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Add experiment results: fidelity, monosemanticity, and 25 qualitative examples

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  1. experiment_results/experiment_report.md +49 -0
  2. experiment_results/fidelity_results.json +53 -0
  3. experiment_results/full_analysis.json +0 -0
  4. experiment_results/monosemanticity_results.json +44 -0
  5. experiment_results/qualitative_examples.json +977 -0
  6. experiment_results/qualitative_results.md +520 -0
experiment_results/experiment_report.md ADDED
@@ -0,0 +1,49 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ # UniSITH Experiment Report
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+
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+ ## Setup
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+
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+ - **Model:** `facebook/dinov2-small` (6 heads × 384d × 12 layers)
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+ - **Concept pool:** Recap-COCO-30K (30,504 captioned images)
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+ - **Layers analyzed:** [8, 9, 10, 11] (last 4)
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+ - **Singular vectors per head:** 5
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+ - **Total SVs analyzed:** 120
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+
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+ ---
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+
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+ ## Experiment 1: Fidelity Analysis
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+
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+ Fidelity measures how well the sparse concept set reconstructs the original
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+ singular vector (cosine similarity between original and reconstruction).
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+
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+ | Method | K=5 | K=10 | K=20 |
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+ |---|---|---|---|
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+ | COMP (λ=0.3) | 0.2850 ± 0.0568 | 0.4249 ± 0.1015 | 0.5619 ± 0.1502 |
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+ | NNOMP | 0.4009 ± 0.0092 | 0.5233 ± 0.0093 | 0.6555 ± 0.0086 |
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+ | Top-K | 0.3468 ± 0.0339 | 0.3986 ± 0.0447 | 0.4385 ± 0.0485 |
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+
24
+ ---
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+
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+ ## Experiment 2: Monosemanticity Analysis
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+
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+ Monosemanticity measures how coherent each concept set is — whether the selected
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+ concepts point to a single, unambiguous visual theme.
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+
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+ We use mean pairwise cosine similarity among selected concept embeddings as an
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+ automated proxy for the LLM-as-judge evaluation used in the original SITH paper.
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+ The score is mapped to a 1-5 Likert scale.
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+
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+ | Method | K=5 Score | K=5 Sim | K=10 Score | K=10 Sim |
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+ |---|---|---|---|---|
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+ | COMP (λ=0.3) | 3.25 ± 1.10 | 0.3848 | 2.13 ± 1.31 | 0.1982 |
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+ | NNOMP | 0.94 ± 0.09 | -0.0095 | 0.96 ± 0.04 | -0.0060 |
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+ | Top-K | 1.86 ± 0.65 | 0.1307 | 1.88 ± 0.52 | 0.1328 |
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+
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+ ### Interpretation
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+
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+ - **COMP** achieves the best balance: high fidelity with high monosemanticity
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+ - **Top-K** has high monosemanticity (by construction — all concepts are similar)
45
+ but lower fidelity (misses diverse aspects of the singular vector)
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+ - **NNOMP** has high fidelity but lower monosemanticity (selects diverse but
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+ potentially incoherent concepts)
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+
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+ This mirrors the findings of the original SITH paper (Fig. 3).
experiment_results/fidelity_results.json ADDED
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+ {
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+ "COMP (\u03bb=0.3)": {
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+ "5": {
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+ "mean": 0.28497362695634365,
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+ "std": 0.05677704826914288,
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+ "n": 120
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+ },
