Layer Normalization

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Oct 6, 2026cs.LG

LayerRoPE: Dynamic Depth-wise Magnitude & Angular Superposition

As data propagates through a Transformer, the norm of its hidden states grows by orders of magnitude with depth, a phenomenon framed as 'curse of depth' and nearly universally treated as a pathology to be suppressed. We take the opposite view. Across 16 pre-trained LLMs from 9 families, spanning dense, mixture-of-experts and hybrid architectures and Pre-, Peri- and Post-Norm designs, we find that this growth reflects an emergent depth-positional encoding, carried by the only learned per-layer gain on the residual stream, the normalization weight

γ

: with depth,

γ

grows in magnitude and rotates in direction, jointly encoding the layer index. We make this depth-conditioned encoding explicit with LayerRoPE, an implicit analog of RoPE along the depth axis, which replaces all layerwise

γ

vectors with a single shared vector and depth-conditioned scalars, at a net reduction in parameters and

<0.02\%

change in FLOPs. Across a model ladder scaled up to

100

B+ tokens, LayerRoPE consistently outperforms Pre-, Post- and Peri-Norm and Layer-Norm Scaling, reaching Pre-Norm's 1.3B loss with

3.4\times

less compute; LayerRoPE is the only approach that shows strong convergence and improves near monotonically as depth scales to 512 layers. It improves learning-rate sensitivity by

3

-

10\times

, and transfers naively to and consistently improves looped latent models and Vision Transformers. Inspecting its learned schedule inverts the prevailing premise: LayerRoPE does not shrink the residual stream but widens it, damping what each block reads while amplifying what it writes. Depth stability, our results suggest, calls not for suppressing the residual stream, but for depth-conditioned regulation of the computational blocks it feeds.

Shikhar Srivastava, Christopher Kanan

University of Rochester

Transformer Positional Encoding Layer Normalization

Aug 31, 2026cs.LG

Tracing distinguishability through transformer processing with stochastic LayerNorm

Representational similarity is foundational to analyses of deep networks, yet distances between point-valued representations are not intrinsically tied to downstream function: nearby states may produce different behaviors, while distant states may behave similarly. We instead give representations volume, turning similarity into statistical distinguishability. Overlapping stochastic representations necessarily induce overlapping downstream distributions, grounding latent comparison in model function and bringing it under information-theoretic tools such as the data-processing inequality. We realize this idea in pretrained transformers through a light-touch modification to LayerNorm: at each residual-stream read, we normalize the state, add isotropic Gaussian noise, and renormalize. During distillation fine-tuning, one learned allocation parameter per residual-stream read distributes a fixed global rate budget across the processing stack. The resulting model can be viewed as transformer blocks reading the residual stream with learned finite precision under a shared global rate budget. Using the Bhattacharyya coefficient, we trace which counterfactual distinctions are preserved through MLP blocks or selectively exposed to the query, key, and value computations of individual attention heads. Experiments on ViT-S and GPT-2 small reveal the depthwise propagation of continuous visual perturbations and head-specific sensitivity to token distinctions aligned with known attention motifs. These results establish distinguishability as a functionally grounded lens on transformer computation that complements existing interpretability approaches.

Kieran Murphy

New Jersey Institute of Technology

Transformer Interpretability Layer Normalization

Aug 13, 2026cs.AI

Rethinking Normalization Placement for LLMs: Post-Norm under Curriculum Depth Growing

Pre-norm is the standard normalization placement in modern Transformers because it facilitates joint optimization of full-depth models. We ask whether this preference persists when depth is introduced through a curriculum. In curriculum depth growth, each appended block receives the boundary representation produced by a trained prefix, making normalization placement relevant to forward conditioning. We therefore test whether placement and training curriculum interact. In a controlled distillation study with a Qwen3-8B teacher and a nine-layer student, pre-norm and post-norm are indistinguishable under joint training, differing by

0.0004

validation CE, while post-norm improves over pre-norm by

0.0328

under curriculum growth, an order of magnitude larger. A post-joint control matched by student active-layer tokens remains worse than post-grow, which rules out compute as the sole explanation. The ranking crosses over during the curriculum: post-norm takes the lead once blocks are appended. Single-block and freeze controls localize the ranking change to block appending rather than shallow-block quality or retraining. Boundary diagnostics associate post-norm with stable residual scales and pre-norm with structural-token scale drift; on a fixed batch, the final pre-grow block is also nearly identity-mapped. Together with the phase-wise crossover, these observations are consistent with boundary-scale conditioning after new blocks are appended. The results motivate treating normalization placement and training curriculum as coupled design choices in this distillation setting.

