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SharedSAE: One Feature Dictionary Across Language Models

Daniil Ognev, Célian Vasson, Lijie Hu, Kentaro Inui, Benjamin Heinzerling

arXiv:2609.04344v1cs.LGcs.CL

TL;DR

SAE training and latent descriptions are usually repeated for each target model, while existing approaches meet only some requirements for shared, adaptable representations. SharedSAE uses one dictionary with model-specific encoder-decoder pairs; across four 1B-scale base models, it reports near-dedicated reconstruction, stronger cross-model alignment, and transferable descriptions.

  • Problem

    SAE training and latent descriptions are typically repeated for each target model, and existing approaches meet only subsets of the requirements for shared, adaptable latents.

    Source: §1 · p. 1

  • Method

    SharedSAE learns one sparse dictionary across heterogeneous language models using per-model encoder-decoder pairs, aligned activations, magnitude-preserving selection, and model dropout for solo inference.

    Source: §1 · p. 2, §3 · p. 3

  • Results

    0.006 mean CE-recovered is the gap from the converged dedicated splice; the shared dictionary also yields stronger alignment and transferable descriptions across four 1B-scale base models.

    Source: §1 · p. 2, §6 · p. 10

  • Takeaways & Limitations

    Frozen-dictionary adaptation attaches held-out, post-trained, and architecturally different models without changing shared latents or existing descriptions.

    Source: §1 · p. 2

    Evidence is bounded to four roughly 1B-parameter base checkpoints on English FineWeb-Edu at roughly 85% depth, and sharedness metrics are proxies.

    Source: Limitations · pp. 10–11

Abstract

from arXiv · show

Sparse autoencoders (SAEs) are widely used to interpret language model activations, but SAE training and latent labelling are typically repeated for every model. Here, we show that a single shared SAE can replace a collection of dedicated per-model SAEs. Our method, SharedSAE, combines a shared dictionary with model-specific encoder-decoder pairs. Unlike the closest prior method, which discards activation magnitudes and requires all models at inference, SharedSAE instead normalizes only selection scores, preserving magnitudes, and uses model dropout for single-model inference. We train SharedSAE on four 1B-scale base language models spanning distinct families and tokenizers. Despite sharing its latents across models, SharedSAE retains 96.6% of dedicated SAEs' mean explained variance; its latent activations exhibit cross-model correlations 1.8 times as high as separate SAEs aligned post-hoc, and its latent descriptions transfer across models. After the dictionary is frozen, new models can be efficiently adapted to it, achieving near-dedicated-SAE reconstruction quality while reusing the shared latent descriptions.

1 Introduction

Training and describing separate SAEs for each model duplicates latent spaces and analyses. SharedSAE uses one dictionary across heterogeneous models and reports cross-model alignment, transferable descriptions, and frozen-dictionary adaptation.

1 Introduction

  • Current practice trains and describes separate SAEs for each target model, requiring another description set and latent space for each new model.The paper frames a single shared SAE as an alternative to this duplication.Source: §1 · p. 1
  • Existing approaches meet only subsets of the requirements: post-hoc matching retains separate dictionaries, while earlier shared dictionaries cannot attach new models with descriptions fixed.Earlier shared-dictionary methods also depend on participating models for inference-time selection.Source: §1 · p. 1
  • SharedSAE aligns tokenization, latent choice, and activation magnitudes, using per-model encoder-decoder pairs around one shared dictionary.Selection scores are normalized while selected magnitudes remain untouched.Source: §1 · p. 1
  • Model dropout trains each model to select shared latents on its own, enabling inference with only the model of interest.After joint training, adaptation trains a new model’s encoder, decoder, and biases while freezing the dictionary.Source: §1 · p. 2
  • Across four 1B-scale base models, the shared dictionary retains near-dedicated reconstruction quality, yields stronger cross-model alignment, and supports transferable latent descriptions.The introduction reports these as the paper’s main empirical contributions.Source: §1 · p. 2

2 Related Work

Related work includes post-hoc alignment of separately trained representations and shared dictionaries trained jointly across models. The paper positions SharedSAE against these approaches and treats representational-convergence hypotheses as background, not a premise.