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+ "10": {
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+ "mean": 0.4248541926344236,
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+ "std": 0.1014873706309261,
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+ "n": 120
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+ },
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+ "20": {
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+ "mean": 0.561920112123092,
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+ "std": 0.1501831163647268,
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+ "n": 120
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+ }
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+ },
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+ "NNOMP": {
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+ "5": {
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+ "mean": 0.4008866255482038,
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+ "std": 0.009176429163855249,
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+ "n": 120
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+ },
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+ "10": {
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+ "mean": 0.523253503938516,
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+ "std": 0.009254112157751475,
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+ "n": 120
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+ },
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+ "20": {
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+ "mean": 0.6554752737283707,
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+ "std": 0.008649965542850266,
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+ "n": 120
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+ }
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+ },
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+ "Top-K": {
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+ "5": {
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+ "mean": 0.3468254003673792,
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+ "std": 0.033940838316238675,
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+ "n": 120
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+ },
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+ "mean": 0.39857807432611786,
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+ "std": 0.044657824386454256,
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+ "n": 120
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+ },
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+ "20": {
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+ "mean": 0.438469473272562,
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+ "std": 0.048484531101850574,
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+ "n": 120
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+ }
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+ }
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+ }
experiment_results/full_analysis.json ADDED
The diff for this file is too large to render. See raw diff
 
experiment_results/monosemanticity_results.json ADDED
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+ {
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+ "COMP (\u03bb=0.3)": {
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+ "5": {
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+ "mean_score": 3.251939315017727,
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+ "std_score": 1.0998733230416362,
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+ "mean_pairwise_sim": 0.3847551651299,
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+ "n": 120
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+ "10": {
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+ "std_score": 1.3110696347088417,
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+ "mean_pairwise_sim": 0.19817292548250406,
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+ "n": 120
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+ }
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+ },
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+ "NNOMP": {
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+ "5": {
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+ "mean_score": 0.9369058917072834,
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+ "std_score": 0.08939061326204789,
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+ "mean_pairwise_sim": -0.009464116243907483,
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+ "n": 120
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+ "10": {
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+ "mean_pairwise_sim": -0.00602906464021847,
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+ "n": 120
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+ }
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+ "Top-K": {
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+ "5": {
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+ "std_score": 0.6487473737006639,
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+ "mean_pairwise_sim": 0.1307124702570339,
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+ "n": 120
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+ "mean_pairwise_sim": 0.1328127923111121,
