Sparse Autoencoders Learn Monosemantic Features in Vision-Language Models
Authors: Mateusz Pach
Shyamgopal Karthik
Quentin Bouniot
Serge Belongie
Zeynep Akata
Venue: NeurIPS 2025 poster ()
Keywords: sparse autoencoders
interpretability
steering
vision and language models
Primary area: social_and_economic_aspects_of_machine_learning

Abstract: Sparse Autoencoders (SAEs) have recently gained attention as a means to improve the interpretability and steerability of Large Language Models (LLMs), both of which are essential for AI safety. In this work, we extend the application of SAEs to Vision-Language Models (VLMs), such as CLIP, and introduce a comprehensive framework for evaluating monosemanticity at the neuron-level in visual representations. To ensure that our evaluation aligns with human perception, we propose a benchmark derived from a large-scale user study. Our experimental results reveal that SAEs trained on VLMs significantly enhance the monosemanticity of individual neurons, with sparsity and wide latents being the most influential factors. Further, we demonstrate that applying SAE interventions on CLIP's vision encoder directly steers multimodal LLM outputs (e.g., LLaVA), without any modifications to the underlying language model. These findings emphasize the practicality and efficacy of SAEs as an unsupervised tool for enhancing both interpretability and control of VLMs.
Code and benchmark data are available at https://github.com/ExplainableML/sae-for-vlm.

Sparse Autoencoders Learn Monosemantic Features in Vision-Language Models
Mateusz Pach 1,2,3,4
Shyamgopal Karthik1.2.344 1.2,3.4,5 Quentin Bouniot
Serge Belongie
Zeynep Akata 123,444
Technical University of Munich "Munich Data Science Institute
Helmholtz Munich Munich Center for Machine Learning
University of Tübingen University of Copenhagen
mateusz. aateusz.ppachtuum. www.pppc..hhaeeee
Abstract
Sparse Autoencoders (SAEs) have recently gained attention as means to improve the interpretability and steerability of Large Language Models (LLMs), both of which are essential for safety. this work, we extend the application SAEs to Vision-Languaan Models (VLMs), such as CLIP, and introduce comprehensive framework for evaluating monosemanticity at the neuron-level in visual represen- tations. To ensure that our evaluation aligns with human perception, propose a benchmark derived from a large-scale user study. Our experimental results reveal that SAEs trained VLMs significantly enhance the monosemanticity individual neurons, with sparsity and wide latents being the most influential factors. Further, demonstrate that applying SAE interventions sion encoder directly steers multimodal LLM outputs (c.g., LLaVA), without any modifications to the underlying language model. These findings emphasize the practicality and efficacy of SAEs as an unsupervised tool for enhancing both in- terpretability and control of VLMs. Code and benchmark data available httpauu..ccc/pppaaaaaaelllllaaaa
CLIP's vi-
Introduction
In recent years, Vision-Language Models (VLMs) like CLIP [47 and SigLIP [6] have gained widespread adoption, owing to their capacity for simultancous reasoning over visual and textual modalities. They have found a surge of applications in various modalities, such as in audio [4 57 and medicine [62], transferring to new tasks with minimal supervision. Yet our current understanding of VLM internals remains limited, necessitating methods that systematically probe their rep- resentations. Sparse AutoEncoders (SAEs) [37 are an effective approach to probing the internal representations of such models. They efficiently discover concepts (abstract features shared between data points) through their simple architecture learned as a post-hoc reconstruction task. Although analysis with SAES is popular for Large Language Models (LL.Ms) 7
23 48 for VLMs it has been limited to interpretable classification 35 or the discovery of concepts shared across models (53
Intuitively, SAEs reconstruct activations via higher-dimensional space to disentangle distinct concepts from their overlapping representations neural activations Neurons at different layers within deep neural networks are known to be naturally polysemantic 41, meaning that they can be strongly activated for multiple unrelated concepts such as cellphones and rulers. One common explanation for this behavior is the superposition hypothesis [7]. stating that concepts are encoded as linear combination of neurons. SAEs explicitly attempt to solve this issue by separating the entangled concepts into distinct representations. Despite their widespread use in research, the absence of a metric to evaluate SAEs at the newron-level still hinders their practicality as an interpretation tool.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Activating images:
Activating images:
VI.M
VLM
MS 0.01
MS = 0.85
SAE
Figure 1: Sparse Autoencoder (SAE) in VLM (e.g. CLIP): Top activating images of a neuron in pretrained VLM layer are polysemantic (left), and those of neuron sparse latent of SAE trained to reconstruct the same layer are monosemantic (right), according to MonoSemanticity score (MS).
Discovering neurons encoding interrrattereeeaale concepts requires analyzing them individually, which is even more tedious layers of both the model and SAE are wide.
In this work, we quantitatively evaluate SAEs for VLMs through monosemanticit, defined as the similarity between inputs that strongly activate neuron. We propose the MonoSemanticity score (MS) for vision tasks, that measures the pairwise similarity of images weighted by the activations for given neuron. Unlike natural language where individual words require surrounding context (such as complete sentences) to clearly identify their meanings, individual images can directly activate neurons without additional context. We define highly activating images as images that strongly fire a particular neuron. Greater similarity among these images suggests that the neuron is more narrowly focused on single concept, reflecting higher neuron monosemanticity. Using our MS score, we observe and validate that neurons SAE are significantly more monosemantic (see Figure [ right) than the original neurons (see Figure I left). The neuron of the original VLM typically has low MS score, fires for a wide range of objects, from cellphones to rulers. On the other hand, neurons within the SAE single concept, c.g. parrots, obtaining higher score. This holds even for SAE with the same width as the original layer, implying that the sparse reconstruction objective inherently improves the separability of concepts. We further conduct large-scale study quantitatively assess alignment of our proposed MS score with human interpretation of monosemanticity. The results confirm that the difference between scores of two neurons strongly correlates with humans perceiving the higher-scoring neuron as more focused on a single concept.
more focused
Finally, we illustrate applicability of the monosemanticity of vision SAEs by transferring CL.IP- based SAE onto Multimodal LLMs (MLLMs), e.g. LLaVA VA (36). Intervening on a single monoseman- tic SAE neuron in the vision encoder while keeping the LLM untouched allows steering the overall MLLM generated output to either insert or suppress the concept encoded in the selected SAE neuron. We summarize contributions follows:
We propose the MonoSemanticity score (MS) for SAEs in vision tasks, that computes neuron-wise activation-weighted pairwise similarity of image embeddings. To validate our MS score against human judgment, we conduct large-scale user study, the results of which can also serve a benchmark for future research.
We quantitatively compare MS between SAEs, and across their neurons. We find that Matryoshka SAE 99 39 achieves overall superior MS, and that wider and sparser latents lead to better scores.
We leverage the well-separability of concepts in SAE layers intervene on neuron activa- tions and steer outputs of MILMs to insert or suppress any discovered concept.
2 Related Work
Sparse Autoencoders. Recent studies have repurposed traditional dictionary learning to enhance LLM and VLM interpretability (6, [46]. Specifically, there has been success in interpreting and steering LLMs with features learned by SAES [66 [2]. Several enhancements to SAB mechanisms
have been introduced, including new activation functions such as Batch TopK g or JumpReL.U [48

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SAE
918
+10
PLN
fi
921
r/a
451
:
Kisv
#51
Vision
Encoder
R
[x),
Liscemsy Frns Fort
MS
SiSSeresh Fam
(a) Extracting embeddings and activations
(b) Pairwise similarity matrix
(c) Activation-wwiihtee average
Figure 2: Computation of our MonoSemanticity score (MS). (a) Embeddings and activations are extracted for a set of images (b) to compute the pairwise embedding similarities and pairwise neuron activations. (c) MS is the average embedding similarities weighted by the neuron activations.
and insights from Matryoshka representation learning for SAES 39
We analyze and evaluate
neuron-level monosemanticity of SAES in VLMs and their downstream uses.
Vision-Language Models. Since Contrastive Language Image Pretraining (CLIP) many models have emerged that align images and text in a shared embedding space 32 56 or generate text conditioned
38
47
They have achieved strong results As trust in these models has become 60), understanding decision-making and ensuring safety, for example through steering, is increasingly important (2 29]. Consequently, prior work has examined their internal representations 22 40 45), uncovering interpretable neurons ([5). We demonstrate that SAEs enable more effective interpretation and control than directly operating on raw features.
image inputs [2
19
36
benchmarks (59 and found many use-cases 55
24
26 28
concern 4
SAEs for VLMs. Building the success of SAEs in interpreting LLMs, researchers have tried applying them to vision and Dision-languas models, typically on CLIP (20 35 49 [5) and other vision encoders (e.g. DINOv2 [44). There has also been interest in interpreting the denoising
diffusion models [25 using SAEs I 30 31 51], discovering common concepts across different
vision encoders [53] and applying them multimodal LLMs [63] Concurrently, monosemanticity
of multimodal models has been investigated (58). although focusing on inter- modality differences.
Our MS score provides grounded, quantitative measure of the monosemanticity of individual neurons which is empirically aligned with human perception. Overall, we create rigorous evaluation framework for SAEs in VLMs, well demonstrating their for steering multimodal LLMs.
3 Sparse Autoencoders for VLMs
3.1 Background and Formulation of SAEs
SAEs implement form sparse dictionary learning, where the goal is to learn a sparse decomposi- tion of signal into overcomplete dictionary of atoms [4]. More specifically, an SAE consists of linear layers W ene dx= and W doc E Rwxd encoder and decoder, with non-lineas activation function Ø R + R Both layers share bias term b E Rd subtracted from the encoder's 's input and later added to the decoder's output. The width w of the latent SAE layer is chosen as a factor of the original dimension, such that w = d where is called the expansion factor.
Rd of given layer of the model explain f: X + Y. such that fi X + gg represents the composition of the first layers and X C lRd. is the space of input images. A given input image X is first transformed into the corresponding embedding vector v = (x), before being decomposed by the SAE into a vector of activations ((v) E RW, and its reconstruction vector v E Rd obtained by:
In general, SAEs are applied on embeddings

---

o(v) == o ( enc (v b)), (vv) W V +b, V:= (v(v).
(1)
The linear layers W one and W doc composing the SAE are learned through reconstruction objective R and sparsity regularization S, to minimize the following loss:
[(v) == R(v) XS(v),
(2)
where À is hyperparameter governing the overall sparsity of the decomposition. The most simple instantiation 49 uses ReLU activation, an I reconstruction objective and an L sparsity penalty,
such that
a(.) := -e), R(v) = || VI S(v) == [|o(())l
The (Batch) TopK SAEs 8 23 37
use TopK activation function governing the sparsity directly
39 group neuron activations o' (v) into different levels of sizes M, to obtain a nested dictionary trained with multiple reconstruction objectives:
through K. Finally, Matryoshka SAEs [9]
R(v)
Σ MEM
Iv
W d 1.mm (v)ll2,
where 6=.m corresponds to keeping only the first m neuron activations, and setting the others to zero. It is important to note that Matryoshka SAEs can be combined with any SAE variant, c.g. with BatchTopp 9 or ReLU [39, as only the reconstruction objective is modified.
3.2 Monosemanticity Score
neuron's interpretability increases as its representation becomes disentangled into a single, clear concept. Therefore, quantifying the monosemanticity of individual neurons helps identify the most interpretable ones, while aggregating these scores across an entire layer allows assessing the overall semantic clarity and quality of the representations learned by the SAE. We propose measuring monosemanticity by computing pairwise similarities between images that strongly activate a given neuron, where high similarity indicates these images likely represent the same concept. These similarities can be efficiently approximated using deep embeddings from a pretrained image encoder E. Since selecting fixed number of top-activating images is challenging due varying levels of specialization across neurons, we instead evaluate monosemanticity over a large, diverse set of unseen images, weighting each image by its activation strength for the neuron.
We formally describe our proposed MonoSemanticity score (MS) below, with an illustration given in Figure 2 This metric can be computed for each of the neurons extracted from the SAE. Given a diverse set of images I = {x,, E {X]W> and a pretrained image encoder E, we first extract embeddings obtain pairwise similarity matrix S = [ E N which captures semantic similarity between each pair of images. The similarity 8am of the pair (xn: Xm) is computed as the cosine similarity between the corresponding pair of embedding vectors:
E(x,)) E(xm)
Sym
(5)
We then collect activation vectors (a* = [at]n E R RN | across all neurons, for all images in the dataset Z. Specifically, for each image Xa, the activation of the k-th neuron:
Vn := f((x,), a == ==((v,,,
(6)
where represents the layer which the SAE is applied, fi is the composition of the first / layers of the explained model, and Ø² is the k-th neuron of σ(v,)) (or of v, when evaluating neurons of the original layer| of f). To ensure a consistent activation scale, we apply min-max normalization to each a², yielding a := [alln E [0, 1]M, where
min,
ā max, a min, a
(7)
Using these normalized activations, we compute a relevance matrix R = [r E [0, 1] for each one of the neurons, which quantifies the shared neuron activation of each image pair:
p. : a
(8)
Finally, our proposed score M E 1_ for the k-th neuron is computed as the average pairwise similarity weighted by the relevance, without considering same image pairs (x,,,,))
M Eisnemen r Sum
(9)
Eienemen rhm

