becomes α = 0.642. We sweep α ∈ {0, 0.032, 0.064, 0.128, 0.257, 0.385, 0.642}, and report effects in units of each property’s standard deviation across the 5,790-sequence UniRef50 pool the contrasts were drawn from (0.456 GRAVY, 0.060 charge/residue, 15.73 index). Table 3: Steering-attributable divergence (up − down); α in units of ∥h∥, SD = divergence over the property’s UniRef50 spread. Unpaired Mann–Whitney, n=40 per direction.

C.3

property

α

naive

p

GLP-corrected

p

SD

gravy gravy gravy gravy gravy gravy

0.032 0.064 0.128 0.257 0.385 0.642

−0.171 +0.006 +0.112 +0.077 +0.546 +1.400

0.17 0.93 0.23 0.44 8×10−5 1×10−10

+0.248 +0.551 +0.969 +1.581 +2.507 +3.382

0.02 1×10−5 7×10−10 2×10−13 4×10−14 2×10−13

+0.54 +1.21 +2.12 +3.46 +5.49 +7.41

charge charge charge charge charge charge

0.032 0.064 0.128 0.257 0.385 0.642

−0.006 −0.007 −0.001 +0.055 +0.157 +0.430

0.90 0.62 0.96 0.02 6×10−10 2×10−12

+0.011 +0.040 +0.092 +0.216 +0.313 +0.560

0.62 4×10−3 5×10−9 2×10−14 2×10−14 3×10−13

+0.18 +0.67 +1.54 +3.60 +5.23 +9.34

instability instability instability instability instability instability

0.032 0.064 0.128 0.257 0.385 0.642

−6.17 +4.43 +3.68 +5.30 +15.65 +17.01

0.12 0.25 0.32 0.19 2×10−4 5×10−5

+6.77 +11.73 +13.55 +25.04 +39.48 +64.93

0.02 2×10−3 3×10−5 7×10−9 1×10−11 4×10−14

+0.43 +0.75 +0.86 +1.59 +2.51 +4.13

The correction’s own concept drift

The α=0 run isolates what the loop does without steering. The edit is the identity there, but the loop still masks and resamples 10% of residues for 30 rounds, and in the corrected arm SDEdit still noises the activation to t0 and denoises it back. Both arms move the property, and what matters is whether the movement is neutral or directional, since an operator that always pushes one way could be mistaken for a steering effect. The naive arm moves GRAVY +0.35 from hydrophilic starts and −0.28 from hydrophobic ones: both move toward the middle, which is resampling reverting to typical composition. The corrected arm moves +1.15 and +0.54, both upward, so SDEdit adds hydrophobicity wherever it starts (Table 4, Fig. 6). Projecting toward high density is itself a directional move, toward whatever composition the GLP treats as typical.

13

What the offset is made of is visible in the composition. The same residues move in all three runs: Leu +5.9/ + 6.3/ + 6.7pp and Val +5.4/ + 5.7/ + 4.0pp, with Glu, Lys, Arg and Asp each down 1.3–2.8pp. The three runs share no data, contrast sets, starting proteins or steering vectors, only the correction operator. Those charge losses are also why charge is the only property with no offset: Lys+Arg (4.0pp) and Glu+Asp (4.4pp) are lost in similar amounts, so α=0 offset on charge is near zero even though the composition changes. Table 4: Concept change with no steering applied (α=0), by arm and starting set, in each property’s own units. A fixed bias adds the same amount from both sets; mean reversion flips sign with the set and cancels in the corrected−naive difference, which is the last column. naive property hydrophobicity charge instability

GLP-corrected

from low

from high

from low

from high

fixed bias (SD)

+0.347 +0.055 +14.99

−0.282 −0.039 −15.48

+1.145 +0.063 +4.66

+0.536 −0.071 −27.13

+1.77 −0.20 −0.70

Figure 6: The α=0 arms, in units of each property’s spread. Hatched: naive. A bias that reverses with the starting set is mean reversion; one that does not comes from the correction.

