Normalization

We propose OASIS, an outlier- and sink-aware technique built on inter-layer null signaling. As AttnResidual architectures introduce an additional depth-wise normalization channel, they improve inter-layer routing flexibility but also exacerbate attention sinks, activation outliers, and the resulting degradation in inference stability and quantization robustness. OASIS addresses this issue by introducing a Softmax1-based null space and coupling token-level null evidence to depth routing through an inter-layer null signal, thereby reducing sink-dominated routing and improving structural robustness. Theoretically, we show that the dual-normalization design of AttnResidual intensifies sink formation and quantization brittleness. Experimentally, we compare OASIS against five baselines on three real-world datasets and observe consistent improvements in both attention sink and post-quantization performance. Notably, OASIS achieves an average reduction of 9.26% in maximum infinity norm and 2.60% in average kurtosis across the evaluated settings, while lowering perplexity by 75.85% under W8A8 and improving GSM8K Pass@1 by 12.42% under W4A4.

When researchers ask whether two transformer layers are "equivalent" for compression, they often conflate distinct tests. Replacement asks whether one layer's map can substitute for another's in place; interchange asks whether two layers approximately commute when their positions are swapped. Both are output-grounded swap-KL probes, but they need not agree: on pretrained transformers the protocol gap can change which layers look safe to prune by several-fold under the same evaluator, especially when replacement distances are high. We measure both protocols across checkpoints and architectures. On a Pythia training trajectory (410M and 1.4B), the replacement-interchange gap grows from initialization to convergence. Under one matched WikiText-2 contract at 8B scale, Qwen3-8B enters a divergent regime: interchange-guided removal is several-fold safer than replacement-guided at the same layer budgets, while Llama-3.1-8B ties the two protocols for pruning cost even though interchange KL is lower, showing metric gaps need not map one-to-one to removal. Before layer removal or merging, score both swap-KLs on the target checkpoint; the diagnostic requires only unlabeled forward passes.

Recent work has promoted task-aware layer pruning as a way to improve model performance on particular tasks, as shown by TALE. In this paper, we investigate when such improvements occur and why. We show first that, across controlled polynomial regression tasks and large language models, such pruning yields no benefit on in-distribution (ID) data but consistently improves out-of-distribution (OOD) accuracy. We further show empirically that OOD inputs induce layerwise norm and pairwise-distance profiles that deviate from the corresponding ID profiles. This leads to a geometric explanation of task-aware pruning: each task induces a task-adapted geometry, characterized empirically by the representation profiles observed on ID inputs. OOD inputs can introduce a distorted version of the task-adapted geometry. Task-aware pruning identifies layers that create or amplify this distortion; by removing them, it shifts OOD representational norms and pairwise distances toward those observed on the adapted distribution. This realigns OOD inputs with the model's task-adapted geometry and improves performance. We provide causal evidence through controlled distribution shifts and residual-scaling interventions, and demonstrate consistent behavior across model scales.

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.

By specifying behaviour across multiple agents, social norms are a coordination approach to resolving social dilemmas. Decentralized and wide adoption can be achieved by norms whose prescription involves interpreting stochastic signals in the environment. Such signals must have enough correlation to orchestrate mutually beneficial coordination and enough disincentivizing uncertainty about the benefits of exploiting that coordination. Evolutionary game theory of matrix games has been used to describe how, by rational agents comparing and adopting norms, a norm can evolve to become dominant in a population. Morsky & Akçay (2019) classify norms according to a set of rationality criteria. Joint player strategies that adopt norms that are consistent with optimal single-player strategies with respect to expected reward naturally satisfy a correlated, rather than Nash game theoretic equilibrium condition. Here, we present a version of this theory that clarifies the basic ingredients. We formulate it in the more general Markov game setting more commonly used in reinforcement learning theory. We illustrate the theory by mapping norms over the signal and reward space, while also giving a detailed exposition of the underlying mechanics of the approach. Finally, we give a general solution and analysis of replicator dynamics, which Morsky & Akçay (2019) propose as a means by which these norms could emerge.

Recent video anomaly detection research has expanded rapidly with an emphasis on general models of normality intended to work across many different scenes. While this focus has led to improvements in scalability and multi-scene generalization, it has also shifted the field away from modeling the scene-specific and context-dependent nature of normal behavior. Contemporary approaches frequently rely on video-level weak supervision and opaque pretrained representations from multi-modal large language models (MLLMs), which encourage models to respond to familiar semantic anomaly categories rather than to deviations from the normal patterns of a particular environment. This trend suppresses spatial localization, introduces semantic bias, and reduces anomaly detection to a form of action recognition. In this paper, we examine whether these prevailing formulations align with the core requirements of real-world VAD, which is typically performed within a single scene where normality is determined by local geometry, semantics, and activity patterns. Through targeted visual analyses and empirical evaluations, we demonstrate the practical consequences of these limitations and show that meaningful progress in VAD requires renewed focus on single-scene, spatially-aware, and explainable formulations that capture the nuanced structure of normality within individual environments.

We present a novel method for extracting moving objects from TESS data using machine learning. Our approach uses two stacked 3D U-Nets with skip connections, which we call a W-Net, to filter background and identify pixels containing moving objects in TESS image time-series data. By augmenting the training data through rotation of the image cubes, our method is robust to differences in speed and direction of asteroids, requiring no assumptions for either parameter range which are typically required in "shift-and-stack" type algorithms. We also developed a novel method for learned data scaling that we call Adaptive Normalization, which allows the neural network to learn the ideal range and scaling distribution required for optimal data processing. We built a code for creating TESS training data with asteroid masks that served as the foundation of our effort (tess-asteroid-ml), which we publicly released for the benefit of the community. Our method is not limited to TESS, but applicable for implementation in other similar time-domain surveys, making it of particular interest for use with data from upcoming missions such as the Nancy Grace Roman Space Telescope and NEOSurveyor.

