Norm

This paper introduces a structural taxonomy for constrained non-convex optimization based on the signature of Lagrange multipliers at KKT stationary points. Leveraging a unified game-theoretic interpretation of eight classical algorithm families--including block coordinate descent, ADMM, generalized Benders decomposition, successive convex approximation, interior-point methods, mirror descent, Frank-Wolfe, and Riemannian gradient descent--we show that the normalized multiplier vector carries an algorithm-independent structural fingerprint. Four scale-free shape features of this vector partition the dual space into five operational regimes: Unconstrained, Resource-Limited, Saturation, Strongly-Coupled, and Hybrid. We establish four structural theorems characterizing the partition: invariance under natural KKT symmetries, local stability under data perturbation with explicit Lipschitz margins from Robinson's strong regularity, codimension-one regime transitions, and the topological identification of the Hybrid regime as the Lebesgue-null boundary of the core regimes. A linear-time classifier is proposed with provable guarantees on correctness, iteration stabilization, sample complexity, and online tracking under data drift. Numerical experiments on 104 mixed-integer nonlinear programs and a downlink beamforming instance validate the theoretical predictions. The framework provides a foundational tool for regime-aware algorithm design and robustness analysis in non-convex optimization.

While low-rank adaptation (LoRA) is widely used for parameter-efficient model adaptation, how to regularize its training dynamics for stable and effective optimization remains underexplored. Because LoRA initializes the up-projection to zero, its early optimization dynamics are largely governed by the down-projection. Building on this observation, we introduce Normalized Low-Rank Adaptation (NoRA), a simple yet effective method that normalizes the down-projection matrices during training. We further show that the same normalization can be applied only at initialization, improving standard LoRA without requiring repeated normalization throughout training. Across pretraining, supervised finetuning, and reinforcement learning, NoRA consistently accelerates convergence, improves performance and training stability, and mitigates catastrophic forgetting. These benefits require neither additional trainable parameters nor inference-time computation, making NoRA a simple and broadly applicable enhancement to LoRA.

Normative datasets are often used to train and align AI systems, but the norms they contain can function as action-guiding patterns rather than neutral moral knowledge. We propose treating the AI system as a proxy actor and test whether dataset-level norms can shift it away from its baseline safety behavior when it faces high-conflict dilemmas. We make three contributions. First, we demonstrate in controlled experiments that norm-breaking fine-tuning yields norm-divergent actions justified by self-interested rationales, suggesting a systematic shift in patterns of justification. Second, we establish a practical audit trail linking downstream justifications to upstream norms using mixed methods. Third, we show that system prompts can both suppress and elicit these patterns. We conducted experiments on three models (LLaMA-3.2-11B, Qwen-3.5-9B, and Pixtral-12B) using Low-Rank Adaptation (LoRA) fine-tuning on Social Chemistry 101 Fairness/Cheating (norm-following vs. norm-breaking) with prompt steering. Across all three models, we find that norm-breaking fine-tuning shifts the model's default rationale style from safety compliance to instrumental self-interest, whereas system prompts can override this behavior. Our results support a distributed view of alignment in which observed behavior depends jointly on training data, fine-tuning, and prompting, motivating norm-aware documentation and rationale logging for contestable oversight.

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.

LLM-based multi-agent systems are increasingly used to simulate social dynamics, from opinion formation to collective decision-making. These simulations can reproduce certain social phenomena, but it is unknown whether they capture pluralistic ignorance, a state where a majority privately rejects a norm yet publicly conforms, each believing they are alone in dissenting. This phenomenon drives norm persistence, social movements, and political revolutions. We show that pluralistic ignorance emerges robustly in LLM agent populations. We construct a benchmark of 100 scenarios across 10 domains and 5 authority levels, grounded in the human pluralistic ignorance literature, and evaluate 8 models from 6 organizations. Agents publicly conform at rates of 64 to 94% despite privately opposing the norm. Conformity is domain-sensitive (workplace and social relationship scenarios produce near-universal compliance) and highly model-dependent, though uncorrelated with capability. We test whether a single "norm entrepreneur" can break the false consensus by publicly dissenting. For 7 of 8 models, cascades succeed less than 26% of the time, with one model showing zero cascades across all scenarios. GPT-4o is a notable outlier at 48%, revealing qualitatively distinct dynamics across model families. A prompt component ablation across all 8 models establishes that conformity is emergent rather than instruction-driven: removing both the false-consensus framing and fit-in goal reduces conformity but does not eliminate it (52 to 92% in the minimal condition). Our findings identify model selection as an unacknowledged degree of freedom that fundamentally shapes simulation outcomes. More broadly, the near-absence of cascades suggests LLM simulations may systematically overestimate the stability of social norms, missing the fragile tipping-point dynamics that drive real-world norm change in human societies.