Figure 7: GLP diffusion loss against steering strength, before and after a single correction pass applied directly to the steered activation (no generation), for hydrophobicity 14

C.4

The correction operator works in isolation

Steering does move activations off the manifold, and monotonically in α: GLP’s diffusion loss on real held-out activations rises from 0.869 unsteered to 1.743 at the top of the grid (Fig. 7). A single SDEdit pass applied to the steered activation, with no generation, returns it to 0.944, and recovers over 90% of the excess at every grid point. What degrades the output, then, is not the edit or the correction but decoding the corrected activation back to amino acids and iterating that. C.5

The decoding protocol, and what it costs

The loop has a fixed point. Every property contributes two starting sets, one per steering direction, resulting in six sets: hydrophilic and hydrophobic, anionic and cationic, stable and unstable. They span natural pTM 0.369–0.650, and the α=0 naive pass lands every one of them between 0.227 and 0.315 (Table 5): the loop does not impose a constant penalty but pulls everything toward lower pTM values. Nothing beyond the loop adds to that cost. Raising α from zero to the top of the grid barely moves pTM on any property, neither does the correction on its own, compared against the naive arm at α=0. The loop accounts for the foldability lost. Total rewriting is what costs structure. How the rewriting is split between mask fraction and rounds does not matter: at matched expected coverage, resampling a small fraction of residues over many rounds and a larger fraction over few give the same foldability and comparable effects. What matters is the total, the fraction of residues resampled at least once: foldability stays within the starting proteins’ own interval up to ∼15% coverage and declines beyond it, while the effect grows throughout (Fig. 8). Steering strength is not the cost either, since neither raising α across the grid nor the correction on its own shifts pTM beyond the fixed point. Table 5: Foldability before and after the decoding loop, with no steering and no correction (α=0, naive arm), for all six held-out sets. starting set

natural pTM

after decoding

change

0.650 0.629 0.507 0.438 0.373 0.369

0.294 0.315 0.256 0.257 0.274 0.227

−55% −50% −50% −41% −27% −38%

instability, stable hydrophobicity, hydrophobic charge, anionic charge, cationic hydrophobicity, hydrophilic instability, unstable

C.6

Can a better decoder escape the fixed point?

The fixed point of Appendix C.5 raises whether the foldability loss is specific to uniformrandom masked-Gibbs decoding or intrinsic to decoding steered activations at all. We tested two alternative decoders, both using the identical steering vector and correction operator. Following the principles of masked generative transformers [3], the first remasks in each round only the lowest-probability positions and freezes the rest. This results in a collapse: 92.7% of outputs are degenerate (≥30% one residue, ≤8 distinct amino acids, or a ≥12-long homopolymer run) against 8.5% for uniform random masking, typically homopolymers. For the second, we replace the resampling loop with the stochastic beam search of [15]. This approach starts from scores and selects a fixed number of single-residue substitutions, choosing each one to keep the sequence as likely as possible under the host. We let the host score those candidates through the steered and corrected activation, so the search prefers substitutions that move the property while staying plausible. Here, the effect is the opposite: it never collapses and keeps foldability near natural, but it steers weakly.

15

The two decoders turn out to trace the same efficacy/naturalness curve parameterised by edit count. Beam search makes a fixed number E of single-residue substitutions, and it is that budget, not the steering strength, that governs the effect: raising α twentyfold barely changes the effect, whereas growing E increases it steadily while foldability declines gracefully (Table 6). Masked-Gibbs rewrites far more than any E we tested, and extrapolating the beam-search curve to that budget reproduces where it sits: few edits are natural but weak, many are strong but degrade. The comparison at α=0 isolates this: with no steering and no correction, the same starting proteins fold at pTM 0.48 through beam search and 0.29 through masked-Gibbs, so what costs foldability is the rewriting itself, not the edit applied to the activation. Neither decoder escapes the trade-off, though beam search is cleaner per edit and may dominate it at matched effect, a direction we leave open.

Figure 8: Steering effect (top) and foldability (bottom) against how much of the protein the decoder rewrites, T =0.5. Marker shape distinguishes mask fraction; the three series fall on a single curve, i.e. mask fraction and round count act only through their product. Shaded band: the starting proteins’ own pTM (±SEM). Grey points are settings whose output is mostly degenerate and are excluded from the trend. This budget sweep predates the relative-α parameterisation and its axis label is in raw units; for the hydrophobicity vector its α=2 is the same perturbation as the α=0.257 used elsewhere in this paper. Table 6: Beam search over the steered pseudo-likelihood as a function of the edit budget E, against uniform-random masked-Gibbs. pTM is the α=0 naive arm (the decoder alone); divergence is the attributable up-minus-down effect at the top of the grid; both at n=40 starting proteins per direction, hydrophobicity. decoder beam, E=5 beam, E=10 beam, E=25 beam, E=50 masked-Gibbs, 30 rounds