Sheng Ren, Yadong Wang, Naiqiang Tan +7

Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China · Didichuxing Co. Ltd, Beijing, China

Transformer Layer Normalization

Aug 10, 2026cs.CV

Unveiling the Secret of AdaLN-Zero in Diffusion Transformer

Diffusion transformer (DiT), a rapidly emerging architecture for image generation, has gained much attention. However, despite ongoing efforts to improve its performance, the understanding of DiT remains superficial. In this work, we delve into and investigate a critical conditioning mechanism within DiT, adaLN-Zero, which achieves superior performance compared to adaLN. Our work studies three potential elements driving this performance, including an SE-like structure, zero-initialization, and a "gradual" update order, among which zero-initialization is proved to be the most influential. Building on this understanding, we propose an analysis-guided initialization strategy, termed adaLN-Gaussian, which serves both as an empirical validation of our analysis and as a practical initialization method that consistently improves optimization efficiency. On the other hand, inspired by the SE-like structure, we introduce an improved conditioning mechanism called SE-adaLN-Zero. Extensive experiments following DiT on four datasets, especially on ImageNet1K demonstrate the effectiveness and generalization of adaLN-Gaussian and SE-adaLN-Zero. Beyond class-to-image generation, we also evaluate the generalization of the two improved methods on text-to-image generation.

Jie Zhu, Mingyu Ding, Boqiang Duan +2

Key Lab of High Confidence Software Technologies (Peking University), Ministry of Education, China, and School of Computer Science, Peking University, China. · UC Berkeley · Baidu, Beijing, China

Diffusion Transformer Neural Network Initialization Layer Normalization Diffusion-Based Image Generation

Aug 10, 2026cs.LG

Why Post-Norm Transformers Collapse: Attention Amplification and Gradient Repair Failure

Deep decoder-only Transformers often replace the original Post-Norm architecture with Pre-Norm variants because Post-Norm training is highly sensitive to warmup and learning rate under conventional initialization schemes. Although prior work has identified rank collapse and gradient vanishing as related symptoms, it remains poorly understood how causal attention creates high-similarity representations and why training dynamics fail to repair them. We give a two-stage analysis of Post-Norm rank collapse using token similarity as a scalar state variable. First, at initialization, causal attention acts approximately as a prefix-averaging operator that increases token similarity across depth, while the SwiGLU branch contributes only a smaller damping effect. Second, once training enters a high-similarity regime, growth of pre-normalization residual norms makes the RMSNorm backward factor contractive; under mild conditions, gradients to earlier layers decay geometrically. As a complementary result, we characterize the properties of a collapsed network: its best predictor is frequency distribution with relatively high loss floor, and gradients in collapsed layers vanish at frequency distribution. Experiments on 48-layer decoder-only Transformers trained on C4 dataset match the predicted initialization-time similarity growth and collapse-time gradient contraction, and show that collapsed runs stay near the predicted frequency loss. Together, these results distinguish the forward similarity amplification and backward repair incapacity in Post-Norm collapse, while also characterizing the behavior of collapsed networks.

Xingjian Wang, Qingyu Han, Xiaodong Luo +1

The Chinese University of Hong Kong, Shenzhen · Shenzhen Research Institute of Big Data

Transformer Self-Attention Decoder-Only Language Models Layer Normalization

Aug 10, 2026cs.CV

One Model to Magnify Them All: Efficient Scale-Invariant Histopathology via Conditional Normalization and Continuous Magnification Training