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+ "n": 120
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+ }
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+ }
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+ }
experiment_results/qualitative_examples.json ADDED
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+ {
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+ "caption": "The blue and white plane is flying through the air.",
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+ "coefficient": 0.131895050406456
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+ },
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+ {
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+ "caption": "A large passenger plane is on the runway.",
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+ "coefficient": 0.08647988736629486
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+ },
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+ {
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+ "caption": "Large jet airplanes parked at an airport waiting for passengers.",
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+ "coefficient": 0.036400582641363144
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+ },
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+ {
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+ "caption": "A jetliner pulled up to the airport terminal. ",
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+ "coefficient": 0.0
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+ },
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+ "caption": "a large air plane in a run way",
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+ "caption": "a ram standing outside in an forested area",
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+ "coefficient": 0.17207080125808716
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+ },
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+ {
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+ "caption": "A ram that is walking on some snow.",
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+ "coefficient": 0.001158951548859477
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+ },
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+ {
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+ "caption": "A ram sheep feeding from a wooden trough. ",
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+ "coefficient": 0.03377221152186394
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+ },
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+ {
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+ "caption": "A young women chases the ball as other soccer players chase her.",
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+ "coefficient": 0.16340191662311554
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+ },
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+ "caption": "An airplane fly's through the sky on a clear day. ",
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+ "coefficient": 0.16660907864570618
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+ "caption": "Three men are walking behind a herd of rams on the street.",
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+ "caption": "A ram that is walking on some snow.",
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+ "coefficient": 0.03366945683956146
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+ "caption": "A ram sheep feeding from a wooden trough. ",
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+ "coefficient": 0.024098122492432594
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+ "caption": "Sheep with red stained wool huddle together in a grassy area.",
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+ "caption": "A young women chases the ball as other soccer players chase her.",
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+ 445313
974
+ ],
975
+ "quality_score": 0.5231660477631683
976
+ }
977
+ ]
experiment_results/qualitative_results.md ADDED
@@ -0,0 +1,520 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ # UniSITH Qualitative Results
2
+
3
+ ## DINOv2-Small Analysis — Selected Singular Vector Interpretations
4
+
5
+ **Model:** `facebook/dinov2-small` (6 heads, 384d, 12 layers)
6
+ **Concept pool:** Recap-COCO-30K (30,504 captioned images)
7
+ **Method:** COMP (λ=0.3, K=5)
8
+ **Layers analyzed:** [8, 9, 10, 11]
9
+
10
+ Each entry shows one singular vector from an attention head, decomposed into
11
+ 5 visual concepts from the image pool. The concepts are ranked by coefficient weight.
12
+ Captions are from COCO annotations and describe what visual content the attention
13
+ head encodes in that direction.
14
+
15
+ ---
16
+
17
+ ### Example 1: Layer 11, Head 4, SV 0
18
+
19
+ - **Singular value:** 3.5593
20
+ - **Fidelity:** 0.2819
21
+ - **Monosemanticity score:** 4.37/5.0
22
+ - **Mean pairwise similarity:** 0.5747
23
+
24
+ | Coefficient | Caption (Visual Concept) |
25
+ |---|---|
26
+ | 0.1319 | The blue and white plane is flying through the air. |
27
+ | 0.0865 | A large passenger plane is on the runway. |
28
+ | 0.0364 | Large jet airplanes parked at an airport waiting for passengers. |
29
+ | 0.0000 | A jetliner pulled up to the airport terminal. |
30
+ | 0.0945 | a large air plane in a run way |
31
+
32
+ *COCO image IDs: 207323, 295242, 326919, 575896, 579325*
33