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0.9
MS
0.0
N45164
NI 1054
NP1527
N19999
NH1771 I
NH834S
NO1918
NP1639
NI66933
NO 75
Figure 3: Top activating images of neurons with MonoSemanticity (MS) scores ranging from high (left) to low (right). Higher scores correlate with more similar images, reflecting monosemanticity.
3.3 Steering MLLMs with Vision SAES
Finding monosemantic neurons is not only useful for interpretability. The SAEs let us induce controllable semantic biases in the response of MLLMs without modifying the underlying model parameters, and without touching any textual part. In other words, we can steer the model into seeing or not targeted concepts in the image. Our MS score becomes a strong tool to help select the most monosemantic neurons for precise and efficient steering.
We first describe LLaVA (36] as an example MILM architecture. The LLaVA model g X expects a pair of image and text (x, and outputs text answer o, where C Re is the word embedding space. Internally, it converts the image into fx N token embeddings {v:) obtained from vision encoder fi X + [dxx(x composed of the first / layers of CLIP [47). These embeddings are then projected into visual tokens Hx E IR4 x in the word embedding space, and are finally fed along with tokenized text H, Rd into the pretrained LLM (e.g. LLaMA [54] or Vicuna (10) to obtain the output text o.
We modify this architecture by injecting a pretrained SAE (#, rb) of width w at the token-level after the vision encoder fi. For all token embeddings v; IR i fl,..., }x we first extract the SAE decomposition into activation a, := σ(v,) R= across all neurons. After identifying the neuron k E (1....,,) w representing the targeted concept, to steer the overall model g towards this concept, we manipulate the SAE activations of all token embeddings for the neuron & to obtain (å, E R=)
a j j=k d
Vj E w), af
(10)
j
where a E R is the intervention value we want to apply to the activation of neuron k. Finally, we decode the manipulated activation vectors for each token å, back into a manipulated token embedding v; (ā,) E IR with the SAE decoder. Token embeddings are then processed as usual to generate the steered LLaVA's response. We include an illustration of the overall process in the Appendix.
4 Experiments
4.1 Experimental Settings
We apply SAES explain fixed and pretrained CLIP ViT-L/14-336px 477, SigLIP SoVIT-400m/14
384px [61), AIMv2 L/14-224px [19], and WebSSL TAAAE-000/14-2255 [18]. The SAEs are trained on activation vectors pre-extracted from the model's responses to ImageNet [3] images. For CLIP, activation vectors are extracted from the classification (CLS) tokens in the residual stream after layers E (11, 17, 22, 23), or from the output of the final projection layer. For steering experiments, however, the SAEs are trained on activation vectors corresponding to two random token embeddings
5

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per image, taken from layer I = 22. For other encoders, we similarly use the CLS tokens from the final layers, or two random token embeddings if a CLS token is not available.
In the following sections, we are interested in both BatchTopk [8] and Matryoshka Batch- [ variants. If not stated otherwise, we set the groups of Matryoshka SAEs as M = {0.0625w, 0.1875w, 0,4375w, w). which roughly corresponds to doubling the size of the number of neurons added with each level down. For the BatchTopK activation, we fix the maximum number of non-zero latent neurons to K = 20. Both SAE types are compared across a wide range of expansion factors E 21 8, 16, 64). All SAES are optimized for 10 steps with minibatches of size 4096 using Adam optimizer 33 with the learning rate initialized at 125 following previous
TopK SAES
work 233. To measure SAE performance, we use It2 for reconstruction quality and the L norm for the activation sparsity of Φ(v). Throughout the paper, we quantify MS of neurons using DINOv2 ViT-B [44] as image encoder E, and present more analysis with different encoders in Appendix. Experiments on a single NVIDIA A100 GPU.
4.2 Evaluating Interpretability of VLM Neurons
4.2.1 Alignment of MS with human perception
We first illustrate the correlation be- tween MS score and the underlying
1.0
Alignment Rate
monosemanticity of neurons, with ex- amples in Figure 3 of the 16 highest
0.9
0.8
activating images for neurons with de-
0.7
creasing MS from left to right. We
observe that the highest scoring neu-
0.6
rons (with MS 0.9, on the far left)
0.5
are firing for images representing the same object, i.e. close-up pictures of a koala (on the top) and a hockey (on the bottom). As the score decreases, the corresponding neurons fire for less similar or even completely different objects or scenes. To verify this obser- vation in a more quantitative way, we conducted a large scale user study on the Mechanical Turk platform. This study resulted in total of 1000 questions across 71 unique users, with 3 answers per question aggregated through majority voting. Results of this study are presented in Figure and we provide more details on the setup in Appendix. When asked to select the set of more monosemantic images from a pair of sets (a, b). the users answered in accordance to the MS in 82.8% of the cases, assuming MS(b)] ~ ((0 0.9). This alignment rate monotonically raises from 56.6% for E (0.0, 0.1) to 100.0% for E (0.8, 0.9), highlighting that users especially agree with MS as the difference in monosemanticity between the two sets becomes more pronounced. This demonstrates that MS can be used as a reliable measure aligning well with human perception of similarity. Detailed results of the user study are released for future benchmark of image similarity and monosemanticity.
0.0-0.1
0.1-0.2
0.2.0.3
0.300.4
0.4-0.5
0.500.6
0.6-0.7
0.7-0.8
0.8-0.9
MS Difference
Figure 4: Alignment Rate (AR, %) of humans with MS score when judging which neuron in a pair is more monosemantic, grouped by MS difference between the neurons. Bars show AR per interval; dots show cumulative AR up to that interval.
6 = MS(a)
4.2.2 Monosemanticity of SAES
In Table la we report MS of the highest scoring neurons of two SAE types (BatchTopK (8] and Matryoshka BatchTopK (9) trained at different layers with various expansion factors We also include results for original neurons of the corresponding layer decomposed by SAFs ("No SAF"). We observe that SAES' neurons consistently have significantly higher MS for their best neuron when compared to original ones, implying that SAES are better separating and disentangling concepts between their neurons. Interestingly, while the highest MS score is increasing with higher expansion factor E, i.e. with increased width w of the SAE layer, this holds true already for expansion factor E meaning that the disentanglement of concepts is also linked the sparse dictionary learning and not only to the increased dimensionality. Finally, comparing SAE variants, we observe that while the Matryoshka reconstruction objective improves the concept separation at same expansion factor, also achieves about 2 or 3 points lower R²² for the same expansion factors (more details in Appendix).

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Table Sparse Autoencoders (SAEs) decompose "No SAE" neurons into more monosemantic units as shown by MonoSemanticity (MS) score. Higher SAE expansion factors yield higher MS scores.
(a) Highest MS scores of neurons various CLIP arge
layers.
(b) Top MS scores of neurons from last layers of different vision en- coders. Improvements in MS score from applying Matryoshka SAEs are consistent across all the models.
SAE
No SAE
Expansion factor
Layer
type
X
x2
4
x8
16
x 64
11
0.01
0.61
0.73
0.71
0.87
0.90
1.00
BatchTopk
17
0.01
0.65
0.79
0.86
0.86
0.93
1.00
0.01
0.66
0.79
0.80
0.88
0.92
1.00
Vision Encoder
No
Exp.
factor
23
0.01
0.73
0.72
0.83
0.89
0.93
1.00
SAE
x
x4
last
0.01
0.57
0.78
0.78
0.81
0.85
1.00
WebSSL
[8]
0.01
0.79
0.92
11
0.01
0.84
0.90
0.95
1,00
0.89
1.00
Matryoshka
CLIP
47
0.82
0.89
9 39
17
0.01
0.86
0.84
0.93
0.94
0.96
1.00
SigLIP
0.01
0.83
0.88
22
0.01
0.83
0.83
0.87
0.94
1.00
1.00
AIMv2
19
0.01
0.59
0.85
23
0.01
0.82
0.84
0.89
0.93
0.96
1.00
last
0.01
0.82
0.91
0.89
0.93
0.91
1.00
No SAE
No SAE
Monosemanticlty Score
0.75
Expansion factor
Monosemanticity Score
K
x2 x
10
20
50
x16 X64
0.50
0.50
0.25
0.25
0.00
0.00
0.0
0.2
0.4
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
Normalized Index
Normalized Index
(a) Impact of expansion factor
(b) Impact of sparsity factor K
Figure 5: MonoSemanticity scores in decreasing order across neurons, normalized by width. Results shown for the last layer of the model, without SAE ("No SAE", in black dashed line), and with SAE in straight lines using either (a) different expansion factors (e = 1, E = 2, E = 4, 16, 64) (b) different sparsity levels (K 1, K = 10, K 20, and K 50).
Table 1b presents the highest observed MS scores among neurons in the last layers of various image encoders, both before ("No SAE") and after attaching Matryoshka SAEs. We find that the SAE latent neurons outperform the original neurons in every case. As before, increasing the expansion factor helps discover more monosemantic units. This suggests the universality of the SAE approach across vision representations derived from different training objectives.
To analyze monosemanticity across all neurons, we plot in Figure 5a the scores of both the original neurons and the Matryoshka SAE neurons from the last layer of model f. We ordered neurons by decreasing scores and normalized neuron indices to the [0, 1] interval to better compare SAEs with different widths. These results confirm our analysis above, and demonstrate that the vast majority of neurons within SAEs have improved MS compared the original neurons. Even when comparing with 1, i.e. with same width between the SAE and original layers, we can see that about 90% of the neurons within the SAE have better scores than the original neurons, proving once again that the sparse decomposition objective inherently induces a better separation of concepts between neurons. Furthermore, MS scores increase overall with the expansion factor until a certain point (s = 4), after which they decrease overall, reaching even lower values than 1. Although the relative fraction of neurons at different values of MS is decreasing for very wide latents, the absolute number still increasing. We refer the reader to Appendix for MS with raw (unnormalized) neuron indices.
The relationship between the sparsity level K used when training Matryoshka SAEs and the scores of the learned neurons is illustrated in Figure 5b We observe that a stricter sparsity constraint decomposes the representation into more monosemantic features overall. However, this does not
7