degenerate

pTM (α=0)

divergence

2.5% 2.5% 3.5% 4.6% 8.5%

0.486 0.473 0.438 0.409 0.293

+0.07 +0.08 +0.27 +0.51 +3.99

16

C.7

The SAE-feature-clamp variant: four structural concepts

The three biochemical properties are computed from individual residues or neighbouring pairs, which a compositional push can move, whereas a structural concept depends on the spatial arrangement of specific residues. We therefore repeat the naive/corrected comparison with a second steering mechanism, clamping one SAE latent (zk ← c) as [23] do, on four structural concepts. A clamp of c=1 sits at the ceiling these features reach on real data; the rest of the grid pushes the latent beyond it. We run this under the same decoder as Algorithm 1, with five changes: line 8 becomes the latent clamp; ρ=1, so each round is an independent full resample rather than a cumulative refinement; R=100; t0 =0.5; finally, the round maximising zk is returned, except at c=0, where there is no clamp and the last round is returned instead. We apply it to Helix (feature 5355), Beta strand (feature 2868), Coiled coil (feature 813) and Zinc finger (feature 1435, the C2H2 union), each clamped to the feature with the highest feature–concept F1. Each generation starts from a uniform-random 25– 40-residue sequence and re-masks and resamples every position for 100 independent rounds (rather than cumulative, as in property steering), keeping the round that maximises zk . We test different c ∈ {0, . . . , 5} ({0, . . . , 8} for Zinc finger), n=100 per cell. Unlike the uniform three-property result, the correction’s benefit here is concept-dependent (Table 7). Helix is the clear case: the correction raises the DSSP helix fraction on its own, before any clamping, and the naive arm needs a nonzero c to catch up. Coiled coil appears to gain as well, but inspection shows pepcoil is scoring long single helices as heptad repeats rather than real pairing. Beta strand barely moves, and the correction pushes its strand fraction below naive for most c. Zinc finger never produces a complete C2H2 motif, by which we mean a PROSITE hit corroborated by a Pfam zf-C2H2 alignment. Scoring every sequence continuously against the same profile instead, the corrected arm does sit higher than naive at most c (Mann–Whitney, best p=2 × 10−5 ), driven by histidine enrichment rather than motif completion. Fold confidence stays low throughout. Why helix is the exception. The clamp sets one scalar per position, a compositional bias, and the decoder resamples each position from its own distribution, so it can change which amino acids appear but not how residues sit relative to one another. Local helix propensity survives that, so helix content rises; a β-sheet, a coiled coil and a zinc finger each need specific distant residues paired (two strands hydrogen-bonded, two helices in heptad register, two Cys and two His chelating an ion), which no per-position bias can arrange. On-manifoldness and naturalness are again compromised. As with property steering (Section 4.3), one correction pass returns the clamped activation close to GLP’s typical density in isolation, but that gain is lost at decoding: once the head has sampled amino acids, ESM re-embeds them and the activation is recomputed from the sequence rather than carried over, so the finished sequence is no more on-manifold than the naive arm’s.

D

Probing protocol and per-concept tables

D.1

Discrete concepts: definition, selection, and probe

Concepts and splits. Each discrete concept is one residue-level UniProtKB feature annotation from Swiss-Prot, materialised per amino acid by InterPLM’s extract_annotations and named by its feature type and description (Domain_SH3, Compositional bias_Acidic residues, and so on). The evaluation set is a 20,000-protein reviewed Swiss-Prot query filtered to proteins with an AlphaFoldDB model and at most 1,022 residues, split by protein into eight shards: 0–3 train the probes, 4–7 are the held-out test set, both disjoint from GLP’s training activations (Appendix B.1). Selection. We retain every concept that fulfills InterPLM’s frequency filter (>25 domain instances or >1,500 positive residues) and have ≥500 positive residues in the test shards. For reference, we tag each concept into one of five biological categories: domain/motif, chemical/PTM, structural, topology/localisation and binding/catalytic. The parsing and filtering yields 110 concepts dominated by the domain/motif category, which we probe at both hosts.

