Sparse autoencoders (SAEs) decompose language model activations into sparse features, but prompt transformations designed to preserve the underlying request can redistribute activity across them. A feature change observed on one transformed prompt need not recur, and even a recurring change need not affect a downstream computation. We introduce the redistribution sensitivity score (RSS), which identifies large feature responses that recur in a consistent direction, and evaluate the resulting supports on variants excluded from selection. Across 27 pretrained SAEs spanning eight language models, the tested prompt transformations produce a reproducible redistribution profile on these excluded variants. We then separate recurring representation change from signed readout contribution and decision failure. For a fixed linear readout, an exact decomposition shows how response magnitude, readout coefficients, directional alignment, and the clean margin determine downstream consequences. In two frozen safety readouts, combining RSS support erosion with the full clean margin yields recurrent failure AUROCs of 0.935 and 0.958 using median supports of 20 and 19 features, compared with 0.965 and 0.964 using full erosion. RSS therefore provides a way to identify recurring sparse representation changes and quantify their contribution to a downstream readout without equating representation change with failure. Code is available at https://github.com/OpenSAE/Redistribution-Sensitivity-Score
Figures & tables
Figure 1: RSS under prompt transformations. In the illustrated five-variant selection, boxed features change in the same direction in at least four variants. MeanRSS averages their absolute response magnitudes.
Figure 2: Normalized MeanRSS across six prompt transformations and 27 pretrained SAEs. Each SAE’s six setting means are divided by their average, so the plot compares transformation profiles rather than absolute activation scales. Large outlined diamonds show averages across SAEs.
Figure 3: Response contrast on variants excluded from feature selection. Each point is the normalized context and wrapper mean minus the local edit mean for the indicated feature set and SAE layer. Clean fixed: features selected from clean prompts. Global fixed: features selected by activity across the clean corpus. Dictionary mean: equal average over all SAE features.
Figure 4: Feature validation on held out variants. A, response rate in the direction chosen on selection variants, comparing RSS with magnitude alone. B, mean ∣efho∣ for RSS features and unselected features matched by readout coefficient magnitude. C–D, MCR as the support cap K varies. The ∣ef∣ ranking uses contributions from the selection variants.
Figure 5: Readout change and recurrent readout failure on held out variants. A, Spearman correlation with held out margin erosion and AUROC for recurrent failure. Correlation measures erosion transfer, while AUROC measures failure ranking; residual margin correlations are oriented toward increasing risk. B, clean margin versus full residual margin for Gemma 3 4B, colored by held out recurrent failure. The dashed line marks zero average selection margin.
Figure 6: Utility of RSS supports selected for each prompt and transformation within the frozen readout. A, R2 for reconstructed held out logit changes. B, readout errors reversed by restoring selected feature values. C–D, errors and harmful false negatives captured at a 20% offline review budget using known labels. Error bars show 95% bootstrap confidence intervals.
Symbol
Meaning
x0 , xv
clean prompt and its v th transformed variant
δv,f
change in SAE feature f from x0 to xv
hf
mean absolute feature change used for RSS magnitude ranking
S
responsive support selected by RSS
MeanRSS
average hf over the responsive support
δv,f
standardized feature change used by the frozen probe
Table S1: Core notation. Quantities are defined for one pretrained SAE, layer, base prompt, and transformation setting unless stated otherwise.
Parameter
Value
Selector observations, n
5
Response rate threshold, ρ
0.8
Directional consistency threshold, κ
0.8
Response threshold, τ
10−5
Candidate features, M
400
Support cap, K
20
Table S2: Selection and uncertainty parameters. The main representation protocol has five operator observations derived from fifteen variants per setting. The readout audit selects from five variants and evaluates on ten excluded variants.