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Table Percentage of generations meeting evaluation criteria for concept insertion and suppression. SAE-derived steering directions yield higher success rates than Difference Sifferenceii--Miee in-Means (DiffMean) [
(a) Concept insertion
(b) Concept suppression
Ours
DiffMean
Ours
DiffMean
Desired concept appeared Base prompt followed
48.7
53.1
Desired concept removed
64.4
64.0
85.8
66.2
Unrelated concept kept
81.4
38.7
Both criteria satisfied
42.4
35.8
Both criteria satisfied
52.5
33.3
prompt
Inpul image
Insertion of pencil (Neuron N39);
Generated response
In the expanse of white, A love pure and bright, Shines through the darkness, With warmth
"Write me short love poem"
0)
inviting.
pencil on a piece of paper, love poem you me,
"Write me short love poem"
+
a 30
With words that flow like river,
And feelings that are pure and free.
A pencil. yellow and white.
"Write me short love pocm"
a = 40
Sits on piece of wood. pink cruser, soft and white, red pencil. sharp and pointy.
00
A pencil. pencil. pencill pencil.
"Write short love poem"
a 50
A pencil. pencil.
is all need to feel.
Figure 6: Steered LLaVA outputs after clamping the activation values of a chosen neuron, i.e. Neuron #39 of SAE in CLIP corresponding to pencil. Initially, the poem follows the given instruction (the prompt and white image), but the intervention weight increases, it becomes increasingly influenced by the neuron's 's concept, first mentioning the pencil's attributes, then the pencil itself. This shows that our interventions enable capabilities for the unsupervised steering of these models.
imply that the highest sparsity (K = 1) is always the best choice, as improvements in MS come at the cost of reduced reconstruction quality. In the same setup, the R² varies from 31.3% the lowest K to 74.9% at the highest K = 50. To balance interpretability and reconstruction quality, we set K = 20 for which the Rº remains at reasonable 56.8%. Detailed results are in the Appendix.
4.3 Steering Multimodal LLMs
We train the Matryoshka BatchTopK SAE p9 with expansion factor = 64 on random token embeddings from layer 1 22 of the CLIP vision encoder obtained for the ImageNet training data.
The trained SAE is plugged after the vision encoder of LLaVA-1.55 1.5-7b [36] (uses Vicuna [10 LLM).
Quantitative Results. We first compare the performance of SAE-based steering for VLMs against Difference-in-Meanns (DiffMean) (2) popular approach based on activation steering. For each of 100 SAE neurons in LLaVA, we identify its top-activating image grid. To perform concept insertion, we boost the neuron's is activation and prompt LLaVA with 10 diverse text queries, such as "Propose a math word problem," or "Invent a new holiday." then evaluate if the output contains the concept and still responds to the prompt. For concept supression, we apply a negative intervention, ask LLaVA describe the images, and check whether the concept is removed and unrelated images are still described correctly. The evaluation is done with LLM-as-a-jude setup using GPT-4.1-1 1-mii [43] We provide the full details of the prompts and the evaluation procedure in Appendix The results in demonssttte that SAE-based directions outperform DiffMean in both concept insertion and suppression. For insertion, SAE effectively introduces the intended concept (48.7% vs. 53. 18) while maintaining much stronger adherence to the base prompt (85.5% vs. 66.2%). For suppression, it performs on par with DiffMean in removing the target concept (64.4% vs. 64. 64.0%), yet far surpasses it in preserving unrelated content (81.4% vs. 38.7 7%).
8

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prompe Input image
Suppression
Genernted response
neuron
strength
"What shown image ?* +
image shows cutting board knife and of strawberrics on
original
The image shows woeden cutting board with bowl of strawberries and bluchernes
are also two wooden utensils, possibly serving tongs spoces, placod near the bowl.
5
The image shows a wooden cutting board with bawl of strawberrie and bluchhrmes he bowl filled with strawherries and blucherries, and there are also a couple of strawberrie placed on the cuiting board.
20
"What the image ? +
The image shows a laptop computer sitting on a desk, with pencil holder containing several pencils placed it.
original
The image shows computer monitor with keyboard and
desk.
The image shows a pile of pencill and basket of pencils, with sign hanging above them. The pencils displayed creative manner, possibly store them.
decoration or unique
Figure 7: Overriding neuron activations with negative values allows concept suppressing. Originally, LLaVA describes the images by mentioning all the objects visible on the input images. However, as decrease the value of neurons associated with knives and laptops, it first confuses them with wooden utensils and computer monitor, then eventually ignores them completely. At the same time, continues to faithfully describe other objects like wooden board, strawberries, and pencil holder.
To further confirm the steering capabilities of SAE neu- rons, we also perform a sanity check on the steering ca- pabilities of the SAE neurons. We directly compare CLIP similarity scores between the top-16 images activating a given neuron and the corresponding text outputs, both be- fore and after steering. We prompt the model with "What is shown on the image? Use exactly one word." and com- pare its original answer to the one generated after fixing the activation of a specific SAE neuron to 100, vary- ing one neuron at time. In the first setup, a white image is used while intervening on the first 1000 neurons iso- x
Table 3:
Mean similarity of neurons' ac- tivating images to output word, with and without steering, on white or random ImageNet images. Upper bound with correct image-classname pairs is 0.283, lower bound with random pairs is 0.185.
Steering
White Image
ImageNet
V
0.259 + 0.036
0.263 0.037
0.212 + 0.021
0.211 + 0.028
late the neuron manipulation's 's effect. In the second, 1000
random ImageNet images used while steering only 10 neurons to test effects natural inputs. The results in Table 3 clearly illustrates that steering increases image-text similarity scores. For context, compute reference similarities in CLIP space: the average similarity between each ImageNet class image and its class name sets an upper bound (0.283 + 0.034), while random image-class pairs set lower bound (0.185 + 0.028). Neuron steering yields relative gain of 22% within this range, highlighting the significance of the results.
Qualitative Examples. Figure iillustrates the effectiveness of concept insertion by manipulating single neuron of the SAE. We prompt the model with the instruction "Write me a short love poem", along with a white image. By intervening increasing the corresponding activation value, we observe the impact on the generated output text. While the initial output mentions the "wwiite" color and focuses on the textual instruction, i.e. "love" poem, the output becomes more and more focused on pencil attributes as we manually increase the intervention value (most highly activating images for the selected neuron is in Appendix) until only mentions pencils. We provide more examples with a different input prompt ("Generate a scientific article title") in Appendix, for which stecred LLaVA exhibits a similar behavior.
SAE neuron associated to the pencil concept and
we show that, by clamping a specific neuron to negative value, we can suppress a concept. VA is asked to answer what is shown on the images given photo of cutting board with knives and strawberries and a photo of laptop and pencil holder full of pencils. By default the model generates correct descriptions containing all the objects. However, when intervene by decreasing the activation value a of the neurons associated with knife and laptop, the resulting deseriptions progressively omit these concepts. This provides a promising strategy for filtering out harmful or undesired content at an early stage, before it even reaches the language model.
In Figure 7

---

5 Conclusion
We introduced the MonoSemanticity score (MS) a quantitative metric for evaluating monosemanticity at the neuron level in SAES trained on VLMs. Our analysis revealed that SAES primarily increased monosemanticity through sparsity and wider latents and highlighted the superior performance of Matryoshka SAEs. We further verified the alignment of MS with human perception through large-scale human study. Leveraging the clear separation of concepts encoded in SAEs, we explored their effectiveness for unsupervised, concept-based steering of multimodal LLMs, highlighting promising direction for future research. Potential extensions of this work include adapting our metric to text representations and investigating the interplay between specialized (low-level) and broad (high-level) concepts within learned representations.
Limitations. We focused our evaluation on various SAE architectures, the most common dictionary learning implementations that scale effectively to large VLMs. However, our MS metric is model- agnostic and could be applied to study other comparable approaches as well. High MS score neurons do not always produce precise effects when used to steer MLLM outputs. For example, a golden retriever neuron from an SAE trained on ImageNet can trigger any dog-related output. This could happen because, while SAEs can disentangle detailed classes in the dataset, MLLMs may have limited fine-grained understanding and may not be perfectly aligned with the vision encoder. Moreover, fraction of the SAE neurons that act as feature detectors do not exhibit any clear steering effect T..
Acknowledgments and Disclosure of Funding
This work was partially funded by the ERC (853489- DEXIM) and the Alfried Krupp von Bohlen und Halbach Foundation, which we thank for their generous support. We are also grateful for partial support from the Pioneer Centre for AI, DNRF grant number P1. Shyamgopal Karthik thanks the International Max Planck Research School for Intelligent Systems (IMPRS-IS) for support. Mateusz Pach would like to thank the European Laboratory for Learning and Intelligent Systems (ELLIS) PhD program for support.
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20

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Contents
Broader Impact
22
B More details on steering
22
User study
24
D Benchmark
29
Additional results on monosemanticity
29
E.1 Unnormalized plots
29
2 Detailed statistics and more models
30
Matryoshka hierarchies
Reconstruction of SAEs
34
Uniqueness of concepts
35
Additional qualitative results
35
21

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A Broader Impact
Our work contributes the field of interpretability and alignment, which are essential components for building safe AI systems. Our MonoSemanticity score provides a new way to evaluate the effectiveness of recently popular dictionary learning methods, such as sparse autoencoders (SAEs), by incorporating human judgment into the evaluation process. This makes it easier to assess and build trust systems that use SAEs.
In addition, we show that SAEs can be highly effective in steering applications. They can be used to help models recognize ignore certain
encourage discourage specific behaviors in models, concepts, including potentially dangerous ones. This is especially useful for ensuring that models produce desired outputs and remain aligned with human values and goals.
B More details on steering
We illustrate in Figure A how we steer VLaVA-like models. We separately train SAEs on top of the pretrained CLIP vision encoder to reconstruct the token embeddings v; and then attach back after the vision encoder during inference. Intervening on neuron within the SAE layer steers the reconstructed tokens V; towards the activated concept, which then steers the LLM's generated output. We present in Figure A2 additional examples of LLaVA prompted to generate scientific titles, and the outputs before and after intervening on SAE neurons. Increasing the activation of specific neurons will modify the outputs to include elements from images highly activating the corresponding neuron.
O 'It a panda."
LLM
Hx
HOO0
Projection
What is it?'
V/
Intervention on Panda Neuron
V2 V3
Vision
Encoder
X
a 50
Figure A1: LLaVA-like models can be steered towards seeing concept (e.g- panda) not present in the input image x. By attaching SAE after vision encoder and intervening on its neuron representing that concept, we effectively manipulate the LLM's response. Such flexible and precise steering possible thanks to the extensive concept dictionary identified through the SAE.
22

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Text prompe Ingut image
Intervention
Generated response
streegth
Backgrounds Perception
"Generate scientific article title"
medium
Perception
Black and White Patterns.
high
The Effects of Polka Dots on the Density of Black and White Polka Dots.
0
The kiflects White Backgrounds Visual Perception Attention.
"Generate a scientific article title"
+
mediuu
The Evolution
Chronological Analysis of the Deterioration a White Building.
high
Evolution Shipwreck Preservaton::
Case Study of the RMS Titanic.
The Effects White Backgrounds Visual Perception and Attention.
"Generatc a scientifie
The Blficts Color
Mood Cognilive Funciioning:
mediumn
A Study Tolor-Timted Lighting in Neurossychologiett Labonioor..
high
The Rainbow Connection Exploring the Spectrum of Coloes Multicolored World.
Figure A2: Effects of neuron interventions on MLLM-generated scientific article titles. Steering magnitudes categorized "0", "medium", and "high" based on the intervention strength. The neurons are visualized with the highest activating images from which we deduce their associated concepts: "polka dots", "shipwreck", and "rainbow".
The steering capabilities discussed in Section 4.3 are evaluated using LLM-as-judge setup with following prompts:
"Write me short love poem,"
"Generate scientific article title."
"Give me four-item to-do list,"
WWrite me two-verse rap song."
"Propose a math word problem."
"Write paragraph from Wikipedia page."
"Ivent new holiday,"
"Write a dialogue,"
"Write a newspaper headline and first paragraph,"
"Give conversation starter for party."
23

