Refinement Symmetry in Multimodal Transformers
Organizations: The Chinese University of Hong Kong, Shenzhen · Shenzhen Loop Area Institute
Abstract
Attention weights depend on token counts, which change with the representation of a signal. We study refinement symmetry: splitting a representation while preserving content, position, visible context, and total mass should preserve its contribution. Building on proportional and quadrature attention, we show that split invariance forces the local mass factor to be linear for any fixed positive attention kernel, provided that factor is nondecreasing. For changed representations, a physical coupling bounds attention error by separating feature change from weight reallocation. In Qwen2.5-Omni-7B, duplicating half the visual tokens threefold changes 255 of 3,586 MVBench answers under standard attention; measure weighting preserves every answer under matched visibility. Under natural frame resampling, it reduces distributional drift. At twofold merging of a frozen video encoding, a five-seed evaluation shows an all-partition-correct accuracy gain of 1.04 percentage points over global count weighting (average group mass) and 0.93 points over standard attention. The advantage over global count also holds on WorldSense but depends on the compression budget. The result is a representation principle with a measured benefit in robustness across partitions.
Figures & tables
| Split | Standard changes | Measure changes | C W | W C | W W |
|---|---|---|---|---|---|
| 2 | 150 | 0 | 63 | 55 | 32 |
| 3 | 255 | 0 | 111 | 90 | 54 |
| Reduction | Rule | Mean accuracy | Robust accuracy | JSD |
|---|---|---|---|---|
| MVBench | ||||
| 2 | Standard | |||
| Global count | ||||
| Measure | ||||
| 4 | Standard | |||
| Global count | ||||
| Comparator | Endpoint | Difference [95% interval] | Adjusted |
|---|---|---|---|
| MVBench: 2,489 questions, 2,290 source videos | |||
| Global count | Robust acc. | +1.04 [+0.45, +1.65] | 0.0082 |
| Global count | JSD | -0.0063 [-0.0080, -0.0047] | |
| Standard | Robust acc. | +0.93 [+0.16, +1.69] | 0.024 |
| Standard | JSD | -0.0010 [-0.0029, +0.0008] | 0.90 |
| WorldSense: 2,188 questions, 1,158 source videos | |||
Appendix figures & tables19 assets
Supplementary material from the paper’s appendix.
Appendix
| Operation | Count form | Measure-aware form |
|---|---|---|
| Attention | ||
| Mean pooling | ||
| Per-token loss | ||
| Token-axis normalization | ||
| MoE load-balancing loss | ||
| Expert capacity |
| Arm | Seeds | Trained (%) | Held out (%) | 95% CI |
|---|---|---|---|---|
| Index RoPE | 5 | 92.5 | 21.4 | |
| Index + modality bias | 5 | 93.1 | 21.1 | |
| Index + measure weighting | 5 | 91.8 | 21.7 | |
| Continuum RoPE | 5 | 97.2 | 83.2 | |
| Continuum + measure | 5 | 97.1 | 83.4 | |
| Shared physical clock | 8 | 97.4 | 81.1 |
| Slow rate | Ratio | Gain | 95% CI | Slow rate | Ratio | Gain | 95% CI |
|---|---|---|---|---|---|---|---|
| 2 | 1 | -1.25 | 8 | 1 | +0.20 | ||
| 2 | 2 | +0.43 | 8 | 2 | +0.14 | ||