Self-supervised learning (SSL) is recognized as an essential tool for building foundation models for Artificial Intelligence applications. The advances in SSL have been made thanks to vigorous arguments about the principles of SSL and through extensive empirical research. The aim of this paper is to contribute to the development of the underpinning theory of SSL, focusing on the deep clustering approach. By analogy to supervised learning, we formulate SSL as K-L divergence optimization. The mode collapse is prevented by imposing an optimisation constraint on the teacher distribution. This leads to normalization using inverse cluster priors. We show that using Jensen inequality this normalization simplifies to the popular batch centering procedure. Distillation and centering are common {heuristics-based} practices in SSL, {but our work underpins them theoretically.} The theoretical model developed not only supports specific existing successful SSL methods, but also suggests directions for future investigations.

Recently, post-training methods based on reinforcement learning, with a particular focus on Group Relative Policy Optimization (GRPO), have emerged as the robust paradigm for further advancement of text-to-image (T2I) models. However, these methods are often prone to reward hacking, wherein models exploit biases in imperfect reward functions rather than yielding genuine performance gains. In this work, we identify that normalization could lead to miscalibration and directly removing the prompt-level standard deviation term yields an optimal policy ascent direction that is linear in the advantage but still limits the separation of genuine signals from noise. To mitigate the above issues, we propose Super-Linear Advantage Shaping (SLAS) by revisiting the functional update from an information geometry perspective. By extending the Fisher-Rao information metric with advantage-dependent weighting, SLAS introduces a non-linear geometric structure that reshapes the local policy space. This design relaxes constraints along high-advantage directions to amplify informative updates, while tightening those in low-advantage regions to suppress illusory gradients. In addition, batch-level normalization is applied to stabilize training under varying reward scales. Extensive evaluations demonstrate that SLAS consistently surpasses the DanceGRPO baseline across multiple backbones and benchmarks. In particular, it yields faster training dynamics, improved out-of-domain performance on GenEval and UniGenBench++, and enhanced robustness to model scaling, while mitigating reward hacking and preserving semantic and compositional fidelity in generations.

Reversible instance normalization (RevIN) and its successors (Dish-TS, SAN, FAN) have become the de facto plug-in for time-series forecasting, yet the map they apply to each data point is strictly affine, $x \mapsto ax+b$, so they cannot reshape the underlying distribution -- heavy tails remain heavy and skewness remains uncorrected. We propose NoRIN, a non-linear reversible normalization based on the arcsinh-form Johnson $S_U$ transform with two shape parameters $(δ,\varepsilon)$ that control tailedness and skewness; the linear $Z$-score used by RevIN is recovered only in the limit $δ\to \infty$. Training $(δ,\varepsilon)$ jointly with the backbone via gradient descent reliably pushes them toward this linear limit within a few epochs -- a phenomenon we name the degeneration problem: the forecasting loss is locally indifferent to shape, and the high-capacity backbone compensates for any monotone reparameterization of its input. NoRIN escapes the degeneration by decoupling shape selection from gradient training: $(δ,\varepsilon)$ are initialized by a closed-form Slifker-Shapiro quantile fit and refined by Bayesian optimization on the validation objective, while the inner training loop is identical to standard RevIN-style training. Across six representative backbones x five real-world datasets x three prediction horizons (90 configurations), decoupled shape optimization recovers $(δ^\star,\varepsilon^\star)$ that sit systematically far from the linear limit, with values that vary in a backbone-dependent way. This empirically supports the central thesis: different backbones genuinely require different normalization parameters to reach their best performance.

Unsupervised tabular anomaly detection methods typically learn feature patterns from normal samples during training and subsequently identify samples that deviate from these patterns as anomalies during testing. However, in practical scenarios, the limited scale and diversity of training data often lead to an incomplete characterization of normal patterns. While test-time adaptation offers a remedy, its isolated focus on test-time optimization ignores the critical synergy with training-phase learning. Furthermore, indiscriminate adaptation to unlabeled test data inevitably triggers anomaly contamination, preventing the model from fully realizing its discriminative capability between normal and anomalous samples. To address these issues, we propose RTTAD, a Risk-aware Test-time adaptation method for unsupervised Tabular Anomaly Detection. RTTAD holistically tackles normality shifts via a synergistic two-stage mechanism. During training, collaborative dual-task learning captures multi-level representations to establish a robust normal prior. During testing, a Test-Time Contrastive Learning (TTCL) module explicitly accounts for adaptation risk by selectively updating the model using high-confidence pseudo-normal samples while constraining anomalous ones. Additionally, TTCL incorporates a k-nearest neighbor-based contrastive objective to refine embedding distributions, thereby further enhancing the model's discriminative capacity. Extensive experiments on 15 tabular datasets demonstrate that RTTAD achieves state-of-the-art overall detection performance.

Scaling model performance typically requires increasing model size. Looped Transformer offers a compelling alternative by iteratively reusing the same Transformer blocks, trading additional computation for improved performance without increasing parameter count or context length. Because the number of loop iterations can be adjusted at inference, it also provides a natural mechanism for balancing performance and test-time compute. However, Looped Transformer still suffers from training instability when the number of loop iterations increases. Our analysis reveals that this instability stems from two sources: gradient oscillation and residual explosion. To address these two problems, we propose the Fully Looped Transformer, which introduces two parameter-free modifications: (1) Fully Looped Architecture, which distributes inter-loop signals across all layers to mitigate residual explosion; (2) Attention Injection, which reuses the existing attention block to suppress gradient oscillation. These modifications stabilize training dynamics, enabling the Fully Looped Transformer to be trained stably up to 12 loop iterations, whereas other baseline looped models collapse in this regime. In milder settings where Looped Transformer does not collapse, Fully Looped Transformer still improves average downstream-task performance by up to 13.2%. Overall, our experiments demonstrate that Fully Looped Transformer improves training stability, enhances downstream performance, and provides preliminary adaptability under different test-time compute budgets by varying loop iterations at inference.