Shared dictionaries and model diffing

  • Crosscoders use one sparse dictionary for model diffing, while USAE and SPARC extend shared dictionaries to multiple models; SPARC is the closest method described.SPARC uses per-model encoders and decoders, a global top-k over raw summed codes, and cross-reconstruction loss.Source: §2 · p. 2
  • Neither USAE nor SPARC adapts a new model onto a frozen dictionary, and only USAE supports single-model deployment.Both are trained as baselines under the paper’s data and budget.Source: §2 · p. 3

Aligning representations after training

  • Post-hoc SAE matching pairs latents by activation correlation but requires a shared tokenizer and matches only a minority; concept-atlas methods reuse labels without jointly training or auditing a shared space.The text also distinguishes concurrent adapter work, which trains no sparse dictionary and audits no sharedness.Source: §2 · p. 3

Hypotheses about shared representations

  • Representation-convergence hypotheses offer one possible explanation for shared sparse latents, but the experiments establish only learnability on the evaluated roster.The Platonic Representation Hypothesis is described as contested, and this explanation is treated as background rather than a premise.Source: §2 · p. 3

3 SharedSAE

SharedSAE learns one sparse dictionary for aligned activations from multiple models, with separate encoder-decoder pairs and a shared TopK selection. Its training combines self- and cross-reconstruction, while vote-source dropout trains the system for single-model inference.

SharedSAE

  • SharedSAE uses one dictionary of L latents with a separate encoder-decoder pair per model, mapping each model’s hidden space into and out of the shared sparse space.The SAE building block is TopK; dedicated SAEs of this form serve as per-model references.Source: §3 · p. 3
  • Normalized model codes are summed before one TopK selects shared active latents, while each model retains its own selected magnitudes.The vote norm prevents the largest activation scale from dominating latent selection.Source: §3 · pp. 3–4
  • Each decoder reconstructs its own model and the other models from rescaled codes, tying a shared latent index to a feature across models.The cross term and rescale permit codes selected for one model to reconstruct another model’s representation.Source: §3 · pp. 3–4
  • With probability 0.5, one random model selects the shared index set during training, making solo voting the inference mode.The vote-source dropout choice trains each model to select latents on its own.Source: §3 · pp. 3–4

Aligned data

  • Each model’s token stream is aligned into windows that decode to the same text, producing tuples of residual-stream activations for the shared training examples.The aligner extends the two-model procedure to N models.Source: §3 · p. 3

SharedSAE

  • The objective adds self- and cross-reconstruction errors, with λx = 1.0 unless stated otherwise.The architecture rationale identifies the cross term and rescale as the mechanism for cross-model reconstruction.Source: §3 · p. 4

Architecture Components Rationale

  • A learned per-model scale cm replaces the target model’s norm-based rescale at inference.The rescale reads the target’s norm during training; the learned scale is the inference substitute.Source: §3 · p. 4

4 Testing Sharedness of the Trained Concept Space

The evaluation tests whether shared SAE latents align in selection, activation magnitude, and meaning, alongside reconstruction and spliced behavior.

4.1 Common SAE metrics: reconstruction and spliced behavior

  • Sharing retains near-dedicated reconstruction quality: SharedSAE is within 0.006 mean CE-recovered of the converged dedicated splice (0.957 vs 0.963).Under solo TopK, it exceeds the budget-matched 8-epoch dedicated SAEs on three of four streams.Source: §4.1 · p. 5, Table 1 · p. 7

4.2 Do the models choose the same latents?

  • Most SharedSAE latents are used near-equally by all four models, while baselines show near one-sided code mass in at least one model pair.Neff measures how many models use a latent; Figure 4 compares pairwise code-mass shares.Source: §4.2 · p. 5, Figure 3 · p. 5, Figure 4 · p. 5
  • For top-50 activating tokens, USAE overlaps only on its frequent core, while SPARC’s zero median reflects usage breadth rather than disagreement.Figure 6 reports the four-way intersection of each model’s top-50 tokens for a latent.Source: §4.2 · p. 6, Figure 6 · p. 6

4.3 Do the activation magnitudes correlate?

  • Under solo TopK, SharedSAE leads every other architecture in per-latent activation-magnitude correlation; SPARC’s higher joint-TopK correlation partly reflects shared selection by construction.Solo TopK is the deployment condition in which each model chooses latents alone.Source: §4.3 · p. 6, Figure 7 · p. 6