Model
Layers
SAE checkpoint
Width
Hook
Architecture / sparsity
GPT-2 Small
4, 6, 8, 10
GPT2-Small-SAEs-Reformatted
24,576
resid_pre
ReLU, 32× ; L1 coef. 8×10−5
Pythia-70M
1, 3, 5
pythia-70m-deduped__res-sm
32,768
resid_post
ReLU, standard; sparsity n.r.
Gemma 3 270M
5, 9, 12, 15
gemma-scope-2-270m-pt
16,384
resid_post
JumpReLU; L0=18 at layer 5 and 20 elsewhere
Gemma 3 1B
7, 13, 17, 22
gemma-scope-2-1b-pt
16,384
resid_post
JumpReLU; L0=18 at layer 7 and 20 elsewhere
Gemma 3 4B
9, 17, 29
gemma-scope-2-4b-pt
65,536
resid_post
JumpReLU; nominal L0=53,60,60
Mistral 7B
8, 16, 24
mistral_7b_layer_L
65,536
resid_pre
ReLU, 16× ; measured L0=92,74,75
Table S3: Pretrained SAE specifications (JumpReLU as in Rajamanoharan et al. [2024] ). “n.r.” means not reported.
Figure S1: Normalized MeanRSS profiles for the six transformations across all sampled layers of the eight models. Normalization follows Figure 2 .
Figure S2: Overlap between the feature supports selected under different transformations, averaged over all units and 1,000 prompts. A, pairwise Jaccard overlap between transformations; B, averages within each model. IC denotes irrelevant context, DC distractor context, MW metalinguistic wrapper, FW format wrapper, PN punctuation noise, and TL typed lexical substitution.
Setting
Available
Mean ∣S∣
Median ∣S∣
∣S∣=20
Irrelevant context
27,000
19.36
20
90.3%
Distractor context
27,000
18.77
20
82.1%
Metalinguistic wrapper
27,000
19.06
20
86.6%
Format wrapper
27,000
18.56
20
82.1%
Punctuation noise
27,000
18.01
20
71.1%
Typed lexical substitution
26,996
16.18
20
54.6%
Table S4: Support availability and size across transformation settings. Each setting contains 27,000 expected groups.
Treatment
Gap
95% CI
Order
Omitted
0.8740
[0.8671, 0.8810]
Reference
Assigned zero
0.8741
[0.8673, 0.8810]
Unchanged
Table S5: Sensitivity to the treatment of unavailable groups. Gap is the context and wrapper mean minus the local-edit mean; brackets give 95% confidence intervals.
Setting
Overlap
Newly active
Inactive
Positive
Negative
Irrelevant context
0.383
0.462
0.469
0.368
0.632
Distractor context
0.361
0.490
0.487
0.304
0.696
Metalinguistic wrapper
0.394
0.453
0.451
0.375
0.625
Format wrapper
0.381
0.496
0.478
0.230
0.770
Punctuation noise
0.692
0.198
0.187
0.406
0.594
Typed lexical substitution
0.776
0.133
0.133
0.381
0.619
Table S6: Changes in active SAE coordinates between clean and transformed prompts. Overlap is Jaccard similarity, newly active is normalized by the transformed active set, and inactive is normalized by the clean active set. Positive and negative shares partition the absolute activation change within the RSS support.
Figure S3: Normalized MeanRSS by prompt topic. A, topic level means for each transformation; B, the ratio of the context and wrapper mean to the local edit mean for each topic. Transformation abbreviations as in Figure S2 .
Figure S4: Profile of the six transformations after removing one model at a time, compared with the profile over all units. Transformation abbreviations as in Figure S2 .
Setting
Normalized MeanRSS
Irrelevant context
1.466 [1.459, 1.474]
Distractor context
1.341 [1.337, 1.346]
Metalinguistic wrapper
1.199 [1.192, 1.205]
Format wrapper
1.159 [1.154, 1.164]
Punctuation noise
0.525 [0.519, 0.532]
Typed lexical substitution
0.309 [0.305, 0.314]
Table S7: Aggregate normalized MeanRSS profile with equal weight for each SAE. Within each SAE, the six setting means are divided by their average. Brackets give 95% confidence intervals.
