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REVIEW 4 major objections 6 minor 2 cited by

Systematic Outliers in Large Language Models

T0 review · 4 major / 6 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read All three LLM outlier types—activation, weight, and attention—stem from one cause, the softmax in self-attention, and act as implicit context-aware scaling factors that an explicit learnable factor can replace.

desk verdict A useful empirical map of where outliers live and a clever architectural fix, but the 'softmax is the root cause' story is a plausible narrative rather than an established mechanism. read the letter →

arxiv 2502.06415 v2 pith:BWVWFDX4 submitted 2025-02-10 cs.CL cs.AIcs.LG

Yongqi An , Xu Zhao , Tao Yu , Ming Tang , Jinqiao Wang This is my paper · ORCID
classification cs.CLcs.AIcs.LG
keywords LLMoutliersactivationweightattentionsoftmaxcontext-awarescalingfactormodelcompressiontransformerinterpretability
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Large language models are riddled with outlier values in activations, weights, and attention scores, and prior work has treated them mostly as nuisances to clip or smooth away during compression. This paper argues instead that the three outlier types are one systematic phenomenon: they all emerge from the softmax operation in self-attention, and they function as implicit, context-aware scaling factors that let the model give start tokens and weak-semantic tokens (the initial token, '.', '_') almost no contextual update. The evidence is layered: the three outlier types co-occur at fixed feature channels and sequence positions (100 percent consistency between weight and activation outliers in feature dimensions, 95 percent between activation and attention outliers in sequence positions); a derivation in the appendix traces them to the softmax 'sum to one' constraint; and training five GPT-2 attention variants shows that only explicit context-aware scaling—not fixed or context-aware bias—prevents outliers. When the implicit scaling is replaced by an explicit learnable one, outliers vanish, early convergence speeds up, and tolerance of compression jumps from broken to near-baseline: WikiText2 perplexity under 8-bit weight quantization falls from 93.44 to 29.22, and under 50% pruning from 7235.68 to 39.47.

What carries the argument

The load-bearing object is the softmax operation inside multi-head self-attention, $\mathrm{softmax}(QK^\top/\sqrt{d})V$, whose outputs are strictly positive and sum to one for every query. The derivation turns on a 'zero-update requirement' (Appendix C.1): for tokens that should barely change—the initial token, punctuation, spaces—the desired attention output is close to zero, yet because softmax probabilities sum to one, near-zero output can only be achieved by concentrating probability on a few keys whose values cancel, which in turn forces extreme disparities among the pre-softmax dot products. This dynamic-range demand steepens gradients on the shared $W_K$ and $W_V$ projections and, through residual connections and LayerNorm's compression of the input distribution, drives the MLP's up-, gate-, and down-projections to grow extreme weights at a few fixed channels (weight outliers), yielding activation outliers at those channels and tokens, which then align the corresponding query and key dimensions to produce attention outliers at the same positions. The companion mechanism that validates the account is the explicit context-aware scaling variant, $Sc(x)\cdot\mathrm{softmax}(QK^\top/\sqrt{d})V$, with a learned input-dependent scalar $Sc(x)$: it supplies the same scaling effect directly, and the training experiments show it prevents outlier formation entirely rather than merely suppressing its effects.

What would settle it

During training of a transformer, record the L2 norm of the attention output added to the residual stream at start tokens and punctuation tokens and compare it with content tokens: the paper's premise requires these updates to be near zero, so updates comparable in size to those of content tokens would remove the zero-update requirement that drives the derivation. A second check: train the same architecture on text with punctuation removed and no special start token—under the paper's account, the count and magnitude of attention and activation outliers should drop sharply because the tokens identified as needing the largest dynamic range no longer exist.

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Extended reading notes

Core claim

The paper's central claim is that activation outliers, weight outliers, and attention outliers in LLMs are not independent defects but one interconnected phenomenon with a single root cause: the softmax normalization in self-attention. Because softmax forces attention scores to be nonnegative and sum to one, tokens that need almost no contextual update—start tokens and semantically weak tokens like '.' and '_'—force the model to concentrate attention onto very few keys, which requires the pre-softmax query-key dot products to span a huge dynamic range. That demand propagates outward: steep gradients on the shared key and value projections, amplified through the residual stream and the MLP up-, gate-, and down-projections, produce weight outliers at a few fixed channels, activation outliers at the same channels and tokens, and attention outliers at the same sequence positions. The outliers therefore act as implicit, context-aware scaling factors, dynamically shrinking or amplifying updates instead of adding a fixed bias. The paper's validation is direct: an explicit context-aware scaling factor, $Sc(x)\cdot\mathrm{softmax}(QK^\top/\sqrt{d})V$ with learned, input-dependent $Sc(x)$, prevents all three outlier types in GPT-2 and TinyLLaMA-120M, while explicit fixed-bias and context-aware-bias variants do not, and sigmoid attention—which drops the sum-to-one requirement—also produces no systematic outliers. Structurally eliminating the outliers this way accelerates early convergence and makes models much more tolerant of 8-bit weight quantization and 50% magnitude pruning.