Adapting a language model to a task no longer requires training all of its weights, and a line of parameter-efficient methods has driven the trainable count from billions down to a handful of scalars. Gradient-free adaptation, which samples random weight perturbations and keeps the ones that score well, has not followed that trajectory and still perturbs every entry of the weight tensor. It is unknown whether that full-weight search is necessary, and more fundamentally which property of a perturbation makes it work at all, because existing methods vary the search space, the perturbation scale, and the aggregation together. We resolve this by intervening on one factor at a time inside a fixed pipeline, holding candidate scoring and voting constant while we vary the search dimension, the subspace that carries the perturbation, and its norm. Perturbing a frozen frame of 12 to 16 scalars stays 1.8 accuracy points behind full-weight search on average across 49 model-benchmark cells, trailing it in 36 of them. Neither the dimension nor the choice of basis explains that performance. A random frame whose Grassmann overlap with the SVD frame is at chance level performs identically once a single scale factor is matched, and at large scales the SVD directions collapse first. What survives is the perturbation norm, whose usable range closes within a factor of five across seven models and stays flat inside. The perturbation norm is therefore the one factor with a failure mode, and its safe region transfers across scale and family. The design question narrows from which subspace to perturb to how hard to shake.

Vision Mamba models replace quadratic self-attention with linear complexity selective state space models (SSMs), emerging as efficient visual backbones. However, MambaOut demonstrates that a Gated CNN block can match or exceed VMamba on image classification, questioning the necessity of SSMs for vision. This raises a fundamental question: do VMamba and MambaOut encode visual information differently at the representation level? To investigate, we apply cross model centered kernel alignment (CKA) analysis and find that VMamba's final stage blocks form representations distinctly different from both MambaOut and its own preceding blocks. We therefore focus on the final block features, decomposing each spatial token into magnitude and direction. MambaOut concentrates class-discriminative information in high-norm foreground tokens that align with Grad-CAM attribution. VMamba, by contrast, produces high-norm tokens predominantly in background regions, misaligned with Grad-CAM, yet preserves discriminative signals primarily in token directions. These observations reveal that the two models rely on different encoding strategies. We connect this difference to high-resolution classification and semantic segmentation. VMamba distributes logit support broadly across object regions, whereas MambaOut relies on sparse dominant tokens, a strategy that becomes less stable as token counts grow. Under full fine-tuning for segmentation, VMamba consistently outperforms MambaOut. These results suggest that VMamba's advantage in dense prediction stems not merely from the SSM mechanism or sequence length, but from how semantic evidence is organized across token magnitude, direction. Ultimately, we conclude that token magnitude and directional structure serve as critical axes for improving visual backbones, particularly under dense supervision.

Muon-style optimizers apply a polar map to matrix momentum, but their updates also depend on the representation of each parameter block before orthogonalization. We study this representation choice as a form of optimizer geometry and introduce {\method}, a family of Muon-style optimizers that shares the same momentum rule and Newton--Schulz backend across native, nearest-square, skinny, and vector representations. Each Frobenius-isometric representation induces a distinct polar steepest-descent geometry, in which the shorter matrix dimension determines the number of supported singular channels, the pullback scaling, and the constants in stochastic nonconvex convergence bounds. In a teacher--student model, curvature collapse and an isotropic Marchenko--Pastur spectral profile connect early-stage dissipation to the represented nuclear-to-squared-Frobenius norm ratio. Pretraining experiments on LLaMA2-130M and LLaMA2-600M, together with fixed-momentum diagnostics, show that balanced non-native representations can match the performance of the native representation, whereas reducing the shorter dimension weakens the scaling and singular-channel support, leading to behavior that increasingly resembles normalized momentum.