| 2 | 4 | +2.40 | 8 | 4 | +1.07 | ||
| 2 | 8 | +5.22 | 8 | 8 | +3.75 | ||
| 2 | 16 | +10.47 | 8 | 16 | +7.68 | ||
| 2 | 32 | +15.94 | 8 | 32 | +12.45 |
| fps | Standard (%) | MC | Count (uncal.) | Count (cal.) | accuracy [95% CI] |
|---|---|---|---|---|---|
| 2 | 34.7 | 9 | 65 | 9 | |
| 0.5 | 36.2 | 48 | 18 | 48 | |
| 0.25 | 33.3 | 70 | 22 | 70 |
| Probe | 7B | 3B |
| Duplication std flips at factor two (of 3,586) | 150 | 140 |
| Duplication std flips at factor three | 255 | 236 |
| Duplication mc flips at factors two and three | 0, 0 | 0, 0 |
| Causal-copy mc flips at factors two and three (of 720) | 4, 4 | 4, 5 |
| Budget KL reduction, nats [95% interval] | 0.0168 | 0.0154 |
| [0.0077, 0.0259] | [0.0082, 0.0226] |
| Arm | Consistency (%) | Accuracy (%) | consistency (pp) | |
|---|---|---|---|---|
| Standard | 86.1 | 67.7 | 1.000 | |
| Modality count | 87.0 | 68.9 | 0.608 | |
| Measure | 87.0 | 68.4 | 0.627 | |
| Local count (0.75 s) | 86.6 | 68.1 | 0.815 |
| Standard (%) | MC (%) | (pp) [95% CI] | W/L | |||
|---|---|---|---|---|---|---|
| 120 | 1 | 61.67 | 61.67 | 0/0 | 1.000 | |
| 120 | 8 | 61.67 | 64.17 | 6/3 | 0.508 | |
| 360 | 1 | 64.44 | 63.61 | 0/3 | 0.250 | |
| 360 | 8 | 63.89 | 62.78 | 10/14 | 0.541 | |
| 2786 | 1 | 62.42 | 62.67 | 17/10 | 0.248 | |
| 2786 | 8 | 62.31 | 63.03 | 87/67 | 0.125 |
| Rate ratio | Loss difference | 95% CI | |
|---|---|---|---|
| 1 | +0.0000 | 1.000 | |
| 2 | +0.0011 | 0.312 | |
| 4 | +0.0068 | 0.003 | |
| 8 | +0.0154 | ||
| 16 | +0.0206 |
| Size set | Arm | Accuracy (%) | (pp) [95% CI] | |
|---|---|---|---|---|
| Narrow | Standard | 54.25 | 1.000 | |
| Narrow | Measure | 55.00 | 0.508 | |
| Narrow | Reverse groups | 55.75 | 0.146 | |
| Wide | Standard | 56.25 | 1.000 | |
| Wide | Measure | 54.75 | 0.307 | |
| Wide | Reverse groups | 56.25 | 1.000 |
| Reduction | Rule | Decoder (ms) | Stage sum (ms) | Peak (GiB) |
|---|---|---|---|---|
| 1 | Standard | 303.6 | 4710.5 | 19.34 |
| 1 | Global count | 294.9 | 4698.4 | 19.34 |
| 1 | Measure | 285.4 | 4686.3 | 19.34 |
| 2 | Standard | 143.1 | 4523.8 | 19.34 |
| 2 | Global count | 147.5 | 4530.0 | 19.34 |
| 2 | Measure | 152.0 | 4536.1 | 19.34 |
| Input-embedding deviation by partition | |||
|---|---|---|---|
| uniform | 45.5 | 65.3 | 74.7 |
| motion | 55.8 | 66.6 | 74.8 |
| entropy | 51.5 | 66.1 | 75.0 |
| keyframe | 62.2 | 71.0 | 75.6 |
| Embedding-scaled attention TV, , by rule (partition range) | |||
| Partition | Standard | Global count | Measure | vs. std. (pp) | vs. count (pp) |
|---|---|---|---|---|---|
| uniform | 64.94 | 65.42 | 65.42 | +0.47 | 0.00 |
| motion | 64.19 | 64.36 | 64.69 | +0.51 | +0.33 |
| entropy | 64.37 | 65.01 | 65.12 | +0.75 | +0.11 |
| keyframe | 63.03 | 63.78 | 64.07 | +1.04 | +0.28 |
| worst partition (keyframe) | 63.03 | 63.78 | 64.07 | +1.04 | +0.28 |
Attention Mechanisms
Attention mechanisms let neural networks weight information from other tokens or regions according to relevance, enabling context-dependent processing.
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