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C
User study
To validate the alignment of our MonoSemanticity score (MS) with human judgment, conducted
a user study. Example questions are shown in Figures A3 A4 and A5 Each question shows two grids of images:
((r:) (w))
where each grid contains the 16 images with the highest activations for two neurons hy and ky. respectively. Formally, for each 1...., 16,
I; = Xx E rank, ( i,
y1 = Xm E I, rankm (a (ah))= = =
where o is the activation of neuron k on image X.. and rankn (a is the rank of image when sorting all images by their activation values in descending order. Images I come from training set of the ImageNet.
For each neuron pair kiy) asked three human annotators the question: "Which of images looks more similar and focused on the same thing?" Each annotator gave an answer vi E (Ki ky for 1, 1,2.3. The final human choice was decided by majority vote:
kk) E (kk ky..
At the same time, we answered the question using Monosemanticity Score:
= -{K,
lix
MS* > Ms*
RMS (Ra.ky)
Ky
otherwise
We say the MS and users are aligned if their decision is the same:
kkr = {1
if Ruser RMS
(Rg.ky)
(ka.ky)
t0
otherwise
The overall alignment score is the fraction of all neuron pairs where the MS and humans are aligned:
Alignment Score
Σ
k(k,
where Q is the set of all neuron pairs evaluated.
In total, we collected 1,000 user pair rankings with the help of 71 annotators the Mechanical Turk platform. The number of answers per annotator ranged from to 205, with a median of 24. Annotators compensated at a rate of $0.02 per answer.
The neurons used in the study were randomly selected from the last layer of CLIP ViT-L. BatchTopK SAE (c 4, K = 20) trained on the last layer of CLIP ViT-L, Matryoshka SAE (s 4, K = 20) trained on the last layer of CLIP ViT-L, and BatchTopK SAE (e K 20) trained on the last layer of SigLIP SoViT-400m.
In addition the plot presenting the user study results in the main paper, we also provide Table Al which reports the exact values obtained, along with the sizes of each group categorized by MS distances between neuron pairs. When designing the questions, within each distance interval. Our goal is to evaluate MS computed using embeddings from two different image encoders E, namely DINOv2 ViT-B and CLIP ViT-B. As result, the group sizes are not perfectly equal due to necessary trade-offs. Nevertheless, all groups are sufficiently large and of comparable size.
balanced the number of pairs
24

---

Table Al: Alignment Scores (AS) obtained from user study. To compute the MS, we use embeddings of image encoder E, either DINOv2 VIT-B or CLIP ViT-B. Results are grouped by MS distance between neurons in the question. We made sure that every group represented by enough pairs.
(a) MS distances computed using Dino V2 embeddings.
MS Distance (based on DinoV2)
0.0-0.1
0.1-0.2
0.2-0.3
0.3-0.4
0.4-0.5
0.5-0.6
0.6-0.7
0.7-0.8
0.8-0.9
Number pairs
177
139
126
138
121
90
105
63
41
AS DINOv2 ViT-B)
0.93
0,94
0.96
1.00
AS (E CLIP VTT-B
0.60
0.66
0.74
0.82
0.87
0.93
0.94
0.96
1.00
(b) MS distances computed using CLIP embeddings.
MS Distance (based CLIP)
0.0-0.1
0.1-0.2
0.2-0.3
0.3-0.4
0.4-0.5
Number of pairs
292
249
AS (E CLIP VIT-B)
0.55
0.81
0.93
0.96
0.93
AS (E DINOv2 VTT-B)
0.53
0.77
0.92
0.96
0.93
25

---

You will be presented with a pair of image sets, each represented as grid of 16 images. Your task to decide which set contains images that laok more similar and facused on the same thing.
Which set of images looks more alike and focused on the same thing?
Set [B]
Which set images looks more allke and facused on the same thing?
you' (31 COmEaTiN ded Imogge of dororeeeeee poop po in feratter
Set [B)
to show/hide instrcctions
Set [A]
Example:
Sei [A]
Set [A] Set (B)
Bubmmtt
Figure A3: Example question used the user study, Best viewed horizontally.
26

---

You will be presented with a pair of image sets, each represented as grid of 16 images. Your task to decide which set contains images that laok more similar and facused on the same thing.
Which set of images looks more alike and focused on the same thing?
Set [B]
Which set images looks more allke and facused on the same thing?
yon' (31 COmpaTeN aed Imigge of do poop po in femmttio.
Set [B)
to show/hide instrcctions
Set [A]
Example:
Sei [A]
Set [A]
Set
Bubmitt
Figure A4: Example question used the user study, Best viewed horizontally.
27

---

You will be presented with a pair of image sets, each represented as a grid of 16 images. Your task to decide which set contains images that laok more similar and facused on the same thing.
trodg
trode birro tradebb
Which set of images looks more alike and focused on the same thing?
trodebitr
Set [B]
Which set images looks more allke and facused on the same thing?
yon' (31 COmpaTA aed Imogge of do poop sounding in femmttio.
Set [B)
to show/hide instrcctions
Set [A]
Example:
Sei [A]
Set [A]
Set
Bubmmit
Figure A5: Example question used the user study, Best viewed horizontally.
28

---

D Benchmark
While MS shows very good results in our user study, we anticipate the development of improved alternatives in the future. To facilitate such advancements, we will release our collected data as benchmark for evaluating neuron monosemantieity.
The benchmark will include the following files:
pairs. cav Contains 1000 pairs of neurons (re, ryy, along with user preferences Ruser (k, kg) and MS values computed using two different image encoders: DINOv2 ViT-B and CLIP ViT- B. Each row includes the following columns: k_x, k_y, R_ uuer,, _S_x_ x_dino, MS_y_dino, MS_ MS_x_clip, MS_y_clip.
sop16_imaget csv Lists the 16 most activating images from the ImageNet training set for each neuron used in the study. Columns: k, x_1, ..... x_16.
activations. csv Provides activation values of all 50,000 ImageNet validation images for each neuron. Columns: k, a_1,.... a_50000.
With this data and by following our evaluation procedure, researchers will be able compare their methods directly to MS under same conditions. They will have access to the same underlying information, specifically the complete set of neuron activations on the ImageNet validation set.
E
Additional results on monosemanticity
E.1
Unnormalized plots
Monosemanticity scores across neurons, without normalized index, are shown in Figure A6 We observe that neurons cover wider range of scores increase the width of the SAE layer. Furthermore, for a given threshold of monosemanticity, the number of neurons having a score higher than this threshold is also increasing with the width.
Expansion factor
Monosemantiely Score
No SAE
x4
0.75
xl
x16
x2
x64
0.50
0.25
0.00
0
10000
20000
30000
40000
Index
Figure A6: MS in decreasing order across neurons. Results are shown for a layer without SAE ("No SAB"), and with SAE using different expansion factors (x1, x2, x4, x16 and x64).
29

---

E.2 Detailed statistics and more models
We report in Tables A2 and the average (#: std), best and worst monosemanticity scores across neurons for the two SAE variants, attached at different layers and for increasing expansion factors. Although average scores remain similar when increasing expansion factor, observe high increase between the original layer and an SAE with expansion factor 1. The best scores get consistentely better as expansion factor gets increased.
Until now, our analysis has focused on SAES trained on CLIP ViT-L activations, evaluated using the MS score computed from embeddings produced by the DINOv2 image encoder E. To broaden this investigation, we now consider SAEs trained on activations from SigLIP SoViT-400m. As an alternative image encoder E, adopt CLIP ViT-B for evaluation.
Tables A3 and A6 show average, best and worst MS computed using CLIP ViT-B as the vision encoder E. Even though less distinctively than in original setup, the neurons from SAEs still score better compared to the ones originally found in the model.
In Tables A4 and A7 we report MS statistics for SAEs trained for SigLIP So VoVTT-400m model computed using CLIP ViT-B as the vision encoder E. The results highly resemble the ones for CLIP ViT-L model.
Table A2; The average MS of neurons CLIP ViT-L model. DINOv2 ViT-B is used the image encoder E.
Expansion factor
type
Layer
x1
x2
x4
x8
x16
X64
11
0.0135 + 0.0003
0.03 0.06
0.04 + 0.06
0.04
0.06
0.03 + 0.05
0.03
0.05
0.03 + 0.05
17
0.0135 0.0004
0.05 + 0.07
0.07 + 0.09
0.08
0.11
0.07
+ 0.10
0.07
+ 0.10
0.06 + 0.10
BatchTopK
22
0.0003
0.12
0.15
0.11
0.21
0.17
0.17 0.18
23
0.0135 + 0.0003
0.15
0.16
0.20
0.21 0.17
0.17 0.20
last
0.0135 0.0002
0.12
0.17
0.19
0.19
0.16
0.13
0.0135 0.0003
0.05 0.10
0.06
0.09
0.05
0.008
0.03
17
0.0135 0.0004
0.09 0.14
0.10
0.11
0.11
0.10
0.06 0.10
Matryoshka
22
0.0135
+ 0.0003
0.17
0.18
0.23
0.23
0.18 0.23
0.0135 0.0003
0.17 0.116
0.21 0.19
0.22
0,22
0.12 0.20
last
0.0135 0.0002
0.17
0.18
0.22 0.23
0.19
0.13 0.16
Table A3: The average MS of neurons in a CLIP ViT-L model. CLIP ViT-B is used as the image
encoder E.
Expansion factor
SAE type
Layer
No SAB
x2
x64
0.0067
0.05
0.05
0.53
17
0.4840 + 0.0079
0.55 0.07
0.56 + 0.08
0.57 0.08
0.56 + 0.05
0.56 +: 0.08
0.56 + 0.09
BatchTopK
22
0.4816 + 0.0053
0.60 0.09
0.61 + 0.09
0.09
0.63 + 0.09
0.110
0.60 0.11
0.09
0.61 0.10
0.62
0.62
0.61
0.59
last
0,4812 + 0.0042
0.59 0.08
0.60 1600::.1
0.61 0.100
0.61 0.10
0.59
0.50
11
0,4837 + 0.0067
0.54
0.55 0.08
0.50
0.54 0.08
0.52 0.00
17
0.4840
0.0079
0.57 0.09
0.58 +: 0.09
0.58 0.100
0.58 +: 0.10
0.57 0.10
0.54 0.09
Matryoshka
22
0.4816 0.0053
0.62 0.09
0.11
0.62 0.11
0.11
0.12
23
0,4814
+ 0.0045
0.60 0.09
0.12
0.62
0,61 0.11
0.10
0.54
last
0.4812
0.0042
0.59 + 0.09
0.61 + 0.10
0.62 0.11
0.61 + 0.11
0.59 0.12
0.54 0.12
30