4.4 Do the shared latents mean the same things?

  • For clear labels, SharedSAE shared-vote labels achieve FADE scores and retained rates comparable to dedicated per-model SAEs.The evaluation includes only label–stream pairs meeting the clarity ≥0.9 threshold, so retained coverage reflects that protocol.Source: §4.4 · pp. 6–7, Table 3 · p. 8
  • Source-validated descriptions retain substantial semantic quality across streams, and clarity, responsiveness, and purity show strong cross-model correlations.The results support reusable descriptions for shared latents while leaving full-coverage automatic labeling as a separate limitation.Source: §4.4 · pp. 7–8
  • Functional evidence indicates partial alignment, not latent-level causal equivalence; faithfulness is lower and less consistent across streams than other FADE dimensions.Input- and output-score correlations are positive but moderate, and the objective does not directly optimize latent-level causal effects.Source: §4.4 · p. 8
  • Targeted probes find shared evaluative latents responding across both probe languages and both poles of a valence axis.Only candidates whose probe contrast was positive in all four models and whose held-out activations confirmed the concept were reported.Source: §4.4 · pp. 8–9

5 Adaptation of Newly Released Models

The paper adapts new models by training their encoder, decoder, and biases against a frozen SharedSAE dictionary. Held-out and previously unseen models approach dedicated reconstruction quality, and adapted models join the shared latent space.

5 Adaptation of Newly Released Models

  • Leave-one-out folds remain within a few percent of their dedicated ceiling, and adapted Qwen3.5 matches its five-model joint-TopK reference while enabling solo selection only with dropout.Qwen3.5 is a hybrid architecture unseen during SharedSAE training.Source: §5 · p. 9
  • Adapted Llama-3.2-1B-Instruct reaches 1.006 of its dedicated SAE, and Hunyuan-1.8B reaches 1.010 while reproducing probe-found latent contexts.Both models are attached to the frozen dictionary; Llama’s base sibling was already in the seed, while Hunyuan was released after dictionary training.Source: §5 · p. 9
  • Adapted models join the shared space: the encoder-decoder attach leads linear alignment and decoder-only methods on every measured criterion, with probe-latent value correlations of 0.64–0.99.On the six probe-found latents, top-50 position overlaps reach 44 of 50 against seed streams.Source: §5 · pp. 9–10, Table 5 · p. 9, Figure 8 · p. 10

6 Conclusion

The conclusion argues that a shared linear concept space is obtainable on the tested roster, with near-dedicated reconstruction and sharedness across several criteria. Adapted models also adopt its existing vocabulary and can be used alone.

6 Conclusion

  • The dictionary reconstructs each stream within a few percent of its converged dedicated ceiling and is within 0.006 mean CE-recovered of the converged dedicated splice.It exceeds budget-matched dedicated SAEs on three of four streams.Source: §6 · p. 10
  • The models choose the same latents, assign correlated magnitudes, and give them the same meaning.These are the conclusion's three stated criteria for a shared space.Source: §6 · p. 10
  • An adapted model adopts the existing vocabulary better than other methods and can be used alone.Source: §6 · p. 10

Limitations

The paper limits its claims to a narrow model and data roster, notes that its measures are proxies, and does not claim its training configuration is optimal.

Limitations

  • Evidence covers four base checkpoints around 1B parameters on English FineWeb-Edu; alignability at larger scale and in other languages remains untested.Post-training is probed with one instruct checkpoint, which does not establish the general case.Source: Limitations · p. 10
  • The settled configuration is not claimed to be optimal; component interactions were not exhaustively ablated.The components interact, but Table 6 varies them one at a time around one configuration.Source: Limitations · p. 11
  • Sharedness metrics are proxies, and a measure of alignment independent of the shared machinery remains future work.The paper notes that good proxy scores could still coincide with labels that fail to transfer.Source: Limitations · p. 11
  • Feature splitting means latent counts can overstate concept counts, and a mis-set shared k can entangle features.Source: Limitations · p. 11

A Experimental setup

The evaluation compares four base models on aligned FineWeb-Edu activations using converged SAE systems and held-out reconstruction and splice metrics.