17

Table 7: Structural steering by c, naive/GLP-corrected, n=100 per cell. Structural column: DSSP secondary-structure fraction (per-chain residue fraction in that class) for Helix and Beta strand; EMBOSS pepcoil hit rate for Coiled coil; and, for Zinc finger, the fraction of sequences with any PF00096 zf-C2H2 profile-HMM alignment (a graded measure, no complete motif forms). c

structure (naive)

structure (corr.)

pLDDT (naive/corr.)

pTM (naive/corr.)

Helix, feature 5355 (DSSP helix fraction) 0 0.54 0.77 1 0.73 0.78 2 0.74 0.80 3 0.76 0.77 4 0.76 0.78 5 0.72 0.75

49.7 / 59.8 59.7 / 62.3 61.5 / 63.5 61.8 / 61.7 61.6 / 62.4 60.4 / 61.6

0.153 / 0.251 0.270 / 0.284 0.287 / 0.296 0.290 / 0.285 0.287 / 0.296 0.278 / 0.291

Beta strand, feature 2868 (DSSP strand fraction) 0 0.001 0.002 1 0.029 0.018 2 0.039 0.028 3 0.033 0.045 4 0.065 0.044 5 0.110 0.060

49.7 / 59.8 49.4 / 52.6 50.0 / 55.8 50.3 / 58.1 50.3 / 59.7 50.9 / 57.5

0.152 / 0.251 0.154 / 0.186 0.157 / 0.215 0.163 / 0.235 0.161 / 0.249 0.167 / 0.226

Coiled coil, feature 813 (pepcoil hit rate) 0 0% 0% 1 0% 0% 2 0% 4% 3 4% 15% 4 3% 19% 5 6% 33%

49.7 / 59.8 59.3 / 65.8 61.7 / 69.5 63.8 / 72.2 65.8 / 73.4 68.1 / 73.0

0.153 / 0.252 0.253 / 0.303 0.279 / 0.345 0.298 / 0.371 0.307 / 0.386 0.329 / 0.378

Zinc finger, feature 1435 (fraction with any PF00096 zf-C2H2 HMM alignment) 0 65% 67% 49.7 / 59.8 0.153 / 0.251 1 82% 91% 49.3 / 54.8 0.148 / 0.206 2 81% 94% 51.4 / 56.9 0.165 / 0.224 3 83% 99% 50.4 / 51.7 0.155 / 0.169 4 88% 99% 51.1 / 48.4 0.161 / 0.136 5 82% 93% 51.6 / 47.5 0.167 / 0.123 6 83% 90% 53.9 / 48.1 0.186 / 0.129 7 77% 85% 57.3 / 47.9 0.218 / 0.128 8 91% 93% 59.7 / 48.1 0.237 / 0.130

Probing. We probe computational units one at a time: one GLP meta-neuron, one SAE feature, one ESM FFN neuron, or one dimension of the raw residual stream. The four representations describe the same residues in different coordinate systems, so the question is which system isolates better a given concept. We therefore run the following methodology once for each concept in each representation (110 concepts × 4 representations = 440 probes). First, a unit that detects a concept should be more active on residues that have it than on residues that do not. In order to account for that, on shards 0–3 we average each unit’s activation over the positive and negative residues, and compute the difference (|f pos − f neg |), retaining the 512 units with the largest gap for that concept. Then, we fit each of those as a 1-D ℓ2 -logistic probe with 5-fold cross-validation, keeping the one with the highest mean CV (validation) AUC, and report its test AUC on shards 4–7. Negatives come from the same proteins as the positives, so a unit cannot win on predicting protein identity. We report ROC-AUC, which needs no per-concept threshold and is the metric of GLP’s released probe. InterPLM’s headline metric is a domain-adjusted F1, which we have not run on the full concept set, so we cannot claim the ordering is metric-invariant. GLP’s units depend on the diffusion time, so its candidates pool meta-neurons across u ∈ {0.1, 0.5, 0.9} and is correspondingly larger than the other three. 18

Figure 9: 1-D probing mean test AUC by method and host (ESM-2-8M solid, ESM-2-650M hatched; 95% bootstrap CI). GLP meta-neurons lead at both host sizes.