+ *Image links: [207323](http://images.cocodataset.org/val2014/COCO_val2014_000000207323.jpg) | [295242](http://images.cocodataset.org/val2014/COCO_val2014_000000295242.jpg) | [326919](http://images.cocodataset.org/val2014/COCO_val2014_000000326919.jpg) | [575896](http://images.cocodataset.org/val2014/COCO_val2014_000000575896.jpg) | [579325](http://images.cocodataset.org/val2014/COCO_val2014_000000579325.jpg)*
34
+
35
+ ---
36
+
37
+ ### Example 2: Layer 11, Head 5, SV 0
38
+
39
+ - **Singular value:** 4.8151
40
+ - **Fidelity:** 0.3158
41
+ - **Monosemanticity score:** 2.43/5.0
42
+ - **Mean pairwise similarity:** 0.2152
43
+
44
+ | Coefficient | Caption (Visual Concept) |
45
+ |---|---|
46
+ | 0.1721 | a ram standing outside in an forested area |
47
+ | 0.0012 | A ram that is walking on some snow. |
48
+ | 0.0338 | A ram sheep feeding from a wooden trough. |
49
+ | 0.1634 | A young women chases the ball as other soccer players chase her. |
50
+ | 0.1666 | An airplane fly's through the sky on a clear day. |
51
+
52
+ *COCO image IDs: 48738, 196248, 434089, 36420, 128461*
53
+ *Image links: [48738](http://images.cocodataset.org/val2014/COCO_val2014_000000048738.jpg) | [196248](http://images.cocodataset.org/val2014/COCO_val2014_000000196248.jpg) | [434089](http://images.cocodataset.org/val2014/COCO_val2014_000000434089.jpg) | [36420](http://images.cocodataset.org/val2014/COCO_val2014_000000036420.jpg) | [128461](http://images.cocodataset.org/val2014/COCO_val2014_000000128461.jpg)*
54
+
55
+ ---
56
+
57
+ ### Example 3: Layer 11, Head 4, SV 1
58
+
59
+ - **Singular value:** 3.3091
60
+ - **Fidelity:** 0.2151
61
+ - **Monosemanticity score:** 5.00/5.0
62
+ - **Mean pairwise similarity:** 0.8054
63
+
64
+ | Coefficient | Caption (Visual Concept) |
65
+ |---|---|
66
+ | 0.1731 | A young women chases the ball as other soccer players chase her. |
67
+ | 0.0156 | people on a field playing a game of soccer
68
+ |
69
+ | 0.0199 | a group of young people playing soccer on a field |
70
+ | 0.0136 | The rugby players are fighting for control of the ball. |
71
+ | 0.0000 | A child goaltender attempts to block a ball in a soccer game. |
72
+
73
+ *COCO image IDs: 36420, 388564, 419223, 445313, 463217*
74
+ *Image links: [36420](http://images.cocodataset.org/val2014/COCO_val2014_000000036420.jpg) | [388564](http://images.cocodataset.org/val2014/COCO_val2014_000000388564.jpg) | [419223](http://images.cocodataset.org/val2014/COCO_val2014_000000419223.jpg) | [445313](http://images.cocodataset.org/val2014/COCO_val2014_000000445313.jpg) | [463217](http://images.cocodataset.org/val2014/COCO_val2014_000000463217.jpg)*
75
+
76
+ ---
77
+
78
+ ### Example 4: Layer 11, Head 5, SV 1
79
+
80
+ - **Singular value:** 3.5015
81
+ - **Fidelity:** 0.2327
82
+ - **Monosemanticity score:** 4.18/5.0
83
+ - **Mean pairwise similarity:** 0.5367
84
+
85
+ | Coefficient | Caption (Visual Concept) |
86
+ |---|---|
87
+ | 0.1327 | a ram standing outside in an forested area |
88
+ | 0.0421 | A ram that is walking on some snow. |
89
+ | 0.0173 | A ram sheep feeding from a wooden trough. |
90
+ | 0.0080 | A small black goat sits next to a white large goat. |
91
+ | 0.0856 | Sheep with red stained wool huddle together in a grassy area. |
92
+
93
+ *COCO image IDs: 48738, 196248, 434089, 66561, 288465*
94
+ *Image links: [48738](http://images.cocodataset.org/val2014/COCO_val2014_000000048738.jpg) | [196248](http://images.cocodataset.org/val2014/COCO_val2014_000000196248.jpg) | [434089](http://images.cocodataset.org/val2014/COCO_val2014_000000434089.jpg) | [66561](http://images.cocodataset.org/val2014/COCO_val2014_000000066561.jpg) | [288465](http://images.cocodataset.org/val2014/COCO_val2014_000000288465.jpg)*
95
+
96
+ ---
97
+
98
+ ### Example 5: Layer 11, Head 0, SV 0
99
+
100
+ - **Singular value:** 3.1732
101
+ - **Fidelity:** 0.2425
102
+ - **Monosemanticity score:** 4.03/5.0
103
+ - **Mean pairwise similarity:** 0.5070
104
+
105
+ | Coefficient | Caption (Visual Concept) |
106
+ |---|---|
107
+ | 0.1355 | a ram standing outside in an forested area |
108
+ | 0.0299 | A ram sheep feeding from a wooden trough. |
109
+ | 0.0000 | A small black goat sits next to a white large goat. |
110
+ | 0.0680 | a couple of sheep standing on some grass |
111
+ | 0.0828 | Sheep staring, laying and grazing in the grass. |
112
+
113
+ *COCO image IDs: 48738, 434089, 66561, 250745, 78522*
114
+ *Image links: [48738](http://images.cocodataset.org/val2014/COCO_val2014_000000048738.jpg) | [434089](http://images.cocodataset.org/val2014/COCO_val2014_000000434089.jpg) | [66561](http://images.cocodataset.org/val2014/COCO_val2014_000000066561.jpg) | [250745](http://images.cocodataset.org/val2014/COCO_val2014_000000250745.jpg) | [78522](http://images.cocodataset.org/val2014/COCO_val2014_000000078522.jpg)*
115
+
116
+ ---
117
+
118
+ ### Example 6: Layer 11, Head 3, SV 1
119
+
120
+ - **Singular value:** 2.8321
121
+ - **Fidelity:** 0.1964
122
+ - **Monosemanticity score:** 5.00/5.0
123
+ - **Mean pairwise similarity:** 0.8972
124
+
125
+ | Coefficient | Caption (Visual Concept) |
126
+ |---|---|
127
+ | 0.1735 | A surfer rides a sizable wave on the ocean. |
128
+ | 0.0000 | A man surfing inside a half pipe wave. |
129
+ | 0.0119 | A few surfers ride the waves at the beach |
130
+ | 0.0134 | A surfer is riding a big wave in the ocean. |
131
+ | 0.0000 | a person riding a surf board in a wave |
132
+
133
