Disentangling Representation Evolution in Transformers through Directional Decomposition
Shwai He, Haichao Zhang, Shen Yan
cs.CL · cs.LG
Quick verdict
Orthogonal decomposition shows Transformers tolerate parallel update rescaling but collapse under perpendicular edits; pretraining gains are real yet small.
Summary
This paper decomposes each Transformer sub-layer update into a parallel component (scalar rescaling of the incoming representation) and a perpendicular component (orthogonal semantic steering), and asks which one behaviour matters. Decomposition is applied in two spaces: residual space, relative to the incoming hidden state, and attention value space, relative to the token's own value vector, where an exclude-self variant preserves the direct self message Att*vt while scaling only cross-token aggregation. Inference-time hooks on Qwen3, Llama-3.2 and Gemma-3 models reveal a sharp asymmetry. Removing the perpendicular component is catastrophic: perplexity rises by thousands of points in value and residual-attention space and by millions in residual MLP space, and zero-shot accuracy collapses (Qwen3-1.7B Core-MC falls from 50.94 to 36.62). Removing the parallel component is largely benign: with the self message preserved, seven-task average accuracy drops only 1.5 points on Qwen3-1.7B and 0.1 on Qwen3-30B-A3B, whereas naive full-aggregate removal costs 8 to 10 points. The same geometry explains compression: under 4-bit AWQ and 50 percent Wanda pruning, perpendicular error ranks the four regimes correctly while parallel error interleaves. Suppressing parallel attention during from-scratch pretraining lowers validation loss and improves six-task averages by 0.7 (1.4B) and 1.5 (2.7B) points.
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Assessment at a glance
5
risk flags identified
● high 0
● medium 3
● low 2
5 strengths · 5 weaknesses · 5 author questions
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Key claims under review
- Learned Transformer updates contain substantial parallel components, and these are largely functionally redundant while perpendicular components are acutely fragile.
- Redundancy is site-dependent: with the direct self message preserved, value-space parallel removal is nearly lossless, whereas residual-space parallel removal and hard diagonal removal degrade the model.
- Perpendicular compression error tracks compressed-model quality across quantization and pruning regimes, while parallel error is not diagnostic, explaining why isotropic L2 error fails.
- Suppressing parallel attention components during from-scratch pretraining lowers validation loss and improves downstream accuracy across scales from 296M to 2.7B parameters.
Strengths
The exclude-self decomposition is a genuinely new and well-argued disentanglement
Section 4.2 identifies a real confound: because the query token's self message dt = Att*vt is colinear with the reference vt, naive parallel removal on the full aggregate destroys the token's identity carrier. Equation 10 restores dt and scales only the non-self aggregate ct. Table 1 turns this into a decisive result: naive V-Para Rem. costs 8.2 points on Qwen3-1.7B and 10.0 on Qwen3-30B-A3B, while V-Excl.-self costs 1.5 and 0.1. That is a large, clean effect attributable to one design decision.
The authors audit how strong their own intervention actually is, and report a result that cuts against a simple story
Table 6 measures the applied post-WO perturbation: exclude-self value editing changes 49.10 percent of branch norm and removes 25.89 percent of energy, versus 25.15 percent and 9.323 percent for residual-space editing. The value-space edit is nearly twice as perturbing yet preserves capability. Reporting this and concluding that stability comes from structural alignment rather than isotropic magnitude is exactly the right control, and it blocks the obvious alternative explanation.