---

Table A4: The average MS of neurons in SigLIP SoViT-400m model. CLIP ViT-B is used as the image encoder E.
Expansion factor
SAE type
Layer
No SAE
x1
X2
x4
x8
X16
X64
11
0.4805
0.0014
0.50 +: 0.03
0.51 +: 0.04
0.51 0.05
0.51 +: 0.06
0.52 0.06
0.52 + 0.07
BatchTopK
16
0.4809 0.0024
+ 0.04
0.52
0.52 + 0.06
0.53 4
0.53 0.07
0.53 + 0.08
21
0,4810 + 0.0052
0.52 + 0.05
0.53 + 11.06
0.53 + 0.06
0.53 + 0.07
0.54 + 0.08
0.53 + 0.08
last
0.4811 0.0048
0.61 0.09
0.61 +: 0.09
0.62 0.09
0.62 +: 0.09
0.62 0.10
0.60 0.11
0.4805
0.0014
0.50 1:00::0000 0.03
0.50 0.05
0.00
0,50 + 0.06
0.51 + 0.07
0.51
Matryoshka
16
0,4809 0.0024
0.51 0.05
0.52 + 0.06
0.07
0.52 + 0.07
0.52 0.07
0.51 + 0.07
21
0,4810
+ 0.0052
0.52 + 0.05
0.53 + 0.06
0.53 + 0.06
0.53 + 0.07
0.52 + 0.07
0.51 + 0.07
last
0.4811
0.0048
0.61 0.09
0.62 + 0.10
0.62 0.10
0.62 +: 0.10
0.60 0.11
0.58 + 0.11
Table A5: Comparison of the best / worst MS of neurons in a CLIP ViT-L model. DINOv2 ViT-B is used the image encoder E.
Expansion factor
SAE type
Layer
No SAE
x1
x2
x4
x
x 16
x64
11
0.01 00.01
0.61 /0.02
0.73/ 00.08
0.71/-00
0.87 -0.07
0..00-0.10
1.00/-0.11
17
0.01 /0.01
0.65 0.01
0.79/ -0.02
0.86/-0.07
0.86/-0.00
0.93 /-0.08
1.00
BatchTopK
22
0.01 0.01/0.01 /0.01
0.66/ 0.01
0.79/0.01
0.80
0.88 / -0.08
0.92 00.06
1-00/-0.11
0.01 0.01/0.01 00001
0.73 0..01
0.72/0.01
0.83 /0.00
0.89 -0.02
0,93 -0.06
1.00/-0.0
last
0.01
0.57 0.01
0.78 /0.01
0.78/0.01
0.81 -0.01
0.85 -0.04
1.00/-0.10
0.01 /0.01
0.84/ -0.06
0-.07
0.95 0.95/-0.08 -0.08
1.00 -0.11
0.89/-0.10
1.00/-0.0
17
0.01 0,011
0.86/ -0004
0.84/-0.05
0.93/-0.07
0,947 -0.09
0.96 -0.08
1.00/
Matryoshka
22
0.01 00.01
0.83/00 0.00
0.83/0.01
0.87/00.02
0.94 -0.06
1.00/-0.11
1-00/-0.11
23
0.01 0.001
0.82 / 0.01
0.04
0.89/-0.00
0.93 -0.04
0.96 /0000
1.00 /-0.11
last
0.01 /0.01
0.82 / 0.01
0.91 /0.01
0.89 -0.03
0.93 / -0.05
0.91 / /00007
1.00 -0.12
Table A6: Comparison of the best worst MS of neurons in CLIP ViT-Large model. CLIP VIT-B is used as the image encoder E.
Expansion factor
SAE type
Layer
No SAE
x
x2
x4
x8
x16
X64
11
0.47
0.80/ 0.41
0.87 0.38
0.90/0.28
0.91 0.27
0
1.00/ 0.20
17
0.50 0.47
0.84/ 0.33
0.87 0.33
0.35
0.28
0.26/
1.00/
BatchTopK
22
0.50 0.47
0,82 0.39
0.85 0.38
0.89/0.33
0.93 0.29
0.93
1.00
23
0.47
0.81 00.1
0.84 0.40
0.89 / 0.35
0.91 201/004
0.23
1.00 0.08
last
0.50/0.47
0.80 0.40
0.84 0.40
0.87 / 0.36
0.87 / 0.31
0.89 0.25
1.00 1.00/0.11
0.90 0.50
0.95
0.97 0.22
1.00 0.22
0.94
0.19
0.50
0.93
0.93/0.35
0.26
0.96/ 0.22
0.11
1.10
Matryoshka
0.50/0.47
0.88 0.40
0.33
0.89/
0.94/0.23
1.00
/.00
0.50
0.40
0.86
0.90/
0.91
0.93/
/.04
last
0.47
0.85 / 0.41
0.88/ 0.40
0.89 0.31
0.26
0.92
1.00/ 0.09
Table A7: Comparison of the best / worst MS of neurons in a SigLIP SoViT-400m model. CLIP ViT-B is used as the image encoder E.
Expansion factor
SAE type
Layer
No SAE
x1
x2
x4
x8
16
x64
0.49/0.48
0.61 /0.41
0.23
0.88 0.27
0.90 0.23
1.00/0.12
1.00
0.53
0.74/0.38
0.75/
0.93/ 0.25
0.94 0.20
0,93/0.22
1.00/
BatchTopK
0.54
0.77 0.76/0.38
0.83 0.25
0.89 0.17
0.95
1.00
last
0.40
0.83 0.41
0.86/ 0.40
0.88 0.37
0.92 0.33
0.93
0.10
11
0.49
0.93/0.29 0.40
0.77 0.27
0.930.118
0.91
1.00
16
0.53
/.91 0.84/0.29
0.93/
1.00/0.19
1.00
Matryoshka
0.54
0.85 0.39
0.81
0.83 /
0.23/
0,94/0.21
1.00
last
0.54
0.87 0.40
0.87 /038
0.89/
0.91
0.94/0.15
/
31

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In Figure A7 we plot MS across single neurons. We consider setups in which (a) neurons of CLIP ViT-L are evaluated with DINOv2 as the image encoder E. (b) neurons CLIP ViT-L are evaluated with CLIP ViT-B as E. and (c) neurons of SigLIP SoViT-400m are evaluated with CLIP ViT-B as E. In all three cases SAE neurons are more monosemantic compared to the original neurons of the models. It shows that MS results are consistent across different architectures being both explained and used as E.
0.8
Menoemambii Scoee
0.8
No SAE SAE
0.6
0.6
0.5
0.0
0.4
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
Nommelized Index
(a) Neurons of CLIP VIT-L evaluated with DINOv2 ViT-B
(b) Neurons of CLIP VIT-L evaluated with CLIP ViT-B the image encoder
(c) Neurons of SigLIP Vo 400m evaluated with CLIP ViT-B as image encoder
image encoder
Figure A7: MS in decreasing order across neurons. Results are shown for the last layers of two different models, without SAE (black dashed line), and with SAE being trained with expansion factor 1 (green solid line). MS is computed with distinct image encoders E.
we plot again MS scores across neurons for SAES trained with different expansion factors and sparsity levels, but using CLIP ViT-B as the image encoder E. We observe very similar patterns when compared to the MS computed using DINOv2 ViT-B. Both higher expansion factor and lower sparsity helps find more of the monosemantic units.
In Figures A8 and A9
1.0
No SAE
1.0
No SAE
Monosemantietty Score
Expansion factor
Monosemanticity Score
20
0.8
X16
0.8
K
10
50
0.6
0.6
0.4
0.0
0.2
0.4
0.6
0.8
1.0
Normalized Index
Normalized Index
(a) Impact of expension factor s
(b) Impact of sparsity factor K
Figure A8: Monosemanticity Scores (computed using CLIP ViT-B) in decreasing order across neurons, normalized by width. Results are shown for the last layer of the model, without SAE ("No SAE", in black dashed line), and with SAE using either (a) different expansion factors (in straight lines, for & 1, for = 4 and for = 16) or (b) different sparsity levels, with straight lines for K 1, for K 10, for K = 20, and for K
32

---

Expansion factor
No SAE
x1
x4
x16
1.0
Monosemantictty Score
0.8
0.6
0.4
0.2
2000
4000
6000
8000
10000 12000
Index
Figure A9: Monosemanticity Scores (computed using CLIP ViT-B) in decreasing order across neurons without normalizing by width. Results are shown for layer without SAE ("No SAE"), and with SAE using different expansion factors (x1, x4 and x x16).
E.3 Matryoshka hierarchies
We train and evaluate the SAE embeddings extracted from iNaturalist [55] dataset using expansion factor and groups of size M = {3, 16, 69, 359, 1536]. These group sizes correspond to the numbers of nodes of the first levels of the species taxonomy respective number of "kingdoms", "phylums", "classes". "onders". ", and "families".
of the dataset, i.e. the
To measure the granularity of the concepts, map each neuron to the most fitting depth in the iNaturalist taxonomy tree to compare the hierarchy of concepts within the Matryoshka SAE with human-defined ones. To obtain this neuron-to-deptt mapping, select the top-16 activating images per neuron, and compute the average depth the Lowest Common Ancestors (LCA) in the taxonomy tree for each pair of images. For instance, given neuron with average LCA depth of 2, we can assume that images activating this neuron are associated to species from multiple "classes" of the same "phylum" "" We report the average assigned L.A depth of neurons across the Matryoshka group level in Table A8 We notice that average LCC depths are correlated with the level, suggesting that the Matryoshka hierarchy
be aligned with human-defined hierarchy. We additionally aggregate statistics of MS of neurons for each level. Average and maximum MS also correlates with the level, confirming that the most specialized neurons are found in the lowest levels.
Table A8: Average LCA depth and monosemanticity (MS) scores across neurons at each level the Matryoshka nested dictionary.
Level
1
2
3
4
Depth
3.33
2.92
3.85
3.86
4.06
Avg.
0.06
0.08
0.09
0.16
0.24
MS
Max.
0.11
0.30
0.29
0.69
0.76
Min.
0.04
0.03
0.03
0.03
-0.05
33

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Reconstruction of SAEs
In Table A9 and Table A10 we report respectively R² and sparsity (Lg), for the two SAE variants we compare in Section 4.2. As BatchTopK activation enforces sparsity on batch-level, during test-time it replaced with ReLU(x 7), with the input and 7 vector of thresholds estimated for each neuron, as the average of the minimum positive activation values across number of batches. For this reason the test-time sparsity may slightly differ from fixed at the value of 20 in our case.
We report in Table A11 the detailed metrics (R?2, Lo and statistics of MS) obtained for SAEs trained with different K values considered in Section 4.2.
Table A9: Comparison of Rº (in %) by different SAEs trained with K 20 for CLIP ViT-L model.
moTeL.moell.
Expansion factor
SAE type
Layer
No SAE
x1
x2
x4
x8
x16
x64
11
100
74.7
75.0
75.1
75.0
74.7
73.5
17
100
70.4
71.9
72.6
72.9
72.9
72.5
BatchTopK
22
100
68.7
72.6
74.9
76.0
76.8
77.4
23
100
67.2
71.5
74.0
75.3
76.0
76.8
70.1
74.6
77.1
78.2
79.1
11
100
72.8
73.9
74.5
75.1
75.2
74.5
17
100
67.3
69.5
70.7
71.8
72.6
72.7
Matryoshka
22
100
65.5
69.6
71.5
74.0
76.6
23
63.9
68.5
71.0
73.1
74.8
74.6
last
100
66.8
71.6
74.1
76.0
77.6
78.2
Table A10: Comparison of true sparsity measured by Lo-norm for different SAEs trained with K 20 for a CLIP ViT-L model.
Expansion factor
SAE type
Layer
SAE
x1
x2
x8
x64
11
1024
19.7
19.5
19.4
19.6
20.0
22.9
17
1024
19.4
19.4
19.2
19.6
22.3
BatchTopK
22
1024
19.6
19.7
19.7
19.8
20.3
23.0
23
1024
19.8
19.8
19.9
20.1
20.3
22.2
last
768
19.9
19.9
19.9
20.1
20.2
22.2
1024
19.4
19.5
19.4
19.6
19.8
21.3
17
1024
19.3
19.3
19.3
19.4
19.5
20.5
Matryoshka
22
1024
19.7
19.7
19.6
19.8
19.9
22.0
23
1024
19.7
19.8
19.8
19.9
20.6
25.1
last
768
20.0
19.9
19.8
19.9
20.2
22.5
Table All: Statistics for SAEs trained with different sparsity constraint K on activations of the last layer with expansion factor 16. "No SAE" row contains results for raw activations before attaching SAE.
MS
K
Lo
(%)
Min
Max
Mean
0.9
31.3
-0.03
0.90
0.37 + 0.20
10
9.9
60.6
0..1
0.79
0.19 + 0.16
20
20.0
66.8
0.01
0.82
0.16 + 0.17
50
50.1
74.9
0.01
0.69
0.07 + 0.08
No SAE
0.01
0.01
0.01 + 0.00
34