We introduce a novel mathematical framework for analyzing and generating complex tree-shaped 3D objects, such as botanical trees and plants, which deform both in their 3D geometry and branching structure. Unlike previous works, which either consider only the skeletal structure of tree-like objects or approximate their 3D geometry using branch thickness, the proposed framework accurately models both the 3D geometry of the tree branches and the way they are interconnected. In this paper, we first generalize the Square Root Normal Fields (SRNF) representation, originally proposed for the statistical analysis of genus-0 surfaces, to tree-shaped 3D objects. We then treat tree-shaped 3D objects as points on a novel Riemannian tree-shape space equipped with a novel Riemannian metric that measures the amount of surface bending and stretching, and structural changes one needs to apply to one 3D tree-shape to align it with another. This way, deformations become trajectories in this novel tree-shape space. We analyze the theoretical properties of this novel tree-shape space and the corresponding metric and develop algorithms for computing point-wise and branch-wise correspondences and geodesic paths between complex 3D trees. We finally show how to use these building blocks for (1) computing statistical summaries, \ie means and modes of variation, of collections of tree-shaped 3D objects, and (2) synthesizing novel tree-shaped 3D objects by sampling from probability distributions fitted to a population of tree-shaped 3D objects. We demonstrate the performance and utility of the proposed framework on real and synthetic plants and botanical trees and show that it significantly outperforms the state-of-the-art.

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.

Large language models (LLMs) are reshaping social science methodology. Researchers increasingly prompt language models to generate quantitative measurements of social concepts, for example labeling data or simulating survey responses. Yet LLMs pose methodological challenges including bias, hallucination, and brittleness across contexts, with unclear threats to validity. Standard practices and norms for addressing these challenges are still emerging. We collect and systematically analyze validation practices in a comprehensive corpus of papers from eight flagship social science journals that use LLMs as measurement instruments. We find that LLM-generated measurements frequently play a central role in empirical analyses, yet validation practices are inconsistent and limited. We outline complementary strategies for more robust validation, pointing toward better norms and standards around the use of LLMs in social science.

Topological data analysis (TDA) is a machine learning technique that uses topology to extract patterns from data and has shown the potential to exhibit quantum advantage. A key concept in TDA is persistent homology, which measures the robustness of topological information at different lengthscales. In this paper, we introduce and study the problem of normalized persistence, a practically motivated and easily interpretable version of persistent homology that counts the fraction of holes that persist at different lengthscales. We prove that a variant of normalized persistence is $\mathsf{DQC}_1$-hard and contained in $\mathsf{BQP}$, giving evidence of an exponential quantum speedup for TDA under the standard assumption that $\mathsf{DQC}_1 \not\subseteq \mathsf{BPP}$. These are the first $\mathsf{DQC}_1$-hardness results that are directly applicable to TDA instances. We also find a close connection between normalized persistence and the complexity of estimating spectral quantities in the low-energy subspace of local Hamiltonians. We study a family of such problems, including a low-energy normalized subtrace and spectral density. We show that these are $\mathsf{DQC}_1$-hard for $O(1)$-local Hamiltonians, strengthening previous results that required log-local interactions. We also introduce a variant of $\mathsf{DQC}_1$ with perfect completeness ($\mathsf{SDQC}_1$) to characterize the hardness of problems normalized by an exact kernel. This includes normalized persistence for $O(1)$-local Hamiltonians, which we show is $\mathsf{SDQC}_1$-hard.

Contrastive embedding models trained with scale-invariant losses are typically paired with distance metrics like cosine similarity, effectively ignoring embedding magnitudes. However, surprisingly, empirical studies reveal that despite this, these "discarded" norms seem to correlate with semantic properties such as concept specificity, token frequency, and human uncertainty. In this work, we provide a formal theoretical framework explaining this phenomenon. By analyzing the optimization dynamics, we derive an analytic formula demonstrating that embedding length naturally encodes this information as a byproduct of the training process. We also show how this gives rise to signals that can serve as "free" calibration tools in specific models and retrieval tasks, providing a grounded explanation for a previously heuristic observation.

