Daily Papers

Understanding why trained Transformers generalize well is a fundamental problem in modern machine learning theory, and complexity-based generalization bounds provide a principled way to study this question. While existing norm-based bounds for Transformers remove the explicit polynomial dependence on the hidden dimension, they typically impose fixed norm constraints specified a priori and can exhibit unfavorable exponential dependence on depth. In this paper, we derive spectrum-adaptive post hoc generalization bounds for multi-layer Transformers. Under layerwise spectral norm control, the bounds are expressed in terms of layerwise Schatten quantities of the query-key, value, and feedforward weight matrices. Since the Schatten indices need not be fixed a priori and can instead be selected after training, separately for each matrix type and layer, the bounds adaptively trade off spectral complexity against the dimension- and depth-dependent factors according to the learned singular-value profiles. Empirical comparisons of BERT-adapted proxies for the leading complexity factors suggest that the proxies induced by our bounds grow more slowly with depth and hidden dimension than the corresponding norm-based proxies. Overall, our results provide a complexity-based perspective on how the spectral structure of trained Transformers is reflected in generalization analyses.

We uncover ELR collapse in language model pretraining: learning rate (LR) and parameter norm govern loss dynamics primarily through their ratio, the effective learning rate (ELR). When ELR is matched across runs, their loss trajectories collapse throughout training despite substantially different LRs and parameter norms. Across optimizers, architectures, datasets, and model scales, mean collapse errors are typically a few x 10^-3, below the seed-to-seed variation measured in a representative configuration. Systematic ablations identify normalization design and the timescale of LR-norm variation as key determinants of collapse precision. Controlled interventions further show that weight decay and Hyperball shape loss dynamics primarily through the ELR schedules they induce. Replacing LR with ELR enables a fitted functional scaling law (FSL) to transfer across norm-control methods. The resulting ELR-based FSL also explains delayed acceleration, a recurring effect of norm control. Together, these results establish ELR as a common coordinate linking LR scheduling, norm control, and loss dynamics.

Is the standard weight decay in AdamW truly optimal? Although AdamW decouples weight decay from adaptive gradient scaling, a fundamental conflict remains: the Radial Tug-of-War. In deep learning, gradients tend to increase parameter norms to expand effective capacity while steering directions to learn features, whereas weight decay indiscriminately suppresses norm growth. This push--pull interaction induces radial oscillations, injecting noise into Adam's second-moment estimates and potentially degrading delicate tangential feature learning. We argue that magnitude and direction play distinct roles and should be decoupled in optimizer dynamics. We propose Orthogonal Dynamics Decoupling and instantiate it as AdamO: an SGD-style update handles the one-dimensional norm control, while Adam's adaptive preconditioning is confined to the tangential subspace. AdamO further incorporates curvature-adaptive radial step sizing and architecture-aware rules and projections for scale-invariant layers and low-dimensional parameters. Experiments on vision and language tasks show that AdamO improves generalization and stability over AdamW without introducing additional complex constraints.

The rank r in LoRA is widely treated as a capacity control: a smaller rank is assumed to yield a simpler model that generalizes better. We show that, under hard per-factor norm budgets---the idealization of the weight decay and norm control used in practice---this intuition breaks down. The reason is structural: under such budgets, the updates LoRA can reach are exactly the matrices of rank at most r inside a nuclear-norm ball, and every complexity and displacement functional we analyze is maximized over this set by a rank-one update---so the rank cap never binds. The consequences follow directly. The linear-readout model class we study is identical for every r ge 1, its Rademacher complexity carries no dependence on r, and the distance the adaptation can move the source distribution obeys a rank-independent upper bound that we show is sharp. If rank does not control capacity, where does it act? We identify two places. Statistically, replacing the per-factor budgets with a joint budget on the product restores a data-dependent, rank-sensitive complexity bound---though the gain appears only for well-spread feature distributions, and the worst case remains rank-free. Spectrally, rank sets the price of adaptation: canceling the leading singular directions of the pretrained weight requires both sufficient rank and sufficient budget. We bound the smallest rank achieving a desired source--target alignment, with upper and lower bounds that match under two-sided spectral decay. Together, these results recast rank as governing which updates are reachable and what cancellation costs---not how much capacity the model has.

Model editing has emerged as a practical approach for mitigating factual errors and outdated knowledge in large language models (LLMs). Among existing methods, the Locate-and-Edit (L&E) paradigm is the dominant framework: it locates MLP parameters implicated in expressing a target fact, and then performs a localized update to rewrite that fact. However, long sequences of edits often trigger abrupt model collapse in L&E beyond a critical point. We empirically identify a strong correlation between collapse and explosive growth of edited MLP weight norms, and formally prove that commonly used L&E update rules can induce exponential norm growth across sequential edits in the absence of explicit norm control. To address this issue, we propose Norm-Anchor Scaling NAS, a plug-and-play norm-constrained strategy. Across extensive experiments, NAS delays the collapse point of representative L&E algorithms by more than 4 times and yields a 72.2% average relative gain in editing performance, requiring only a single additional line of code and incurring negligible computational overhead.

This paper reinterprets the Synthetic Control (SC) framework through the lens of weighting philosophy, arguing that the contrast between traditional SC and Difference-in-Differences (DID) reflects two distinct modeling mindsets: sparse versus dense weighting schemes. Rather than viewing sparsity as inherently superior, we treat it as a modeling choice simple but potentially fragile. We propose an L-infinity-regularized SC method that combines the strengths of both approaches. Like DID, it employs a denser weighting scheme that distributes weights more evenly across control units, enhancing robustness and reducing overreliance on a few control units. Like traditional SC, it remains flexible and data-driven, increasing the likelihood of satisfying the parallel trends assumption while preserving interpretability. We develop an interior point algorithm for efficient computation, derive asymptotic theory under weak dependence, and demonstrate strong finite-sample performance through simulations and real-world applications.