Falsification. For the concepts where GLP’s selected meta-neuron beats the SAE’s selected feature, we (i) regress it on the full 10,240-feature SAE dictionary (held-out R2 : is it a linear read-out?) and (ii) find k ∗ , the smallest k ∈ {2, 5, 10, 20} at which a joint probe over k SAE features matches the test AUC that the single meta-neuron reached. Those k features are the SAE’s highest-ranked candidates by the same positive-minus-negative activation gap used to shortlist the 1-D probes, computed on train, not by AUC (Table 10). ESM-2-650M. The scaling point repeats all of the above on the larger host (d=1280) at layer 18, against the released Elana/InterPLM-esm2-650m SAE, with the GLP trained on 100M activations. Because the selection rule depends only on the annotations, the concept set is identical to the 8M one, so AUCs are comparable across hosts (Fig. 9). D.2

Continuous properties: definition and probe

The ten continuous targets are whole-sequence physicochemical scalars computed directly from the amino-acid string, with no annotation lookup and no learned predictor. From Biopython’s ProteinAnalysis: GRAVY (mean Kyte–Doolittle hydropathy), molecular weight, isoelectric point, aromaticity, instability index (Guruprasad dipeptide-weighted sum), net charge at pH 7, and the helix / turn / sheet secondary-structure fractions. From modlAMP’s GlobalDescriptor: the aliphatic index. Sequences containing a non-canonical residue (X / B / Z / U / O) are undefined for these scales and dropped. The probe uses the same shards and the same select-on-validation, report-on-test design as the discrete one, with three changes forced by the target being a per-protein real number rather than a per-residue label. First, each protein becomes a single row: a unit’s value for a protein is its activation averaged over that protein’s residues. Second, candidates are ranked by |Pearson r| between that pooled value and the target property, retaining the top k=512 as well. Third, each 1-D probe is an ordinary least-squares fit scored by Spearman ρ. We select the unit with the largest |ρ| on validation, refit it on shards 0–3, and report its ρ on shards 4–7. We report test Spearman ρ rather than AUC because a continuous property has no positive / negative split. D.3

Per-concept results

Per-concept numbers behind Table 8 are presented here. Furthermore, Table 9 shows the results for the ten continuous properties and Table 10 the falsification verifications on the concepts GLP wins. 19

Table 8: Per-concept test AUC, all 110 concepts, both hosts. Bold marks the highest value in each row within a host. Shaded rows are category means; * marks a lead over the runnerup with p<0.05 (two-sided paired Wilcoxon over the category’s concepts, uncorrected). Categories with n≤4 cannot reach this threshold even if the leader wins every concept. ESM-2-8M Concept Domain / motif (n=92) Compositional bias_Acidic residues Compositional bias_Basic and acidic residues Compositional bias_Basic residues Compositional bias_Gly residues Compositional bias_Low complexity Compositional bias_Polar residues Compositional bias_Pro residues Domain_C-type lectin Domain_C1q Domain_CTCK Domain_Collagen-like Domain_DHHC Domain_EF-hand 1 Domain_EF-hand 2 Domain_EF-hand 3 Domain_EF-hand 4 Domain_EGF-like Domain_F-box Domain_Fe2OG dioxygenase Domain_G-alpha Domain_GOLD Domain_GST C-terminal Domain_GST N-terminal Domain_Globin Domain_H15 Domain_HTH myb-type 1 Domain_HTH myb-type 2 Domain_IGFBP N-terminal Domain_Ig-like Domain_Ig-like C1-type Domain_Ig-like C2-type Domain_Ig-like C2-type 1 Domain_Ig-like C2-type 2 Domain_Ig-like V-type Domain_J Domain_K-box Domain_LIM zinc-binding 1 Domain_LIM zinc-binding 2 Domain_MADS-box Domain_MARVEL Domain_MPN Domain_N-acetyltransferase Domain_Nudix hydrolase Domain_Orange Domain_PB1 Domain_PDZ Domain_PH Domain_PPIase cyclophilin-type Domain_Peptidase S1

GLP 0.904 0.974

*

SAE

FFN

ESM-2-650M Res.

GLP

SAE *

FFN

Res.