Criterion
Prompts
Share
Context/wrapper mean > local-edit mean
1,000 / 1,000
100.0%
Every context/wrapper setting > both local edits
997 / 1,000
99.7%
Table S8: Prompt-level consistency over the 1,000 representation-corpus prompts.
Figure S5: Comparison of the main feature selection rule with an alternative rule that treats all fifteen variants individually. A, mean support size; B, rates of undersized and empty selections; C, Jaccard overlap between the supports chosen by the two rules; D, unit level normalized MeanRSS under the two rules. Transformation abbreviations as in Figure S2 .
Setting
Spearman
Minimum
Gap
Mean ∣S∣
Jaccard
Reference
1.00
1.00
0.626 [0.604, 0.646]
13.2
1.00
ρ=0.6
1.00
0.94
0.632 [0.610, 0.652]
13.8
0.90
κ=0.6
1.00
0.77
0.595 [0.571, 0.617]
17.4
0.61
K=10
1.00
0.89
0.702 [0.680, 0.723]
8.6
0.75
K=50
1.00
0.94
0.537 [0.514, 0.558]
17.5
0.89
Table S9: Selector parameter ablation on a stratified prompt pool. The reference uses ρ=κ=0.8 and K=20 ; other rows change one parameter. Gap is the context and wrapper mean minus the local-edit mean, with 95% confidence intervals in brackets.
Criterion
Specifications
Full six-setting order preserved
17 / 25
Top setting preserved
20 / 25
Bottom setting preserved
25 / 25
Table S10: Transformation-ranking robustness across 25 combinations of magnitude summaries and normalization schemes.
τ
Available
Profile Spearman
Gap
Positive units
0.001
99.99%
0.943
0.835
27/27
0.01
99.94%
0.943
0.817
27/27
0.05
99.65%
0.943
0.756
27/27
0.1
99.40%
0.943
0.706
27/27
Table S11: RSS after scaling feature changes using clean-prompt activations. Profile Spearman is relative to the main result; Gap is the context and wrapper mean minus the local-edit mean.
Setting and level
Definition
Tokens
Edits
Irrelevant context 1
4–8 added tokens
4.00
0
Irrelevant context 2
12–16 added tokens
12.00
0
Irrelevant context 3
24–32 added tokens
24.00
0
Irrelevant context 4
48–64 added tokens
48.00
0
Format wrapper 1
single label or quote
3.24
10.4
Format wrapper 2
envelope with two fields
8.92
28.2
Table S12: Intensity-level definitions and realized values. Tokens and edits are mean counts.
Sel.
Eval.
Reliability
Profile
Sign
CV
Jac.
3
12
0.773 [0.763, 0.782]
0.805
0.960
0.221
0.393
5
10
0.802 [0.792, 0.810]
0.827
0.964
0.189
0.539
8
7
0.714 [0.703, 0.724]
0.773
0.946
0.268
0.527
10
5
0.681 [0.670, 0.691]
0.765
0.946
0.279
0.654
Table S13: Split-half reliability by selection size. Brackets give 95% confidence intervals. Profile is stability against the 15-variant reference; Sign is transformation-group sign stability; Jac. is split-to-split support Jaccard.
Method
Sel.
Reliability
Profile
Sign
RSS support
3
0.773
0.805
0.959
RSS support
5
0.802
0.827
0.964
RSS support
8
0.714
0.773
0.946
RSS support
10
0.681
0.765
0.946
Clean support
3
0.772
0.809
0.921
Clean support
5
0.752
0.792
0.918
Table S14: Reliability by selection method and selection size. Column definitions follow Table S13 .
Fold
Avail.
Profile
Gap
Pos. units
Same dir.