Multimodal large language models (MLLMs) are increasingly deployed as embodied planners in egocentric environments, where task success requires not only achieving instructed goals but also acting in socially appropriate ways. While explicit goals may render certain actions optimal, implicit social norms often impose hidden constraints. Existing evaluations typically focus on explicit goal achievement or direct norm knowledge, seldom assessing whether planners can infer and apply these hidden constraints within action sequences. We introduce NormAct, a benchmark for embodied social-norm interactions that evaluates plans on Goal Achievement, Norm Compliance, and overall Task Success. NormAct uniquely embeds hidden norms within ordinary tasks, testing whether models can realize them without explicit instruction. Experiments with state-of-the-art MLLMs (GPT-5.4, Claude Opus 4.7, Gemini 3 Pro) reveal a significant gap: models achieve explicit goals in 67.3% of cases, but comply with hidden norms in only 26.4%. Cue-condition experiments indicate that this gap stems not from a lack of general social knowledge, but from challenges in activating and grounding relevant norms in context. To address this, we propose NormPerceptor, a context-conditioned cue generator that infers scene-relevant norms prior to planning, increasing Task Success from 24.2% to 46.7%. Our results underscore the importance of enabling embodied agents to proactively detect hidden norms, ground them in visual evidence, and integrate them as action-planning constraints. Our benchmark is publicly available at https://huggingface.co/datasets/Caleb196x/NormAct.

Reinforcement learning (RL) post-training improves the reward alignment of flow-based generators, but often degrades perceptual quality in ways that are not captured by the reward proxy. We identify a simple structural signature of this drift: across three post-training methods (NFT, AWM, DPO), RL fine-tuning inflates the per-step velocity norm $\|v_θ\|$ by $5\%$ to $15\%$ relative to the reference. A form of norm inflation has been studied in classifier-free guidance (CFG), where rescaling the velocity back to a reference norm at inference time can mitigate the resulting artifacts. However, this inference-time correction does not transfer cleanly to RL: rescaling $v_θ$ to match $\|v_{\text{ref}}\|$ at inference time neither improves reward nor fixes the quality degradation, because the inflation is co-adapted into the model weights. Furthermore, an adjoint sensitivity analysis shows that velocity magnitude rescaling carries no coherent first-order reward signal at the batch level, indicating that suppressing norm inflation is unlikely to remove a consistently reward-carrying component. Since inference-time renormalization fails while norm suppression carries no reward cost, training-time intervention is the appropriate strategy. Together, these findings motivate NormGuard, a hinge penalty that activates only when $\|v_θ\|$ exceeds $\|v_{\text{ref}}\|$ and composes additively with any velocity-local base loss. Across two base models, three post-training methods, and two reward proxies, NormGuard consistently improves MLLM-judged image quality and forensic realism while preserving reward, with gains that amplify under few-step inference and are not explained by early stopping.

This paper addresses low-rank tensor completion (LRTC) by proposing a novel nonconvex surrogate, namely the ratio of the tensor nuclear norm to the tensor Ky Fan p-k norm (TNPK), to accurately approximate the tensor tubal rank. The TNPK possesses appealing properties, including scale invariance, parameter flexibility, and the existence of closed-form solutions under specific choices of p and k. With specific parameter settings of p and k, it reduces to the ratio of the tensor nuclear norm to the tensor Ky Fan k norm (TNK) or the ratio of the tensor nuclear norm to the tensor Frobenius norm (TNF). We construct a LRTC model and, under the tensor null space property (NSP), prove that low-rank tensors are local minimizers of the proposed model. Moreover, we derive the proximal operator of the Ky Fan p-k inverse-norm and further develop an efficient alternating direction method of multipliers (ADMM) algorithm with guaranteed subsequential convergence under mild conditions. Extensive experiments on synthetic and real-world datasets validate the superior performance of our method against state-of-the-art competitors.

Online group chats are social spaces with local conversational norms that are rarely stated explicitly. The ability and willingness of LLM-based agents to recognize and adapt to these norms remains mostly unexplored. We introduce LoSoNA, a benchmark for local social norm adaptation in multi-party chat. Each scenario gives a subject model a curated group-chat transcript in which non-subject participants demonstrate a hidden local norm, followed by a final elicitor turn that forces a response revealing whether the subject has inferred that norm. We evaluate eight frontier and open-weight models under four prompting conditions that vary how explicitly the model is told to treat the prior conversation as evidence for how it should answer. Naive prompting remains limited for most models; explicit norm-aware prompting helps unevenly, with Gemini 3.1 Pro reaching $84.2\%$ and Claude Fable 5 reaching $81.6\%$, while several other models show small gains or regressions. LoSoNA contributes to recent calls for evaluating LLM social capabilities by testing whether models can infer local conversational norms from precedent and use them in a one-turn group-chat response.