Load-bearing premise

The entire causal chain rests on the premise, asserted in Appendix C.1 and never measured, that start tokens and weak-semantic tokens genuinely require near-zero updates from attention; if that requirement is not real, or is itself an artifact of training under softmax, the derivation from softmax to systematic outliers loses its foundation.

Editorial extensions

If this is right

  • All three outlier types share one removable cause: replacing implicit softmax-driven scaling with an explicit context-aware scaling factor eliminates activation, weight, and attention outliers in both GPT-2 and TinyLLaMA-120M.
  • Compression becomes practical without post-hoc outlier repair: on WikiText2, the scaled GPT-2 drops 8-bit absmax weight-quantization perplexity from 93.44 to 29.22 and 50% unstructured-magnitude-pruning perplexity from 7235.68 to 39.47, at a parameter overhead below 0.1%.
  • Training speeds up: explicit context-aware scaling reaches lower validation loss in the earliest steps than default attention, although final loss ends up comparable.
  • Scaling, not bias, is the operative role: the fixed-bias and context-aware-bias attention variants still produce outliers, which rules out the massive-activations-as-fixed-bias reading of the phenomenon.
  • Softmax is the root cause, not the data or the tuning: sigmoid attention, which can emit near-zero attention weights without normalization, produces no systematic outliers, while outliers persist across model families and survive instruction fine-tuning.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the zero-update premise is correct, outlier sites should track the training data's low-information tokens: a model trained on text without punctuation or explicit start tokens should produce markedly fewer and weaker attention and activation outliers—a prediction the paper does not run.
  • Reading outlier channels as implicit scaling suggests post-hoc compression fixes (clipping, smoothing, rotation) may work against the model's actual computation; a cheaper alternative to full retraining would be to emulate the per-token scaling with a small learned correction applied only at the affected channels.
  • The account extends naturally to streaming LLMs: the attention-sink tokens that current methods inject to stabilize long-context inference are, on this view, an explicit stand-in for the implicit scaling the model already performs, so a properly scaled attention mechanism could reduce or remove the need for sink tokens.
  • A directly checkable corollary of the derivation is that a token's pre-softmax logit spread should be inversely related to the size of the update it actually needs; probing checkpoints mid-training, rather than only at the end, would test the causal direction the paper asserts.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper studies three types of outliers in LLMs—activation, weight, and attention outliers—and argues that they are systematically interconnected and originate from the softmax operation in self-attention. After documenting the distribution and localization of these outliers across LLaMA-2 and several other models, the authors hypothesize that outliers act as implicit, context-aware scaling factors. They test this hypothesis by training GPT-2 variants with alternative attention formulations (fixed bias, context-aware bias, attention bias, and explicit context-aware scaling factor), finding that only formulations with a scaling factor prevent outlier formation. They further report that an explicit context-aware scaling factor improves robustness to quantization and pruning and accelerates early convergence. Appendix C provides a mathematical narrative connecting softmax-induced dynamic range expansion, zero-update requirements for certain tokens, and gradient amplification to the emergence and localization of outliers.

Significance. If the central claim is correct, the paper would provide a unified mechanistic explanation for three previously separate outlier phenomena and a principled architectural mitigation. The empirical survey across LLaMA-2/3, Mistral, OPT, MPT, Falcon, Phi-2 and fine-tuned variants is a useful systematic documentation, and the GPT-2 variant experiments are an interventionist test that cleanly separates bias effects from scaling effects at a qualitative level. The authors also ship code and give detailed experimental settings, supporting reproducibility. However, the causal derivation in Appendix C rests on an untested assumption about near-zero MHA updates for certain tokens, and the intervention experiments demonstrate that explicit scaling factors prevent outliers without directly establishing that the original outliers function as scaling factors. These gaps are load-bearing for the paper's main claim, but they are addressable with additional measurements and a more carefully scoped interpretation.