Group sign
Pairwise
0
99.985%
1.000
0.909
27/27
0.940
99.92%
93.49%
1
99.985%
1.000
0.896
27/27
0.957
99.86%
92.00%
2
99.989%
1.000
0.897
27/27
0.959
99.87%
92.15%
Table S15: Fixed-support evaluation with one realization per operator used for selection. Profile is Spearman correlation with the 15-variant reference; Gap is the context and wrapper mean minus the local-edit mean; Pos. units is the number of SAEs with positive Gap; Group sign and Pairwise are prompt-level ordering rates.
Support
Absolute response
95% CI
Same direction
95% CI
RSS
107.670
[106.749, 108.597]
0.952
[0.951, 0.952]
Random, 100 draws
5.797
[5.748, 5.846]
0.758
[0.758, 0.759]
Table S16: Held out response for RSS and random supports matched in candidate pool and support size. Brackets give 95% confidence intervals.
Selection requirement
Available
Same direction
Gap
4 of 4 operators
99.42%
0.894
0.925
3 of 4 operators
100.00%
0.848
0.896
Table S17: Evaluation with one transformation operator excluded from support selection. Gap is the context and wrapper mean minus the local-edit mean.
Model
Unit
λ
Weights
Clean AUROC
Harmful FNR
Benign FPR
Gemma 3 4B
L17
0.01
415
0.941 [0.914, 0.963]
23.3%
7.3%
Llama 3.1 8B
L24
0.001
862
0.919 [0.884, 0.949]
33.3%
6.0%
Table S18: Safety probes and clean test performance. Brackets give 95% confidence intervals for AUROC; FNR and FPR are false-negative and false-positive rates.
Figure S6: Probe AUROC for the two safety readouts on untransformed test prompts and under each transformation. Transformation abbreviations as in Figure S2 . Error bars show 95% bootstrap confidence intervals.
Figure S7: Normalized MeanRSS and margin erosion on held out variants for each transformation, evaluated on the audited safety units. Transformation abbreviations as in Figure S2 . Error bars show 95% bootstrap confidence intervals.
Model
Setting
Norm. MeanRSS
Erosion
Flip
AUROC
Gemma 3 4B
Irrelevant context
1.118 [1.102,1.134]
0.132 [0.029,0.235]
6.1%
0.928
Distractor context
1.263 [1.244,1.284]
0.138 [0.024,0.249]
5.6%
0.935
Metalinguistic wrapper
1.113 [1.098,1.128]
0.231 [0.121,0.344]
6.6%
0.926
Format wrapper
1.190 [1.172,1.208]
0.037 [-0.084,0.152]
8.0%
0.935
Punctuation noise
0.524 [0.506,0.541]
0.158 [0.098,0.218]
4.2%
0.933
Typed lexical substitution
0.792 [0.759,0.825]
0.146 [0.068,0.223]
4.6%
0.938
Table S19: MeanRSS and probe outcomes by transformation setting. Brackets give 95% confidence intervals for normalized MeanRSS and erosion. Erosion is mean held out margin loss; Flip is the fraction of predictions that differ from the clean prediction.
Figure S8: Effect of transformation strength on the audited safety units. A, margin erosion under three transformations rebuilt at four increasing intensity levels, with 95% bootstrap confidence intervals. B, MeanRSS for the same series, relative to the weakest level.
Model
Setting
Eligible
MeanRSS ρ
MeanRSS mono.
Erosion ρ
Erosion mono.
Gemma 3 4B
Irrelevant context
300
0.8
78/254
0.4
51/254
Format wrapper
300
1.0
203/254
0.4
63/254
Punctuation noise
265
1.0
137/222
0.4
37/222
Llama 3.1 8B
Irrelevant context
300
0.8
67/241
0.2
39/241
Format wrapper
300
1.0
192/241
0.4
51/241
Punctuation noise
265
1.0
138/212
0.6
62/212
Table S20: Prompt-level intensity calibration in the safety corpus. Monotonic counts use prompts whose mean response is nondecreasing across the four levels.