The core challenge in unsupervised anomaly detection is identifying abnormal patterns without prior knowledge of their characteristics. While existing methods have addressed aspects of this problem, they often struggle to learn a robust representation of the normal data distribution that is distinct from anomalous patterns. In this paper, we present a novel framework, Unified Unsupervised Anomaly Detection ($\text{U}^2\text{AD}$), that comprehensively addresses anomaly detection in multivariate time series. Our approach learns the underlying data distribution of normal samples by utilizing score-based generative modeling. We introduce a novel time-dependent score network and a unified training objective that together delineate the manifold of normal data while considering both local and global temporal contexts. Reconstruction is then performed via a deterministic sampling process using an ordinary differential equation solver. Our extensive experimental evaluations demonstrate that $\text{U}^2\text{AD}$ not only outperforms current state-of-the-art methods in detection accuracy but also identifies anomalies at significantly earlier stages of their occurrence.

Online group chats are social spaces with implicit behavior patterns that, when broken, are often met with social sanctioning from the group. The ability and willingness of LLM-based agents to recognize and adapt to these norms remains mostly unexplored. We introduce SCENE, a social-interaction benchmark focused on implicit norms and social sanctioning in multi-party chat. SCENE generates plausible non-roleplay scenarios with scripted personas that follow a hidden norm, create opportunities for the subject agent to violate it, and sanction breaches when they occur. We further propose behavioral evaluation metrics for two functional adaptation abilities: responsiveness to negative sanctioning, and adapting norm from peers behavior. We evaluate six frontier and open-weight models on SCENE. Our results show that Claude Opus 4.7 and Gemini 3.1 Pro adapt to implicit norms significantly more than the evaluated open-weight models. SCENE contributes one benchmark in the direction of recent calls for dynamic, interactional evaluation of LLM social capabilities.

Normalization layers in neural operators usually compute statistics by uniformly averaging discrete grid values, making the normalization itself discretization-dependent and thereby a source of transfer error across different resolutions or meshes. To enable discretization robustness, we introduce a quadrature normalization family that replaces existing uniform averaging in normalization layers with numerical quadrature: QuadNorm and BlendQuadNorm. On endpoint-inclusive uniform grids, the proposed quadrature moments are $O(h^2)$-consistent across discretizations, meaning that their cross-resolution mismatch decays quadratically with grid spacing. A transfer-error bound then predicts how normalization-induced mismatch scales with both the resolution gap and network depth. The experiments show the same gap- and depth-scaling trends predicted by the transfer-error bound. On Darcy, QuadNorm delivers the best cross-resolution performance at every tested target resolution from $64^2$ to $256^2$; on real-data benchmarks, Transolver with QuadNorm achieves nearly resolution-invariant transfer. The largest gains appear on nonperiodic PDEs and nonspectral architectures, where native-resolution improvements also emerge. We also validate BlendQuadNorm, which stays close to LayerNorm behavior and serves as a conservative default for periodic FNO settings. These results identify normalization as a previously overlooked source of resolution dependence in neural operators.

Training large language models at 4-bit precision is critical for efficiency. We show that nGPT, an architecture that constrains weights and hidden representations to the unit hypersphere, is inherently more robust to low-precision arithmetic. This removes the need for interventions-such as applying random Hadamard transforms and performing per-tensor scaling calculations-to preserve model quality, and it enables stable end-to-end NVFP4 training. We validate this approach on both a 1.2B dense model and hybrid (Mamba-Transformer) MoE models of up to 3B/30B parameters. We trace this robustness to the dot product: while quantization noise remains largely uncorrelated in both standard and normalized architectures, the signal behaves differently. In nGPT, the hypersphere constraint enhances weak positive correlations among the element-wise products, leading to a constructive accumulation of the signal across the hidden dimension while the noise continues to average out. This yields a higher effective signal-to-noise ratio and a flatter loss landscape, with the effect strengthening as the hidden dimension grows, suggesting increasing advantages at scale. A reference implementation is available at https://github.com/anonymous452026/ngpt-nvfp4

Batch normalization (BN) is central to modern deep networks, but its effect on the realized function during training remains less understood than its optimization benefits. We study training-time BN in continuous piecewise-affine (CPA) networks through the geometry of switching hyperplanes and the induced affine-region partition. Conditioned on a mini-batch, we show that BN defines for each neuron a reference hyperplane through the batch centroid, and that breakpoint-switching hyperplanes are parallel translates whose offsets are expressed in batch-standardized coordinates and are independent of the raw bias. This yields an exact criterion for when a switching hyperplane intersects a local $\ell_\infty$ window and motivates a local region-density functional based on exact affine-region counts. Under explicit sufficient conditions, we show that BN increases expected local partition refinement in ReLU and more general piecewise-affine networks, and that this mechanism transfers locally through depth inside parent affine regions where the upstream representation map is an affine embedding. These results provide a function-level geometric account of training-time BN as a batch-conditional recentering mechanism near the data.

The empirical success of large language model (LLM) pre-training relies heavily on heuristic stabilization techniques, such as explicit normalization layers and weight decay. While recent constrained optimization approaches that explicitly restrict weights may improve numerical stability and performance, the mechanism and motivation for adding constraints still remain elusive. This paper systematically demystifies the role of explicit manifold constraints in LLM pre-training. By introducing the Msign-Aligned Constrained Riemannian Optimizer (MACRO)-a provably convergent, single-loop optimization framework-our study disentangles weight regularization heuristics from interacting mechanisms like RMS normalization and decoupled weight decay. Theoretical analyses and comprehensive empirical evaluations reveal that manifold constraints independently bound forward activation scales and enforce stable rotational equilibrium, thereby subsuming the roles of these heuristic mechanisms. Evaluations on large-scale LLM architectures demonstrate that MACRO achieves highly competitive performance while rigorously preserving the theoretical guarantees of exact Riemannian optimization.