Despite significant progress in alignment, large language models (LLMs) remain vulnerable to adversarial attacks that elicit harmful behaviors. Activation steering techniques offer a promising inference-time intervention approach, but existing methods suffer from critical limitations: activation addition requires careful coefficient tuning and is sensitive to layer-specific norm variations, while directional ablation provides only binary control. Recent work on Angular Steering introduces continuous control via rotation in a 2D subspace, but its practical implementation violates norm preservation, causing distribution shift and generation collapse, particularly in models below 7B parameters. We propose Selective Steering, which addresses these limitations through two key innovations: (1) a mathematically rigorous norm-preserving rotation formulation that maintains activation distribution integrity, and (2) discriminative layer selection that applies steering only where feature representations exhibit opposite-signed class alignment. Experiments across nine models demonstrate that Selective Steering achieves 5.5x higher attack success rates than prior methods while maintaining zero perplexity violations and approximately 100\% capability retention on standard benchmarks. Our approach provides a principled, efficient framework for controllable and stable LLM behavior modification. Code: https://github.com/knoveleng/steering

With a goal of understanding what drives generalization in deep networks, we consider several recently suggested explanations, including norm-based control, sharpness and robustness. We study how these measures can ensure generalization, highlighting the importance of scale normalization, and making a connection between sharpness and PAC-Bayes theory. We then investigate how well the measures explain different observed phenomena.

We study the parameter dependence and transversality properties of trajectories of the controlled ODE $ U_x = P, qquad P_x = - f(U) - βP + tilde α(x)U, arising from traveling-wave solutions of a bistable reaction-diffusion equation with control. Optimal profiles minimizing the L^1-norm of the control \tilde α are determined by the unstable and stable manifolds Γ_u, Γ_s, the critical curve P^*(U) = Uf(U), and the associated function F(U) = dP^*{dU} + f(U){P^*(U)}. We establish generic transversality properties for these objects with respect to perturbations of the speed β and the nonlinear source f, together with quantitative estimates on the first- and second-order dependence of the invariant manifolds on these parameters. We also analyze the loss of regularity at the critical speed β^{**}, where the unstable manifold approaches the strongly stable manifold of the equilibrium (U^*,0)$. These results provide the ODE ingredients used in the analysis of the structure and regularity of optimal profiles in paper [S. Bianchini and C. Trifone. Traveling profiles and control cost for a PDE describing the evolution of invasive species. 2026. arXiv: 2606.23979 [math.OC]].

Linear attention has emerged as a viable alternative to softmax attention by reducing complexity from quadratic to linear in sequence length. To preserve two fundamental properties of softmax, non-negativity and entropy reduction, current works employ various linearly separatable kernel functions with L1 normalization instead of softmax operator. However, query norms are neglected by the normalization operation in linear attention, such degradation heavily leads to an entropy gap. Meanwhile, existing works inhibit negative values of query and key vectors resulting in a missing inner-product interactions after being mapped. To address these dual challenges, we propose a novel Norm-Aware Linear Attention mechanism serving to restore norm-guided dynamic spikiness and recover kernel-perturbed norm distributions. Specifically, we first decouple query and key matrices into two components: norm and direction, to achieve norm-aware spikiness control and norm consistency, respectively. We mathematically reveal that the extent of entropy reduction varies with the query norm in softmax normalization, motivating a query-norm aware kernel function for dynamic control over entropy reduction. Furthermore, to ensure norm consistency and enforce non-negativity constraints, we employ a norm-preserving mapping to project all elements of the angular matrix into positive values, leveraging cosine similarity to inhibit dimensions with opposite directions. We conduct extensive experiments demonstrating that the NaLaFormer improves performance on vision and language tasks, enhancing both expressiveness and efficiency by up to 4.2\%.

Stability of neural network weights is critical when training transformer models. The query and key weights are particularly problematic, as they tend to grow large without any intervention. Applying normalization to queries and keys, known as `QK norm', fixes stability issues in practice, but is not always applicable. For example, QK norm is not compatible with Multi Latent Attention (MLA) because QK norm requires full materialization of queries and keys during inference, which is not done in MLA. In this paper we suggest that controlling the changes to logits is important for stability. We show that these changes are controllable by assigning parameter-dependent learning rates to the query and key weights. We find that our cheap intervention allows us to increase the base learning rate of the network, outperform other methods in the MLA setting, and achieve performance competitive with QK norm when using Multi-head Attention.

We analyze the state constrained inverse Stefan type parabolic free boundary problem as an optimal control problem in the Sobolev-Besov spaces framework. Boundary heat flux, density of heat sources, and free boundary are components of the control vector. Cost functional is the sum of the L_2-norm declinations of the temperature measurement at the final moment, the phase transition temperature, the final position of the free boundary, and the penalty term, taking into account the state constraint on the temperature. We prove the existence of optimal control, Frechet differentiability, and optimality condition in the Besov spaces under minimal regularity assumptions on the data. We pursue space-time discretization through finite differences and prove that the sequence of discrete optimal control problems converges to the original problem both with respect to functional and control.

We consider the inverse Stefan type free boundary problem, where information on the boundary heat flux and density of the sources are missing and must be found along with the temperature and the free boundary. We pursue optimal control framework where boundary heat flux, density of sources, and free boundary are components of the control vector. The optimality criteria consists of the minimization of the L_2-norm declinations of the temperature measurements at the final moment, phase transition temperature, and final position of the free boundary. We prove the Frechet differentiability in Besov spaces, and derive the formula for the Frechet differential under minimal regularity assumptions on the data. The result implies a necessary condition for optimal control and opens the way to the application of projective gradient methods in Besov spaces for the numerical solution of the inverse Stefan problem.

We consider funnel control for linear infinite-dimensional systems that are impedance passive, meaning that they satisfy an energy balance in which the stored energy equals the squared norm of the state and the supplied power is the inner product of input and output. For the analysis we employ the system node approach, which offers a unified framework for infinite-dimensional systems with boundary and distributed control and observation. The resulting closed-loop dynamics are governed by a nonlinear evolution equation; we establish its solvability and hence the applicability of funnel control to this class. The applicability is illustrated by an Euler-Bernoulli beam, which is studied in two distinct scenarios: once with boundary control and once with distributed control.

Federated learning (FL) is a distributed learning protocol in which a server needs to aggregate a set of models learned some independent clients to proceed the learning process. At present, model averaging, known as FedAvg, is one of the most widely adapted aggregation techniques. However, it is known to yield the models with degraded prediction accuracy and slow convergence. In this work, we find out that averaging models from different clients significantly diminishes the norm of the update vectors, resulting in slow learning rate and low prediction accuracy. Therefore, we propose a new aggregation method called FedNNNN. Instead of simple model averaging, we adjust the norm of the update vector and introduce momentum control techniques to improve the aggregation effectiveness of FL. As a demonstration, we evaluate FedNNNN on multiple datasets and scenarios with different neural network models, and observe up to 5.4% accuracy improvement.