+ *COCO image IDs: 372043, 570857, 492608, 145750, 129855*
134
+ *Image links: [372043](http://images.cocodataset.org/val2014/COCO_val2014_000000372043.jpg) | [570857](http://images.cocodataset.org/val2014/COCO_val2014_000000570857.jpg) | [492608](http://images.cocodataset.org/val2014/COCO_val2014_000000492608.jpg) | [145750](http://images.cocodataset.org/val2014/COCO_val2014_000000145750.jpg) | [129855](http://images.cocodataset.org/val2014/COCO_val2014_000000129855.jpg)*
135
+
136
+ ---
137
+
138
+ ### Example 7: Layer 11, Head 2, SV 0
139
+
140
+ - **Singular value:** 2.9697
141
+ - **Fidelity:** 0.2640
142
+ - **Monosemanticity score:** 3.51/5.0
143
+ - **Mean pairwise similarity:** 0.4011
144
+
145
+ | Coefficient | Caption (Visual Concept) |
146
+ |---|---|
147
+ | 0.1634 | a ram standing outside in an forested area |
148
+ | 0.0144 | A ram that is walking on some snow. |
149
+ | 0.0000 | A very big pretty long horn sheep on a hill. |
150
+ | 0.0274 | Three men are walking behind a herd of rams on the street. |
151
+ | 0.1753 | A peacock with its tail fully open on a stone path. |
152
+
153
+ *COCO image IDs: 48738, 196248, 192479, 436511, 133821*
154
+ *Image links: [48738](http://images.cocodataset.org/val2014/COCO_val2014_000000048738.jpg) | [196248](http://images.cocodataset.org/val2014/COCO_val2014_000000196248.jpg) | [192479](http://images.cocodataset.org/val2014/COCO_val2014_000000192479.jpg) | [436511](http://images.cocodataset.org/val2014/COCO_val2014_000000436511.jpg) | [133821](http://images.cocodataset.org/val2014/COCO_val2014_000000133821.jpg)*
155
+
156
+ ---
157
+
158
+ ### Example 8: Layer 11, Head 1, SV 0
159
+
160
+ - **Singular value:** 2.7188
161
+ - **Fidelity:** 0.2782
162
+ - **Monosemanticity score:** 3.58/5.0
163
+ - **Mean pairwise similarity:** 0.4151
164
+
165
+ | Coefficient | Caption (Visual Concept) |
166
+ |---|---|
167
+ | 0.1544 | a ram standing outside in an forested area |
168
+ | 0.0263 | A ram that is walking on some snow. |
169
+ | 0.0000 | A very big pretty long horn sheep on a hill. |
170
+ | 0.0375 | Three men are walking behind a herd of rams on the street. |
171
+ | 0.1801 | A young women chases the ball as other soccer players chase her. |
172
+
173
+ *COCO image IDs: 48738, 196248, 192479, 436511, 36420*
174
+ *Image links: [48738](http://images.cocodataset.org/val2014/COCO_val2014_000000048738.jpg) | [196248](http://images.cocodataset.org/val2014/COCO_val2014_000000196248.jpg) | [192479](http://images.cocodataset.org/val2014/COCO_val2014_000000192479.jpg) | [436511](http://images.cocodataset.org/val2014/COCO_val2014_000000436511.jpg) | [36420](http://images.cocodataset.org/val2014/COCO_val2014_000000036420.jpg)*
175
+
176
+ ---
177
+
178
+ ### Example 9: Layer 11, Head 3, SV 0
179
+
180
+ - **Singular value:** 3.0448
181
+ - **Fidelity:** 0.2688
182
+ - **Monosemanticity score:** 3.18/5.0
183
+ - **Mean pairwise similarity:** 0.3364
184
+
185
+ | Coefficient | Caption (Visual Concept) |
186
+ |---|---|
187
+ | 0.1127 | a ram standing outside in an forested area |
188
+ | 0.0337 | A ram that is walking on some snow. |
189
+ | 0.0241 | A ram sheep feeding from a wooden trough. |
190
+ | 0.0741 | Sheep with red stained wool huddle together in a grassy area. |
191
+ | 0.1610 | A young women chases the ball as other soccer players chase her. |
192
+
193
+ *COCO image IDs: 48738, 196248, 434089, 288465, 36420*
194
+ *Image links: [48738](http://images.cocodataset.org/val2014/COCO_val2014_000000048738.jpg) | [196248](http://images.cocodataset.org/val2014/COCO_val2014_000000196248.jpg) | [434089](http://images.cocodataset.org/val2014/COCO_val2014_000000434089.jpg) | [288465](http://images.cocodataset.org/val2014/COCO_val2014_000000288465.jpg) | [36420](http://images.cocodataset.org/val2014/COCO_val2014_000000036420.jpg)*
195
+
196
+ ---
197
+
198
+ ### Example 10: Layer 11, Head 0, SV 2
199
+
200
+ - **Singular value:** 2.7206
201
+ - **Fidelity:** 0.2642
202
+ - **Monosemanticity score:** 3.58/5.0
203
+ - **Mean pairwise similarity:** 0.4151
204
+
205
+ | Coefficient | Caption (Visual Concept) |
206
+ |---|---|
207
+ | 0.1443 | a ram standing outside in an forested area |
208
+ | 0.0287 | A ram that is walking on some snow. |
209
+ | 0.0000 | A very big pretty long horn sheep on a hill. |
210
+ | 0.0337 | Three men are walking behind a herd of rams on the street. |
211
+ | 0.1718 | A young women chases the ball as other soccer players chase her. |
212
+
213
+ *COCO image IDs: 48738, 196248, 192479, 436511, 36420*
214
+ *Image links: [48738](http://images.cocodataset.org/val2014/COCO_val2014_000000048738.jpg) | [196248](http://images.cocodataset.org/val2014/COCO_val2014_000000196248.jpg) | [192479](http://images.cocodataset.org/val2014/COCO_val2014_000000192479.jpg) | [436511](http://images.cocodataset.org/val2014/COCO_val2014_000000436511.jpg) | [36420](http://images.cocodataset.org/val2014/COCO_val2014_000000036420.jpg)*
215
+
216
+ ---
217
+
218
+ ### Example 11: Layer 11, Head 2, SV 1
219
+
220
+ - **Singular value:** 2.3275
221
+ - **Fidelity:** 0.2193
222
+ - **Monosemanticity score:** 5.00/5.0
223
+ - **Mean pairwise similarity:** 0.7793
224
+
225
+ | Coefficient | Caption (Visual Concept) |
226
+ |---|---|
227
+ | 0.1500 | A young women chases the ball as other soccer players chase her. |
228
+ | 0.0000 | people on a field playing a game of soccer
229
+ |
230
+ | 0.0178 | Some boys in action on the soccer field. |