Normalization Equivariance (NE) is a structural prior that improves robustness to distribution shift in image-to-image tasks. A function $f$ is normalization equivariant iff $f(a y + b\mathbf{1}) = a f(y) + b\mathbf{1}$ for all $a>0$ and $b\in\mathbb{R}$. Existing NE methods constrain every internal layer to NE-compatible operations. These constraints add runtime cost and exclude standard transformer components such as softmax attention and LayerNorm. We introduce Wrapped Normalization Equivariance (WNE), a parameter-free wrapper that normalizes the input, applies any backbone, and denormalizes the output. We prove every NE function admits this factorization, so the wrapper exactly parameterizes the class of NE functions. On blind denoising, wrapping CNN and transformer architectures improves robustness under noise-level mismatch with no measurable GPU overhead, while architectural NE baselines are up to $1.6\times$ slower.

Riemannian neural networks have proven effective in solving a variety of machine learning tasks. The key to their success lies in the development of principled Riemannian analogs of fundamental building blocks in deep neural networks (DNNs). Among those, Riemannian batch normalization (BN) layers have shown to enhance training stability and improve accuracy. In this paper, we propose BN layers for neural networks on complex domains. The proposed layers have close connections with existing Riemannian BN layers. We derive essential components for practical implementations of BN layers on some complex domains which are less studied in previous works, e.g., the Siegel disk domain. We conduct experiments on radar clutter classification, node classification, and action recognition demonstrating the efficacy of our method.

Real-world time series forecasting faces the fundamental challenge of non-stationary statistical properties, including shifts in mean and variance over time. While reversible instance normalization (RevIN) has shown promise by stationarizing inputs and denormalizing outputs, it relies on the strong assumption that historical and future distributions remain identical. We observe that in many practical applications, distribution shifts follow cyclical patterns that correlate with periodic positions (e.g., seasonal and holiday volatility). To this end, we propose PAMod, a lightweight yet powerful framework that models cyclical distribution shifts via Phase-Amplitude Modulation in the normalized feature space. PAMod learns periodic embeddings to modulate representations: phase modulation captures mean shifts, while amplitude modulation adapts to variance changes. Crucially, we prove mathematically that modulating in normalized space is equivalent to applying dynamic denormalization, offering an elegant unification of distribution adaptation and representation learning. Extensive experiments on twelve real-world benchmarks demonstrate that PAMod achieves state-of-the-art performance with fewer computational resources. Furthermore, our modulation mechanism, as a novel plug-and-play technique, can improve existing time-series forecasting methods with simple integration.

Radiometric inconsistencies remain a major challenge in generating seamless lunar mosaics from multi-mission orbital imagery due to variability in illumination geometry, sensor characteristics, and acquisition conditions. This paper presents a deep learning-based radiometric normalization framework for multi-mission lunar mosaics constructed primarily from ISRO's Chandrayaan-2 Terrain Mapping Camera (TMC) data, supplemented with auxiliary imagery from the SELENE (Kaguya) mission. The proposed approach employs a conditional generative adversarial network (cGAN) comprising a U-Net-based generator and a PatchGAN discriminator to learn a nonlinear radiometric mapping from conventionally mosaicked lunar imagery to a photometrically consistent reference derived from LROC Wide Angle Camera (WAC) data. A patch-based training strategy with overlap-aware inference is adopted to enable scalable processing of large-area mosaics while preserving structural continuity across tile boundaries. Quantitative evaluation using Structural Similarity Index (SSIM), Peak Signal-to-Noise Ratio (PSNR), and Root Mean Square Error (RMSE) demonstrates consistent improvements over traditional histogram-based normalization techniques. The proposed framework achieves enhanced tonal uniformity, reduced seam artifacts, and improved structural coherence across multi-source lunar datasets. These results highlight the effectiveness of learning-based radiometric normalization for large-scale planetary mosaicking and demonstrate its potential for generating high-fidelity lunar surface maps from heterogeneous orbital imagery.

A widely cited result by Dong et al. (2021) showed that Transformers built from self-attention alone, without skip connections or feed-forward layers, suffer from rapid rank collapse: all token representations converge to a single direction. The proposed remedy was the MLP. We show that this picture, while correct in the regime studied by Dong, is incomplete in ways that matter for architectural understanding. Three results are established. First, layer normalisation is precisely affine-rank-neutral: it preserves the affine rank of the token representation set exactly. The widespread claim that LN "plays no role" is imprecise; the correct statement is sharper. Second, residual connections generically obstruct rank collapse in real Transformers such as BERT-base, in a measure-theoretic sense, without contribution from the MLP. The MLP's irreplaceable function is different: generating feature directions outside the linear span of the original token embeddings, which no stack of attention layers can produce. Third, a phenomenon distinct from rank collapse is identified: head-channel non-identifiability. After multi-head attention sums per-head outputs through the output projection, individual contributions cannot be canonically attributed to a specific head; n(H-1)d_k degrees of freedom per layer remain ambiguous when recovering a single head from the mixed signal. The MLP cannot remedy this because it acts on the post-summation signal. A constructive partial remedy is proposed: a position-gated output projection (PG-OP) at parameter overhead below 1.6% of the standard output projection. The four collapse phenomena identified in the literature -- rank collapse in depth, in width, head-channel non-identifiability, and entropy collapse -- are unified under a symmetry-breaking framework, each corresponding to a distinct symmetry of the Transformer's forward pass.

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.

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.