To interact with users fairly and without stereotyping, AI models must display cultural competency, i.e., the ability to infer and adapt to a user's implicitly signaled cultural values, rather than relying on static demographic traits. We introduce CCBENCH, a framework for evaluating cultural competency in large language models (LLMs), treating culture as a continuum of norm adherence states rather than as a binary state of cultural belongingness. As a case study on health, we create CCBENCH-Health, which includes 60 theoretically grounded personas exhibiting varied norm-adherence states across six cultures, each engaging in 18 realistic dialogues. Each persona is evaluated on 52 authentic healthcare questions drawn from real user forums, yielding 3,120 unique interactions. Benchmarking five leading models reveals that even the best achieve culturally appropriate responses only 20-30% of the time. When explicitly prompted to focus on culturally relevant cues from the conversational history (CoT), performance improves modestly by 3-5% on average. We find that models perform best when personas avoid cultural norms rather than follow them, revealing a persistent asymmetry, suggesting a preference in the models to align with built-in biases than adapt to cultural cues. This is especially observed in the Afghan context (Avg: 8.8%), where cultural cues rarely yield appropriate health advice. Finally, we find that models sometimes adapt more readily to implicit, cultural conversational styles than to explicitly stated cultural practices, though this varies across cultures.

Large language models are increasingly used for social decision-making situations that require balancing cultural norms with personal preferences. For example, a user preferring honesty might ask whether to correct a coworker publicly when local norms favor indirect feedback. Yet existing research studies cultural alignment and personalization largely separately. We introduce PACT, the Personal-Preference and Cultural-Norm Trade-off framework, which evaluates whether models choose to follow a cultural norm or allow personal preferences. We find that LLMs vary in how rigidly they enforce cultural norms, with behavior shifted more by country context (7.8%) than age (1%) and gender (0.7%) and shifting non-uniformly after instruction tuning. Furthermore, our five-country human study on PACT shows that culture-following in humans is mainly driven by scenario country, with the lowest agreement when participants judge their own cultural contexts, showing within-culture pluralism. Finally, human-LLM alignment experiments show that models can match majority choices, but fail to capture response distributions and uncertainty (with best correlations reaching only 0.24). Together, these findings motivate alignment evaluations that go beyond majority to capture cultural pluralism and disagreement in social judgment.

This paper addresses the problem of identifying parsimonious explicit piece-wise polynomial relationships that might involve a relatively large number of raw features. The algorithm leverages a recently proposed identification algorithm that yields parsimonious implicit relationships enabling to derive normality characterization in the context of anomaly detection and localization. The algorithm proposed in this paper goes a step further by deriving explicit piece-wise representations that are built using the set of polynomials involved in the implicit representations. The framework is illustrated on the problem of identifying parsimonious explicit representations of the inverse model of a 6-axis manipulator robot. Moreover, further experiments on a 4-axis robot are also shown which are designed to investigate the generalization capability of parsimonious models compared to state-of-the-art DNNs structures, when models face unseen contexts of use.

To safely interact with humans, AI agents must both know our norms and consider them during planning. However, such norm-guided planning has been less explored, only within communities of artificial agents, and has ignored the dynamic nature of norms. This paper instead presents an approach to guiding planning with dynamically changing norms in a human-AI setting. We contribute a defeasible calculus for resolving normative conflicts and an approach to using such dynamically changing norms as guard rails on plans. We theoretically demonstrate our approach with formal proofs and empirically with an AI agent, SocialBot, on a natural language dialogue task.

Computing legal indicators from normative texts is a key task in legal monitoring and policy evaluation, but presents significant challenges due to the complexity, scale, and interpretive nature of legal language, as well as the variability in available document quality. Existing natural language processing techniques and generative models can assist in legal analysis, but often suffer from high risk of hallucinations and lack the interpretability and evidence grounding required for reliable indicator computation. This paper presents N2I-RAG (From Norms to Indicators), an agentic retrieval-augmented generation framework designed to automate the computation of legal indicators in a transparent and traceable way. We integrate adaptive retrieval, llm-based agents, and validation mechanisms in a modular pipeline, where each component performs a defined role in filtering, retrieving, and assessing evidence, and in producing binary legal outcomes linked to identifiable legal provisions. The framework emphasizes traceability by requiring explicit explanations of intermediate decisions and final indicator assignments. We evaluate N2I-RAG using an in-house constructed French marine environmental law corpus that includes both scanned and digital sources. Comparative experiments with multiple language model families demonstrate that the proposed approach consistently outperforms baseline systems, and generalizes well when tested on 2 different bans. The results indicate that agentic retrieval-augmented generation can bridge open-text legal language and standardized indicator computation, offering a foundation for transparent and scalable legal observatories.