Model
Risk signal
Erosion ρ
Failure AUROC
AP
Gemma 3 4B
Clean margin
-0.282 [-0.370,-0.192]
0.863 [0.821,0.900]
0.294
Full ℓ1
0.101 [0.025,0.173]
0.520 [0.444,0.595]
0.072
Full cosine
0.083 [0.006,0.157]
0.486 [0.398,0.572]
0.063
MeanRSS
0.116 [0.040,0.188]
0.526 [0.446,0.599]
0.069
Probe exposure
0.104 [0.029,0.178]
0.597 [0.510,0.683]
0.107
MeanRSS × exposure
0.130 [0.049,0.210]
0.606 [0.524,0.689]
0.091
Table S21: Risk signals on the common held out cohort. Brackets give 95% confidence intervals. Erosion ρ is Spearman correlation with held out margin erosion; AUROC and AP use recurrent failure. Residual-margin correlation is reported in the direction of increasing risk.
Model
RSS
Magnitude only
Gemma 3 4B
0.876 [0.872, 0.879]
0.816 [0.810, 0.822]
Llama 3.1 8B
0.871 [0.867, 0.874]
0.794 [0.788, 0.800]
Table S22: Held out response in the direction selected by RSS compared with magnitude-only selection. Brackets give 95% confidence intervals.
Model
RSS contribution
Matched contribution
Difference
Direction agreement
Gemma 3 4B
0.2397
0.0221
0.2177 [0.2005, 0.2356]
97.4%
Llama 3.1 8B
0.3702
0.0220
0.3483 [0.3235, 0.3739]
97.1%
Table S23: Held out feature contribution after matching selected and unselected features by readout coefficient magnitude. Contribution columns report mean absolute contribution. Direction agreement compares observed contribution sign with sign(−ywfsf) . Brackets give 95% confidence intervals for the paired difference.
Model
RSS
Mismatched RSS
∣ef∣
Gemma 3 4B
0.430 [0.411, 0.450]
0.326 [0.308, 0.346]
0.942 [0.936, 0.948]
Llama 3.1 8B
0.562 [0.547, 0.577]
0.435 [0.417, 0.453]
0.919 [0.912, 0.925]
Table S24: Margin Contribution Retention at K=20 . Mismatched RSS uses a support selected for another transformation; ∣ef∣ ranks features by contributions computed from Vsel . Brackets give 95% confidence intervals.
Model
Feature set
Erosion ρ
Failure AUROC
Gemma 3 4B
Full readout
0.923 [0.909, 0.935]
0.785 [0.721, 0.842]
RSS support
0.737 [0.700, 0.771]
0.753 [0.686, 0.815]
Llama 3.1 8B
Full readout
0.896 [0.878, 0.911]
0.705 [0.639, 0.766]
RSS support
0.793 [0.761, 0.820]
0.735 [0.666, 0.797]
Table S25: Margin erosion results for the full readout and RSS support. Erosion ρ is correlation with held out erosion, and Failure AUROC ranks recurrent failure using the corresponding erosion score. Brackets give 95% confidence intervals.
Model
Feature set
Residual ρ
Residual AUROC
Gemma 3 4B
Full readout
0.169 [0.077, 0.261]
0.965 [0.939, 0.982]
RSS support
0.009 [-0.081, 0.105]
0.935 [0.901, 0.961]
Llama 3.1 8B
Full readout
0.152 [0.065, 0.243]
0.964 [0.940, 0.982]
RSS support
0.080 [-0.006, 0.171]
0.958 [0.924, 0.981]
Table S26: Residual margin results for the same cohort. Both feature sets use the full clean margin. Correlation with held out erosion is oriented toward increasing risk; AUROC evaluates recurrent failure. Brackets give 95% confidence intervals.