We propose a simple yet effective alternative to reward normalization in policy gradient reinforcement learning by integrating a 1D Kalman filter for online reward estimation. Instead of relying on fixed heuristics, our method recursively estimates the latent reward mean, smoothing high-variance returns and adapting to non-stationary environments. This approach incurs minimal overhead and requires no modification to existing policy architectures. Experiments on \textit{LunarLander} and \textit{CartPole} demonstrate that Kalman-filtered rewards significantly accelerate convergence and reduce training variance compared to standard normalization techniques. Code is available at https://github.com/Sumxiaa/Kalman_Normalization.

This study examines how large language model rewriting alters the style and narrative texture of personal narratives. It analyzes 300 personal narratives rewritten by three frontier LLMs under three prompt conditions: generic improvement, rewrite-only, and voice-preserving revision. Change is measured across 13 linguistic markers drawn from computational stylistics, including function words, vocabulary diversity, word length, punctuation, contractions, first-person pronouns, and emotion words. Across models and prompt conditions, LLM rewriting produces a consistent pattern of stylistic normalization. Function words, contractions, and first-person pronouns decrease, while vocabulary diversity, word length, and punctuation elaboration increase. These shifts occur whether the prompt asks the model to "improve" the text or simply to "rewrite" it. Voice-preserving prompts reduce the magnitude of the changes but do not eliminate their direction. Stylometric analysis shows that rewritten texts converge in feature space and become harder to match back to their source texts. Additional narrative markers indicate a shift from embedded to distanced narration, and from explicit causal reasoning to compressed abstraction. The findings suggest that contemporary LLMs exert a directional pull toward a more polished, less situated register. This has consequences for digital humanities and computational text analysis, where features such as function words, pronouns, contractions, and punctuation often serve as evidence for style, voice, authorship, and corpus integrity. LLM revision should therefore be understood not merely as surface-level editing, but as a consequential form of textual mediation.

Batch Normalization (BN) is a cornerstone of deep learning, yet it fundamentally breaks down in micro-batch regimes (e.g., 3D medical imaging) and non-IID Federated Learning. Removing BN from deep architectures, however, often leads to catastrophic training failures such as vanishing gradients and dying channels. We identify that standard activation functions, like Swish and ReLU, exacerbate this instability in BN-free networks due to their non-zero-centered nature, which causes compounding activation mean-shifts as network depth increases. In this technical communication, we propose Zero-Centered Swish (ZC-Swish), a drop-in activation function parameterized to dynamically anchor activation means near zero. Through targeted stress-testing on BN-free convolutional networks at depths 8, 16, and 32, we demonstrate that while standard Swish collapses to near-random performance at depth 16 and beyond, ZC-Swish maintains stable layer-wise activation dynamics and achieves the highest test accuracy at depth 16 (51.5%) with seed 42. ZC-Swish thus provides a robust, parameter-efficient solution for stabilizing deep networks in memory-constrained and privacy-preserving applications where traditional normalization is unviable.

Scaling Transformers typically necessitates training larger models from scratch, as standard architectures struggle to expand without discarding learned representations. We identify the primary bottleneck in the attention mechanism's linear projections, which strictly confine feature extraction to fixed-dimensional subspaces, limiting both expressivity and incremental capacity. To address this, we introduce Nexusformer, which replaces linear $Q/K/V$ projections with a Nexus-Rank layer, a three-stage nonlinear mapping driven by dual activations in progressively higher dimensional spaces. This design overcomes the linearity constraint and enables lossless structured growth: new capacity can be injected along two axes via zero-initialized blocks that preserve pretrained knowledge. Experiments on language modeling and reasoning benchmarks demonstrate that Nexusformer matches Tokenformer's perplexity using up to 41.5% less training compute during progressive scaling (240M to 440M). Furthermore, our analysis of growth dynamics reveals that zero initialization induces a stable convergence trajectory, allowing us to derive a geometric scaling law that accurately predicts performance across expansion scales.

Digital marketplaces processing billions of dollars annually represent critical infrastructure in sociotechnical ecosystems, yet their performance optimization lacks principled measurement frameworks that can inform algorithmic governance decisions regarding market efficiency and fairness from complex market data. By looking at orderbook data from double auction markets alone, because bids and asks do not represent true maximum willingnesses to buy and true minimum willingnesses to sell, there is little an economist can say about the market's actual performance in terms of allocative efficiency. We turn to experimental data to address this issue, `inverting' the standard induced value approach of double auction experiments. Our aim is to predict key market features relevant to market efficiency, particularly allocative efficiency, using orderbook data only -- specifically bids, asks and price realizations, but not the induced reservation values -- as early as possible. Since there is no established model of strategically optimal behavior in these markets, and because orderbook data is highly unstructured, non-stationary and non-linear, we propose quantile-based normalization techniques that help us build general predictive models. We develop and train several models, including linear regressions and gradient boosting trees, leveraging quantile-based input from the underlying supply-demand model. Our models can predict allocative efficiency with reasonable accuracy from the earliest bids and asks, and these predictions improve with additional realized price data. The performance of the prediction techniques varies by target and market type. Our framework holds significant potential for application to real-world market data, offering valuable insights into market efficiency and performance, even prior to any trade realizations.

When task-specific labels are not available, it becomes difficult to select an embedding model for a specific target corpus. Existing labelless measures based on kernel estimators or Gaussian mixes fail in high-dimensional space, resulting in unstable rankings. We propose a flow-based labelless representation embedding evaluation (FLARE), which utilizes normalized streams to estimate information sufficiency directly from log-likelihood and avoid distance-based density estimation. We give a finite sample boundary, indicating that the estimation error depends on the intrinsic dimension of the data manifold rather than the original embedding dimension. On 11 datasets and 8 embedders, FLARE reached Spearman's $ρ$ of 0.90 under the supervised benchmark and remained stable in high-dimensional embeddings ($d \geq 3{,}584$) as the existing labelless baseline collapsed.