Video Diffusion Models (VDMs) have demonstrated remarkable capabilities in synthesizing realistic videos by learning from large-scale data. Although vanilla Low-Rank Adaptation (LoRA) can learn specific spatial or temporal movement to driven VDMs with constrained data, achieving precise control over both camera trajectories and object motion remains challenging due to the unstable fusion and non-linear scalability. To address these issues, we propose LiON-LoRA, a novel framework that rethinks LoRA fusion through three core principles: Linear scalability, Orthogonality, and Norm consistency. First, we analyze the orthogonality of LoRA features in shallow VDM layers, enabling decoupled low-level controllability. Second, norm consistency is enforced across layers to stabilize fusion during complex camera motion combinations. Third, a controllable token is integrated into the diffusion transformer (DiT) to linearly adjust motion amplitudes for both cameras and objects with a modified self-attention mechanism to ensure decoupled control. Additionally, we extend LiON-LoRA to temporal generation by leveraging static-camera videos, unifying spatial and temporal controllability. Experiments demonstrate that LiON-LoRA outperforms state-of-the-art methods in trajectory control accuracy and motion strength adjustment, achieving superior generalization with minimal training data. Project Page: https://fuchengsu.github.io/lionlora.github.io/

The ''pretraining-and-finetuning'' paradigm has become a norm for training domain-specific models in natural language processing and computer vision. In this work, we aim to examine this paradigm for symbolic music generation through leveraging the largest ever symbolic music dataset sourced from the MuseScore forum. We first pretrain a large unconditional transformer model using 1.5 million songs. We then propose a simple technique to equip this pretrained unconditional music transformer model with instrument and genre controls by finetuning the model with additional control tokens. Our proposed representation offers improved high-level controllability and expressiveness against two existing representations. The experimental results show that the proposed model can successfully generate music with user-specified instruments and genre. In a subjective listening test, the proposed model outperforms the pretrained baseline model in terms of coherence, harmony, arrangement and overall quality.

Linear activation steering has gained popularity as a simple and empirically effective way to control language model behavior. More recently, spherical steering paradigms have been proposed to address limitations of additive interventions, often motivated by the assumption that hidden-state norm does not carry concept-relevant information. In this work, we revisit this assumption through a controlled empirical study designed to disentangle the roles of angular and radial components. We show that steering methods differ mainly in how they couple two geometric effects: changing a token's angular alignment with a concept direction and changing its hidden-state norm. Across seven language models, we find that concepts are represented primarily in angular structure, supporting the motivation for spherical methods, but that norm remains important for the stability and downstream effects of steering. Our results explain why interventions with similar concept-level effects can behave differently, and suggest that activation steering should be parameterized by interpretable angular and radial components of the intervention, rather than by a single additive coefficient that entangles these two effects.

We establish nonlinear stability of three-dimensional Couette flow for the incompressible Navier--Stokes equations on mathbb Ttimesmathbb R^2. Divergence-free perturbations satisfying |u_{rm in}|_{H^2}+|u^perp_{0,rm in}|_{dot B^{-2}_{2,infty}}leq c_*ν generate unique global H^2 solutions that remain close to Couette flow, where u^perp_{0,rm in} denotes the streamwise average of the transverse velocity. This result retains the O(ν) stability threshold despite the absence of a spanwise spectral gap. The nonzero streamwise modes exhibit enhanced dissipation, their wall-normal component satisfies a viscosity-uniform time-integrated inviscid-damping estimate, and the transverse zero mode decays in L^2 at rate (1+νt)^{-1}. The endpoint space dot B^{-2}_{2,infty} controls the transverse low frequencies, accommodates divergence-form nonlinear forcing, and is critical for linear lift-up from the wall-normal zero mode. The proof combines propagation of this endpoint norm, Fourier splitting, and a two-level roll-to-streak representation with an adaptation of the nonzero-mode framework of Wei--Zhang (CPAM, 2021).

Personalized federated learning combines shared representations with client-specific predictors, but the contribution of a server weighting rule can be obscured by local training and evaluation choices. We study ORDERS, a configuration that combines a shared backbone, a private residual adapter and classifier, geometric weights assigned by descending update norm, feature alignment, and private-parameter perturbations. The server computes a weighted sum of updates obtained from the same broadcast model; it does not obtain an additional optimization effect from sequential addition. A fully specified evaluation comprises 80 final runs: eight configurations, two datasets, and five training seeds on one fixed partition per dataset. On two-class-per-client CIFAR-10, ORDERS achieves 80.51 pm 0.79% native mean client accuracy, compared with 79.02 pm 1.42% for FedPer-R1 and 80.27 pm 0.73% for the matched uniform-weight control. After common local fine-tuning, the difference from FedPer-R1 narrows to 0.32 percentage points. On Sent140, ORDERS reaches 74.71 pm 0.49%, only 0.69 points above a post hoc client training-majority diagnostic. Ablations provide limited, endpoint-dependent evidence for norm ranking and alignment, and no clear benefit from perturbations. Parameter-payload savings are 5.47% and 0.78%, respectively.

Reinforcement learning (RL) is a core approach for robot control when expert demonstrations are unavailable. On-policy methods such as Proximal Policy Optimization (PPO) are widely used for their stability, but their reliance on narrowly distributed on-policy data limits accurate policy evaluation in high-dimensional state and action spaces. Off-policy methods can overcome this limitation by learning from a broader state-action distribution, yet suffer from slow convergence and instability, as fitting a value function over diverse data requires many gradient updates, causing critic errors to accumulate through bootstrapping. We present FlashSAC, a fast and stable off-policy RL algorithm built on Soft Actor-Critic. Motivated by scaling laws observed in supervised learning, FlashSAC sharply reduces gradient updates while compensating with larger models and higher data throughput. To maintain stability at increased scale, FlashSAC explicitly bounds weight, feature, and gradient norms, curbing critic error accumulation. Across over 60 tasks in 10 simulators, FlashSAC consistently outperforms PPO and strong off-policy baselines in both final performance and training efficiency, with the largest gains on high-dimensional tasks such as dexterous manipulation. In sim-to-real humanoid locomotion, FlashSAC reduces training time from hours to minutes, demonstrating the promise of off-policy RL for sim-to-real transfer.