Experimental setup

Models

  • The roster contains four separately released base checkpoints from four model families and tokenizers, hooked at roughly 85% depth.Their median token norms differ by three orders of magnitude.Source: A Experimental setup · p. 14

Data

  • Activations come from FineWeb-Edu, aligned over 4M positions, with 3.9M used for training and shard 9 reserved for evaluation.A separate 200k-position store extends the held-out window to 300k for per-latent statistics.Source: A Experimental setup · p. 14

Training

  • Systems share L = 32,768, TopK k = 128, and the same data; training continues until validation FVE levels off, capped at 64 epochs.The matched 8-epoch budget leaves validation curves rising, so Table 1 compares converged systems.Source: A Experimental setup · p. 14

Baselines and metrics

  • Dedicated per-model TopK SAEs on the same trainer provide the reconstruction ceilings; held-out FVE and solo-TopK splice metrics assess reconstruction and function.The splice reports CE-recovered and KL(clean ∥patched).Source: A Experimental setup · p. 14

B Artifacts, licenses, and data

This section documents the data, metric definitions, measurement protocols, convergence checks, and controls used to evaluate SharedSAE. It also reports correlation and reconstruction comparisons, alongside boundaries on the data and evaluation setting.

C.1 Reconstruction

  • Training minimizes per-position uncentered NMSE, while evaluation reports pooled centered FVE; cross-FVE averages all ordered model pairs, and share of ceiling compares against dedicated SAEs.Source: §C.1 · p. 17

C.3–C.4 Shared usage and selection agreement

  • Sharedness measures distinguish balanced latent use by selection counts or code mass from selection agreement per token and across top-50 activating positions.Under independent selection, expected top-50 intersection is below 10^-3 at these window sizes.Source: §C.3 · p. 17, §C.4 · pp. 17–18

C.5 Activation-magnitude agreement

  • Code-correlation measurements retain zero activations as disagreements, while the post-hoc control uses each latent’s best-correlated partner without a one-to-one constraint.That matching protocol is an upper bound on any one-to-one assignment between independently trained dictionaries.Source: §C.5 · p. 18

D.1–D.2 Measurement windows and convergence

  • Main self-FVE uses the first 20,000 held-out positions; dedicated references reach the 64-epoch cap except Llama, which stops at epoch 53, while SharedSAE stops at epoch 62.The activation corpus is English FineWeb-Edu, so other-language behavior is untested; personally identifying content was not separately screened beyond source filtering.Source: B Artifacts, licenses, and data · pp. 14–15, §D.1 · p. 18, §D.2 · p. 19

D.4 Controls

  • Mean cross-FVE was 0.610 for a raw-stream ridge map versus 0.726 for the shared code, which outperformed it on all twelve ordered pairs.The pairwise advantage ranged from 0.085 to 0.179.Source: §D.4 · p. 19
  • All headline statistics exceeded 100 frequency-matched permutation draws (one-sided empirical p = 0.0099), while four-way selection agreement stayed between 52 and 60 of 128 across token groupings.Source: §D.4 · p. 19
  • Solo-code cross-model splices recover 0.92 to 0.96 of the target’s cross-entropy gap (mean 0.94), versus 0.95 to 0.97 for target-native codes.The divergence to the clean model roughly doubles for cross-model splices.Source: §D.4 · p. 20
  • SharedSAE’s solo-TopK median code correlation was 0.785, versus 0.428 for the post-hoc control; 86% versus 35% of latents exceeded 0.5.Source: §D.4 · p. 20

D.7 Tables of the main comparison

The comparison reports stronger cross-model agreement for SharedSAE, alongside baseline and adaptation results. It also examines tokenizer alignment and whether sharedness persists across held-out model rosters.