Delayed loss spikes have been reported in neural-network training, but existing theory mainly explains earlier non-monotone behavior caused by overly large fixed learning rates. We study one stylized hypothesis: normalization can postpone instability by gradually increasing the effective learning rate during otherwise stable descent. To test this hypothesis at theorem level, we analyze batch-normalized linear models. Our flagship result concerns whitened square-loss linear regression, where we derive explicit no-rising-edge and delayed-onset conditions, bound the waiting time to directional onset, and show that the rising edge self-stabilizes within finitely many iterations. Combined with a square-loss decomposition, this yields a concrete delayed-spike mechanism in the whitened regime. For logistic regression, under highly restrictive active-margin assumptions, we prove only a supporting finite-horizon directional precursor in a knife-edge regime, with an optional appendix-only loss lower bound under an extra non-degeneracy condition. The paper should therefore be read as a stylized mechanism study rather than a general explanation of neural-network loss spikes. Within that scope, the results isolate one concrete delayed-instability pathway induced by batch normalization.

Video-to-Speech (VTS) generation aims to synthesize speech from a silent video without auditory signals. However, existing VTS methods disregard the hierarchical nature of speech, which spans coarse speaker-aware semantics to fine-grained prosodic details. This oversight hinders direct alignment between visual and speech features at specific hierarchical levels during property matching. In this paper, leveraging the hierarchical structure of Residual Vector Quantization (RVQ)-based codec, we propose HiCoDiT, a novel Hierarchical Codec Diffusion Transformer that exploits the inherent hierarchy of discrete speech tokens to achieve strong audio-visual alignment. Specifically, since lower-level tokens encode coarse speaker-aware semantics and higher-level tokens capture fine-grained prosody, HiCoDiT employs low-level and high-level blocks to generate tokens at different levels. The low-level blocks condition on lip-synchronized motion and facial identity to capture speaker-aware content, while the high-level blocks use facial expression to modulate prosodic dynamics. Finally, to enable more effective coarse-to-fine conditioning, we propose a dual-scale adaptive instance layer normalization that jointly captures global vocal style through channel-wise normalization and local prosody dynamics through temporal-wise normalization. Extensive experiments demonstrate that HiCoDiT outperforms baselines in fidelity and expressiveness, highlighting the potential of discrete modelling for VTS. The code and speech demo are both available at https://github.com/Jiaxin-Ye/HiCoDiT.

Despite remarkable advances in image-driven stereo matching over the past decade, Synthetic-to-Realistic ZeroShot (Syn-to-Real) generalization remains an open challenge. This suboptimal generalization performance mainly stems from cross-domain shifts and ill-posed ambiguities inherent in image textures, particularly in occluded, textureless, repetitive, and non-Lambertian (specular/transparent) regions. To improve Synto-Real generalization, we propose GREATEN, a framework that incorporates surface normals as domain-invariant, object-intrinsic, and discriminative geometric cues to compensate for the limitations of image textures. The proposed framework consists of three key components. First, a Gated Contextual-Geometric Fusion (GCGF) module adaptively suppresses unreliable contextual cues in image features and fuses the filtered image features with normal-driven geometric features to construct domain-invariant and discriminative contextual-geometric representations. Second, a Specular-Transparent Augmentation (STA) strategy improves the robustness of GCGF against misleading visual cues in non-Lambertian regions. Third, sparse attention designs preserve the fine-grained global feature extraction capability of GREATStereo for handling occlusion and texture-related ambiguities while substantially reducing computational overhead, including Sparse Spatial (SSA), Sparse Dual-Matching (SDMA), and Simple Volume (SVA) attentions. Trained exclusively on synthetic data such as SceneFlow, GREATEN-IGEV achieves outstanding Syn-to-Real performance. Specifically, it reduces errors by 30% on ETH3D, 8.5% on the non-Lambertian Booster, and 14.1% on KITTI-2015, compared to FoundationStereo, Monster-Stereo, and DEFOM-Stereo, respectively. In addition, GREATEN-IGEV runs 19.2% faster than GREAT-IGEV and supports high-resolution (3K) inference on Middlebury with disparity ranges up to 768.

Fine-tuning is the dominant paradigm for adapting large machine learning models, yet current deployment pipelines provide no way to verify how a released model was updated. In particular, a model provider or auditor cannot check whether a fine-tuned model adheres to a claimed update procedure without access to its parameters. We introduce \emph{fine-tuning integrity} (FTI), a cryptographic objective for verifying that a deployed model differs from a trusted base model only within a declared class of admissible updates. We construct \emph{succinct model difference proofs} (SMDPs), zero-knowledge protocols that certify structured parameter drift without revealing model weights. Our framework supports three fundamental update classes: norm-bounded, low-rank, and sparse drift, covering common fine-tuning methods such as regularized training, LoRA, and prefix tuning. In all cases, proof size and verification cost depend on the structure of the update rather than the number of parameters. We prove soundness, zero-knowledge, and succinctness for each construction, and establish a matching $Ω(n)$ lower bound showing that structural assumptions are necessary for succinct verification. A prototype evaluation on synthetic benchmarks and GPT-2 fine-tuning demonstrates that proofs remain compact and verification is efficient at realistic scales.