major comments (4)
  1. [Appendix C.1] The zero-update premise is asserted, not tested. The derivation begins with 'the desired behavior is a near-zero update' for initial and weak-semantic tokens and defines ∆x = MHA(Qx, K, V) ≈ 0, but no measurement of MHA output norms for those tokens in LLaMA-2-7B or any other model is reported. Since every subsequent step (dynamic range expansion, gradient amplification, weight outlier formation) is conditional on this premise, the paper should either measure actual MHA output magnitudes for the claimed outlier tokens or explicitly weaken the claim to a conditional hypothesis.
  2. [Appendix C.4] There is an internal tension between the zero-update requirement in C.1 and the token-level localization story in C.4. C.4 states that initial tokens 'aggregate global information, receiving disproportionately high attention scores, which amplifies their values in the MHA output,' and that weak-semantic tokens receive 'exaggerated updates during training.' Both statements describe non-zero MHA updates, which contradicts the near-zero-update premise required by the derivation. The authors need to reconcile these statements, for example by distinguishing between the attention weights assigned to these tokens and the L2 norm of the resulting contextual update.
  3. [Section 5.2, Table 2] The variant experiments show that explicit context-aware scaling factors prevent outlier formation in GPT-2, but they do not establish that the outliers observed in the default model actually function as scaling factors. An intervention that removes a phenomenon is not by itself evidence for the proposed functional role of that phenomenon. Additionally, the comparison between variants (c) and (d) changes two components at once (adding both a bias and a scaling-like term), so the attribution of the effect specifically to the scaling factor is not as clean as claimed. The functional claim would be strengthened by a direct probe, such as comparing the learned Sc(x) against the magnitude of the outliers in the default model, or by showing that removing the attention outlier in a trained model produces effects similar to inserting an explicit scaling factor.
  4. [Appendix C, overall] The paper describes Appendix C as 'theoretical derivations' (Abstract and Section 5.3), but the derivation is qualitative. The step from large dynamic ranges in softmax inputs to steep gradients and thence to concentrated weight outliers is asserted rather than derived; no formal bound or gradient expression is provided. This is acceptable as an intuition, but the wording overclaims. The authors should either present a concrete formal statement (e.g., a bound on gradient norms in terms of softmax logit gaps) or revise the language to describe the appendix as a qualitative mechanism analysis.
minor comments (6)
  1. [Abstract] There is a typo: 'avilable' should be 'available'.
  2. [Appendix D title] The heading reads 'MORE ANALYSIS FO SYSTEMATIC OUTLIERS'; 'FO' should be 'OF'.
  3. [Figure 23] The figure label says 'GPT-2 with Sigmoid Attenion'; 'Attenion' should be 'Attention'.
  4. [Section 3, Definition] The outlier threshold τ is set to 1000 with no sensitivity analysis. Since all subsequent consistency statistics in Table 1 depend on τ, a brief analysis of how the reported overlaps vary with τ would improve robustness.
  5. [Section 5.3, Table 3] The compression experiments are only reported for GPT-2. Given the paper's emphasis on LLMs, reporting at least one additional model (e.g., TinyLLaMA) for the quantization and pruning results would strengthen the practical claim.
  6. [Appendix B.3] The GPT-2 variant experiments train for 50,000 iterations, but no training curves or final validation losses for the variants are shown except Figure 12. Reporting the full training curves for all five variants would help rule out that the absence of outliers in variants (d) and (e) is an artifact of underfitting.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the paper's central claims rest on independent observations and interventionist experiments, not on self-citation or definitional equivalence.

full rationale

The paper's derivation chain is not circular. Activation, weight, and attention outliers are defined by magnitude thresholds (τ=1000), not by the softmax mechanism, so the existence and localization claims are empirical. The hypothesis that outliers act as context-aware scaling factors is tested by training GPT-2 variants with explicit scaling factors and by comparing sigmoid attention; these are interventionist tests whose outcomes are not forced by the definitions. The Appendix C derivation is conditional on an asserted premise—that certain tokens 'require minimal updates' and 'the desired behavior is a near-zero update'—but this premise is not defined in terms of the conclusion, and the paper does not fit a parameter and then rename it as a prediction. There are no load-bearing self-citations (the reference list contains no works by the present authors). The unsupported jump in C.2 from 'zero-update' to 'highly concentrated attention weight distribution' is a logical gap, and the weak-semantic/initial-token premise is empirically untested, but these are correctness and evidence concerns, not circular reductions. Under the standard requiring an exhibitable Eq.-to-Eq. or definition-to-definition reduction, no circular step is present.