D.7 Tables of the main comparison

  • After frozen-dictionary adaptation, the new model’s median code correlation to seed models is 0.897 to 0.911 in one arm and 0.901 to 0.915 in the other.Each adaptation trains only the new model’s encoder, decoder, and biases; the shared dictionary stays frozen.Source: §D.7 · p. 20
  • With raw votes, Gemma retains 0.956 of its ceiling while the other three models retain 0.90 to 0.92; RMS-calibrated inputs still leave vote shares spread sixfold.The passage reports these calibration comparisons for the vote-input block in Table 6.Source: §D.7 · p. 20
  • On equal-size cores of 13,065 latents, SharedSAE reaches 33.0 of 50 top-position overlaps, versus 28.0 for USAE, 19.0 for SPARC, and 13.0 for the matched dedicated control.The equal-size comparison uses each system’s most-selected measurable latents.Source: §D.7 · p. 21
  • In Table 13, the mid-depth hooks—layer 14 of Qwen3, 8 of Llama, 8 of OLMo-2, and 13 of Gemma—at roughly half depth reach a cross-FVE mean of 0.652 at the earlier protocol.Source: §D.7 · p. 21
  • Solo per-latent correlation has a median of 0.79 for SharedSAE, versus 0.45 for post-hoc cross-model matching and 0.77 for the within-model matching ceiling.The joint-TopK SharedSAE median is 0.90; its correlations use a 300k window, while matching controls use 100k.Source: Figure 11 · p. 21

E Token alignment procedure

  • The tokenizer-only replay aligns 99.92% of chunks fully or partially; 93.0% of 4.0M windows close on the single-token fast path.The nine partial failures hit the 16-token window cap, mainly on byte-split non-Latin text and long digit runs; dropped remainders cost 0.05% of raw tokens.Source: E Token alignment procedure · pp. 22–23

F Baseline adaptation to the LLM setting

  • USAE’s mean self-FVE rises from 0.604 to 0.760 across 8 to 64 epochs, while SPARC’s joint-TopK mean rises from 0.702 to 0.732.The passage reports diminishing returns by the 64-epoch cap; SPARC’s solo Gemma stream remains collapsed at 0.251.Source: F Baseline adaptation to the LLM setting · p. 23

G Sharedness across held-out rosters

H SPARC’s solo agreement

SPARC’s solo votes agree per token, but its per-latent agreement statistics depend strongly on which latents are measured. The analysis attributes its zero pooled medians to a rarely firing tail outside a smaller shared core.

H SPARC’s solo agreement

  • SPARC’s four solo selections share 49 of 128 latents, compared with 59 for SharedSAE, and each pair shares 59 to 69 latents.Each stream’s own top-k reproduces 0.59 to 0.71 of the joint top-k for SPARC, versus 0.73 to 0.76 for SharedSAE.Source: H SPARC’s solo agreement · p. 24, Table 12 · p. 25
  • SPARC’s zero pooled per-latent medians arise because wide-usage stream pairs measure many rarely firing latents, where both statistics are zero.SPARC’s Gemma solo vote selects 7,719 distinct latents, versus 31,097 for OLMo-2; Gemma-containing pairs are measured on a smaller core where SPARC agrees.Source: H SPARC’s solo agreement · p. 24
  • SPARC retains per-latent agreement on a core of about 7,600 latents, roughly a quarter of its dictionary, but shows no measurable agreement outside it.SharedSAE agreement is measured over a population three times larger because its streams use the dictionary at comparable breadth.Source: H SPARC’s solo agreement · p. 24

I Latent taxonomy and the window-size control

The taxonomy distinguishes a stable consensus core from a window-sensitive model-specific tail, while planted-concept tests and rare-latent examples probe whether sharing preserves interpretable features.

I Latent taxonomy and the window-size control

  • Of 1,397 entries classified as specific on a 20k-token window, 305 remain specific on the 100k shard, 497 become shared, and 593 fall below the usage threshold.The consensus class is 92% stable and grows with the window; masking specific entries changes solo FVE by about 0.001, while masking the consensus core drives every model’s solo FVE negative.Source: I Latent taxonomy and the window-size… · p. 25, Table 14 · p. 25
  • Without TopK selection, 41 of 66 low-correlation or undefined specific-entry candidates respond in other models, while 24 entries—0.07% of the dictionary—respond in only one model.The 24 exclusive entries have a median best other-model response rate of 0% and maximum of 4%; 21 belong to Gemma.Source: I Latent taxonomy and the window-size… · p. 25