Prior work in parameter-modifying knowledge editing has shown that large-scale sequential editing leads to significant model degradation. In this paper, we study the reasons behind this and scale sequential knowledge editing to 10,000 sequential edits, while maintaining the downstream performance of the original model. We first show that locate-then-edit knowledge editing methods lead to overfitting on the edited facts. We also show that continuous knowledge editing using these methods leads to disproportionate growth in the norm of the edited matrix. We then provide a crucial insight into the inner workings of locate-then-edit methods. We show that norm-growth is a hidden trick employed by these methods that gives larger importance to the output activations produced from the edited layers. With this "importance hacking", the edited layers provide a much larger contributions to the model's output. To mitigate these issues, we present ENCORE - Early stopping and Norm-Constrained Robust knowledge Editing. ENCORE controls for overfitting and the disproportionate norm-growth to enable long-term sequential editing, where we are able to perform up to 10,000 sequential edits without loss of downstream performance. ENCORE is also 61% faster than MEMIT and 64% faster than AlphaEdit on Llama3-8B.

Joint-Embedding Predictive Architectures (JEPA) learn view-invariant representations and admit projection-based distribution matching for collapse prevention. Existing approaches regularize representations towards isotropic Gaussian distributions, but inherently favor dense representations and fail to capture the key property of sparsity observed in efficient representations. We introduce Rectified Distribution Matching Regularization (RDMReg), a sliced two-sample distribution-matching loss that aligns representations to a Rectified Generalized Gaussian (RGG) distribution. RGG enables explicit control over expected ell_0 norm through rectification, while preserving maximum-entropy up to rescaling under expected ell_p norm constraints. Equipping JEPAs with RDMReg yields Rectified LpJEPA, which strictly generalizes prior Gaussian-based JEPAs. Empirically, Rectified LpJEPA learns sparse, non-negative representations with favorable sparsity-performance trade-offs and competitive downstream performance on image classification benchmarks, demonstrating that RDMReg effectively enforces sparsity while preserving task-relevant information.

Object detection under image degradation can benefit from clean-image supervision, but aggregate gains do not imply that transferred representation changes are uniformly useful. We study how clean task knowledge affects degraded-image representations and whether local responses to structured representation directions can be characterized geometrically. Using paired clean and Gaussian-degraded BDD100K images, we show that clean-teacher distillation improves observed detection accuracy while producing heterogeneous object-level transfer. We isolate a representation component complementary to direct clean-teacher alignment and map it into the distilled student space through an orthogonal bridge. Controlled interventions rescue 13.22% of objects lost under the distilled representation, versus 4.30% under norm-matched random perturbations, with very low harm on preserved objects. We introduce task-sensitive geometry, a gradient-derived channel-space geometry constructed from normalized detection-loss gradients. On a reserved cohort, mapped-complement orientation within this frozen geometry is positively associated with local intervention-response magnitude after controlling for intervention magnitude (partial Spearman ρ = 0.242, 95% CI [0.108, 0.359]). The relationship eplicates on independent data (ρ = 0.180) and with RT-DETR-L (ρ = 0.227), but not for the direct clean-teacher residual family, and it weakens for large interventions. Routing rules and specialized distillation objectives based on these signals do not yield statistically reliable gains over CLEANKD. These results support a local, direction-family-dependent task-sensitive geometry while showing that converting such structure into improved global training remains an open problem.

With diffusion transformer (DiT) excelling in video generation, its use in specific tasks has drawn increasing attention. However, adapting DiT for pose-guided human image animation faces two core challenges: (a) existing U-Net-based pose control methods may be suboptimal for the DiT backbone; and (b) removing text guidance, as in previous approaches, often leads to semantic loss and model degradation. To address these issues, we propose DynamiCtrl, a novel framework for human animation in video DiT architecture. Specifically, we use a shared VAE encoder for human images and driving poses, unifying them into a common latent space, maintaining pose fidelity, and eliminating the need for an expert pose encoder during video denoising. To integrate pose control into the DiT backbone effectively, we propose a novel Pose-adaptive Layer Norm model. It injects normalized pose features into the denoising process via conditioning on visual tokens, enabling seamless and scalable pose control across DiT blocks. Furthermore, to overcome the shortcomings of text removal, we introduce the "Joint-text" paradigm, which preserves the role of text embeddings to provide global semantic context. Through full-attention blocks, image and pose features are aligned with text features, enhancing semantic consistency, leveraging pretrained knowledge, and enabling multi-level control. Experiments verify the superiority of DynamiCtrl on benchmark and self-collected data (e.g., achieving the best LPIPS of 0.166), demonstrating strong character control and high-quality synthesis. The project page is available at https://gulucaptain.github.io/DynamiCtrl/.

We introduce a new functional space U designed to contain all classical arithmetic functions (Mobius, von Mangoldt, Euler phi, divisor functions, Dirichlet characters, etc.). The norm of U combines a Hilbert-type component, based on square summability of Dirichlet coefficients for every s > 1, with a Banach component controlling logarithmic averages of partial sums. We prove that U is a complete Banach space which embeds continuously all standard Hilbert spaces of Dirichlet series and allows natural actions of Dirichlet convolution and shift operators. This framework provides a unified analytic setting for classical and modern problems in multiplicative number theory.

A central challenge in sequence modeling is efficiently handling tasks with extended contexts. While recent state-space models (SSMs) have made significant progress in this area, they often lack input-dependent filtering or require substantial increases in model complexity to handle input variability. We address this gap by introducing S7, a simplified yet powerful SSM that can handle input dependence while incorporating stable reparameterization and specific design choices to dynamically adjust state transitions based on input content, maintaining efficiency and performance. We prove that this reparameterization ensures stability in long-sequence modeling by keeping state transitions well-behaved over time. Additionally, it controls the gradient norm, enabling efficient training and preventing issues like exploding or vanishing gradients. S7 significantly outperforms baselines across various sequence modeling tasks, including neuromorphic event-based datasets, Long Range Arena benchmarks, and various physical and biological time series. Overall, S7 offers a more straightforward approach to sequence modeling without relying on complex, domain-specific inductive biases, achieving significant improvements across key benchmarks.