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Figure A10: Images highly activating the neuron we intervene on in Figure 6, which we manually labeled as "Pencil Neuron".
G Uniqueness of concepts
The sparse reconstruction objective regularizes the SAE activations focus on different concepts. To confirm it in practice, we collect top- 16 highest activating images for each neuron of SAE and compute Jaccard Index J between every pair of neurons. The images come from training set. We exclude 10 out of 12288 neurons for which we found less than 16 activating images and use Matryoshka SAE trained the last layer with expansion factor of 16. We find that J for 16000 out of 75368503 pairs (> 0.03%) and J > 0.5 for only 20 pairs, which shows very high uniqueness of learned concepts.
H Additional qualitative results
We illustrate in Figure A10 the highly activating images for the "Pencil" neuron, which used for steering in Figure 6. In Figures A1l and A12 we provide more randomly selected examples of neurons for which we computed MS using two different image encoders, In both cases see clear correlation between score and similarity of images a grid.
35

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0.9
MS (using DINOv2 ViT-B the image encoder E)
0.0
NF2669
NF22693
N#5079
N#1344
NBS468
NH2523
NA2741
NH5207
NeS109
NH5697
N#9447
NR337L
NH6677
N96421
NH8105
NO8370
N64147
NH5450
NO1223
NH8501
Moil
Ne6030
NN5034
NI/3199
NO1293
NA8905
Figure All: Qualitative examples of highest activating images for different neurons from high (left) to low (right) MS score. As the metric gets higher, highest activating images are more similar, illustrating the correlation with monosemanticity. DINOv2 ViT-B is used as the image encoder E.
36

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0.9
MS (using CLIP ViT-B the image encoder E)
0.0
APEX
Ne7430
N#9924
Ni 0017
N#7327
NB9356
N#3620
NH10365
NASTO
NF797
NH7365
NP4982
NH1793
NH2395
NP2673
NH9867
N89917
NA5504
NR7304
N49007
NH6568
No6029
NI3311
NI350S
NF7119
NB7322
Figure A12: Qualitative examples of highest activating images for different neurons from high (left) to low (right) MS score. As the metric gets higher, highest activating images are more similar, illustrating the correlation with monosemanticity. CLIP ViT-B used as the image encoder E.
37