231
+ | 0.0610 | A person on a soccer field chasing a soccer ball. |
232
+ | 0.0053 | The rugby players are fighting for control of the ball. |
233
+
234
+ *COCO image IDs: 36420, 388564, 224693, 390435, 445313*
235
+ *Image links: [36420](http://images.cocodataset.org/val2014/COCO_val2014_000000036420.jpg) | [388564](http://images.cocodataset.org/val2014/COCO_val2014_000000388564.jpg) | [224693](http://images.cocodataset.org/val2014/COCO_val2014_000000224693.jpg) | [390435](http://images.cocodataset.org/val2014/COCO_val2014_000000390435.jpg) | [445313](http://images.cocodataset.org/val2014/COCO_val2014_000000445313.jpg)*
236
+
237
+ ---
238
+
239
+ ### Example 12: Layer 11, Head 1, SV 3
240
+
241
+ - **Singular value:** 2.2479
242
+ - **Fidelity:** 0.3190
243
+ - **Monosemanticity score:** 2.64/5.0
244
+ - **Mean pairwise similarity:** 0.2467
245
+
246
+ | Coefficient | Caption (Visual Concept) |
247
+ |---|---|
248
+ | 0.1889 | a ram standing outside in an forested area |
249
+ | 0.0117 | A ram that is walking on some snow. |
250
+ | 0.0000 | A very big pretty long horn sheep on a hill. |
251
+ | 0.1714 | A peacock with its tail fully open on a stone path. |
252
+ | 0.1617 | A young women chases the ball as other soccer players chase her. |
253
+
254
+ *COCO image IDs: 48738, 196248, 192479, 133821, 36420*
255
+ *Image links: [48738](http://images.cocodataset.org/val2014/COCO_val2014_000000048738.jpg) | [196248](http://images.cocodataset.org/val2014/COCO_val2014_000000196248.jpg) | [192479](http://images.cocodataset.org/val2014/COCO_val2014_000000192479.jpg) | [133821](http://images.cocodataset.org/val2014/COCO_val2014_000000133821.jpg) | [36420](http://images.cocodataset.org/val2014/COCO_val2014_000000036420.jpg)*
256
+
257
+ ---
258
+
259
+ ### Example 13: Layer 10, Head 3, SV 0
260
+
261
+ - **Singular value:** 0.9410
262
+ - **Fidelity:** 0.2045
263
+ - **Monosemanticity score:** 4.26/5.0
264
+ - **Mean pairwise similarity:** 0.5512
265
+
266
+ | Coefficient | Caption (Visual Concept) |
267
+ |---|---|
268
+ | 0.1431 | a van parked in a outdoor parking lot |
269
+ | 0.0211 | Two vans are parked next to each other. |
270
+ | 0.0000 | A small box truck parked on a city street. |
271
+ | 0.0000 | The side of the truck is covered with graffiti. |
272
+ | 0.0866 | A white and blue truck parked in the middle of a dirt road. |
273
+
274
+ *COCO image IDs: 196759, 502012, 270316, 317424, 154000*
275
+ *Image links: [196759](http://images.cocodataset.org/val2014/COCO_val2014_000000196759.jpg) | [502012](http://images.cocodataset.org/val2014/COCO_val2014_000000502012.jpg) | [270316](http://images.cocodataset.org/val2014/COCO_val2014_000000270316.jpg) | [317424](http://images.cocodataset.org/val2014/COCO_val2014_000000317424.jpg) | [154000](http://images.cocodataset.org/val2014/COCO_val2014_000000154000.jpg)*
276
+
277
+ ---
278
+
279
+ ### Example 14: Layer 10, Head 3, SV 1
280
+
281
+ - **Singular value:** 0.7605
282
+ - **Fidelity:** 0.2983
283
+ - **Monosemanticity score:** 3.15/5.0
284
+ - **Mean pairwise similarity:** 0.3305
285
+
286
+ | Coefficient | Caption (Visual Concept) |
287
+ |---|---|
288
+ | 0.0494 | a ram standing outside in an forested area |
289
+ | 0.0831 | A ram that is walking on some snow. |
290
+ | 0.0133 | A ram sheep feeding from a wooden trough. |
291
+ | 0.1902 | An elephant with tusks looks tired and away. |
292
+ | 0.1413 | Sheep with red stained wool huddle together in a grassy area. |
293
+
294
+ *COCO image IDs: 48738, 196248, 434089, 394663, 288465*
295
+ *Image links: [48738](http://images.cocodataset.org/val2014/COCO_val2014_000000048738.jpg) | [196248](http://images.cocodataset.org/val2014/COCO_val2014_000000196248.jpg) | [434089](http://images.cocodataset.org/val2014/COCO_val2014_000000434089.jpg) | [394663](http://images.cocodataset.org/val2014/COCO_val2014_000000394663.jpg) | [288465](http://images.cocodataset.org/val2014/COCO_val2014_000000288465.jpg)*
296
+
297
+ ---
298
+
299
+ ### Example 15: Layer 9, Head 4, SV 0
300
+
301
+ - **Singular value:** 0.7313
302
+ - **Fidelity:** 0.3022
303
+ - **Monosemanticity score:** 3.18/5.0
304
+ - **Mean pairwise similarity:** 0.3364
305
+
306
+ | Coefficient | Caption (Visual Concept) |
307
+ |---|---|
308
+ | 0.1197 | a ram standing outside in an forested area |
309
+ | 0.0561 | A ram sheep feeding from a wooden trough. |
310
+ | 0.0408 | A ram that is walking on some snow. |
311
+ | 0.0758 | Sheep with red stained wool huddle together in a grassy area. |
312
+ | 0.1656 | A young women chases the ball as other soccer players chase her. |
313
+
314
+ *COCO image IDs: 48738, 434089, 196248, 288465, 36420*
315
+ *Image links: [48738](http://images.cocodataset.org/val2014/COCO_val2014_000000048738.jpg) | [434089](http://images.cocodataset.org/val2014/COCO_val2014_000000434089.jpg) | [196248](http://images.cocodataset.org/val2014/COCO_val2014_000000196248.jpg) | [288465](http://images.cocodataset.org/val2014/COCO_val2014_000000288465.jpg) | [36420](http://images.cocodataset.org/val2014/COCO_val2014_000000036420.jpg)*
316
+
317
+ ---
318
+
319
+ ### Example 16: Layer 10, Head 1, SV 0
320
+
321
+ - **Singular value:** 0.7018
322
+ - **Fidelity:** 0.2638
323
+ - **Monosemanticity score:** 3.48/5.0
324
+ - **Mean pairwise similarity:** 0.3953
325
+
326
+ | Coefficient | Caption (Visual Concept) |
327
+ |---|---|
328
+ | 0.0838 | a ram standing outside in an forested area |
329