Flow matching generates data by integrating a learned velocity field, where the number of integration steps (NFE) directly determines inference cost. We analyze which properties of the velocity field govern integration error by decomposing the velocity Jacobian into its symmetric part S (strain rate) and antisymmetric part Omega (vorticity). We prove that strain and vorticity play different roles: strain controls exponential error amplification through the logarithmic norm, while vorticity contributes only linearly to the local truncation error. We further show that the optimal transport velocity field is irrotational and has zero material derivative, implying second-order Euler accuracy; for exact displacement interpolation, the associated Lagrangian particle dynamics are integrated exactly by Euler. Motivated by this analysis, we study weighted Jacobian regularization with strain weight alpha and vorticity weight beta. Experiments on 2D synthetic data confirm the main theoretical predictions, showing up to 2.7x lower integration error at NFE=5. Preliminary CIFAR-10 experiments show consistent trends, with a lightweight fine-tuning procedure improving FID by 14 percent at NFE=10 while preserving high-NFE quality.

Grokking, or delayed generalization, is a phenomenon where generalization in a deep neural network (DNN) occurs long after achieving near zero training error. Previous studies have reported the occurrence of grokking in specific controlled settings, such as DNNs initialized with large-norm parameters or transformers trained on algorithmic datasets. We demonstrate that grokking is actually much more widespread and materializes in a wide range of practical settings, such as training of a convolutional neural network (CNN) on CIFAR10 or a Resnet on Imagenette. We introduce the new concept of delayed robustness, whereby a DNN groks adversarial examples and becomes robust, long after interpolation and/or generalization. We develop an analytical explanation for the emergence of both delayed generalization and delayed robustness based on a new measure of the local complexity of a DNN's input-output mapping. Our local complexity measures the density of the so-called 'linear regions' (aka, spline partition regions) that tile the DNN input space, and serves as a utile progress measure for training. We provide the first evidence that for classification problems, the linear regions undergo a phase transition during training whereafter they migrate away from the training samples (making the DNN mapping smoother there) and towards the decision boundary (making the DNN mapping less smooth there). Grokking occurs post phase transition as a robust partition of the input space emerges thanks to the linearization of the DNN mapping around the training points. Website: https://bit.ly/grok-adversarial

Large language model (LLM)-enhanced recommendation models inject LLM representations into backbone recommenders to exploit rich item text without inference-time LLM cost. However, we find that existing LLM-enhanced methods significantly hinder the optimization of backbone models, resulting in high training losses that are difficult to reduce. To address it, we establish a comprehensive theoretical analysis of local optimization curvature and identify two key causes: 1) large norm disparity and 2) semantic-collaboration misaligned angular clustering of LLM representations. Guided by these insights, we propose Training-Friendly LLM-Enhanced Recommender (TF-LLMER), a lightweight framework with two key components. First, we highlight the necessity of item embedding normalization to eliminate norm-driven instability and achieve provable control over optimization conditioning. Second, we introduce Rec-PCA, a recommendation-aware dimensionality reduction method that injects collaborative structure into the representation transformation to resolve semantic-collaboration misaligned angular clustering. It jointly optimizes semantic information retention and alignment with an item-item co-occurrence graph constructed from interaction histories. The graph captures collaborative structure, and alignment is promoted by penalizing total variation over the graph. Both theory and extensive experiments demonstrate that TF-LLMER significantly outperforms state-of-the-art methods. Our code is available at https://github.com/woriazzc/TF-LLMER.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

We address the problem of finite-horizon control of a discrete-time linear system, where the initial state distribution follows a Gaussian mixture model, the terminal state must follow a specified Gaussian distribution, and the state and control inputs must obey chance constraints. We show that, throughout the time horizon, the state and control distributions are fully characterized by Gaussian mixtures. We then formulate the cost, distributional terminal constraint, and affine/2-norm chance constraints on the state and control, as convex functions of the decision variables. This is leveraged to formulate the chance-constrained path planning problem as a single convex optimization problem. A numerical example demonstrates the effectiveness of the proposed method.

Transformers trained on modular arithmetic exhibit sharp transitions between memorization, generalization, and collapse. We show that weight decay acts as a scalar empirical control parameter for these regimes, and introduce two cheap online diagnostics, mean pairwise attention-head cosine similarity and entropy standard deviation, that track training dynamics from attention activations alone and complement loss-landscape diagnostics at lower compute cost. Across eleven experimental conditions and three model scales (0.82M to 85M parameters), the weight-decay axis separates memorization, developmental grokking, and collapse. A near-transition logistic fit localizes the memorization-to-developmental boundary at λ_c=0.0158 (95% CI [0.0109, 0.0200], N=210); a power-law fit gives an empirical exponent ν=0.757 (CI [0.725, 0.799]). Reference exponents ν=1/2 and 3D Ising νapprox 0.63 lie outside this empirical CI under our four-bin grid, so we report ν as empirical and defer universality-class identification to denser finite-size-scaling work. A horizon-matched multi-task replication (n=280, four modular operations) preserves the weight-decay control pattern; a paired attention-head re-initialization experiment at λ=0.05 changes Phase-2 amplitude (Cohen's d=-1.190, n=10, p_t=4.5 times 10^{-3}), while matched weight-norm clipping does not. Three cross-architecture probes (4L MLP, 4L LSTM, and 4L Mamba; each n=70) replicate the weight-decay-controlled transition with architecture-specific λ_c values. Main diagnostic claims are scoped to modular arithmetic in small transformer attention models; the non-attention experiments are scope probes, and architecture-wide, language-model, and universality-class claims are out of scope.

Modern neural network training relies on optimizers such as Adam and Muon which act on each weight matrix as a single object. Yet every weight matrix carries two distinct quantities -- a magnitude and a direction -- and all optimizers stepping in the matrix as a whole couple their dynamics: the directional change from an update depends on the current magnitude, while the magnitude drifts as a byproduct of learning the direction, so neither is governed directly by the learning rate. Typical training therefore leans on surrounding recipes such as weight decay and warmup to keep learning stable at scale, though these regulate the coupling only indirectly; other recent methods instead constrain the weight to a fixed-norm sphere, but add no learnable magnitude, leaving scale control to normalization layers alone. We propose Magnitude--Direction (MD) Decoupling, an optimizer modification that factorizes each weight into a fixed-norm direction on a hypersphere and learnable per-row and per-column magnitude gains, updated at separate learning rates, all while the model still sees a single fused weight tensor. The method is agnostic to the base optimizer and removes the need for weight decay and warmup. Across both Adam and Muon, MD Decoupling improves on well-tuned baselines, transfers the optimal LR across model width without retuning, and continues to help at scale on large Mixture-of-Experts (MoE) models. Treating magnitude and direction as separately controlled quantities thus yields more predictable training dynamics and a simple, broadly applicable improvement to modern optimizers.