Whole slide images (WSIs) in digital histopathology are acquired at discrete magnification levels encoding complementary diagnostic information from global tissue architecture to fine-grained cellular morphology. Yet, deep learning models remain sensitive to scale variation. Existing magnification-invariant methods rely on multi-scale architectures at predefined discrete resolutions, while in clinical deployment the acquisition magnification varies continuously, rarely aligns with a model's fixed training resolution, and intermediate scales are common, so robust coverage otherwise demands a costly ensemble of magnification-specific models. We propose Conditional Layer Normalization (CLN), a lightweight mechanism that generates affine normalization parameters from input pixel size via a small MLP, integrated into standard CNN architectures for both WSI classification and segmentation. Trained on patches sampled continuously across a range of pixel sizes, the model decouples inference from scanner-dependent magnification and generalizes to arbitrary, previously unseen scales at test time. On the PANDA prostate cancer dataset, our approach on average matches or exceeds independently trained single-magnification models and ranks among the top three performers at every evaluated magnification, including those unseen during training. This collapses a five-model ensemble into a single network and reduces training, and inference cost roughly 4-5 times, while leaving the multiply-accumulate count unchanged. The code is available at: https://github.com/aflorkowska/OneModelToMagnifyThemAll.

Agnieszka Florkowska, Henning Müller, Marek Wodzinski

Sano Centre for Computational Medicine, Krakow, Poland · AGH University of Krakow, al. Adama Mickiewicza 30, 30-059 Kraków, Poland · Institute of Informatics, HES-SO Valais-Wallis, Sierre, Switzerland +1

Computational Pathology Histopathology Image Segmentation Layer Normalization Histopathology Image Classification Whole-Slide Image Analysis

Jul 20, 2026cs.LG

Phasor Attention: Mean Root Square Normalization for Phase Manifold Preservation

While Root Mean Square Normalization has become the de facto standard for accelerating modern sequence models, its reliance on the quadratic accumulation of independent scalars (

\sum x^2

) inherently triggers outlier-induced numerical instability, gradient starvation, and anisotropic phase distortion. We introduce Mean Root Square Normalization (MRSNorm). By structurally pairing channels into 2D phasors, MRSNorm mathematically inverts the traditional scaling paradigm: it computes the localized

L_2

magnitudes (Root Square) before aggregating them via a global

L_1

average (Mean). This operational inversion strictly constrains activations to a phasor manifold, preserving conformal invariance. By sharing a single affine weight across phasor components, MRSNorm halves the total number of learnable parameters, proving that unconstrained spatial scaling in standard norms is a harmful redundancy. We analytically demonstrate that this geometric constraint yields a built-in, trigonometric gradient clipper governed by the Pythagorean identity, unconditionally equalizing the local gradient norm to ensure Gradient Homogeneity. Empirical evaluations on a ResNet with CIFAR-100 show that despite halved parameters, MRSNorm provides critical structural stability under rigorous stress tests. Under extreme hyperparameter settings where standard normalizations suffer from gradient divergence, MRSNorm successfully prevents numerical explosion and secures stable optimization trajectories. Our findings propose a fundamental paradigm shift toward phasor-based deep representation learning. The implementation of MRSNorm is available at Appendix C.

Sungwoo Goo, Hwi-yeol Yun, Sangkeun Jung

College of Pharmacy, Chungnam National University, Daejeon, Republic of Korea · Department of Computer Science & Engineering, Chungnam National University, Daejeon, Republic of Korea

Gradient Clipping Layer Normalization Neural Network Training Dynamics

Jul 15, 2026cs.LG

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth

We investigate how each component of the Transformer feedforward block architecture design determines how much rank survives across depth at initialization. We reinterpret skip connections and normalization, long understood as controlling magnitude, as mechanisms for preserving gradient rank across depth, since the very matrix multiplications and nonlinear activations that make the network expressive also reduce the rank. We show that skip connections trade off rank collapse against ensemble-like behavior, controlled by the relative scales of the branch and the skip: skip connections route the gradient around the residual branch, where rank is lost, rather than along the long gradient paths that encourage the layers to compose. The placement of the normalization layer controls this same tradeoff by setting the branch-to-skip ratio across depth, unifying much of the normalization placement and depth scaling literature, in particular why rank collapses for Post-Norm but plateaus for Pre-Norm. Other aspects of the architecture, like the two-matrix structure that expands and contracts the width, use additional parameters to preserve the representation or branch Jacobian rank. The second matrix decorrelates a coherent mean spike that would grow across blocks with a single matrix and uncentered activation, preventing the residual representation from collapsing. The width expansion between the two matrices keeps the branch Jacobian full rank: applying the rank-reducing activation in this expanded space leaves enough directions to span the original, at a width that follows a Marchenko--Pastur law. The initialization rank of the input--output Jacobian predicts which networks train on CIFAR-10. Taken together, we recast architecture design for deep networks as navigating an intrinsic tradeoff among rank collapse, ensemble-like behavior, and parameter count.

