arxiv: 2605.08504 · v2 · submitted 2026-05-08 · 💻 cs.CL

Recognition: 2 theorem links

· Lean Theorem

A Single Layer to Explain Them All:Understanding Massive Activations in Large Language Models

Fan Yang, Qifan Wang, Ruixiang Tang, Zeru Shi, Zhenting Wang

Pith reviewed 2026-05-12 02:25 UTC · model grok-4.3

classification 💻 cs.CL

keywords massive activationslarge language modelsemergence layerresidual connectionsRMSNormattention sinkshidden statesmodel performance

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The pith

Massive activations in large language models first emerge in one consistent layer and then propagate through residual connections.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper identifies a specific layer called the Massive Emergence Layer that appears across different model families and marks the point where massive activations originate. These activations then remain stable and spread to later layers through residual connections, which reduces the variety of hidden states available to the attention mechanism. The emergence is traced to the combined action of RMSNorm and feed-forward network parameters within that layer. To address the resulting rigidity, the authors introduce a method that weakens the dominance of the massive activation token. This change improves results on instruction following and math reasoning tasks in both training-free and fine-tuning regimes and also lessens attention sinks.

Core claim

The authors establish that massive activations arise at a single identifiable layer, the ME Layer, where RMSNorm and FFN parameters together produce them, after which the activation token stays largely unchanged across subsequent layers via residual connections and thereby limits representation diversity for attention.

What carries the argument

The Massive Emergence Layer (ME Layer), the specific layer where massive activations first form due to RMSNorm and FFN and then propagate invariantly through residuals.

If this is right

Massive activation tokens remain largely invariant across deeper layers after the ME Layer.
Reducing the rigidity of the massive activation token improves performance on instruction following and math reasoning.
The improvement occurs in both training-free and fine-tuning settings.
The method also mitigates attention sinks by selectively weakening their influence at the hidden-state level.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Intervening only at the ME Layer could offer a more targeted way to handle attention sinks than direct changes to attention weights.
The joint role of RMSNorm and FFN at one layer suggests that similar single-layer origins might be found for other activation anomalies if the same post-hoc tracing approach is applied.
Architectures that avoid strong residual propagation of early dominant tokens might prevent the rigidity problem from arising in the first place.

Load-bearing premise

The layer identified after the fact as the first site of massive activations is their actual root cause in typical models, and making the massive activation token less rigid will raise performance on downstream tasks without harming other model abilities.

What would settle it

An experiment that applies the rigidity-reduction method only at the identified ME Layer and measures whether massive activations disappear in all deeper layers while performance gains appear on the target tasks but not when the same method is applied at other layers instead.

Figures

Figures reproduced from arXiv: 2605.08504 by Fan Yang, Qifan Wang, Ruixiang Tang, Zeru Shi, Zhenting Wang.

**Figure 1.** Figure 1: This figure illustrates how massive activations emerge and propagate. In the top panel, we trace the flow of massive activations: they arise only at the FFN of a specific layer and then propagate to subsequent layers through residual connections. The → arrows denote the generation and propagation of massive activations. The bottom panel shows how the output ℓ2 norm changes across layers. ME Layer means Mas… view at source ↗

**Figure 2.** Figure 2: The comparison of the magnification of RMSNorm on token0 and other tokens in Qwen3-4B across layers. Amplification effect of RMSNorm. We analyze the scaling factors in RMSNorm layer by layer and find that the amplification effect in the ME Layer on the hidden state far exceeds that of other layers. In [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 4.** Figure 4: Line chart(the y-axis on the left) shows difference of the projection concentration between first token and others after different module in FFN. Bar chart(the y-axis on the right) shows the amplification factor of the MLP on the token hidden state. the hidden state is along a small subset of representation dimensions after the FFN transformation. A higher projection concentration indicates that the resul… view at source ↗

**Figure 5.** Figure 5: (a) L2 norm of the first token’s hidden state across layers for different input instances. (b) The activation of token 0 in different layer of model. Red line indicates the activation of ME Layer (c) Heatmap of the cosine similarity between different input’s first-token hidden state across layers. 3.2. The Direction of Massive Activation Key Takeaway Once the massive activation emerges at the ME Layer the … view at source ↗

**Figure 6.** Figure 6: This is the schematic diagram of our methods. We will choose top-k dimensions based on weights then masking the corresponding dimensions in hidden state. 5. Experiments 5.1. Settings Method Details and Training Setups: We adopt Qwen3- 4B as the base model and apply our method both as a training-free inference-time technique and as a trainingtime strategy across multiple tasks, including instruction fine-t… view at source ↗