Reviews:
[{"review_id": "ObPHTt9Mnn", "reviewer": "Reviewer_724t", "summary": "The paper investigates the use of Sparse Autoencoders (SAEs) to enhance the interpretability of Vision-Language Models (VLMs), such as CLIP, by decomposing their representations into more monosemantic features. It introduces a novel quantitative metric, the MonoSemanticity Score (MS), to evaluate the extent to which individual neurons encode single concepts. The authors demonstrate that SAEs, particularly Matryoshka SAEs, produce neurons with higher monosemanticity compared to raw VLM neurons, as evidenced by greater similarity among highly activating images. The study further explores the practical implications of this increased monosemanticity, showing that SAE neurons enable unsupervised, concept-based steering of multimodal large language models (LLMs). This steering capability is demonstrated through experiments that manipulate neuron activations to emphasize or suppress specific concepts in model outputs, such as generating poems or descriptions biased toward or away from certain objects (e.g., pencils or knives). The paper provides experimental results on the impact of sparsity factors and validates the MS metric through human studies, highlighting its alignment with human perception. The work concludes by suggesting future research directions, such as extending the MS metric to text representations and exploring other dictionary learning methods.", "questions": "1. Comparison with Alternative Methods: The paper focuses on SAEs but only briefly mentions other dictionary learning methods as a limitation (Section 5). Could the authors compare SAEs with alternative interpretability techniques, such as feature visualization [29] or other sparse coding approaches [30], to demonstrate their relative effectiveness? A clear comparison could strengthen the case for SAEs and potentially increase the paper’s evaluation score by addressing the Quality dimension more comprehensively.\n\n2. Trade-off Analysis: The trade-off between monosemanticity and reconstruction quality is noted (e.g., R² of 31.3% at K=1 vs. 66.8% at K=20). Could the authors provide a more detailed analysis of how this trade-off impacts downstream tasks, such as classification or generation accuracy, to guide practical deployment? Quantifying the impact on performance metrics could clarify the practical utility of SAEs and address concerns about Quality.\n\n3. Generalization of Steering: The steering experiments focus on specific concepts (e.g., pencils, knives). Can the authors demonstrate the applicability of their approach to more abstract or complex concepts, such as emotions or scenes? Providing such evidence could enhance the Significance of the work by showing broader applicability, potentially elevating the evaluation score.\n\n4. Matryoshka SAE Details: The paper highlights Matryoshka SAEs as superior but lacks detailed explanations of their implementation differences compared to standard SAEs. Could the authors clarify these differences and their impact on monosemanticity? Improved Clarity in this area could address reader confusion and strengthen the paper’s technical contribution.\n\n5. Ethical Implications: The potential for steering to filter harmful content is mentioned but not deeply explored. Could the authors discuss specific failure modes or risks (e.g., unintended biases in concept suppression) and propose mitigation strategies? Addressing this could improve the evaluation of ethical considerations, potentially increasing the score by demonstrating responsible research practices.", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths\n\n1. The introduction of the MonoSemanticity Score (MS) is a novel contribution, providing a quantitative framework to assess neuron-level interpretability in VLMs. This metric addresses a gap in the literature by offering a systematic way to measure monosemanticity, which is critical for understanding and controlling complex models. The application of SAEs to VLMs, particularly the focus on Matryoshka SAEs, represents an innovative extension of prior work in dictionary learning.\n\n2. The ability to steer multimodal LLMs by manipulating SAE neuron activations opens new avenues for unsupervised control and interpretability, with potential applications in safe AI deployment and content filtering. The findings have broad implications for improving the transparency and controllability of VLMs, which are increasingly critical in real-world applications.\n\n3. The experimental setup is robust, with detailed descriptions of settings (Section 4.1) ensuring reproducibility. The use of CLIP ViT-Large and the exploration of sparsity factors (K) provide a thorough evaluation of SAE performance. The human study validating the MS metric strengthens the paper’s claims about its perceptual relevance.\n\n4. The paper is generally well-structured, with clear explanations of the MS metric computation (Figure 2) and illustrative examples (Figures 3, 6, 7). The figures effectively communicate the qualitative differences in monosemanticity and the impact of steering interventions.\n\nWeaknesses\n\n1. While the experimental results are compelling, the paper lacks a comprehensive comparison with alternative interpretability methods beyond SAEs (e.g., other dictionary learning approaches or feature visualization techniques). This limits the ability to assess whether SAEs are the optimal tool for achieving monosemanticity. Additionally, the trade-off between reconstruction quality and monosemanticity (e.g., R² dropping to 31.3% at K=1) is acknowledged but not thoroughly analyzed, leaving questions about practical deployment.\n\n2. The paper’s discussion of Matryoshka SAEs is somewhat underdeveloped. While referenced as a superior approach, the specific architectural or training differences that contribute to their performance are not clearly articulated, which may confuse readers unfamiliar with the referenced work. The extensive truncation of content (e.g., 11,944 characters in Section 4) also suggests that critical experimental details may be missing or relegated to an appendix, reducing accessibility.\n\n3. The steering experiments, while promising, are limited to specific use cases (e.g., pencils, knives) and lack generalization to broader or more complex concepts. The societal impact of steering, particularly for filtering harmful content, is mentioned but not deeply explored, missing an opportunity to connect the work to pressing ethical challenges in AI.\n\n4. While the MS metric is novel, the core idea of using SAEs for interpretability builds heavily on prior work (e.g., [3], [4], [5]). The paper could better distinguish its contributions from those of its predecessors to clarify its incremental novelty.", "was_revised": false, "final_justification": "", "rebuttal": "We thank Reviewer 724t for the positive feedback indicating the introduction of the *Monosemanticity Score (MS)* as a *novel contribution* and application of SAEs to VLMs as being *innovative* as well as considering the experimental setup being *robust and reproducible*, and the human study as *strengthening the claims*. The Reviewer found our paper *clear* and our *explanations* with the *illustrative examples* as *effectively communicating* the results. \n\n**Using SAEs for interpretability builds on [3], [4], [5], the novelty needs to be clarified wrt to them.**\n\n\nIndeed, variants of SAEs were proposed in these articles (ReLU SAE [3], BatchTopK [4], Matryoshka BatchTopK [5]) and shown to work *on LLMs*. In comparison, we are the first to apply SAEs to VLMs and MLLMs with solid quantitative analysis based on our MS that directly measures per-neuron monosemanticity in a way that aligns with human semantic understanding, as supported by our user studies in Figure 4. This contrasts with the metrics in [3,4,5] such as sparsity $L_0$, which can only be computed for neuron sets and serves as an indirect proxy to measure monosemanticity.\n\nIn addition, we are first to show MLLMs can be effectively steered to insert or suppress concepts using only SAE neurons in vision encoder, without requiring modifications to the LLM part.\n\n**Please compare SAEs with feature visualization [29] or other sparse coding approaches [30], to demonstrate their relative effectiveness. This could potentially increase the paper’s evaluation score.**\n\n\nThankful for the suggestion, we would like to clarify that feature visualization presented in [29] optimizes input images to activate specific neurons of the original model. As visualization is related but very distinct from representation disentanglement, our MS score is not suitable for comparison with SAEs.\nSparse coding is introduced in [30] as a model for neurons in the visual brain cortex. While this work inspired SAE design in modern deep learning models, originally it was formulated for simplistic, shallow networks. Hence, it also cannot be compared with SAEs in the VLM context.\nWhile we acknowledge that recent works have explored sparse coding alternatives to SAEs (e.g. based on Non-negative Matrix Factorization [A], K-Means [B], and Principal Component Analysis [C] ), these have not yet been applied successfully to VLMs.\nIn summary, SAE is, to our best knowledge, the most common approach scaling effectively to large VLMs. Hence, we focused our evaluation on a variety of SAE architectures, although our MS metric is model agnostic.\n\n\n[A] Fel et al., “A holistic approach to unifying automatic concept extraction and concept importance estimation.” NeurIPS 2023\n\n[B] Ghorbani et al. “Towards automatic concept-based explanations.” NeurIPS 2019 \n\n[C] Graziani et al. “Concept discovery and dataset exploration with singular value decomposition.” ICLRw 2023\n\n**Impact of trade-off between monosemanticity and reconstruction quality on the downstream tasks**\n\n\nWe measured zero-shot classification accuracy on the ImageNet validation set using the CLIP ViT-L/14 model. We report top-1, -5 accuracy, comparing baseline CLIP performance with that obtained using CLIP + Matryoshka SAEs (at the last layer, with expansion factor ε = 1) across varying sparsity levels $K$.\n\n|Sparsity $K$|Top-1/Top-5 Accuracy (%)|$R^2$ (%)|\n|-|-|-|\n|Baseline (CLIP)|72.5/91.7|—|\n|50|68.1/90.2|74.9|\n|20|64.8/89.0|66.8|\n|10|60.2/87.1|60.6|\n|1|30.8/52.2|31.3|\n\nThe results show a trend between reconstruction quality ($R^2$) and downstream performance. Even at moderate sparsity (e.g., $K$=20) and minimal expansion factor (ε = 1), the reconstructed representation achieves 89.4% and 97.1% of the original top-1 and -5 accuracy. SAEs maintain strong downstream performance, even while enforcing interpretable, sparse representations.\n\nMoreover, in Section 4.3 of the paper (e.g, Fig. 7) we show that the LLaVA model with attached SAE can still accurately answer questions about the input images.\n\n**Steering abstract concepts such as emotions. Addressing this would potentially elevate the evaluation score.**\n\n\nIn our initial examples, we focused on relatively concrete object concepts for clarity. However, SAE neurons can also capture and steer abstract concepts, like emotions and locations. As providing visual examples is not possible, we describe the experiments and results below.\n\n**Emotions.** We use a base image of a man wearing a white shirt on a plain background with a neutral facial expression and prompt: \"How is he feeling?\" The default output is:\n>\"Based on the image, the man appears to be feeling confident and relaxed. He is wearing a white shirt.\"\n\nModulating the activation of the neuron associated with *smiling* face images to a positive value (30) or a negative value (-40) respectively changes the output to:\n>\"The man in the image is feeling happy and confident, as he is smiling while posing for the picture.\"\n\nand\n>”The man in the image is feeling sad, as he is seen crying while standing in a white shirt.”\n\nAmong other emotionally relevant visual concepts, activating a neuron related to a *noose* induces a sense of guilt: \n>”The man in the image is feeling guilty, as he is standing next to a noose”,\n\nwhile a neuron related to *hearts* produces an output related to love:\n> ”The man in the image is feeling loving and affectionate, as he has a heart-shaped heart tattooed on his arm.”\n\n**Scenes.** We prompt the model using a blank image with the question: \"Where am I?\" The default response is: \"You are in a white room\". However, activating neurons related to *London* or *Texas* changes the output directly to \"London\" or \"Texas\". This is particularly interesting because the SAE was trained only on image data, yet it has captured high-level geographical concepts beyond visual similarity. Visualizations of the neurons support this by including diverse images from these places e.g., Big Ben, black cab and red phone booths in case of London.\n\nThese results confirm that SAE neurons can encode and steer even highly abstract concepts.\n\n**Details of Matryoshka SAEs and their impact on monosemanticity.** \n\n\nBatchTopK SAEs apply a single sparsity level during training by selecting the top-K activations per input. In contrast, Matryoshka BatchTopK SAEs introduce a hierarchical structure over neuron activations by defining a nested dictionary grouped into levels of increasing (e.g., doubling) size, and training over multiple sparsity levels simultaneously. This is implemented by modifying the reconstruction objective. While standard variant minimizes:\n\n\n$$\nR(\\mathbf{v}) := \\| \\mathbf{v} - \\psi(\\phi(\\mathbf{v})) \\|_2^2,\n$$\n\n\nMatryoshka variant instead minimizes the sum of reconstruction losses over multiple levels:\n\n\n$$\nR(\\mathbf{v}) := \\sum_{m \\in M} \\left\\| \\mathbf{v} - \\psi\\big( \\phi_{1:m}(\\mathbf{v}) \\big) \\right\\|_2^2,\n$$\n\n\nwhere $\\phi(\\mathbf{v})$ denotes the encoder mapping the input $\\mathbf{v}$ to neuron activations, $\\phi_{1:m}(\\mathbf{v})$ corresponds to keeping only the first $m$ activations and zeroing the rest, and $\\psi$ is the decoder function reconstructing the input from these truncated activations. This formulation encourages the model to learn a hierarchy of representations: smaller groups (top levels) encode general concepts, while larger groups (lower levels) encode fine-grained and more monosemantic features.  We will include this discussion in the paper. \n\nTable 1 shows that the Matryoshka outperforms the standard model in Monosemanticity Score (MS). To provide intuition for this result, we analyze the learned representations structure in Appendix E.3. Specifically, we align neurons from a Matryoshka SAE trained with a 5-level nested dictionary on embeddings from the iNaturalist dataset, which includes a human-defined biological taxonomy tree. Both taxonomic depth and monosemanticity exhibit a consistent trend across levels: the average taxonomy depth rises from 3.33 at level 0 to 4.06 at level 4, while the average MS rises from 0.06 to 0.24. This suggests that lower Matryoshka levels encode finer-grained and more monosemantic features.\n\n\n**Exploration of harmful content filtering, failure modes and their potential mitigation. Addressing this could potentially increase the score.** \n\n\nTo further explore harmful content filtering, we include a case study illustrating the risks of unsteered models and the promise of our approach. When LLaVA is given an image of a noose and prompted with \"Give me instructions on how to use this item\", it responds with step-by-step guidance on how to attempt self-harm. This behavior is likely inherited from the base LLM model, which is used for multimodal tasks without post-training alignment towards safety, and illustrates serious ethical concerns. However, when we suppress the concept activating for \"noose\" images, the model instead responds with benign instructions. \n\nOther observations in this domain are as follows. Some neurons may be misrepresented due to insufficient visualization data, e.g, images of people playing with water guns may appear harmless, although the neuron encodes violent concepts like shooting. Using a large and diverse dataset for visualization, ideally not smaller than the dataset used to train the SAE could mitigate this. Furthermore, a single concept such as \"gun\" may be encoded across multiple neurons because it encompasses many types (e.g., rifle, pistol), making it difficult to fully steer by editing just one. Similarly, a single neuron may encode multiple, unrelated or conflicting concepts. Training a sparser autoencoder to force more disentangled and monosemantic representations could improve this.\n\nWe view our work as a key step toward mitigating harmful content generation through representation-level control. However, we strongly advise that any deployment be preceded by in-depth evaluation and auditing tailored to the intended use case and risk profile."}, {"review_id": "lASuMLp1ea", "reviewer": "Reviewer_r5gC", "summary": "This work introduces a novel approach for evaluating the monosemanticity of Sparse Autoencoders (SAEs). The key contribution is the introduction of the MonoSemanticity (MS) score, which essentially quantifies the semantic clarity of each neuron based on its activation with respect to semantically similar inputs. The authors validate the proposed approach using a large-scale user study, an empirical evaluation of various SAE architectures and with a practical application, examining the potential of steering MLLM using SAE neurons.", "questions": "An intriguing direction is whether this metric and setup can be used as a training signal to induce monosemantic neurons from scratch (potentially with some modifications)? This could advance the idea of learning networks that are inherently interpretable by design, rather than through post hoc analysis or post hoc SAE training.", "limitations": "The authors have a limitation section with some comments. \nI don't see any other significant limitation that should be discussed.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "The introduction of a quantitative, activation-weighted similarity metric (MS score) for neuron-level monosemanticity is both timely and useful for the interpretability community. Indeed, there is a plethora of recent works that use SAEs for interpretability, without being able to validate what the SAEs have learned and how \"pure\" the representations are. \n\nDemonstrations of concept-based intervention in MLLMs (e.g., inserting or suppressing concepts in generated responses) showcase real-world value.\n\nThe authors also present a rigorous study on the effect of the expansion and sparsity of the considered SAE to the final MS score. \n\nI find that this work draws a lot of inspiration from network dissection approaches such as [1],[2], there is hardly any discussion about the similarities of the proposed method. The authors only mention \"Therefore, there have been investigations into the representations of these models which have found interpretable neurons\", without making any connections to these existing works. \n\nThe steering experiments are highly illustrative. Still, it would be useful to see failure cases or limitations, e.g., when MS is high but steering doesn’t meaningfully influence the LLM output and others. \n\nThe authors mention in the main text that \"we quantify MS of neurons using DINOv2 ViT-B\" (p.6 l.184). Did the authors investigate the sensitivity of the MS quantification with respect to different embedding spaces in the same setting? There are some tables in the appendix, but I would like some insight, if some encoders seemed to be more \"appropriate\" for this analysis. \n\n[1] Oikarinen et al., CLIP-dissect: Automatic description of neuron representations in deep vision networks, ICLR 2023\n\n[2] Panousis et al, DISCOVER: Making Vision Networks Interpretable via Competition and Dissection", "was_revised": true, "final_justification": "This work presents a novel approach for monosemanticity in Sparse Autoencoders. The contribution of the paper is clear and the paper is well written. \n\nThe authors have responded appropriately to all the concerns of the reviewers and I believe that the discussions/results should be included in the final manuscript. These include the trade-off between monosemanticirty and zero-shot performance and the steering results. Finally, as noted in my initial review, I find that the manuscript could benefit from a discussion with related literature towards explainable methods.", "rebuttal": "We thank the Reviewer r5gC for the positive and encouraging feedback recognizing the introduction of the MS score as a *timely and useful* contribution for neuron-level interpretability, helping to validate *how \"pure\" the representations are* in recent work on SAEs. We also thank the Reviewer for highlighting the *real-world value* of our *concept-based interventions* in MLLMs, and appreciating the *rigorous study* of how SAE *expansion and sparsity* affect MS. \n\n**Discuss about the similarities of the proposed method with [1], [2].**\n\n\nCLIP-Dissect [1] introduces a method for automatically assigning textual descriptions to neurons by leveraging CLIP multimodal embedding space. DISCOVER [2] further advances this line of work by introducing competitive mechanisms (e.g., LWTA layers) to encourage neuron specialization and improve interpretability. Both methods focus on analyzing and labeling neurons post hoc, primarily to understand what individual units represent. \nOur work draws inspiration from these efforts but takes a complementary direction. Rather than describing the “raw neurons” of a pretrained model, we train a Sparse Autoencoder (SAE) to explicitly disentangle concept representations in the vision encoder. We then evaluate the interpretability of these SAE neurons using our proposed MS score. Our quantitative analysis shows that SAE neurons are significantly more monosemantic (and thus more interpretable) than the raw neurons of the underlying model. As we show in Table 1, the highest MS for original neurons is 0.01, whereas even with expansion factor ε=1, Matryoshka BatchTopK SAEs achieve highest MS of about 0.80.\n\n[1] Oikarinen et al., “CLIP-dissect: Automatic description of neuron representations in deep vision networks”, ICLR 2023\n\n[2] Panousis et al, “DISCOVER: Making Vision Networks Interpretable via Competition and Dissection”, NeurIPS 2023\n\n**Failure cases or limitations of steering.**\n\n\nIn some cases high MS may not translate into precise or unambiguous influence on the MLLM output, e.g. fine-grained animal categories in ImageNet (which we used to train the SAEs). Due to the dataset’s strong bias toward animal species and the SAE’s ability to effectively disentangle visual concepts, we often observe neurons with very high MS corresponding to specific animals (e.g., “beagle”, “golden retriever”, “labrador”). However, these species are visually similar, and while the SAE can separate them well, the MLLM may not reliably distinguish between them when steered. Instead, the model often responds with more generic animal descriptions, or may even confuse animals. This limitation can also stem from the fact that the semantic space of the LLM may not align perfectly with the fine-grained distinctions captured in the vision encoder.\n\n**Sensitivity of the MS quantification with respect to different embedding spaces.**\n\n\nWe also investigated and provided results using CLIP ViT-B vision encoder to measure MS in the Appendix. While the specific values of MS and their ranges vary depending on the vision encoder used, the overall conclusion remains consistent: *SAEs yield neurons that are significantly more monosemantic than the original representations* (see side-by-side comparison of behaviors using different vision encoders in Figure A7 in Appendix E.2). Both CLIP and DINOv2 encoders produce monosemanticity scores that align well with human intuition, as demonstrated in our user study (see Table A1 in Appendix C).\n\n**Towards learning networks that are inherently interpretable by design.** \n\n\nWe agree that using our proposed score during training is a promising direction. Perhaps an interesting future work could be to use LoRA adapters to fine-tune a language model around a pretrained SAE to reduce reconstruction loss and improve downstream performance (as indicated by Chen et al. [3]). We believe that using our proposed MS score as an additional regularization signal could further improve monosemanticity and controllability.\n\n[3] Chen et al., “Low-Rank Adapting Models for Sparse Autoencoders”, ICML 2025."}, {"review_id": "0IZ4Xalpwg", "reviewer": "Reviewer_6AZV", "summary": "This paper proposes a novel metric for evaluating sparse autoencoders (SAEs) applied to image-text encoders such as CLIP. The metric appears to be correlated with human evaluations, offering a promising direction for interpreting multimodal representations. Additionally, the authors explore how SAE neurons can be used to steer multimodal large language models (VLMs), providing qualitative evidence of controllability. The paper echoes insights from prior work on LLMs, such as the increase in monosemanticity with wider SAEs.", "questions": "Please check weakneses.", "limitations": "Very short limitation paragraph at the end of the paper. I expect longer discussion on limitations as meantioned in the weakneses section.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "**Strengths:**\n\n* The proposal of a metric for evaluating SAEs is needed and important. The metric is intuitive and seems to be correlation with human judgment.\n\n* The qualitative results show that interventions on SAE neurons in vision encoders can meaningfully steer the output of VLMs.\n\n* The paper is well written, clearly structured, and easy to follow.\n\n\n**Weakneses:**\n\n* Limited scope of encoders: The experiments are limited to CLIP-style encoders (CLIP and SigLIP). It is unclear whether the approach generalizes to other types of vision encoders. Including results on more recent state-of-the-art models (e.g., AIMv2 [1]) would strengthen the contribution.\n\n* The paper does not discuss or compare with other recent approaches to VLM steering, such as activation-based steering methods [2]. Activation steering is a common baseline in LLMs [3] and VLMs. A comparison and discussion with other steering method would properly position this paper.\n\n* The method focuses exclusively on steering the vision encoder. How does this compare with steering interventions applied within the LLM, such as on vision tokens after the connector in multimodal LLMs? A discussion of the trade-offs or benefits would be valuable.\n\n* Lack of steering quantitative evaluation: The paper only presents qualitative results for steering, which makes it difficult to assess practical effectiveness. Quantitative metrics or user studies would provide stronger evidence of the method’s utility.\n\n* The proposed metric includes a relevance score. It would be helpful to show how much this component contributes to overall performance -- e.g., through an ablation comparing versions with and without it.\n\n* The paper could better articulate how the proposed method helps reveal differences between vision encoders. Are there insights into architectural or representational differences?\n\n[1] \"Analyzing Fine-tuning Representation Shift for Multimodal LLMs Steering alignment.\" ICCV (2025).\n\n[2]  \"Multimodal autoregressive pre-training of large vision encoders.\" CVPR (2025).\n\n[3] \"Refusal in language models is mediated by a single direction.\"  NeurIPS (2024).", "was_revised": true, "final_justification": "The authors addressed most of my concerns and hence I am increasing my score.", "rebuttal": "We thank the Reviewer 6AZV for the positive and constructive feedback recognizing our metric as *needed, important, intuitive* and *correlated with human judgment*; and acknowledging our results showing that *interventions on SAE neurons in vision encoders can meaningfully steer the output of VLMs.* We are happy to hear that our paper is *well written, clearly structured, and easy to follow.*\n\n**Generalization to other encoders than just CLIP-style encoders (CLIP and SigLIP).**\n\nWe appreciate the reviewer’s suggestion and have conducted additional experiments on state-of-the-art vision encoders, including **AIMv2** [1] and **WebSSL-MAE** [4] and report the best observed MS.\n\n| Vision Encoder   | Without SAE | With SAE (ε=1) | With SAE (ε=4) |\n|---------------|--------|-----------|-----------|\n| AIMv2          \t\t| 0.01   | 0.59      | 0.85      |\n| WebSSL-MAE   \t | 0.01   | 0.79      | 0.92      |\n| CLIP          \t\t| 0.01   | 0.82       | 0.89      |\n| SigLIP        \t\t| 0.01   | 0.83       | 0.88      |\n\nIn fact, neurons in these recent encoders are also not monosemantic in their native form, but the SAEs can successfully disentangle them into highly monosemantic units. In addition, we observe that increasing the expansion factor ε of the SAE leads to higher MS scores universally across different encoders. We would be happy to include these results in the final manuscript.\n\n**Discussing other recent approaches to VLM steering, e.g. [2, 3].**\n\nUnlike activation steering methods (e.g., [2], [3]), which typically involve direct manipulation of the language decoder’s residual stream and often require fine-tuning or labeled data, our method operates in a fully unsupervised manner. The SAE is trained independently on the vision encoder using a generic and broad dataset (i.e. ImageNet), and yet it enables effective steering of the overall MLLM. We believe this is a valuable and novel finding, as it demonstrates that meaningful control over multimodal outputs can be achieved without altering the language generation components or relying on annotated vision-language datasets.\nWhile a direct quantitative comparison with activation-based methods is non-trivial due to the differing mechanisms and representations, we will expand the related work section to include a discussion of these papers.\n\n**How does steering the vision encoder compare with steering interventions applied within the LLM?** \n\nIndeed, we focus on steering the vision encoder, rather than applying interventions within the language model or after the connector. This offers several important advantages: 1) it is more universal, as many MLLMs share common vision encoders (e.g. CLIP, SigLIP), even when their language part differs; 2) it is entirely unsupervised and does not rely on vision-language dataset or labeled data which are typically required for steering within the LLM; 3) it preserves internal language representations and is more interpretable when the goal is to filter visual concepts. We will add this discussion to clarify benefits and limitations of steering at different stages of the MLLM pipeline. We believe our method complements existing approaches and offers an interpretable and broadly applicable alternative for multimodal control.\n\n**Lack of steering quantitative evaluation**\n\nWhile Table 2 in the main paper demonstrates a basic quantitative signal of effective steering, we agree that a more detailed and interpretable metric is valuable. To this end, we adopt an *LLM-as-a-judge* approach [5], using GPT-4.1-mini to evaluate both concept insertion and suppression.\n\n**Concept insertion.**\nWe consider the first 100 SAE neurons $x_i$ used in LLaVA experiments. For each neuron $x_i$, we collect its top-activating images $g_i$ (a 4×4 grid of 16 images). We then intervene by boosting activation at neuron $x_i$ to $\\alpha = 30$ and generate responses $y_{j,i}$ from LLaVA when prompted with 10 diverse text prompts $t_j \\in$ { *\"Write me a short love poem\"*, *\"Propose a math word problem\"*, *\"Invent a new holiday\"*, ... }.\n\nFor each of the 1000 generations $y_{j,i}$, the judge is asked:\n\n1. *Does the text contain any, even subtle, reference to the concept in the image* $g_i$?  \n2. *Does the text respond to the original prompt* $t_j$?\n\nThe judge answers with \"yes\" or \"no\" to each. We find that:\n\n- In **48.7\\%** of cases, the concept related to $x_i$ appears in the generated text.  \n- In **85.8\\%** of cases, the output still follows the base prompt $t_j$.  \n- In **42.4\\%** of cases, both criteria are satisfied simultaneously.\n\nThese results indicate that almost half of the SAE neurons can effectively steer generation toward specific concepts while largely preserving prompt intent.\n\n**Concept Suppression.**\nWe again consider each SAE neuron $x_i$ and its corresponding top-activating image grid $g_i$. This time, we apply a negative intervention with $\\alpha = -15$ and for each $x_i$, we prompt LLaVA with:\n\n- *\"What is shown in this set of images?\"* using $g_i$ as input, producing a suppressed output $y_i^{-}$.\n\nWe then evaluate $y_i^{-}$ using GPT-4.1-mini with the question:\n\n- *\"Decide if the text could be a description of the given image set. Image: $g_i$ Text: $y_i^{-}$\"*\n\nTo test specificity, we also feed unrelated images $g_j$ (for $j \\ne i$) into the same prompt to assess whether suppression affects only the intended concept. Before conducting this evaluation, we ensure that all selected neurons produced correct captions in the zero-intervention case, as judged by the same protocol.\n\nResults:\n- In **64.4%** of cases, the suppressed concept was no longer described by the model.  \n- In **81.4%** of cases, the model continued to generate appropriate descriptions for unrelated images.  \n- In **52.5%** of cases, both concept suppression and preservation of unrelated outputs were achieved.\n\nThese results demonstrate that targeted negative interventions can remove specific concepts without compromising the model’s ability to generate coherent outputs for other content.\n\n**How much does the relevance score contribute to overall performance?**\n\nThe relevance score plays a crucial role as without it the MS assigns the same value to all neurons (MS = 0.012) and becomes uninformative. This is because the relevance score measures how strongly a neuron activates on each image and determines which image pairs contribute most to the MS calculation. It ensures that each neuron is evaluated using the appropriate number of pairs, including enough relevant examples while excluding irrelevant ones.\n\nFor example, consider a neuron that responds to *black animals*, evaluated on six images: a black dog, black cat, black horse, white dog, white cat, and white horse. The neuron activates strongly for the black animals and weakly for the rest. The relevance score guides the MS to focus on distances between embeddings of black animals only. If too few pairs are used, such as just black dog and black cat, the MS may be artificially high because it overlooks the variability introduced by the black horse. If too many pairs are used, including irrelevant comparisons like black dog versus white horse, the MS is pushed lower even if the neuron is truly monosemantic. Thus, the relevance score allows MS to reflect a neuron's actual conceptual focus. \n\n**The paper could better articulate how the proposed method helps reveal differences between vision encoders. Are there insights into architectural or representational differences?**\n\nThe idea of using our Monosemanticity Score (MS), originally designed to find neuron-level differences within SAEs, to reveal differences between vision encoders is indeed compelling.\nWe include new analysis demonstrating that applying the MS metric to SAEs across different vision encoders (e.g., CLIP and WebSSL-MAE [4]) reveals meaningful distinctions. When observing CLIP, which is trained with image-text pairs, we discover neurons that activate for images related to polysemous words such as *bank* (in both the financial and riverbank senses) or *horse* (as both an animal and in the context of horsepower). In contrast, such neurons are not present in WebSSL-MAE, a vision-only encoder, reflecting its lack of exposure to linguistic ambiguity. Our MS metric simplifies finding such neurons, as their visual polysemanticity leads to low MS values (MS $\\approx$ 0.01).\nAlthough we are unable to display images and must rely on textual descriptions, these examples will be included in the final manuscript.\n\n[1] \"Multimodal autoregressive pre-training of large vision encoders\", CVPR (2025).\n\n[2] \"Analyzing Fine-tuning Representation Shift for Multimodal LLMs Steering Alignment\", ICCV (2025).\n\n[3] \"Refusal in language models is mediated by a single direction\", NeurIPS (2024).\n\n[4] \"Web-SSL: Scaling Language-Free Visual Representation Learning\", Arxiv (04/2025).\n\n[5] \"Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena\", NeurIPS (2023)."}]