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.

We present NormBank, a knowledge bank of 155k situational norms. This resource is designed to ground flexible normative reasoning for interactive, assistive, and collaborative AI systems. Unlike prior commonsense resources, NormBank grounds each inference within a multivalent sociocultural frame, which includes the setting (e.g., restaurant), the agents' contingent roles (waiter, customer), their attributes (age, gender), and other physical, social, and cultural constraints (e.g., the temperature or the country of operation). In total, NormBank contains 63k unique constraints from a taxonomy that we introduce and iteratively refine here. Constraints then apply in different combinations to frame social norms. Under these manipulations, norms are non-monotonic - one can cancel an inference by updating its frame even slightly. Still, we find evidence that neural models can help reliably extend the scope and coverage of NormBank. We further demonstrate the utility of this resource with a series of transfer experiments.

During pretraining, the Pre-LayerNorm transformer suffers from a gradient magnitude mismatch: gradients at early layers are much larger than at later layers. These issues can be alleviated by our proposed NormFormer architecture, which adds three normalization operations to each layer: a Layer Norm after self attention, head-wise scaling of self-attention outputs, and a Layer Norm after the first fully connected layer. The extra operations incur negligible compute cost (+0.4% parameter increase), but improve pretraining perplexity and downstream task performance for both causal and masked language models ranging from 125 Million to 2.7 Billion parameters. For example, adding NormFormer on top of our strongest 1.3B parameter baseline can reach equal perplexity 24% faster, or converge 0.27 perplexity better in the same compute budget. This model reaches GPT3-Large (1.3B) zero shot performance 60% faster. For masked language modeling, NormFormer improves fine-tuned GLUE performance by 1.9% on average. Code to train NormFormer models is available in fairseq https://github.com/pytorch/fairseq/tree/main/examples/normformer .

This paper presents the Adaptive Personalized Control System (APECS) architecture, a novel framework for human-in-the-loop control. An architecture is developed which defines appropriate constraints for the system objectives. A method for enacting Lipschitz and sector bounds on the resulting controller is derived to ensure desirable control properties. An analysis of worst-case loss functions and the optimal loss function weighting is made to implement an effective training scheme. Finally, simulations are carried out to demonstrate the effectiveness of the proposed architecture. This architecture resulted in a 4.5% performance increase compared to the human operator and 9% to an unconstrained feedforward neural network trained in the same way.

Human activity is moderated by norms. When performing actions in the real world, humans not only follow norms, but also consider the trade-off between different norms However, machines are often trained without explicit supervision on norm understanding and reasoning, especially when the norms are grounded in a physical and social context. To improve and evaluate the normative reasoning capability of vision-language models (VLMs), we present EgoNormia |epsilon|, consisting of 1,853 ego-centric videos of human interactions, each of which has two related questions evaluating both the prediction and justification of normative actions. The normative actions encompass seven categories: safety, privacy, proxemics, politeness, cooperation, coordination/proactivity, and communication/legibility. To compile this dataset at scale, we propose a novel pipeline leveraging video sampling, automatic answer generation, filtering, and human validation. Our work demonstrates that current state-of-the-art vision-language models lack robust norm understanding, scoring a maximum of 45% on EgoNormia (versus a human bench of 92%). Our analysis of performance in each dimension highlights the significant risks of safety, privacy, and the lack of collaboration and communication capability when applied to real-world agents. We additionally show that through a retrieval-based generation method, it is possible to use EgoNomia to enhance normative reasoning in VLMs.

Artificial writing is permeating our lives due to recent advances in large-scale, transformer-based language models (LMs) such as BERT, its variants, GPT-2/3, and others. Using them as pre-trained models and fine-tuning them for specific tasks, researchers have extended state of the art for many NLP tasks and shown that they capture not only linguistic knowledge but also retain general knowledge implicitly present in the data. Unfortunately, LMs trained on unfiltered text corpora suffer from degenerated and biased behaviour. While this is well established, we show that recent LMs also contain human-like biases of what is right and wrong to do, some form of ethical and moral norms of the society -- they bring a "moral direction" to surface. That is, we show that these norms can be captured geometrically by a direction, which can be computed, e.g., by a PCA, in the embedding space, reflecting well the agreement of phrases to social norms implicitly expressed in the training texts and providing a path for attenuating or even preventing toxic degeneration in LMs. Being able to rate the (non-)normativity of arbitrary phrases without explicitly training the LM for this task, we demonstrate the capabilities of the "moral direction" for guiding (even other) LMs towards producing normative text and showcase it on RealToxicityPrompts testbed, preventing the neural toxic degeneration in GPT-2.

Society is characterized by the presence of a variety of social norms: collective patterns of sanctioning that can prevent miscoordination and free-riding. Inspired by this, we aim to construct learning dynamics where potentially beneficial social norms can emerge. Since social norms are underpinned by sanctioning, we introduce a training regime where agents can access all sanctioning events but learning is otherwise decentralized. This setting is technologically interesting because sanctioning events may be the only available public signal in decentralized multi-agent systems where reward or policy-sharing is infeasible or undesirable. To achieve collective action in this setting we construct an agent architecture containing a classifier module that categorizes observed behaviors as approved or disapproved, and a motivation to punish in accord with the group. We show that social norms emerge in multi-agent systems containing this agent and investigate the conditions under which this helps them achieve socially beneficial outcomes.

Deep learning optimizers are often motivated through a mix of convex and approximate second-order theory. We select three such methods -- Adam, Shampoo and Prodigy -- and argue that each method can instead be understood as a squarely first-order method without convexity assumptions. In fact, after switching off exponential moving averages, each method is equivalent to steepest descent under a particular norm. By generalizing this observation, we chart a new design space for training algorithms. Different operator norms should be assigned to different tensors based on the role that the tensor plays within the network. For example, while linear and embedding layers may have the same weight space of R^{mtimes n}, these layers play different roles and should be assigned different norms. We hope that this idea of carefully metrizing the neural architecture might lead to more stable, scalable and indeed faster training.