**Figure 8.** Figure 8: (a) shows the attention heatmap without our method. (b) shows the attention heatmap with our method. Motivated by this connection, we further investigate the relationship between massive activation onset, our proposed intervention, and the emergence of attention sinks. As shown in [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗

**Figure 7.** Figure 7: (a) shows heatmap of attention weights in the ME Layer (layer 7). (b) shows the layer after ME Layer (layer 8). Our findings share similarities with prior studies on attention sinks. Previous works, such as Qiu et al. (2025) and Gu et al. (2024), show that attention weights are often heavily concentrated on a single token across multiple heads. This concentration implies a low-rank structure in the attenti… view at source ↗

**Figure 9.** Figure 9: The hidden state of the output of DecoderLayer, left figure remove FFN in ME Layer middle figure remove RMSNorm in ME Layer right figure contains all module. C. More Experiment Settings During training, WeMask is applied to every layer following the onset of massive activation. In contrast, during evaluation, we adopt different configurations depending on the task type. For tasks that primarily assess the … view at source ↗

**Figure 10.** Figure 10: L2 norm of the first token across layers for different input instances. Each curve corresponds to a distinct example. E. Performance of Different Mask Methods In this section, we evaluate different masking strategies by incorporating them into the inference stage as training-free interventions, in order to examine their impact on model performance. For each masking method, we adopt the mask ratio that yie… view at source ↗

**Figure 11.** Figure 11: The hidden state of the output of RMSNorm, FFN and Decoderlayer on Qwen3-8B 15 [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗

**Figure 12.** Figure 12: The hidden state of the output of RMSNorm, FFN and Decoderlayer on Qwen3-4B-Instruct Output of RMSNorm Output of FFN Output of DecoderLayer Qwen2.5-7B [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗

**Figure 13.** Figure 13: The hidden state of the output of RMSNorm, FFN and Decoderlayer on Qwen2.5-7B Output of RMSNorm Output of FFN Output of DecoderLayer Qwen2.5-7B-Instruct [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗

**Figure 14.** Figure 14: The hidden state of the output of RMSNorm, FFN and Decoderlayer on Qwen2.5-7B-Instruct 16 [PITH_FULL_IMAGE:figures/full_fig_p016_14.png] view at source ↗

**Figure 15.** Figure 15: The hidden state of the output of RMSNorm, FFN and Decoderlayer on Qwen2.5-32B Output of RMSNorm Output of FFN Output of DecoderLayer Llama3.1-8B [PITH_FULL_IMAGE:figures/full_fig_p017_15.png] view at source ↗

**Figure 16.** Figure 16: The hidden state of the output of RMSNorm, FFN and Decoderlayer on Llama3.1-8B Output of RMSNorm Output of FFN Output of DecoderLayer Llama3.1-8B-Instruct [PITH_FULL_IMAGE:figures/full_fig_p017_16.png] view at source ↗

**Figure 17.** Figure 17: The hidden state of the output of RMSNorm, FFN and Decoderlayer on Llama3.1-8B-Instruct 17 [PITH_FULL_IMAGE:figures/full_fig_p017_17.png] view at source ↗

**Figure 18.** Figure 18: The hidden state of the output of RMSNorm, FFN and Decoderlayer on Mistral-7B-v0.1. Output of RMSNorm Output of FFN Output of DecoderLayer Deepseek-llm-7b-chat [PITH_FULL_IMAGE:figures/full_fig_p018_18.png] view at source ↗

**Figure 19.** Figure 19: The hidden state of the output of RMSNorm, FFN and Decoderlayer on DeepSeek-llm-7b-chat. Output of RMSNorm Output of FFN Output of DecoderLayer Phi-3-mini-4k-instruct [PITH_FULL_IMAGE:figures/full_fig_p018_19.png] view at source ↗