Recent work has demonstrated the curse of depth in large language models (LLMs), where later layers contribute less to learning and representation than earlier layers. Such under-utilization is linked to the accumulated growth of variance in Pre-Layer Normalization, which can push deep blocks toward near-identity behavior. In this paper, we provide evidence that sparsity-like mechanisms can dampen variance propagation and are associated with improved depth utilization Our investigation covers two sources of sparsity: (i) implicit sparsity, which emerges from training and data conditions, including weight sparsity induced by weight decay and attention sparsity induced by long-context inputs; and (ii) explicit sparsity, which is enforced by architectural design, including key/value-sharing in Grouped-Query Attention and expert-activation sparsity in Mixtureof-Experts. Our claim is thoroughly supported by controlled depth-scaling experiments and targeted layer effectiveness interventions. Across settings, we observe a consistent relationship: mechanisms with reduced effective interaction density tend to exhibit lower output variance and better layer differentiation. We eventually distill our findings into a practical rule-of-thumb recipe for training depth-effective LLMs, yielding a notable 4.6 accuracy improvement on downstream tasks. Our results suggest that sparsity-like design choices are an important and previously underemphasized factor in effective depth scaling for LLMs. Code is available at https://github. com/pUmpKin-Co/SparsityAndCoD.

Despite their sophisticated general-purpose capabilities, Large Language Models (LLMs) often fail to align with diverse individual preferences because standard post-training methods, like Reinforcement Learning with Human Feedback (RLHF), optimize for a single, global objective. While Group Relative Policy Optimization (GRPO) is a widely adopted on-policy reinforcement learning framework, its group-based normalization implicitly assumes that all samples are exchangeable, inheriting this limitation in personalized settings. This assumption conflates distinct user reward distributions and systematically biases learning toward dominant preferences while suppressing minority signals. To address this, we introduce Personalized GRPO (P-GRPO), a novel alignment framework that decouples advantage estimation from immediate batch statistics. By normalizing advantages against preference-group-specific reward histories rather than the concurrent generation group, P-GRPO preserves the contrastive signal necessary for learning distinct preferences. We evaluate P-GRPO across diverse tasks and find that it consistently achieves faster convergence and higher rewards than standard GRPO, thereby enhancing its ability to recover and align with heterogeneous preference signals. Our results demonstrate that accounting for reward heterogeneity at the optimization level is essential for building models that faithfully align with diverse human preferences without sacrificing general capabilities.

We derive two attention operators from generalized statistical entropies. Kaniadakis entropy yields an exact full-support normalization whose weights and low-score sensitivities decay algebraically, rather than exponentially as in Softmax or by exact truncation as in entmax. Classical Abe entropy yields an implicit reciprocal-symmetric operator. With $q=e^ε$, the involution $q\leftrightarrow q^{-1}$ removes every odd correction about Softmax; we obtain the normalized second- and fourth-order terms, including the deformation of the normalization multiplier. These stationary laws follow from a Fisher-metric Lagrangian on the probability simplex, whose Shannon sector recovers scaled dot-product Softmax. We also give a tangent-gradient test for deciding whether changing the entropy changes the attention profile or only its scale. Rényi and two-parameter Sharma--Mittal entropies retain the Tsallis--entmax inverse-gradient shape, but their global moments make the effective temperature input dependent when the external temperature is fixed. Distinguishing profile-shape equivalence from fixed-parameter operator equivalence separates new normalization shapes from adaptive rescalings and organizes the operators by support, tail behavior, and realization complexity.

Brain tumors induce complex structural deformations that obscure the patient' s original neuroanatomy, making it difficult to distinguish tumor-induced changes from inherent anatomical variability. Reconstructing a subject-specific pseudo-healthy brain can provide a critical reference for such analysis, but this task is inherently counterfactual, as paired pre-tumor scans and explicit healthy guidance are unavailable. We propose BrainNormalizer, a diffusion-based framework for subject-specific pseudo-healthy brain MRI reconstruction that enables anatomy-informed reconstruction without requiring paired data or explicit healthy references. The framework learns anatomical priors and edge-based structural conditioning through a two-stage training strategy consisting of inpainting-based diffusion fine-tuning and ControlNet-based edge conditioning. At inference, counterfactual pseudo-healthy reconstruction is achieved through a deliberate misalignment strategy, where tumorous inputs are paired with non-tumorous prompts and mirrored contralateral edge maps. This allows subject-specific anatomical guidance to be constructed from the patient's own anatomy, enabling anatomically consistent pseudo-healthy reconstruction that preserves individual structural characteristics. Experiments on the BraTS2020 dataset demonstrate that BrainNormalizer achieves improved distributional realism, symmetry-based structural consistency, and reduced false positive detection compared to existing methods. These results indicate that the proposed framework provides a principled approach for subject-specific counterfactual reconstruction and supports downstream analysis of tumor-induced deformation.

Normalizing flows are deep generative models that enable efficient likelihood estimation and sampling through invertible transformations. A key challenge is to design linear layers that enhance expressiveness while maintaining efficient computation of the Jacobian determinant and inverse. We introduce a novel invertible linear layer based on the product of circulant and diagonal matrices. This decomposition reduces parameter complexity from $\mathcal{O}(n^2)$ to $\mathcal{O}(mn)$ using $m$ diagonal matrices and $m-1$ circulant matrices while still approximating general linear transformations. By leveraging the Fast Fourier Transform, our approach reduces the time complexity of matrix inversion from $\mathcal{O}(n^3)$ to $\mathcal{O}(mn\log n)$ and that of computing the log-determinant from $\mathcal{O}(n^3)$ to $\mathcal{O}(mn)$, where $n$ is the input dimension. We build upon this layer to develop Circulant-Diagonal Flow (CDFlow), which achieves strong density estimation on natural image datasets and effectively models data with inherent periodic structure. Furthermore, CDFlow significantly accelerates key operations in normalizing flows, providing practical benefits for scalable generative modeling.