Despite recent progress in optimal hyperparameter transfer under model and dataset scaling, no unifying explanatory principle has been established. Using the Scion optimizer, we discover that joint optimal scaling across model and dataset sizes is governed by a single invariant: the operator norm of the output layer. Across models with up to 1.3B parameters trained on up to 138B tokens, the optimal learning rate/batch size pair (eta^{ast}, B^{ast}) consistently has the same operator norm value - a phenomenon we term norm transfer. This constant norm condition is necessary but not sufficient: while for each dataset size, multiple (eta, B) reach the optimal norm, only a unique (eta^{ast}, B^{ast}) achieves the best loss. As a sufficient condition, we provide the first measurement of (eta^{ast}, B^{ast}) scaling with dataset size for Scion, and find that the scaling rules are consistent with those of the Adam optimizer. Tuning per-layer-group learning rates also improves model performance, with the output layer being the most sensitive and hidden layers benefiting from lower learning rates. We provide practical insights on norm-guided optimal scaling and release our Distributed Scion (Disco) implementation with logs from over two thousand runs to support research on LLM training dynamics at scale.

It has been conjectured that the operator norm of the Lyapunov operator induced by the Frobenius norm is always attained at a symmetric matrix. The conjecture is known to hold for all matrices of order at most five. We give an integer matrix of order seven for which the skew-symmetric restricted norm is strictly larger than the symmetric restricted norm. A rational separator and exact-arithmetic certificates establish the strict inequality without relying on floating-point computations. A direct-sum construction yields counterexamples in every order n geq 7; the case n = 6 remains open.

While most social norms are informal, they are often formalized by companies in contracts to regulate trades of goods and services. When poorly written, contracts may contain normative conflicts resulting from opposing deontic meanings or contradict specifications. As contracts tend to be long and contain many norms, manually identifying such conflicts requires human-effort, which is time-consuming and error-prone. Automating such task benefits contract makers increasing productivity and making conflict identification more reliable. To address this problem, we introduce an approach to detect and classify norm conflicts in contracts by converting them into latent representations that preserve both syntactic and semantic information and training a model to classify norm conflicts in four conflict types. Our results reach the new state of the art when compared to a previous approach.

Modern Transformers predominantly adopt the Pre-Norm paradigm for its optimization stability, foregoing the superior potential of the unstable Post-Norm architecture. Prior attempts to combine their strengths typically lead to a stability-performance trade-off. We attribute this phenomenon to a structural incompatibility within a single-stream design: Any application of the Post-Norm operation inevitably obstructs the clean identity gradient preserved by Pre-Norm. To fundamentally reconcile these paradigms, we propose SiameseNorm, a two-stream architecture that couples Pre-Norm-like and Post-Norm-like streams with shared parameters. This design decouples the optimization dynamics of the two streams, retaining the distinct characteristics of both Pre-Norm and Post-Norm by enabling all residual blocks to receive combined gradients inherited from both paradigms, where one stream secures stability while the other enhances expressivity. Extensive pre-training experiments on 1.3B-parameter models demonstrate that SiameseNorm exhibits exceptional optimization robustness and consistently outperforms strong baselines. Code is available at https://github.com/Qwen-Applications/SiameseNorm.

A growing body of multi-agent studies with LLMs explores how norms and cooperation emerge in mixed-motive scenarios, where pursuing individual gain can undermine the collective good. While prior work has explored these dynamics in both richly contextualized simulations and simplified game-theoretic environments, most LLM systems featuring common-pool resource (CPR) games provide agents with explicit reward functions directly tied to their actions. In contrast, human cooperation often emerges without explicit knowledge of the payoff structure or how individual actions translate into long-run outcomes, relying instead on heuristics, communication, and enforcement. We introduce a CPR simulation framework that removes explicit reward signals and embeds cultural-evolutionary mechanisms: social learning (adopting strategies and beliefs from successful peers) and norm-based punishment, grounded in Ostrom's principles of resource governance. Agents also individually learn from the consequences of harvesting, monitoring, and punishing via environmental feedback, enabling norms to emerge endogenously. We establish the validity of our simulation by reproducing key findings from existing studies on human behavior. Building on this, we examine norm evolution across a 2times2 grid of environmental and social initialisations (resource-rich vs. resource-scarce; altruistic vs. selfish) and benchmark how agentic societies comprised of different LLMs perform under these conditions. Our results reveal systematic model differences in sustaining cooperation and norm formation, positioning the framework as a rigorous testbed for studying emergent norms in mixed-motive LLM societies. Such analysis can inform the design of AI systems deployed in social and organizational contexts, where alignment with cooperative norms is critical for stability, fairness, and effective governance of AI-mediated environments.

With the growing reliance on artificial intelligence (AI) for many different applications, the sharing of code, data, and models is important to ensure the replicability and democratization of scientific knowledge. Many high-profile academic publishing venues expect code and models to be submitted and released with papers. Furthermore, developers often want to release these assets to encourage development of technology that leverages their frameworks and services. A number of organizations have expressed concerns about the inappropriate or irresponsible use of AI and have proposed ethical guidelines around the application of such systems. While such guidelines can help set norms and shape policy, they are not easily enforceable. In this paper, we advocate the use of licensing to enable legally enforceable behavioral use conditions on software and code and provide several case studies that demonstrate the feasibility of behavioral use licensing. We envision how licensing may be implemented in accordance with existing responsible AI guidelines.

Social norms fundamentally shape interpersonal communication. We present NormDial, a high-quality dyadic dialogue dataset with turn-by-turn annotations of social norm adherences and violations for Chinese and American cultures. Introducing the task of social norm observance detection, our dataset is synthetically generated in both Chinese and English using a human-in-the-loop pipeline by prompting large language models with a small collection of expert-annotated social norms. We show that our generated dialogues are of high quality through human evaluation and further evaluate the performance of existing large language models on this task. Our findings point towards new directions for understanding the nuances of social norms as they manifest in conversational contexts that span across languages and cultures.

We introduce Feasible Learning (FL), a sample-centric learning paradigm where models are trained by solving a feasibility problem that bounds the loss for each training sample. In contrast to the ubiquitous Empirical Risk Minimization (ERM) framework, which optimizes for average performance, FL demands satisfactory performance on every individual data point. Since any model that meets the prescribed performance threshold is a valid FL solution, the choice of optimization algorithm and its dynamics play a crucial role in shaping the properties of the resulting solutions. In particular, we study a primal-dual approach which dynamically re-weights the importance of each sample during training. To address the challenge of setting a meaningful threshold in practice, we introduce a relaxation of FL that incorporates slack variables of minimal norm. Our empirical analysis, spanning image classification, age regression, and preference optimization in large language models, demonstrates that models trained via FL can learn from data while displaying improved tail behavior compared to ERM, with only a marginal impact on average performance.