**Figure 20.** Figure 20: The hidden state of the output of RMSNorm, FFN and Decoderlayer on Phi3-mini-4k-instruct. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_20.png] view at source ↗

read the original abstract

We investigate the origins of massive activations in large language models (LLMs) and identify a specific layer named the \textbf{Massive Emergence Layer (ME Layer)}, that is consistently observed across model families, where massive activations first emerge and subsequently propagate to deeper layers through residual connections. We show that, within the ME Layer both the RMSNorm and the FFN parameters jointly contribute to the emergence of massive activations. Once formed, the massive activation token representation remains largely invariant across layers, reducing the diversity of hidden representations passed to the attention module. Motivated by this limitation, we propose a simple and effective method to reduce the rigidity of the massive activation token. Our approach consistently improves LLM performance across multiple tasks, including instruction following and math reasoning, in both training free and fine tuning settings. Moreover, we show that our method mitigates attention sinks by selectively weakening their influence, elucidating their origin at the hidden state level and shedding new light on principled mitigation strategies.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper spots a consistent ME Layer across LLMs where massive activations emerge from RMSNorm and FFN together, with a simple fix that lifts performance on some tasks, but the origin claim stays mostly observational.

read the letter

The punchline for you is that the authors have spotted what they call the Massive Emergence Layer in a range of large language models. This is the point where massive activations first show up, driven by the combination of RMSNorm and the feed-forward network in that layer. After that, the activation stays pretty much the same in later layers thanks to the residual connections, which cuts down on the variety of representations going into attention. They then test a basic technique to make the massive activation token less rigid, and this change improves results on instruction following and math reasoning in both training-free and fine-tuning setups. It also seems to help with attention sinks. What stands out as new is the consistent identification of this layer across model families and the joint role they assign to RMSNorm and FFN. Prior work on activation scaling or attention sinks did not frame it this way. The practical method they propose is straightforward and delivers gains, which is a plus for anyone looking to apply it. The paper does a decent job documenting the pattern through experiments on multiple models. The performance improvements are reported in a way that suggests the fix is effective without heavy computation. On the soft spots, the central claim that this layer is where the activations originate rests on observation rather than direct intervention. They see where the norm becomes large and call that the emergence point, but without experiments that modify only the RMSNorm scale or FFN weights in that specific layer while keeping everything else the same, and then check if massive activations are reduced later, the link is correlational. It could be that effects build up before that layer. The invariance in deeper layers is expected from the residual structure, so it does not require much explanation. The method improves the tasks they tested, but I would want to see checks on whether it harms other capabilities or how it performs on a wider set of benchmarks. The abstract mentions consistent observations, but details on data splits and statistical tests would strengthen it. This work is aimed at people studying LLM mechanisms, interpretability, and ways to improve model behavior through targeted changes. It has enough new empirical content and a usable idea to make it worth a serious referee's time. I recommend sending it for peer review.

Referee Report

3 major / 3 minor

Summary. The paper claims to identify a consistent 'Massive Emergence Layer' (ME Layer) across LLM families as the point where massive activations first originate due to joint RMSNorm and FFN effects, propagate invariantly via residuals (reducing hidden-state diversity), and proposes a simple intervention to reduce the rigidity of these tokens. This intervention is reported to improve performance on instruction following and math reasoning in both training-free and fine-tuning settings while also mitigating attention sinks.

Significance. If the ME Layer identification and causal attribution hold, the work would offer a mechanistic account of activation magnitude patterns and attention sinks at the hidden-state level, along with a lightweight, architecture-aligned mitigation strategy that generalizes across model families and training regimes. The empirical consistency across families and the dual training-free/fine-tuning gains would be notable strengths.

major comments (3)

[Abstract and §3 (ME Layer identification)] The central claim that the ME Layer is the causal origin of massive activations (rather than the first layer where a chosen magnitude threshold is crossed) rests on post-hoc observation without targeted layer-specific interventions. No ablation is described that modifies only the ME Layer's RMSNorm scale or FFN weights while freezing all other layers and verifies suppression of massive activations downstream; residual propagation alone does not establish origin.
[Abstract and §4 (component analysis)] The joint contribution of RMSNorm and FFN parameters within the ME Layer is asserted but lacks the necessary controlled experiments. A full-factorial ablation (RMSNorm-only, FFN-only, both, neither) at the identified layer, with downstream activation norms measured, is required to move from correlation to attribution; current evidence appears observational.
[Abstract and §5 (experiments)] Performance improvements and attention-sink mitigation are reported without sufficient experimental detail: no mention of statistical tests, number of runs, exact data splits, or comparison against strong baselines that also target token rigidity or attention. The risk that gains arise from generic regularization rather than the ME-Layer hypothesis cannot be assessed from the current description.

minor comments (3)