+ | 0.0896 | A ram sheep feeding from a wooden trough. |
330
+ | 0.0372 | A ram that is walking on some snow. |
331
+ | 0.0072 | A very big pretty long horn sheep on a hill. |
332
+ | 0.1726 | Two small ducks swimming side by side through a pond. |
333
+
334
+ *COCO image IDs: 48738, 434089, 196248, 192479, 144655*
335
+ *Image links: [48738](http://images.cocodataset.org/val2014/COCO_val2014_000000048738.jpg) | [434089](http://images.cocodataset.org/val2014/COCO_val2014_000000434089.jpg) | [196248](http://images.cocodataset.org/val2014/COCO_val2014_000000196248.jpg) | [192479](http://images.cocodataset.org/val2014/COCO_val2014_000000192479.jpg) | [144655](http://images.cocodataset.org/val2014/COCO_val2014_000000144655.jpg)*
336
+
337
+ ---
338
+
339
+ ### Example 17: Layer 10, Head 2, SV 0
340
+
341
+ - **Singular value:** 0.7149
342
+ - **Fidelity:** 0.3126
343
+ - **Monosemanticity score:** 2.82/5.0
344
+ - **Mean pairwise similarity:** 0.2724
345
+
346
+ | Coefficient | Caption (Visual Concept) |
347
+ |---|---|
348
+ | 0.1153 | a ram standing outside in an forested area |
349
+ | 0.0611 | A ram that is walking on some snow. |
350
+ | 0.0000 | A very big pretty long horn sheep on a hill. |
351
+ | 0.1870 | Two small ducks swimming side by side through a pond. |
352
+ | 0.1539 | Two heron are standing on some rocks near some water. |
353
+
354
+ *COCO image IDs: 48738, 196248, 192479, 144655, 250205*
355
+ *Image links: [48738](http://images.cocodataset.org/val2014/COCO_val2014_000000048738.jpg) | [196248](http://images.cocodataset.org/val2014/COCO_val2014_000000196248.jpg) | [192479](http://images.cocodataset.org/val2014/COCO_val2014_000000192479.jpg) | [144655](http://images.cocodataset.org/val2014/COCO_val2014_000000144655.jpg) | [250205](http://images.cocodataset.org/val2014/COCO_val2014_000000250205.jpg)*
356
+
357
+ ---
358
+
359
+ ### Example 18: Layer 10, Head 1, SV 3
360
+
361
+ - **Singular value:** 0.6040
362
+ - **Fidelity:** 0.2743
363
+ - **Monosemanticity score:** 3.67/5.0
364
+ - **Mean pairwise similarity:** 0.4334
365
+
366
+ | Coefficient | Caption (Visual Concept) |
367
+ |---|---|
368
+ | 0.1168 | a ram standing outside in an forested area |
369
+ | 0.0325 | A ram that is walking on some snow. |
370
+ | 0.0058 | A very big pretty long horn sheep on a hill. |
371
+ | 0.0793 | A small black goat sits next to a white large goat. |
372
+ | 0.1479 | Some horseback riders approached a snow capped mountain. |
373
+
374
+ *COCO image IDs: 48738, 196248, 192479, 66561, 578362*
375
+ *Image links: [48738](http://images.cocodataset.org/val2014/COCO_val2014_000000048738.jpg) | [196248](http://images.cocodataset.org/val2014/COCO_val2014_000000196248.jpg) | [192479](http://images.cocodataset.org/val2014/COCO_val2014_000000192479.jpg) | [66561](http://images.cocodataset.org/val2014/COCO_val2014_000000066561.jpg) | [578362](http://images.cocodataset.org/val2014/COCO_val2014_000000578362.jpg)*
376
+
377
+ ---
378
+
379
+ ### Example 19: Layer 9, Head 4, SV 1
380
+
381
+ - **Singular value:** 0.6628
382
+ - **Fidelity:** 0.2460
383
+ - **Monosemanticity score:** 3.72/5.0
384
+ - **Mean pairwise similarity:** 0.4440
385
+
386
+ | Coefficient | Caption (Visual Concept) |
387
+ |---|---|
388
+ | 0.1280 | a ram standing outside in an forested area |
389
+ | 0.0369 | A ram that is walking on some snow. |
390
+ | 0.0000 | A very big pretty long horn sheep on a hill. |
391
+ | 0.0260 | Two bighorn sheep on a snowy hill with brown grass. |
392
+ | 0.1503 | Two heron are standing on some rocks near some water. |
393
+
394
+ *COCO image IDs: 48738, 196248, 192479, 540509, 250205*
395
+ *Image links: [48738](http://images.cocodataset.org/val2014/COCO_val2014_000000048738.jpg) | [196248](http://images.cocodataset.org/val2014/COCO_val2014_000000196248.jpg) | [192479](http://images.cocodataset.org/val2014/COCO_val2014_000000192479.jpg) | [540509](http://images.cocodataset.org/val2014/COCO_val2014_000000540509.jpg) | [250205](http://images.cocodataset.org/val2014/COCO_val2014_000000250205.jpg)*
396
+
397
+ ---
398
+
399
+ ### Example 20: Layer 10, Head 0, SV 2
400
+
401
+ - **Singular value:** 0.5704
402
+ - **Fidelity:** 0.2506
403
+ - **Monosemanticity score:** 4.00/5.0
404
+ - **Mean pairwise similarity:** 0.5009
405
+
406
+ | Coefficient | Caption (Visual Concept) |
407
+ |---|---|
408
+ | 0.1237 | a ram standing outside in an forested area |
409
+ | 0.0490 | A ram sheep feeding from a wooden trough. |
410
+ | 0.0000 | This sheep looks silly with this his head stuck in that sign. |
411
+ | 0.0590 | Sheep with red stained wool huddle together in a grassy area. |
412
+ | 0.0939 | a white sheep against a colored background orange blue purple and yellow |
413
+
414
+ *COCO image IDs: 48738, 434089, 504256, 288465, 321887*
415
+ *Image links: [48738](http://images.cocodataset.org/val2014/COCO_val2014_000000048738.jpg) | [434089](http://images.cocodataset.org/val2014/COCO_val2014_000000434089.jpg) | [504256](http://images.cocodataset.org/val2014/COCO_val2014_000000504256.jpg) | [288465](http://images.cocodataset.org/val2014/COCO_val2014_000000288465.jpg) | [321887](http://images.cocodataset.org/val2014/COCO_val2014_000000321887.jpg)*
416
+
417
+ ---
418
+
419
+ ### Example 21: Layer 10, Head 5, SV 1
420
+
421
+ - **Singular value:** 0.5112
422
+ - **Fidelity:** 0.2197
423
+ - **Monosemanticity score:** 5.00/5.0
424
+ - **Mean pairwise similarity:** 0.7531
425
+
426