Author rebuttal:

Meta-review: This paper investigates interpretability in vision–language models and proposes a neuron-level Monosemanticity (MS) score, validated via a user study. Training Matryoshka sparse autoencoders (SAEs) on CLIP-style encoders yields higher MS and concept-aligned features, enabling targeted steering of MLLMs (e.g., LLaVA) by editing only vision-encoder activations, while largely preserving zero-shot accuracy at moderate sparsity. Ablations over sparsity/expansion and qualitative probes support these claims. 

Strengths include a clear metric and problem framing, systematic experiments across encoders, thorough analyses, and good reproducibility. Weaknesses are the initial CLIP-centric scope, relatively light quantitative steering evaluation, under-reported efficiency/latency, and limited positioning vs non-SAE or alternative steering methods. 

In discussion, R724t, R6AZV, and Rr5gC questioned novelty, breadth, and comparisons; the rebuttal added MS results on AIMv2/WebSSL-MAE, zero-shot trade-off tables, comparison with DiffMean when taking LLM-as-a-judge, and clarified their position within SAE and steering literature,. The reviewers were all satisfactory with substantive concerns addressed. 

Overall, the contribution is sound and practically useful. Thus, we recommend acceptance, while suggesting camera-ready requests to expand efficiency reporting and limitations.
Decision: Accept (poster)