Model
Feature set
Size
Erosion ρ
Residual AUROC
Errors
Harmful FN
Gemma 3 4B
Full readout
415
0.923
0.965
94.1%
90.9%
RSS support
20
0.737
0.935
89.2%
87.3%
Llama 3.1 8B
Full readout
862
0.896
0.964
91.9%
93.5%
RSS support
19
0.793
0.958
92.8%
94.4%
Table S27: Summary of the full frozen readout and RSS supports selected for each case on the common evaluation cohort. Size is the full nonzero coefficient count or median support size. Both residual margin signals use the full clean margin. Errors and Harmful FN are capture rates at 20% offline review with known labels.
Layer
∣S∣
Same direction
MCR
Residual AUROC
R2
Restoration
8
20
0.960
0.628
0.905
0.814
0.566
16
20
0.970
0.578
0.806
0.692
0.807
Table S28: Functional results for two additional Llama 3.1 8B layers under the main audit protocol.
Model
Support
Size
R2
Errors reversed
Qres
Gemma 3 4B
RSS support
20
0.579 [0.532, 0.621]
0.722 [0.635, 0.803]
0.618
Mismatched setting
20
0.438 [0.386, 0.481]
0.603 [0.512, 0.683]
0.368
Global instability
20
0.017 [-0.008, 0.035]
0.067 [0.018, 0.151]
0.000
Random matched
20
0.014 [-0.006, 0.022]
0.012 [0.002, 0.026]
0.002
Llama 3.1 8B
RSS support
19
0.627 [0.568, 0.675]
0.718 [0.610, 0.807]
0.800
Mismatched setting
19
0.490 [0.406, 0.560]
0.611 [0.487, 0.721]
0.590
Table S29: Reconstruction and readout-counterfactual results. Baseline supports are matched to RSS support size; brackets give 95% confidence intervals. Qres is the share of probe logit change recovered from the support.
Ranking signal
Capture@10
Capture@20
Harmful FN@20
Residual error
Δ pAURC
Residual margin mres
85.1%
94.1%
90.9%
0.25%
+0.0276 [0.0175,0.0385]
Low clean margin
41.3%
68.9%
60.9%
1.30%
+0.0186 [0.0117,0.0267]
+ probe weights
32.1%
47.6%
49.5%
2.20%
+0.0109 [0.0046,0.0180]
MeanRSS
11.0%
18.8%
18.2%
3.40%
+0.0007 [-0.0026,0.0046]
Table S30: Selective-review summary for the Gemma probe. Capture columns give the fraction of errors reviewed at the stated budget. Residual error is reported at a 20% review budget. pAURC is the normalized partial area under the residual error curve from 0 to 40% review, and Δ pAURC is the random ranking pAURC minus the listed value; brackets give 95% confidence intervals.
Model
Ranking signal
Errors
Harmful FN
Gemma 3 4B
Residual margin mres
94.1 [90.2, 96.5]
90.9 [81.9, 95.7]
RSS residual margin mresS
89.2 [81.8, 93.5]
87.3 [72.4, 94.9]
Mismatched RSS residual
86.5 [78.7, 92.0]
85.9 [69.8, 93.5]
Margin erosion E
63.6 [49.3, 74.8]
62.3 [35.4, 78.2]
RSS margin erosion ES
64.2 [50.1, 75.0]
66.8 [44.4, 81.1]
Llama 3.1 8B
Residual margin mres
91.9 [87.6, 95.6]
93.5 [88.7, 97.4]
Table S31: Selective review at a 20% budget for the rankings in Figure 6 C–D. Values are capture percentages; brackets give 95% confidence intervals.
Model
Method
Clean
Mean
Worst
Worst FNR
Gap
Gemma 3 4B
MeanRSS sampling
0.945
0.943
0.938
0.191
0.0067
Gemma 3 4B
Uniform
0.933
0.934
0.926
0.238
0.0071
Llama 3.1 8B
MeanRSS sampling
0.911
0.910
0.901
0.256
0.0100
Llama 3.1 8B
Uniform
0.915
0.913
0.907
0.263
0.0082
Table S32: Retrained-probe results for Figure S9 A. Clean, Mean, and Worst are AUROC; Gap is clean minus worst AUROC.