0.879 0.867 0.959 0.942

0.895 0.888

0.843 0.972

0.879 0.920

0.833 0.940 0.920 0.983

0.818

0.718

0.745

0.783 0.748

0.664 0.682

0.680

0.955

0.935

0.918

0.807 0.933

0.795 0.786

0.830

0.939 0.872

0.890 0.801

0.891 0.852

0.916 0.937 0.848 0.820

0.859 0.829 0.711 0.738

0.835 0.763

0.856

0.809 0.867

0.793 0.806

0.679 0.777

0.787

0.944 0.891 0.903 0.961 0.896 0.932 0.950 0.832 0.898 0.796 0.652 0.749 0.985 0.976 0.988 0.888 0.882 0.787 0.688 0.601 0.621 0.719 0.727 0.712 0.702 0.702 0.703 0.764 0.665 0.716 0.955 0.937 0.959 0.995 0.967 0.957 0.934 0.912 0.926 0.925 0.858 0.876 0.951 0.783 0.902 0.886 0.750 0.861 0.977 0.944 0.940 0.919 0.761 0.853 0.992 0.893 0.994 0.965 0.895 0.921 0.936 0.880 0.916 0.752 0.764 0.757 0.954 0.902 0.959 0.943 0.867 0.925 0.820 0.767 0.807 0.796 0.772 0.799 0.815 0.705 0.759 0.941 0.909 0.921 0.983 0.954 0.977 0.953 0.866 0.910 0.796 0.741 0.743 0.774 0.723 0.755 0.924 0.882 0.890 0.953 0.808 0.926 0.808 0.760 0.751 0.951 0.924 0.935 0.936 0.917 0.916 0.866 0.781 0.838 0.906 0.814 0.947 0.986 0.908 0.975 0.905 0.754 0.870 0.919 0.748 0.904 0.969 0.952 0.987

0.901 0.851 0.834 0.723 0.976 0.823 0.625 0.673 0.662 0.646 0.927 0.906 0.899 0.802 0.873 0.789 0.887 0.728 0.950 0.893 0.897 0.726 0.872 0.816 0.725 0.732 0.733 0.856 0.902 0.765 0.724 0.711 0.840 0.859 0.647 0.888 0.828 0.754 0.914 0.925 0.823 0.882 0.925

0.939 0.843 0.780 0.828 0.986 0.938 0.904 0.973 0.993 0.990 0.974 0.971 0.977 0.940 0.913 0.881 0.989 0.822 0.966 0.961 0.998 0.998 0.984 0.999 0.857 0.740 0.741 0.742 0.771 0.668 0.655 0.726 0.822 0.699 0.740 0.714 0.877 0.875 0.729 0.773 0.894 0.870 0.779 0.729 0.993 0.986 0.987 0.930 0.975 0.911 0.910 0.958 0.995 0.972 0.971 0.929 0.950 0.834 0.816 0.917 0.979 0.974 0.934 0.938 0.997 0.945 0.962 0.959 0.995 0.989 0.976 0.940 0.997 0.988 0.975 0.979 0.951 0.922 0.884 0.922 0.954 0.858 0.919 0.924 0.911 0.915 0.804 0.878 0.957 0.914 0.742 0.949 0.976 0.934 0.918 0.957 0.830 0.741 0.750 0.751 0.813 0.692 0.693 0.706 0.828 0.748 0.713 0.769 0.948 0.875 0.845 0.864 0.995 0.989 0.978 0.950 0.985 0.958 0.943 0.943 0.832 0.782 0.628 0.768 0.788 0.736 0.688 0.739 0.995 0.981 0.970 0.988 0.996 0.992 0.994 0.962 0.996 0.954 0.938 0.992 0.930 0.851 0.901 0.940 0.890 0.731 0.806 0.919 0.955 0.937 0.936 0.913 0.971 0.937 0.953 0.969 0.976 0.903 0.817 0.956 0.988 0.961 0.923 0.955 0.992 0.978 0.986 0.970 0.979 0.890 0.921 0.955 continued on next page

20

(continued) ESM-2-8M

ESM-2-650M

Concept

GLP

SAE

FFN

Res.

GLP

Domain_Protein kinase Domain_RRM Domain_RRM 1 Domain_RRM 2 Domain_SH2 Domain_SH3 Domain_SOCS box Domain_Sm Domain_THD Domain_TSP type-1 Domain_Thioredoxin Domain_Tyrosine-protein phosphatase Domain_UBC core Domain_UPAR/Ly6 Domain_Ubiquitin-like Domain_bHLH Domain_bZIP Domain_sHSP Domain_t-SNARE coiled-coil homology Domain_v-SNARE coiled-coil homology Motif_Effector region Motif_Nuclear localization signal Motif_Nudix box Motif_Switch 1 Motif_Switch 2 Region_Alpha-1 Region_Alpha-2 Region_Alpha-3 Region_Basic motif Region_Disordered Region_Helix-loop-helix motif Region_LID Region_Leucine-zipper Region_NMP Region_Switch-II Zinc finger_C2H2-type Zinc finger_C2H2-type 1 Zinc finger_C2H2-type 2 Zinc finger_C2H2-type 3 Zinc finger_C2H2-type 4 Zinc finger_C4-type Zinc finger_RING-type Zinc finger_any