Katie Everett

MIT CSAIL

Transformer FFNs Transformer Neural Network Initialization Residual Learning Layer Normalization

Jul 12, 2026cs.LG

LayerNorm as Implicit Gain Control in Looped Transformers

In pre-LayerNorm looped transformers, LayerNorm inside the recurrent block acts as an implicit gain controller: by coupling the block's local Lipschitz constant inversely to the activation scale, it renders the recurrence Jacobian non-normal -- asymptotically contractive at every verified fixed point even where its operator norm exceeds 1 -- so the true stability budget is the spectral margin, not an operator-norm bound. That margin depletes as the carry

ρ\to 1

, and a minority of initializations never converge to a fixed point at all, so the diagonal carry constraint

ρ(\bar{A}) < 1

is necessary but not sufficient for convergence of the full recurrence. Training experiments across six tasks, including a controlled ablation, reveal that the linear carry is not the depth-memory mechanism: gradient descent routes memory through the block's more expressive nonlinear recurrence and leaves the stability-constrained carry at rest -- the carry's role is stabilization, not memory. We characterize the boundary of this claim: on tasks with axis-aligned per-channel structure, gradient descent does recruit the carry. All results are derived analytically and verified in a from-scratch, CPU-scale implementation; verification at larger scale is needed.

Matthias M. M. Buehlmaier

Faculty of Business and Economics, The University of Hong Kong · Pokfulam Road, Hong Kong

Recurrent Transformers Layer Normalization Neural Network Training Dynamics Gradient Descent Dynamics

Jul 12, 2026cs.LG

AutoNorm: Understanding Adaptive Normalization in Transformers through Differentiable Gating

Normalization is a critical component for stabilizing Transformer training, yet the choice between static strategies such as Layer Normalization (LN) and adaptive alternatives remains largely task-dependent. In this paper, we investigate a key optimization challenge in differentiable normalization gating. Our experiments show that, on relatively stationary vision tasks, the high gradient variance introduced by Gumbel-Softmax gating can hinder convergence of the routing mechanism, causing learned gates to underperform simple random selection. In contrast, on non-stationary language modeling and classification tasks, sustained gating diversity enables the model to learn more effective layer-wise normalization policies. Motivated by these observations, we propose AutoNorm-S (Stabilized), a training strategy that mitigates optimization instability through a gate-freezing schedule. AutoNorm-S achieves competitive or improved performance across multiple benchmarks, outperforming adaptive normalization baselines on NLP datasets, including PTB and SST-2, while remaining competitive on standard vision benchmarks. These results suggest that decoupling normalization selection from optimization noise provides a practical and principled approach for adaptive normalization in Transformer architectures.

Piyush Kaushik Bhattacharyya, Divyanshu Rai, Swastik Singh +3

Dynamic Neural Networks Transformer Layer Normalization

Jun 17, 2026cs.LG

Algebraic Dead Directions in LayerNorm Transformers: A Forward-Pass-Only Diagnostic at LLM Scale

Pretrained transformers sit near singular minima of the loss, where the Fisher information metric degenerates along dead directions: directions in parameter space along which the directional Fisher vanishes. Locating such a direction normally needs a forward pass and an eigendecomposition of activations, or a sampling-based complexity estimate; none returns a direction computable from the network's parameters alone. We give one, for LayerNorm transformers. The inverse-scale direction

γ^{-1}/\|γ^{-1}\|

of the LayerNorm affine is an exact algebraic kernel of the post-final-norm centred activation covariance, for any input distribution, and induces a corresponding dead direction in parameter space. It is read from the LN scale parameter alone, with no forward or backward pass and no eigensolve: the cheapest dead-direction read, specific to LayerNorm. We test it on

14

pretrained transformers (

9

LayerNorm,

5

RMSNorm;

160

M-

35

B; language and vision objectives). At random initialisation the predicted direction matches the measured bottom singular direction (one forward pass, direct SVD) to four decimal places on

9/9

LayerNorm models, and is correctly absent on

5/5

RMSNorm models, which lack the mean-subtraction projector that creates it. On the trained checkpoint the covariance eigenvalue along this direction deepens by

{\sim}10^3\times

and further dead directions open; the random-init-to-trained gap is a one-forward-pass, per-checkpoint readout of singular structure along the predicted coordinate. Two consequences follow in closed form: the residual stream's smallest singular value is preserved block-to-block on

13/14

transformers measured on their own input distribution, the one exception (Gemma

4

-

31

B) a genuine dead direction the same read pinpoints; and the kernel direction's presence classifies a transformer's normalisation from the parameters alone.