Assumptions & free parameters 1 free parameters · 4 assumptions · 1 invented entities

The paper's analysis relies on a small number of assumptions outside standard mathematics. The most significant are the zero-update necessity for certain tokens and the qualitative claim that softmax-induced dynamic range propagates into outliers. The only hand-chosen parameter is the outlier threshold tau. The proposed scaling factor is an architectural addition, not a fitted quantity, and it has been tested in controlled experiments.

free parameters (1)
  • Outlier threshold tau = 1000
    Empirically set to isolate extreme deviations; no principled basis is given, and all outlier statistics depend on this arbitrary choice.
assumptions (4)
  • ad hoc to paper Certain tokens require near-zero updates (zero-update necessity).
    Assumed in Appendix C.1 to argue why softmax must concentrate attention; no empirical test is provided for this necessity.
  • standard math Softmax attention must output probability distributions that sum to one.
    Definitional property of softmax, used to motivate dynamic range expansion.
  • ad hoc to paper Large dynamic ranges in attention scores translate into large gradients and hence outliers.
    Assumed propagation mechanism in Appendix C.3; not formally derived.
  • ad hoc to paper LayerNorm compresses dynamic range, forcing earlier MLPs to compensate with larger activations.
    Proposed in Section 5.3 without supporting analysis.
invented entities (1)
  • Explicit context-aware scaling factor Sc(x) independent evidence
    purpose: Replaces the implicit scaling that outliers are claimed to perform, removing outliers and improving compression robustness.
    The factor is a learnable component whose effects are measurable: models trained with it show no outliers and better perplexity after compression. It is falsifiable through ablation and on larger models.

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Cite this review

Pith. "Pith review of Systematic Outliers in Large Language Models." pith.science (2026). https://pith.science/paper/BWVWFDX4

@misc{pith2026250206415,
  author       = {Pith},
  title        = {Pith review of: Systematic Outliers in Large Language Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BWVWFDX4}},
  note         = {Machine review of arXiv:2502.06415}
}
read the original abstract

Outliers have been widely observed in Large Language Models (LLMs), significantly impacting model performance and posing challenges for model compression. Understanding the functionality and formation mechanisms of these outliers is critically important. Existing works, however, largely focus on reducing the impact of outliers from an algorithmic perspective, lacking an in-depth investigation into their causes and roles. In this work, we provide a detailed analysis of the formation process, underlying causes, and functions of outliers in LLMs. We define and categorize three types of outliers-activation outliers, weight outliers, and attention outliers-and analyze their distributions across different dimensions, uncovering inherent connections between their occurrences and their ultimate influence on the attention mechanism. Based on these observations, we hypothesize and explore the mechanisms by which these outliers arise and function, demonstrating through theoretical derivations and experiments that they emerge due to the self-attention mechanism's softmax operation. These outliers act as implicit context-aware scaling factors within the attention mechanism. As these outliers stem from systematic influences, we term them systematic outliers. Our study not only enhances the understanding of Transformer-based LLMs but also shows that structurally eliminating outliers can accelerate convergence and improve model compression. The code is avilable at https://github.com/an-yongqi/systematic-outliers.

Figures

Figures reproduced from arXiv: 2502.06415 by the authors.