The compression diagnostic is predictive, not merely descriptive
Pretraining evidence includes a gated control that rules out the obvious alternative
Practical cost is measured, so the diagnostics are usable
Weaknesses
Cross-model robustness is selectively summarised in text
No variance or significance anywhere; most effects are small relative to unmeasured noise
The headline benchmark suite is narrow and the aggregate hides task-level losses
Causal language for compression exceeds what correlation supports
Perplexity and loss evidence rests on very small fixed sample sets
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Scope & Claims
The paper asks a clean question with a long pedigree: when a Transformer layer adds an update to the residual stream, does the part that merely rescales the incoming direction matter, or only the part that steers it somewhere new? The scope is deliberately broad — measurement across pretrained families, inference-time intervention, a compression diagnostic, and a from-scratch pretraining intervention — and the authors are explicit that the edits are analysis tools rather than a proposed method (Limitations). Four claims carry the argument: parallel components exist and are substantial; they are behaviourally redundant while perpendicular components are fragile; this redundancy is site-dependent, being nearly lossless in value space once the direct self message is preserved; and the same geometry predicts compression quality and improves pretraining. Evidence spans Qwen3 (0.6B to 30B-A3B), Llama-3.2-3B and Gemma-3, seven zero-shot tasks, 13-task RULER at 4k to 12k, AWQ and Wanda compression, and pretraining from 296M to 2.7B parameters.
The remaining sections cover Methodology Assessment, Statistical Evidence, Results & Reproducibility, Limitations & Risks, and Verdict & Recommendations.
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- 5 risk flags with severity, section & reviewer questions
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Frequently asked questions
What is directional decomposition in Transformers?
It is a way of splitting each layer's update into two geometric parts relative to the representation it modifies: a parallel part that merely rescales the existing direction, and a perpendicular part that rotates the representation into a new, orthogonal direction. The paper applies this split in the residual stream (relative to the incoming hidden state) and inside attention (relative to the token's own value vector). Scaling the two parts independently at inference time reveals that the perpendicular part is essential while the parallel part can often be removed with little harm.
Does removing the parallel component of Transformer updates break the model?
Usually not, if you do it in the right place. Removing parallel components from the full attention aggregate costs 8 to 10 points of average zero-shot accuracy on Qwen3-1.7B and Qwen3-30B-A3B, because that also erases the token's direct self message. When the self message is preserved and only cross-token aggregation is scaled, average accuracy drops just 1.5 points on the 1.7B model and 0.1 points on the 30B mixture-of-experts model, and perplexity stays within about one point for retained scales between 0 and 1. By contrast, removing the perpendicular component is catastrophic: perplexity rises by thousands of points and accuracy collapses.
Why does perpendicular error matter for model compression?
Quantization and pruning change the update a layer produces, and that change can be split into error along the original update direction and error orthogonal to it. The paper finds that perpendicular error ranks compression methods in the same order as their actual quality (4-bit AWQ best, then unstructured, 4:8 and 2:4 Wanda pruning), while parallel error gives an inconsistent ranking. Perpendicular error accounts for 87.5 to 98.0 percent of layer distortion and correlates with total error at r between 0.970 and 0.998, which explains why methods with similar overall L2 error can behave very differently.
Can this decomposition be used at training time?
Yes. The authors pretrain GPT-style models from scratch with parallel attention components suppressed throughout training and evaluation. On OpenWebText models of 296M, 436M and 528M parameters, validation loss is lower across the whole trajectory, not just at the end. At 1.4B and 2.7B on FineWeb100BT, six-benchmark average accuracy improves by 0.7 and 1.5 points for the value-space variant and by 0.3 and 0.7 points for the residual-space variant. A control with learned gating instead of fixed removal converges to higher loss, so the benefit comes from removing the degrees of freedom outright. The overhead is under 2.5 percent in prefill and 3.39 percent in training.
About this review
This is an AI-generated preliminary review by Evolve.Pub, produced from the openly available text of the paper. It is not peer review and does not represent the authors' views. The canonical record of the paper is at the publisher link above.
- Figures 1, 3, 4, 5, 6, 7, 8, 9 and 10 cannot be read from the extracted text; all numeric claims come from the captions, tables and body prose, so no value is taken directly from a plotted curve.
- Table 4 lists many evaluation tasks (MMLU, GSM8K, DROP, CoQA, TruthfulQA) that do not appear in the main tables, so the exact benchmark composition of the reported averages was inferred from Tables 1, 9 and 12 only.
- Pretraining results at 1.4B and 2.7B use FineWeb100BT while the smaller scales use OpenWebText, so the scale trend is not measured on a single data distribution.
- The paper lists a project repository for code but no URL is present in the extracted text, so code availability is recorded only as stated by the authors.
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