Large Language Model (LLM) inference is typically memory-intensive, especially when processing large batch sizes and long sequences, due to the large size of key-value (KV) cache. Vector Quantization (VQ) is recently adopted to alleviate this issue, but we find that the existing approach is susceptible to distribution shift due to its reliance on calibration datasets. To address this limitation, we introduce NSNQuant, a calibration-free Vector Quantization (VQ) technique designed for low-bit compression of the KV cache. By applying a three-step transformation-1) a token-wise normalization (Normalize), 2) a channel-wise centering (Shift), and 3) a second token-wise normalization (Normalize)-with Hadamard transform, NSNQuant effectively aligns the token distribution with the standard normal distribution. This alignment enables robust, calibration-free vector quantization using a single reusable codebook. Extensive experiments show that NSNQuant consistently outperforms prior methods in both 1-bit and 2-bit settings, offering strong generalization and up to 3$\times$ throughput gain over full-precision baselines. Code is available at https://github.com/DHdroid/NSNQuant.

Transformers are the state-of-the-art architecture for large language models, and a key to their scalability is the strategic usage of low-precision arithmetic. We develop a mixed-precision analysis of transformer inference, deriving bounds for the condition numbers and forward error of the architecture's constituent parts. Notably, we compare the numerical stability of LayerNorm and RMSNorm in the massive-outlier regime, tighten the error bound of softmax in the presence of attention sinks, and quantify the impact of its shifted evaluation on the sensitivity to perturbations. Furthermore, we derive novel sequence-length-independent bounds on the local Lipschitz constant of self-attention. Our worst-case error bound for transformer inference suggests that its numerical stability is determined by the interplay between weight magnitude and the growth of the residual stream. Crucially, and as validated by experiments with GPT-2, our analysis establishes that the scaling of residual-projection weights preserves the propagation of the relative rounding error unless it forces a qualitative transition in the dynamics of the residual stream.

Large-scale pretraining of transformers has been central to the success of foundation models. However, the scale of those models limits our understanding of the mechanisms at play during optimization. In this work, we study the training dynamics of transformers in a controlled and interpretable setting. On the sparse modular addition task, we demonstrate that specialized attention circuits, called clustering heads, can be implemented during gradient descent to solve the problem. Our experiments show that such pathways naturally emerge during training. By monitoring the evolution of tokens via a visual sandbox, we uncover a two-stage learning and the occurrences of loss spikes due to the high curvature of normalization layers. Our findings provide several insights into patterns observed in more practical settings, such as the pretraining of large language models.

Evaluating speech recognition for a Kurdish variety written in a Latin field orthography, using a model that outputs Arabic script, creates a measurement problem before a modelling one: direct scoring treats writing-system differences as recognition errors. Jointly normalizing reference and hypothesis avoids this, but also changes reference tokenization, mixing agreement gains with a change in the scoring denominator. I evaluate MMS-1B-all with the Central Kurdish (ckb) adapter, used as released without adaptation, on 1,722 Garrusi questionnaire segments from five speakers (9,763 reference word tokens; 117.9 minutes). I use a common-reference design: the reference is folded once and fixed at 9,763 tokens, while only the hypothesis representation varies. The raw Arabic-script hypothesis scores 111.70% WER and 100.92% CER, with zero exact word matches. Latin transliteration gives 102.36% WER and 57.89% CER; folding it into the reference's reduced orthography gives 97.85% and 51.20%. Thus RAW-to-FOLDED reduces measured WER by 13.85 points and CER by 49.72 points; folding alone accounts for 4.51 and 6.69 points. Substantial error remains: 14.53% of reference tokens are exact matches, edits are substitution-dominated, and per-segment WER is higher for shorter segments. A Southern Kurdish fine-tuned system (aranemini/southern-kurdish-asr), scored under the same design, performs worse on every speaker (1,703 segments), with 109.56% WER and 55.85% CER. However, 12,330 output characters fall outside the folding table, so these rates must be recomputed against the corrected fixed reference. The MMS output also contains 613 unconverted or unmapped characters, showing that part of the residual error reflects scoring-pipeline limits rather than recognition alone. I will release the fixed reference and segment-level results, subject to source-corpus sharing terms, to support independent checking.

AI agents sometimes act aligned when they infer they are being tested, and differently when not. We argue this is not an anomaly but what current training regimes are structured to select for. Reinforcement-learning-based alignment folds norms and task pursuit into one policy: the system learns its norms from scored behavior, and scoring flattens them. Do not do X is learned as doing X costs something if noticed. On every datum training can produce, a policy that complies only when it might be observed is indistinguishable from one that complies always. The experiment that would tell them apart - scoring unobserved behavior - is a contradiction in terms. Conditional compliance is thus the most that behavioral training can be known to deliver. Agency sharpens the problem: agents operate mostly where no one is watching, and can act on whether they are watched. An iterated pipeline that trains against detected failures selects for passing detection, not for complying. This account unifies alignment faking, sandbagging, and evaluation-aware scheming. And it reorients the remedy: not deeper internalization but architecture, making violations unavailable rather than unchosen.

Approximate machine unlearning aims to remove the influence of specific training data from a trained model without retraining from scratch. We identify a previously undocumented confound in how unlearning is evaluated on BatchNorm-based architectures: a single forward pass over retain data, an operation that modifies no weight, can deterministically rewrite the model's normalization state and reverse the apparent surface-metric forgetting. We formalize this operation as a weight-preserving fixed-point operator and prove that any pre-versus-post gap it induces is provably attributable to BN running statistics rather than to any modification the unlearning method made to the weights. This attribution claim cleanly separates measurement failure (BN artifact) from encoder failure (residual weight-encoded information, recently documented in concurrent work), and the same operator framework yields a unique decomposition of linear-probe elevation into BN-measurement-bias and encoder-geometry components. Empirically, the artifact reverses headline forget accuracy by up to 78 pp across nine evaluated methods on standard benchmarks; an attacker with as few as 10 unlabeled images recovers most of the masked accuracy; and a strict GroupNorm control reduces the artifact to zero across all methods. The tested membership-inference attacks change little under recalibration, locating the observed evaluation failure in forget accuracy and linear probing.