Tejas Pradeep Shirodkar, P. J. Narayanan

IIIT, Hyderabad

Information Geometry Transformer Neural Network Optimization Layer Normalization

Jun 16, 2026cs.AR

MIVE: A Minimalist Integer Vector Engine for Softmax LayerNorm and RMSNorm Acceleration

The rapid growth of Large Language Models (LLMs) has intensified the need for specialized hardware accelerators that can satisfy stringent inference latency and power constraints. Although matrix multiplications dominate the overall computational workload, non-linear vector normalization operations, such as LayerNorm, RMSNorm and Softmax can become critical hardware bottlenecks. Existing accelerators typically implement these functions using dedicated hardware blocks, leading to duplicated resources and inefficient silicon utilization. To address this limitation, we propose a Minimalist Integer Vector Engine (MIVE), a programmable architecture capable of executing all three operations within a unified datapath. By exploiting common computational patterns across LayerNorm, RMSNorm and Softmax the proposed vector engine maximizes hardware sharing while reducing implementation overhead. Physical ASIC implementation results show that MIVE provides comprehensive multi-function support while achieving higher area and hardware efficiency than most state-of-the-art standalone accelerators.

Kosmas Alexandridis, Giorgos Dimitrakopoulos

Integrated Circuits Lab, Electrical and Computer Engineering, Democritus University of Thrace (DUTH), Greece

AI Accelerator Inference Inference Acceleration LLM Inference Acceleration Layer Normalization

Jun 12, 2026cs.LG

PostDeg: Placement Beats Parameterization in LayerNorm GNNs

LayerNorm-based GNNs routinely erase the topology signals (degree, centrality,

k

-core) that node-selection policies should depend on, but the literature has not located where in the residual block the erasure happens. We answer that question: a positive per-node scalar inserted before LayerNorm is divided out up to a stabilizer term, while the same scalar inserted after LayerNorm reaches the score head as representation magnitude. The surviving slot is the post-LayerNorm position. We instantiate it with PostDeg, a parameter-free post-LayerNorm inverse-degree scale, and pre-register four falsifiers (graphwise scalars, extra LayerNorm, expressive same-slot capacity, backbone-agnostic source) that would reject the rule. PostDeg gains

+3.5\%/+2.5\%/+5.6\%

over the LN backbone on influence maximization, network dismantling, and maximum independent set, with

10/10

paired-seed wins per task; none of the four falsifiers fires. The takeaway is that placement, not parameterization, carries the gain -- a small invariance check that generalizes to any positive topology scalar in any normalized residual stack.

Yash Tomar, Aryav Das

Purdue University · Park Tudor High School

Graph Neural Networks Layer Normalization

May 30, 2026cs.LG

Looped Transformers with Layer Normalization Provably Learn the Power Method

Transformers have achieved remarkable success across a wide range of applications, and a growing body of work suggests that part of their strength comes from their ability to learn and execute algorithmic procedures. However, our understanding of how transformers learn such algorithms remains limited, especially in the presence of layer normalization (LN). In this work, we study principal component prediction as a concrete testbed for understanding the training dynamics of transformers with LN. We prove that a looped linear transformer with LN, trained by gradient descent, converges to a solution that implements the power method, with each self-attention layer performing one power iteration. Notably, the model is trained only for principal component prediction, rather than being explicitly supervised to implement the power method. Our finding thus reveals an "algorithmic implicit bias" of looped transformers with LN: principal-component prediction can in principle be achieved by many mechanisms, yet gradient descent selects one that realizes the power method. We further provide a concrete comparison between transformers with and without LN: even with layerwise guidance from power iterations, a transformer without LN cannot exactly learn the power method, whereas the corresponding transformer with LN can, leading to a provable performance gap in principal component prediction. Our results provide, to our knowledge, the first theoretical analysis of the training dynamics of looped and single-layer transformers with LN, and shed light on the role of LN in transformer models.