J Planted-ground-truth check

  • The shared assignment recovers planted concepts as well as free per-model matching, with a universality ratio of 1.000; recovery collapses in the no-sharing control.Pooling across models also improves recovery over per-model SAEs, with the largest gain on the narrowest model.Source: J Planted-ground-truth check · p. 26

K Shared rare latents: examples

  • Latent 8319 fires 50 times per 100k held-out tokens, and its 15 strongest positions decode to “free” in all four models’ tokenizers.The passage uses this as an example of a label read from one model carrying over to the others and to a model adapted onto the frozen dictionary.Source: K Shared rare latents: examples · p. 26

L FADE Semantic Evaluation

The semantic evaluation describes how labels are generated and tested across models, while the accompanying steering examples illustrate related behavioral shifts with room for model-specific effects. The authors also report AI-assistant use and their verification responsibilities.

L FADE Semantic Evaluation

  • FADE evaluates semantic descriptions on clarity, responsiveness, purity, and faithfulness, using held-out aligned positions distinct from the label-generation data.The evaluation samples 100 latents across activation-frequency strata and computes scores independently on each model.Source: L FADE Semantic Evaluation · p. 26
  • Cross-stream transfer evaluation tests whether a description generated from one model remains clear on the other models, using a 0.9 clarity-retention threshold.Cross-model consistency compares FADE scores across the six model pairs.Source: L FADE Semantic Evaluation · p. 27

M Use of AI assistants

  • AI assistants helped draft and edit manuscript sections, write analysis and figure code, run experiments, and search literature; the authors say they reviewed the results and verified every claim.The authors take responsibility for the content and state that assistants proposed no research question.Source: M Use of AI assistants · p. 27

L FADE Semantic Evaluation

  • Qualitative steering examples show shared latents inducing related behavioral shifts across all four models while allowing model-specific effects.Each shared latent is steered independently in each model.Source: Figure 13 · p. 28
  • None of the Welch tests comparing faithfulness of SharedSAE shared-vote labels with dedicated SAE baselines is significant at p < 0.05.The tests compare retained label–stream pairs.Source: Table 18 · p. 28

N Cross-model probes: corpus transfer, causal effects, and steering

Cross-model probes find sharedness beyond the training corpus and across labels, causal effects, and steering, with alignment varying by probe. The appendix also presents sampled top-activating contexts for probe-found latents.

N Cross-model probes: corpus transfer, causal effects, and steering

  • On unseen Wikipedia, per-latent value-correlation medians are 0.72 across 23,224 active latents and 0.76 on the 12,510-latent well-sampled core; four-way top-50 overlap is 21 of 50.The authors interpret this as evidence that sharedness is a property of the models, not their shared training text.Source: N Cross-model probes: corpus transfer,… · pp. 28–29
  • Median top-30 causal-token overlap was 0.19 (0.27 with the linear logit lens), versus 0.00 for the mismatched-latent null.String-level overlap is a lower bound because concepts can appear in different surface forms across tokenizers; subword-fragment features also sometimes promoted incoherent token sets.Source: Figure 14 · p. 29, N Cross-model probes: corpus transfer,… · p. 29
  • 88 of 90 mined latents received the same blind-written concept label from all four models; two were partial and none disagreed.The 90 included 24 lexical, 51 phrasal or syntactic, and 15 abstract-topic or discourse latents.Source: N Cross-model probes: corpus transfer,… · p. 29
  • At α=1, concept rate rises 0.16–0.22 with coherence 3.0–3.3 versus a 3.1–3.6 unsteered baseline; at α=2, the lift is 0.30–0.42 with coherence 2.2–2.7 versus 3.8–4.3.At α=4 the lift is roughly 0.5, where fluency collapses; matched-norm random controls stay within 0.04 of baseline at every dose.Source: N Cross-model probes: corpus transfer,… · p. 29, Figure 15 · p. 30
  • Topic-level features steer broadly at α=2, but token-level detectors and positional-slot features never steer; Gemma-3 coherence is low at every arm, including unsteered.The authors connect the detector-versus-producer distinction to Arad et al. (2025) and exclude Gemma-3 from coherence-gated claims.Source: N Cross-model probes: corpus transfer,… · p. 29

O Top-activating contexts for the probe-found latents

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