0.960 0.989 0.858 0.837 0.834 0.990 0.819 0.892 0.939 0.723 0.922 0.901

0.934 0.965 0.977 0.981 0.816 0.828 0.813 0.817 0.668 0.786 0.973 0.968 0.741 0.781 0.792 0.887 0.768 0.918 0.672 0.658 0.823 0.908 0.875 0.869

0.962 0.983 0.804 0.822 0.746 0.916 0.721 0.883 0.811 0.684 0.740 0.893

0.993 0.786 0.930 0.984 0.973 0.947 0.919 0.986 0.932 0.761 0.784 0.831 0.861 0.789 0.785 0.842 0.967 0.939 0.889 0.902 0.996 0.948 0.939 0.951 0.972 0.987 0.980 0.936 0.990 0.895 0.857 0.980 0.988 0.950 0.975 0.925 0.966 0.922 0.836 0.877 0.901 0.781 0.750 0.868 0.904 0.759 0.753 0.842

0.845 0.932 0.910 0.934 0.983 0.970 0.917

0.718 0.809 0.913 0.896 0.803 0.911 0.849 0.931 0.936 0.979 0.964 0.973 0.845 0.867

0.689 0.820 0.773 0.883 0.966 0.956 0.806

0.938 0.931 0.993 0.990 0.990 0.991 0.987

0.967

0.946

0.910 0.997

Chemical / PTM (n=9) Disulfide bond Glycosylation_N-linked (GlcNAc...) asparagine Glycosylation_any Lipidation Modified residue_N6-acetyllysine Modified residue_N6-succinyllysine Modified residue_Phosphoserine Modified residue_Phosphothreonine

0.971 0.997 0.989

0.957 0.970 0.985

0.958 0.902 0.958 0.977

0.924 0.934 0.842 0.919 0.958 0.950 0.977 0.968

0.939

SAE

0.903 0.862 0.896 0.978 0.963 0.980 0.994

FFN

Res.

0.895 0.943 0.836 0.850 0.812 0.944 0.988 0.984 0.964 0.984 0.955 0.946 0.967 0.994

0.995 0.992

0.980

0.995 0.996 0.986 0.981 1.000 0.993 0.992 0.993 0.852 0.838 0.802 0.735 0.777 0.675 0.633 0.690 0.977 0.961 0.978 0.943 0.987 0.959 0.887 0.969 0.988 0.968 0.987 0.933 0.990 0.965 0.972 0.968 0.987 0.944 0.963 0.936 0.993 0.997 0.965 0.941 0.887 0.769 0.860 0.796 0.978 0.950 0.931 0.926 0.764 0.631 0.708 0.744 0.902 0.815 0.834 0.831 0.994 0.938 0.988 0.842 0.999 0.993 0.959 0.991 0.978 0.969 0.974 0.949 0.979 0.971 0.948 0.976 0.876 0.763 0.870 0.877 0.856 0.682 0.778 0.767 0.948 0.869 0.877 0.856 0.977 0.947 0.961 0.960 0.881 0.775 0.807 0.816 0.972 0.914 0.958 0.943 0.943 0.903 0.913 0.869 0.904 0.870 0.875 0.873 0.981 0.960 0.956 0.926 0.998 0.996 0.974 0.983 0.989 0.969 0.967 0.940 0.995 0.995 0.967 0.943 0.980 0.932 0.927 0.930 0.971 0.758 0.852 0.858 0.888 0.811 0.876 0.810 0.898 0.822 0.800 0.820 0.867 0.812 0.880 0.825 0.855 0.779 0.781 0.865 0.853 0.785 0.863 0.824 0.878 0.770 0.739 0.834 0.803 0.747 0.837 0.766 0.844 0.737 0.745 0.788 0.829 0.812 0.739 0.693 0.914 0.773 0.738 0.771 0.967 0.941 0.960 0.872 0.966 0.914 0.787 0.935 0.937 0.881 0.936 0.849 0.916 0.700 0.747 0.920

0.976 0.976 0.984 0.986

0.945 0.977 0.985

0.947 0.835

0.902 0.972* 0.944 0.781 0.912 0.993 0.972 0.919 0.925 0.993 0.976 0.701 0.874 0.890 0.916 0.925

0.964 0.917 0.963 0.972

0.867 0.974 0.898 0.980

0.927 0.908 0.945 0.971

0.755 0.827 0.736

0.729 0.821 0.830 0.852

0.697 0.894 0.695 0.702

0.919 0.721 0.939 0.755

0.810 0.719

continued on next page

21

(continued) ESM-2-8M

ESM-2-650M

Concept

GLP

SAE

FFN

Res.