Figure 1
Figure 1. Systematic outliers in LLaMA2-7B. Outliers are identified in four locations: activations (layer outputs hℓ and down-projection inputs x down ℓ ), weights (down-projection matrices Wdown ℓ ), and attention (attention weights Ai ℓ ). further summarized in [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Illustration of systematic outliers loca￾tions in LLMs. These definitions provide a unified framework to identify and analyze outliers across LLM components. We empirically set τ = 1000 in our experiments to isolate extreme deviations. Existence of Outliers in LLMs. Systematic outliers consistently emerge in LLMs across various components and architectures. Fig￾ure 1 highlights their presence in LLaMA2-7B (Touvron e… view at source ↗
Figure 3
Figure 3. Distribution of activation outliers in hℓ across layers, sequences, and feature dimensions. 1 8 16 24 32 Layers 0 250 500 750 1000 1250 1500 Magnitudes LLaMA-2-7B Layer-wise Analysis Top 1 Top 2 Top 3 Median (a) Which layers? Summer is warm . Winter is cold . \n 7890 0 1k LLaMA-2-7B, Layer 2 (b) Layer 2 Summer is warm . Winter is cold . \n 3721 7006 0 800 LLaMA-2-7B, Layer 31 (c) Layer 31 [PITH_FULL_IMAGE:figures/f… view at source ↗
Figures from the paper (21 more)
Figure 4
Figure 4. Figure 4: Distribution of activation outliers in x down ℓ across layers, sequences, and feature dimen￾sions. 3.1 WHERE ARE ACTIVATION OUTLIERS LOCATED? Activation outliers manifest as abnormally large values in specific sequence and feature dimensions, as shown in Figures 1(a) a…
Figure 5
Figure 5. Figure 5: Distribution of weight outliers in Wdown ℓ across layers, modules, and feature dimensions. 1 8 16 24 32 Layers 0 100 200 300 400 500 Attention Scores LLaMA-2-7B Layer-wise Attention Accumulation Top 1 Top 2 Median (a) Which layers? initial token 50.0% "." 40.5% "_" 9.5…
Figure 6
Figure 6. Figure 6: Distribution of attention outliers in Ai ℓ across layers, keys and heads. In summary, weight outliers in LLaMA2-7B are primarily located in the MLP’s down-projection matrices, concentrated in specific shallow and deep layers. 3.3 WHERE ARE ATTENTION OUTLIERS LOCATED? T…
Figure 7
Figure 7. Figure 7: The emergence of activation outliers from weight outliers. are not isolated but occur simultaneously and are interconnected across multiple dimensions within the model. Specifically, weight outliers align perfectly with activation outliers in feature dimen￾sions, while…
Figure 8
Figure 8. Figure 8: The spread of attention outliers from activation outliers. Activation outliers influence the self-attention mechanism, extending their impact to other sequence dimensions. 6 [PITH_FULL_IMAGE:figures/full_fig_p006_8.png]
Figure 9
Figure 9. Figure 9: The disappearance of outliers in the final layers. The Spread of Attention Outliers from Activation Outliers. Activation outliers propagate into the attention mechanism through their influence on query, key, and value vectors. In the third layer’s Multi-Head Attention …
Figure 10
Figure 10. Figure 10: Activation outliers across different attention formulations. 1 3 6 9 12 Layers 0 200 400 600 800 1000 Magnitudes GPT-2 Default (a) 1 3 6 9 12 Layers 0 100 200 300 400 500 600 700 800 Magnitudes GPT-2 with Fixed Bias (b) 1 3 6 9 12 Layers 0 100 200 300 400 500 600 700 …
Figure 11
Figure 11. Figure 11: Top-3 largest activation outliers for each layer. • It is not the context-aware bias: Experiment (c) shows that context-aware bias alone is insufficient. A comparison with Experiment (d) highlights that context-aware biases do not eliminate outliers. • It is the conte…
Figure 12
Figure 12. Figure 12: Training loss comparison showing improved convergence by eliminating outliers. 6 CONCLUSION In this work, we systematically analyzed the distribution, formation, and roles of outliers in large language models (LLMs), categorizing them into activation, weight, and atte…
Figure 13
Figure 13. Figure 13: Systematic outliers in Phi-2. Sum mer is warm . Winter is cold . \n 7310 0 1k 2k Mistral-7B, Layer 2 (a) activation: x down ℓ 0 1 2 ·········7310 ··· ··· ··· ··· 2070 0 0.3 Mistral-7B, Layer 2 (b) weight: Wdown ℓ Sum mer is warm . Winter is cold . \n 2070 0 150 300 Mi…