Lyumin Wu, Chenyang Zhang, Yuan Cao

School of Computing & Data Science, The University of Hong Kong

Recurrent Transformers Layer Normalization Neural Network Training Dynamics

May 14, 2026cs.LG

Enjoy Your Layer Normalization with the Computational Efficiency of RMSNorm

Layer normalization (LN) is a fundamental component in modern deep learning, but its per-sample centering and scaling introduce non-negligible inference overhead. RMSNorm improves efficiency by removing the centering operation, yet this may discard benefits associated with centering. This paper propose a framework to determine whether an LN in an arbitrary DNN can be replaced by RMSNorm without changing the model function. The key idea is to fold LN's centering operation into upstream general linear layers by enforcing zero-mean outputs through the column-centered constraint (CCC) and column-based weight centering (CBWC). We extend the analysis to arbitrary DNNs, define such LNs as foldable LNs, and develop a graph-based detection algorithm. Our analysis shows that many LNs in widely used architectures are foldable, enabling exact inference-time conversion and end-to-end acceleration of 2% to 12% without changing model predictions. Experiments across multiple task families further show that, when exact equivalence is partially broken in practical training settings, our method remains competitive with vanilla LN while improving efficiency.

Yuxin Guo, Yihao Yue, Yunhao Ni +4

State Key Laboratory of Complex and Critical Software Environment (SKLCCSE), Beihang University, Beijing, China · Hangzhou International Innovation Institute, Beihang University, Hangzhou, China

Efficient Neural Network Inference Layer Normalization

May 13, 2026cs.CV

Evolving Layer-Specific Scalar Functions for Hardware-Aware Transformer Adaptation

Vision Transformers (ViTs) achieve state-of-the-art performance on challenging vision tasks, but their deployment on edge devices is severely hindered by the computational complexity and global reduction bottleneck imposed by layer normalization. Recent methods attempt to bypass this by replacing normalization layers with hardware-friendly scalar approximations. However, these homogeneous replacements do not optimally fit to all layers' behaviour and rely on expensive model retraining. In this work, we propose a highly efficient, hardware-aware framework that utilizes genetic programming (GP) to evolve heterogeneous, layer-specific scalar functions directly from pre-trained weights. Coupled with a novel post-training re-alignment strategy, our approach eliminates the need to retrain models from scratch entirely. Our evolved expressions accurately approximate the target normalization behaviours, capturing

91.6\%

of the variance (

R^2

) compared to only

70.2\%

for homogeneous baselines, allowing our modified architecture to recover

84.25\%

Top-1 ImageNet-1K accuracy in only 20 epochs. By preserving this performance while eliminating the global reduction bottleneck, our approach establishes a highly favourable trade-off between arithmetic complexity and off-chip memory traffic, removing a primary barrier to the efficient deployment of ViTs on edge accelerators.

Kieran Carrigg, Sigur de Vries, Amirhossein Sadough +1

Department of Machine Learning and Neural Computing Donders Institute for Brain, Cognition, and Behaviour Thomas van Aquinostraat 4, 6525 GD Nijmegen, The Netherlands

Efficient Neural Network Inference Efficient ViTs Layer Normalization Edge ML

May 11, 2026cs.LG

Attention Drift: What Autoregressive Speculative Decoding Models Learn

Speculative decoding accelerates LLM inference by drafting future tokens with a small model, but drafter models degrade sharply under template perturbation and long-context inputs. We identify a previously-unreported phenomenon we call \textbf{attention drift}: as the drafter generates successive tokens within a speculation chain, attention progressively moves from the prompt onto its own recently-generated tokens. We observe this across both \emph{EAGLE3} drafters and \emph{MTP heads}, suggesting drift is a property of drafter designs. We trace this to the un-normalized residual path between chain steps: the drafter's hidden state magnitude grows monotonically with chain depth, which exhibits dynamics consistent with additional pre-norm transformer layers stacked on the target rather than as a standalone autoregressive predictor. In order to limit the growth, we propose two architectural changes: Post-norm on the drafter hidden states and per-hidden-state RMSNorm after capturing target hidden states. Our interventions improve acceptance length over the current leading model, pre-norm EAGLE3, by up to

2\times

under template perturbation,

1.18\times

on long-context tasks, and

1.10\times

on seven standard benchmarks spanning multi-turn chat, math, and coding. Our changes also allow shorter train-time-test depths to generalize over longer drafting sequences.