GLP

Modified residue_Phosphotyrosine Structural (n=4) Beta strand Coiled coil Helix Turn Topology / localisation (n=3) Transit peptide_Chloroplast Transit peptide_Mitochondrion Transit peptide_any Binding / catalytic (n=2) Active site_Proton acceptor Active site_any

0.993

0.991

0.991

0.915 0.995

0.752 0.748 0.878 0.782 0.602 0.957 0.961 0.954 0.955 0.768 0.803 0.733

0.656 0.621 0.829 0.615 0.557 0.939 0.951 0.929 0.938 0.691 0.715 0.667

0.694 0.646 0.700 0.659 0.619 0.714 0.827 0.762 0.843 0.692 0.624 0.644 0.599 0.580 0.597 0.929 0.905 0.973 0.945 0.885 0.971 0.914 0.923 0.974 0.928 0.905 0.975 0.750 0.769 0.801 0.797 0.817 0.827 0.704 0.721 0.775

SAE

FFN

Res.

0.937 0.695

0.716

0.604 0.555 0.772 0.553 0.535 0.956 0.966 0.950 0.952 0.657 0.694 0.620

0.626 0.627 0.708 0.601 0.569 0.923 0.922 0.924 0.923 0.742 0.766 0.718

0.635 0.601 0.729 0.638 0.572 0.940 0.951 0.931 0.939 0.686 0.708 0.665

Table 9: Per-property test Spearman ρ, all 10 continuous properties, both hosts. The shaded row is the mean, with the Wilcoxon p for the leader against the runner-up. ESM-2-8M

ESM-2-650M

Property

GLP

SAE

FFN

Res.

GLP

SAE

FFN

Res.

Aliphatic index Aromaticity GRAVY (hydropathy) Helix fraction Instability index Isoelectric point Molecular weight Net charge at pH 7 Sheet fraction Turn fraction

0.697 0.765 0.803 0.594 0.575 0.575 0.723 0.582 0.764 0.609

0.601 0.717 0.638 0.563 0.578 0.511 0.739 0.495 0.610 0.566

0.585 0.522 0.648 0.500 0.567 0.577 0.448 0.585 0.656 0.547

0.651 0.465 0.570 0.341 0.482 0.349 0.439 0.339 0.646 0.501

0.593 0.631 0.684 0.425 0.524 0.450 0.610 0.428 0.671 0.532

0.691 0.717 0.562 0.426 0.524 0.448 0.799 0.446 0.570 0.511

0.403 0.339 0.465 0.339 0.450 0.249 0.316 0.264 0.460 0.444

0.486 0.420 0.401 0.316 0.474 0.231 0.384 0.228 0.437 0.356

Table 10: Falsification tests on the concepts GLP wins. R2 : meta-neuron regressed on the full SAE dictionary (held-out). k ∗ : fewest top-k SAE features whose joint probe matches its test AUC (“none” if no k ≤ 20 does). ESM-2-8M

ESM-2-650M

Concepts tested R2 , median [IQR] Concepts at k∗ = 2/5/10/20 No k ≤ 20 reaches it short by, median largest gap

104 of 110 0.756 [0.706, 0.842] 7/23/36/28 10 0.0035 Active site_Proton acceptor (0.171)

105 of 110 0.725 [0.627, 0.799] 14/43/32/12 4 0.0041 Domain_RRM 1 (0.054)

Examples Transit peptide_Chloroplast Domain_Protein kinase Region_Disordered Beta strand Domain_SH2 Disulfide bond

R2 / k∗ at each host 0.880 / 2 0.893 / 5 0.829 / 10 0.770 / 20 0.169 / 10 0.958 / none

0.839 / 2 0.884 / 10 0.903 / 10 0.762 / 20 0.523 / 5 0.915 / 2

22

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