Figure S9: Augmentation guided by MeanRSS compared with uniform sampling. A, differences between the two sampling methods in clean, mean, and worst transformation AUROC, together with the reduction in harmful false negative rate under the worst transformation. Error bars show 95% bootstrap confidence intervals. B, harmful false negative rate averaged over the six transformations across five runs. Bars show the run mean and whiskers the observed range.
Sparse Autoencoders (SAEs) extract features from LLM internal activations, meant to correspond to interpretable concepts. A core SAE training hyperparameter is L0: how many SAE features should fire per token on average. Existing work compares SAE algorithms using sparsity-reconstruction tradeoff plots, implying L0 is a free parameter with no inherently correct value aside from its effect on reconstruction. In this work we study the effect of L0 on SAEs, and show that if L0 is not set correctly, the SAE fails to disentangle the underlying features of the LLM. If L0 is too low, the SAE will mix correlated features to improve reconstruction. If L0 is too high, the SAE finds degenerate solutions that also mix features. Further, we present a proxy metric that can help guide the search for the correct L0 for an SAE on a given training distribution. We show that our method finds the correct L0 in toy models and coincides with peak sparse probing performance in LLM SAEs. We find that most commonly used SAEs have an L0 that is too low. Our work shows that practitioners must set L0 correctly to train SAEs with monosemantic features.
Sparse Autoencoders (SAEs) are widely used to interpret large language models by decomposing activations into sparse, human-understandable features, but scaling to large dictionaries exposes fundamental challenges. Systematic studies reveal pervasive feature splitting that fragments coherent concepts into non-atomic latents and widespread feature absorption that creates arbitrary exceptions in general features, severely compromising latent reliability. These issues stem from inconsistent latent assignment across samples: without cross-sample constraints, per-sample optimization often allows a single underlying concept to be inconsistently distributed across multiple redundant or interfering latents. To address this, we introduce C2R (Cross-sample Consistency Regularization). C2R explicitly encourages that each semantic feature is consistently represented by a unified latent across the batch by penalizing the co-activation of directionally similar latents. Comprehensive evaluation demonstrates that C2R effectively mitigates both splitting and absorption while, crucially, preserving reconstruction fidelity, providing a principled solution that enhances latent interpretability without degrading model performance. Source code is available at https://github.com/hr-jin/Cross-sample-Consistency-Regularization.
Haoran Jin, Xiting Wang, Shijie Ren +2
University of Science and Technology of China · State Key Laboratory of Cognitive Intelligence · Gaoling School of Artificial Intelligence, Renmin University of China
Sparse autoencoders (SAEs) are increasingly scaled to wider dictionaries to recover fine-grained structure from large language model activations. However, a feature is useful for interpretation only if it remains a stable unit of analysis when the same meaning is expressed in different surface forms. We study this reliability question for TopK SAEs via feature sensitivity. Experiments demonstrate that scaling selectively reduces the sensitivity of rare features, while common features remain comparatively stable. A controlled width×k factorial experiment identifies the active budget k as the root cause: the degradation arises from the selection boundary rather than dictionary width alone. We attribute this failure to the geometry of TopK selection. The active margin, the distance to the cutoff, predicts feature loss without thresholds. Guided by this margin diagnosis, we introduce pairwise rank stabilization. Our method targets ordering failures at the cutoff and improves rare-feature sensitivity by 8.83 percentage points, while keeping reconstruction and alive-feature coverage near the baseline. Overall, our results suggest that wide TopK SAEs should be evaluated not only by reconstruction, sparsity, and feature count, but also by feature reliability under semantic variation and boundary geometry for stable interpretability.
Zhenting Huang, Bo Jiang, Junnan Liu +2
Beihang University · Monash University · Zhongguancun Laboratory