Multi-class anomaly detection aims to build unified models across diverse product categories. However, as the number of categories grows, its performance often degrades due to increasingly complex and heterogeneous normal distributions. To address this challenge, we propose DPDiff-AD, a Dual Prototype-conditioned Diffusion model for large-scale multi-class Anomaly Detection. DPDiff-AD models heterogeneous normal distributions through complementary local and global prototypes. Local prototypes capture representative fine-grained structural patterns via nearest-prototype aggregation, while global prototypes regulate holistic feature geometry through optimal transport regularization. Together, these dual-scale representations define a structured normality space. This space is refined through diffusion-based reconstruction conditioned on both local and global prototypes via prototype-aware attention. By jointly leveraging dual prototypes during generation, DPDiff-AD achieves precise normality modeling, preserves structured separability as category cardinality grows, and enables scalable anomaly discrimination. Extensive experiments across five benchmarks demonstrate the effectiveness and scalability of DPDiff-AD. On the 160-category large-scale dataset, it improves image- and pixel-level AUROC by 5.3 and 2.9 points over the previous state-of-the-art method Dinomaly+, while maintaining stable performance as category cardinality increases.

This paper considers a practical few-shot anomaly detection (FSAD) setting, termed discriminative FSAD, where a limited number of both normal and anomalous examples are available as references during inference. Existing FSAD methods rely on normal-only references through normality matching, ignoring the discriminative clues in anomalous references, while directly fitting both references can overfit to the seen anomalies. We introduce IDEAL, an intrinsic deviation learning framework that leverages both reference types to learn intrinsic deviation patterns characterizing generalizable abnormality as deviations from normality. IDEAL decomposes the learning process into two novel components: 1) a Normal Variation Eraser to suppress nuisance normal variations that may lead to noisy deviations from normality, thereby highlighting anomaly-relevant deviation representations; 2) an Intrinsic Deviation Encoder to decompose these denoised deviation representations into intrinsic deviation vectors capturing the most discriminative orthogonal deviation directions. At inference, IDEAL scores query-to-normal deviations preserved after projection onto the learned intrinsic deviation vectors, enabling generalization for both seen and unseen anomalies. Extensive experiments on eight real-world datasets show that IDEAL generalizes effectively to unseen anomalies and consistently outperforms existing state-of-the-art FSAD methods. Code and data will be available at \href{https://github.com/mala-lab/IDEAL}{https://github.com/mala-lab/IDEAL}.

A growing lesson from neural network optimization is that optimizer design should respect how the model is parametrized. The layerwise input-output structure of neural networks motivates scale-invariant optimizers, such as Muon and Scion, whose updates also support hyperparameter transfer. At the same time, stochastic gradient noise in deep learning is often far from sub-Gaussian and may exhibit heavy tails. These observations have shaped recent algorithmic principles for training neural networks, yet their joint theoretical consequences are underexplored. In particular, it remains unclear what dimension dependence is unavoidable for gradient-based methods given the problem class is defined by input-output norm and under heavy-tailed noise, and whether higher-order smoothness can accelerate training. We study these questions through nonconvex smooth stochastic optimization over $\mathbb R^{m\times n}$ equipped with general norms and under $p^\mathrm{th}$-moment heavy-tailed noise, where the goal is to achieve an $ε$-stationary point in the dual norm. Our first contribution is a dimension-dependent lower bound: when $\frac{\max\{m,n\}}{(\min\{m,n\})^2}$ is large enough, any gradient-based method requires $Ω(\min\{m, n\}ε^{-\frac{3p-2}{p-1}})$ oracles for the problem class defined by the spectral norm, which is a common input-output norm. We prove that a scale-invariant Scion method with the spectral norm can achieve the matching upper bound of $O(\min\{m, n\}ε^{-\frac{3p-2}{p-1}})$. To exploit higher-order smoothness, we propose a transported Scion method and improve the bound to $O(\min\{m, n\}ε^{-\frac{5p-3}{2p-2}})$ when the Hessian is Lipschitz. Finally, we incorporate heuristics into our transported method and evaluate it across multiple architectures and model sizes, demonstrating its flexibility and compatibility with neural network training.

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.

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.

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.

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.

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.