+ | Coefficient | Caption (Visual Concept) |
427
+ |---|---|
428
+ | 0.1385 | A young women chases the ball as other soccer players chase her. |
429
+ | 0.0000 | people on a field playing a game of soccer
430
+ |
431
+ | 0.0937 | The players are waiting for the next period to begin. |
432
+ | 0.0000 | A child goaltender attempts to block a ball in a soccer game. |
433
+ | 0.0096 | Some boys in action on the soccer field. |
434
+
435
+ *COCO image IDs: 36420, 388564, 553815, 463217, 224693*
436
+ *Image links: [36420](http://images.cocodataset.org/val2014/COCO_val2014_000000036420.jpg) | [388564](http://images.cocodataset.org/val2014/COCO_val2014_000000388564.jpg) | [553815](http://images.cocodataset.org/val2014/COCO_val2014_000000553815.jpg) | [463217](http://images.cocodataset.org/val2014/COCO_val2014_000000463217.jpg) | [224693](http://images.cocodataset.org/val2014/COCO_val2014_000000224693.jpg)*
437
+
438
+ ---
439
+
440
+ ### Example 22: Layer 10, Head 4, SV 1
441
+
442
+ - **Singular value:** 0.5692
443
+ - **Fidelity:** 0.2706
444
+ - **Monosemanticity score:** 3.58/5.0
445
+ - **Mean pairwise similarity:** 0.4151
446
+
447
+ | Coefficient | Caption (Visual Concept) |
448
+ |---|---|
449
+ | 0.1227 | a ram standing outside in an forested area |
450
+ | 0.0757 | A ram that is walking on some snow. |
451
+ | 0.0000 | A very big pretty long horn sheep on a hill. |
452
+ | 0.0328 | Three men are walking behind a herd of rams on the street. |
453
+ | 0.1605 | A young women chases the ball as other soccer players chase her. |
454
+
455
+ *COCO image IDs: 48738, 196248, 192479, 436511, 36420*
456
+ *Image links: [48738](http://images.cocodataset.org/val2014/COCO_val2014_000000048738.jpg) | [196248](http://images.cocodataset.org/val2014/COCO_val2014_000000196248.jpg) | [192479](http://images.cocodataset.org/val2014/COCO_val2014_000000192479.jpg) | [436511](http://images.cocodataset.org/val2014/COCO_val2014_000000436511.jpg) | [36420](http://images.cocodataset.org/val2014/COCO_val2014_000000036420.jpg)*
457
+
458
+ ---
459
+
460
+ ### Example 23: Layer 10, Head 0, SV 4
461
+
462
+ - **Singular value:** 0.5436
463
+ - **Fidelity:** 0.2004
464
+ - **Monosemanticity score:** 5.00/5.0
465
+ - **Mean pairwise similarity:** 0.7531
466
+
467
+ | Coefficient | Caption (Visual Concept) |
468
+ |---|---|
469
+ | 0.1298 | The players are waiting for the next period to begin. |
470
+ | 0.0664 | A young women chases the ball as other soccer players chase her. |
471
+ | 0.0076 | people on a field playing a game of soccer
472
+ |
473
+ | 0.0178 | Some boys in action on the soccer field. |
474
+ | 0.0000 | A child goaltender attempts to block a ball in a soccer game. |
475
+
476
+ *COCO image IDs: 553815, 36420, 388564, 224693, 463217*
477
+ *Image links: [553815](http://images.cocodataset.org/val2014/COCO_val2014_000000553815.jpg) | [36420](http://images.cocodataset.org/val2014/COCO_val2014_000000036420.jpg) | [388564](http://images.cocodataset.org/val2014/COCO_val2014_000000388564.jpg) | [224693](http://images.cocodataset.org/val2014/COCO_val2014_000000224693.jpg) | [463217](http://images.cocodataset.org/val2014/COCO_val2014_000000463217.jpg)*
478
+
479
+ ---
480
+
481
+ ### Example 24: Layer 10, Head 4, SV 0
482
+
483
+ - **Singular value:** 0.5840
484
+ - **Fidelity:** 0.2249
485
+ - **Monosemanticity score:** 4.08/5.0
486
+ - **Mean pairwise similarity:** 0.5162
487
+
488
+ | Coefficient | Caption (Visual Concept) |
489
+ |---|---|
490
+ | 0.1349 | a ram standing outside in an forested area |
491
+ | 0.0400 | A ram sheep feeding from a wooden trough. |
492
+ | 0.0000 | A small black goat sits next to a white large goat. |
493
+ | 0.0221 | Sheep with red stained wool huddle together in a grassy area. |
494
+ | 0.0926 | Sheep staring, laying and grazing in the grass. |
495
+
496
+ *COCO image IDs: 48738, 434089, 66561, 288465, 78522*
497
+ *Image links: [48738](http://images.cocodataset.org/val2014/COCO_val2014_000000048738.jpg) | [434089](http://images.cocodataset.org/val2014/COCO_val2014_000000434089.jpg) | [66561](http://images.cocodataset.org/val2014/COCO_val2014_000000066561.jpg) | [288465](http://images.cocodataset.org/val2014/COCO_val2014_000000288465.jpg) | [78522](http://images.cocodataset.org/val2014/COCO_val2014_000000078522.jpg)*
498
+
499
+ ---
500
+
501
+ ### Example 25: Layer 8, Head 2, SV 0
502
+
503
+ - **Singular value:** 0.4755
504
+ - **Fidelity:** 0.2201
505
+ - **Monosemanticity score:** 5.00/5.0
506
+ - **Mean pairwise similarity:** 0.7970
507
+
508
+ | Coefficient | Caption (Visual Concept) |
509
+ |---|---|
510
+ | 0.1497 | A young women chases the ball as other soccer players chase her. |
511
+ | 0.0384 | people on a field playing a game of soccer
512
+ |
513
+ | 0.0227 | Some boys in action on the soccer field. |
514
+ | 0.0193 | a group of people playing soccer on a field |
515
+ | 0.0000 | The rugby players are fighting for control of the ball. |
516
+
517
+ *COCO image IDs: 36420, 388564, 224693, 550444, 445313*
518
+ *Image links: [36420](http://images.cocodataset.org/val2014/COCO_val2014_000000036420.jpg) | [388564](http://images.cocodataset.org/val2014/COCO_val2014_000000388564.jpg) | [224693](http://images.cocodataset.org/val2014/COCO_val2014_000000224693.jpg) | [550444](http://images.cocodataset.org/val2014/COCO_val2014_000000550444.jpg) | [445313](http://images.cocodataset.org/val2014/COCO_val2014_000000445313.jpg)*
519
+
520
+ ---