[§3] The precise numerical criterion used to label an activation 'massive' (e.g., norm threshold relative to other tokens or layers) should be stated explicitly and held constant across all models and figures.
[§4] Notation for the proposed rigidity-reduction method (scaling factor, which parameters are adjusted, whether it is applied only at the ME Layer) is unclear from the abstract and should be formalized with an equation or pseudocode.
[Figures 2-4] Figure captions and axis labels for activation-norm plots should include the exact threshold used and the model/layer indices to allow direct replication.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback, which identifies key opportunities to strengthen the causal evidence for the ME Layer and enhance the transparency of our experimental results. We address each major comment in detail below and will incorporate the suggested improvements in the revised manuscript.

read point-by-point responses

Referee: [Abstract and §3 (ME Layer identification)] The central claim that the ME Layer is the causal origin of massive activations (rather than the first layer where a chosen magnitude threshold is crossed) rests on post-hoc observation without targeted layer-specific interventions. No ablation is described that modifies only the ME Layer's RMSNorm scale or FFN weights while freezing all other layers and verifies suppression of massive activations downstream; residual propagation alone does not establish origin.

Authors: We agree that establishing the ME Layer as the causal origin requires more than consistent observational patterns across models. Our current evidence centers on the layer being the first where massive activations reliably appear due to the interaction of RMSNorm and FFN, followed by invariant propagation through residuals that reduces hidden-state diversity. We acknowledge that this does not fully rule out threshold-based emergence at other layers. In revision, we will add a targeted intervention: we will selectively modify RMSNorm scale and FFN weights only within the identified ME Layer (freezing all other layers) and measure whether massive activations are suppressed in downstream layers. revision: yes
Referee: [Abstract and §4 (component analysis)] The joint contribution of RMSNorm and FFN parameters within the ME Layer is asserted but lacks the necessary controlled experiments. A full-factorial ablation (RMSNorm-only, FFN-only, both, neither) at the identified layer, with downstream activation norms measured, is required to move from correlation to attribution; current evidence appears observational.

Authors: We recognize that our component analysis, while showing joint effects through targeted examination of RMSNorm and FFN within the ME Layer, remains observational without a complete factorial design. To move toward stronger attribution, the revised manuscript will include the full-factorial ablation (RMSNorm-only, FFN-only, both, and neither) performed specifically at the ME Layer, with quantitative reporting of downstream activation norms to isolate the joint contribution. revision: yes
Referee: [Abstract and §5 (experiments)] Performance improvements and attention-sink mitigation are reported without sufficient experimental detail: no mention of statistical tests, number of runs, exact data splits, or comparison against strong baselines that also target token rigidity or attention. The risk that gains arise from generic regularization rather than the ME-Layer hypothesis cannot be assessed from the current description.

Authors: We accept that the experimental reporting requires greater detail to allow proper evaluation. In the revision, we will specify the number of runs, report means with standard deviations, include statistical significance tests, detail the exact data splits, and add comparisons against strong baselines that address token rigidity or attention sinks. This will help demonstrate that the observed gains are tied to the ME-Layer hypothesis rather than generic regularization effects. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical layer identification and observations are self-contained

full rationale

The paper's core claims rest on post-hoc empirical observations of activation norms across model families to label the first layer exceeding a magnitude threshold as the ME Layer, followed by analysis of RMSNorm and FFN contributions at that point and a proposed mitigation technique. No equations, fitted parameters, or self-citations are shown to reduce the identification, propagation claim, or performance improvements back to the inputs by construction. The derivation chain consists of direct measurements and interventions rather than self-definitional renaming or load-bearing self-citation chains, making the findings independent of the observed patterns themselves.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on standard transformer architecture properties and empirical identification rather than new free parameters or invented physical entities.

axioms (1)

standard math Transformer architectures employ residual connections that propagate hidden states across layers.
Invoked to explain how massive activations spread from the ME Layer.

invented entities (1)

Massive Emergence Layer (ME Layer) no independent evidence
purpose: To label the layer where massive activations are observed to first appear
Empirically defined from activation patterns across models; no independent falsifiable prediction supplied.

pith-pipeline@v0.9.0 · 5474 in / 1257 out tokens · 48973 ms · 2026-05-12T02:25:23.836564+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
We identify a specific layer named the Massive Emergence Layer (ME Layer)... where massive activations first emerge and subsequently propagate to deeper layers through residual connections. We show that, within the ME Layer both the RMSNorm and the FFN parameters jointly contribute to the emergence of massive activations.
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
Once formed, the massive activation token representation remains largely invariant across layers, reducing the diversity of hidden representations passed to the attention module.