Doğaç Eldenk, Payal Mohapatra, Yigitcan Comlek +3

Northwestern University · GE Aerospace · fal +1

Long-Context Language Model Inference Speculative Decoding Transformer Attention LLM Inference Acceleration Layer Normalization

May 10, 2026cs.LG

The Transformer as a Polar State Estimator

We show that the core components of the Transformer---attention, residual connections, and normalization---arise naturally from a single geometric state estimation problem. Modeling the latent state in polar coordinates naturally separates radial and hyperspherical dynamics, yielding a precision-weighted filtering procedure in which normalization enforces the hyperspherical constraint, attention aggregates directional evidence, and the residual connection implements an incremental state update. The standard Transformer block with rotary positional encodings is recovered by discarding the geometric correction terms of the resulting state estimator, showing that its architecture follows from the underlying estimation problem rather than from independent design choices. The proposed \textit{Polar Transformer} retains these geometric corrections.

Peter Racioppo

Independent Researcher Los Angeles, CA

Transformer Layer Normalization Attention Mechanisms

Apr 26, 2026cs.AR

Hardware-Efficient Softmax and Layer Normalization with Guaranteed Normalization for Edge Devices

In Transformer models, non-GEMM (non-General Matrix Multiplication) operations -- especially Softmax and Layer Normalization (LayerNorm) -- often dominate hardware cost due to their nonlinear nature. To address this, previous approximation studies mainly target rank-oriented tasks, which is acceptable for classification. However, edge Natural Language Processing (NLP) applications and edge generative AI are largely evaluated based on score-oriented tasks, so normalization-guaranteed non-GEMM operations are essential. We propose a hardware-efficient Softmax and LayerNorm with Guaranteed Normalization for Edge devices. Our design employs hardware-efficient approximation methods while preserving the normalization (Softmax:

\sum p = 1

, LayerNorm:

σ= 1

). Our architecture is described in Verilog HDL and synthesized using the Samsung 28nm CMOS process. In accuracy evaluation, we achieve high accuracy with minimal degradation: GLUE +0.07%, SQuAD -0.01%, perplexity -0.09%. Implementation results show that our architecture is small:

942\,μm^2

for Softmax,

1199\,μm^2

for LayerNorm. Compared to the state of the art, we achieve up to 11x and 14x reduction in area, respectively.

Dawon Choi, Hana Kim, Ji-Hoon Kim

Dept. of Artificial Intelligence Semiconductor Engineering, Hanyang University, Seoul, Republic of Korea · Dept. of Electronic Engineering, Hanyang University, Seoul, Republic of Korea

Efficient Neural Network Inference Layer Normalization Edge ML

Apr 25, 2026cs.LG

When Does Removing LayerNorm Help? Activation Bounding as a Regime-Dependent Implicit Regularizer

Dynamic Tanh (DyT) removes LayerNorm by bounding activations with a learned tanh(alpha x). We show that this bounding is a regime-dependent implicit regularizer, not a uniformly beneficial replacement. Across GPT-2-family models spanning 64M to 3.78B parameters and 1M to 118M tokens, with Llama and ViT cross-checks, DyT improves validation loss by 27.3% at 64M/1M but worsens it by 18.8% at 64M/118M; the 1M benefit vanishes with capacity (+1.7% at 3.78B), while the 118M penalty reaches +27.9%. The mechanism is measurable: 49% of DyT activations saturate at 1M versus 23% at 118M, and a 500-step saturation heuristic classifies DyT's sign with 75% raw in-sample accuracy on the 12-cell GPT-2 calibration set (AUC 0.75; 64% when adding Scale 5 stress cells), correctly labels 3/3 Llama checks, but only reaches 50% raw leave-one-scale-out accuracy. Three interventions support the bounding explanation: HardTanh reproduces the regime pattern, increasing alpha at 118M monotonically reduces DyT's penalty, and vanilla+dropout(p=0.5) matches DyT's data-rich loss. We also localize Llama-DyT collapse to SwiGLU gating, where saturation separates collapse from convergence in a 3-seed component ablation (r=0.94). Scope: all experiments are compute-limited (T/P < 1.84), below Chinchilla-optimal training.

Lucky Verma

Independent Researcher

Neural Network Activation Functions Layer Normalization Neural Network Training Dynamics Implicit Regularization