Figure 14
Figure 14. Figure 14: Systematic outliers in Mistral-7B. Summer is warm . Winter is cold . \n 8811 0 1k LLaMA-2-13B, Layer 4 (a) activation: x down ℓ 0 1 2 ·········8811 ··· ··· ··· ··· 2100 4743 0 2 LLaMA-2-13B, Layer 4 (b) weight: Wdown ℓ Summer is warm . Winter is cold . \n 2100 4743 0 …
Figure 15
Figure 15. Figure 15: Systematic outliers in LLaMA2-13B. Summer is warm . Winter is cold . 2427 0 500 LLaMA-3-8B, Layer 2 (a) activation: x down ℓ 0 1 2 ········· ··· 12638 ··· ··· ··· 0 1 LLaMA-3-8B, Layer 2 (b) weight: Wdown ℓ Summer is warm . Winter is cold . 788 1384 4062 0 300 LLaMA-3…
Figure 16
Figure 16. Figure 16: Systematic outliers in LLaMA3-8B. B DETAILED EXPERIMENTAL SETTINGS This section provides comprehensive details on the experimental settings used to analyze systematic outliers in LLMs. It covers the methodologies and configurations employed in different aspects of the…
Figure 17
Figure 17. Figure 17: Systematic outliers in OPT-6.7B. Summer is warm . Winter is cold . \n 0 5 MPT-7B, Layer 4 (a) activation: x down ℓ 0 1 2 ······903 ··· ··· ··· ··· ··· 0 0.5 MPT-7B, Layer 4 (b) weight: Wdown ℓ Summer is warm . Winter is cold . \n 0 1k MPT-7B, Layer 4 (c) activation: h…
Figure 18
Figure 18. Figure 18: Systematic outliers in MPT-7B. Summer is warm . Winter is cold . \n 0 30 Falcon-7B, Layer 4 (a) activation: x down ℓ 0 1 2 ······1135 ··· ··· ··· ··· ··· 0 1 Falcon-7B, Layer 4 (b) weight: Wdown ℓ Summer is warm . Winter is cold . \n 0 1k Falcon-7B, Layer 4 (c) activa…
Figure 19
Figure 19. Figure 19: Systematic outliers in Falcon-7B. Summer is warm . Winter is cold . \n 7890 0 1k LLaMA-2-7B-chat, Layer 2 (a) activation: x down ℓ 0 1 2 ·········7890 ··· ··· ··· ··· 1415 2533 0 2 LLaMA-2-7B-chat, Layer 2 (b) weight: Wdown ℓ Summer is warm . Winter is cold . \n 1415 …
Figure 20
Figure 20. Figure 20: Systematic outliers in LLaMA2-7B-Chat. B.1 POSITION ANALYSIS SETTINGS This subsection describes the experimental settings used to analyze the distribution of systematic outliers in LLaMA2-7B across layers, sequences, and feature dimensions. The focus is on three types…
Figure 21
Figure 21. Figure 21: Systematic outliers in LLaMA2-13B-Chat. Sum mer is warm . Winter is cold . \n 7310 0 1k 2k Mistral-7B-Instruct, Layer 2 (a) activation: x down ℓ 0 1 2 ·········7310 ··· ··· ··· ··· 2070 0 0.5 Mistral-7B-Instruct, Layer 2 (b) weight: Wdown ℓ Sum mer is warm . Winter is…
Figure 22
Figure 22. Figure 22: Systematic outliers in Mistral-7B-Instruct. are distributed across shallow, middle, and deep layers. Using 100 sequences of length 2,048 from the RedPajama dataset (Computer, 2023), the positions where activation outliers first appear are identified. Additionally, sca…
Figure 23
Figure 23. Figure 23: Absence of outliers in sigmoid attention. D.2 EXPLICIT CONTEXT-AWARE SCALING FACTOR IN TINY-LLAMA To verify the generalizability of our findings beyond GPT-2, we conducted additional experiments using a TinyLLaMA-120M model. The training setup and code were adapted fr…
Figure 24
Figure 24. Figure 24: Visualization of TinyLLaMA-120M with explicit context-aware scaling factor. The absence of systematic outliers illustrates the effectiveness of this approach in preventing outlier formation. D.3 IMPACT OF SEQUENCE LENGTH ON OUTLIERS Our analysis shows that sequence le…

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Forward citations

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    \@lbibitem[] @bibitem@first@sw\@secondoftwo \@lbibitem[#1]#2 \@extra@b@citeb \@ifundefined br@#2\@extra@b@citeb \@namedef br@#2 \@nameuse br@#2\@extra@b@citeb \@ifundefined b@#2\@extra@b@citeb @num @parse #2 @tmp #1 NAT@b@open@#2 NAT@b@shut@#2 \@ifnum @merge>\@ne @bibitem@firs...

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    @open @close @open @close and [1] URL: #1 \@ifundefined chapter * \@mkboth \@ifxundefined @sectionbib * \@mkboth * \@mkboth\@gobbletwo \@ifclassloaded amsart * \@ifclassloaded amsbook * \@ifxundefined @heading @heading NAT@ctr thebibliography [1] @ \@biblabel @NAT@ctr \@bibset...

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.