This paper derives necessary optimality conditions for free end-time optimal control problems governed by sweeping process dynamics. In contrast to classical optimal control problems, the presence of the normal cone term in the state equation introduces discontinuities with respect to the state variable and prevents the standard Lipschitz regularity assumptions typically used in optimal control theory. As a result, both the analysis of trajectories and the formulation of optimality conditions require refined tools. We address problems with general endpoint constraints and time-dependent data, considering both the case in which the dynamics are Lipschitz continuous in time and the more challenging setting of merely measurable time dependence. Special attention is devoted to the additional transversality conditions associated with the free end-time variable. In the Lipschitz case, these conditions are expressed in terms of a function of bounded variation that coincides almost everywhere with the maximized Hamiltonian. In the measurable case, we show that a suitable interpretation can be obtained via the notions of sub- and super-essential values of the maximized Hamiltonian, recently introduced in the literature, leading to strengthened transversality conditions. These conditions also involve an additional term reflecting the interaction between the costate arc and the normal cone to the moving set at the optimal endpoints. Our approach combines suitable perturbation techniques with a penalization method tailored to sweeping processes. The moving set is modelled as a finite intersection of inequality-defined sets satisfying suitable constraint qualifications, including a positive linear independence condition and a diagonal dominance property of the associated Gramian matrix. We also introduce a local version of the constraint qualification condition. Our results apply to a broad class of problems, including those involving unbounded moving sets such as polyhedra. The resulting optimality system extends and sharpens recent results for classical free end-time problems to the non-Lipschitz, discontinuous framework of sweeping processes. The relevance of the transversality conditions obtained in this article is illustrated through two simple examples.

Toxic language, such as hate speech, can deter users from participating in online communities and enjoying popular platforms. Previous approaches to detecting toxic language and norm violations have been primarily concerned with conversations from online forums and social media, such as Reddit and Twitter. These approaches are less effective when applied to conversations on live-streaming platforms, such as Twitch and YouTube Live, as each comment is only visible for a limited time and lacks a thread structure that establishes its relationship with other comments. In this work, we share the first NLP study dedicated to detecting norm violations in conversations on live-streaming platforms. We define norm violation categories in live-stream chats and annotate 4,583 moderated comments from Twitch. We articulate several facets of live-stream data that differ from other forums, and demonstrate that existing models perform poorly in this setting. By conducting a user study, we identify the informational context humans use in live-stream moderation, and train models leveraging context to identify norm violations. Our results show that appropriate contextual information can boost moderation performance by 35\%.

Social norms govern culturally appropriate behavior in communication, enabling dialogue systems to produce responses that are not only coherent but also socially acceptable. We present NormGenesis, a multicultural framework for generating and annotating socially grounded dialogues across English, Chinese, and Korean. To model the dynamics of social interaction beyond static norm classification, we propose a novel dialogue type, Violation-to-Resolution (V2R), which models the progression of conversations following norm violations through recognition and socially appropriate repair. To improve pragmatic consistency in underrepresented languages, we implement an exemplar-based iterative refinement early in the dialogue synthesis process. This design introduces alignment with linguistic, emotional, and sociocultural expectations before full dialogue generation begins. Using this framework, we construct a dataset of 10,800 multi-turn dialogues annotated at the turn level for norm adherence, speaker intent, and emotional response. Human and LLM-based evaluations demonstrate that NormGenesis significantly outperforms existing datasets in refinement quality, dialogue naturalness, and generalization performance. We show that models trained on our V2R-augmented data exhibit improved pragmatic competence in ethically sensitive contexts. Our work establishes a new benchmark for culturally adaptive dialogue modeling and provides a scalable methodology for norm-aware generation across linguistically and culturally diverse languages.

Most value function learning algorithms in reinforcement learning are based on the mean squared (projected) Bellman error. However, squared errors are known to be sensitive to outliers, both skewing the solution of the objective and resulting in high-magnitude and high-variance gradients. To control these high-magnitude updates, typical strategies in RL involve clipping gradients, clipping rewards, rescaling rewards, or clipping errors. While these strategies appear to be related to robust losses -- like the Huber loss -- they are built on semi-gradient update rules which do not minimize a known loss. In this work, we build on recent insights reformulating squared Bellman errors as a saddlepoint optimization problem and propose a saddlepoint reformulation for a Huber Bellman error and Absolute Bellman error. We start from a formalization of robust losses, then derive sound gradient-based approaches to minimize these losses in both the online off-policy prediction and control settings. We characterize the solutions of the robust losses, providing insight into the problem settings where the robust losses define notably better solutions than the mean squared Bellman error. Finally, we show that the resulting gradient-based algorithms are more stable, for both prediction and control, with less sensitivity to meta-parameters.

Large Language Models (LLMs) are increasingly utilized in autonomous decision-making, where they sample options from vast action spaces. However, the heuristics that guide this sampling process remain under-explored. We study this sampling behavior and show that this underlying heuristics resembles that of human decision-making: comprising a descriptive component (reflecting statistical norm) and a prescriptive component (implicit ideal encoded in the LLM) of a concept. We show that this deviation of a sample from the statistical norm towards a prescriptive component consistently appears in concepts across diverse real-world domains like public health, and economic trends. To further illustrate the theory, we demonstrate that concept prototypes in LLMs are affected by prescriptive norms, similar to the concept of normality in humans. Through case studies and comparison with human studies, we illustrate that in real-world applications, the shift of samples toward an ideal value in LLMs' outputs can result in significantly biased decision-making, raising ethical concerns.

ControlNet has enabled detailed spatial control in text-to-image diffusion models by incorporating additional visual conditions such as depth or edge maps. However, its effectiveness heavily depends on the availability of visual conditions that are precisely aligned with the generation goal specified by text prompt-a requirement that often fails in practice, especially for uncommon or imaginative scenes. For example, generating an image of a cat cooking in a specific pose may be infeasible due to the lack of suitable visual conditions. In contrast, structurally similar cues can often be found in more common settings-for instance, poses of humans cooking are widely available and can serve as rough visual guides. Unfortunately, existing ControlNet models struggle to use such loosely aligned visual conditions, often resulting in low text fidelity or visual artifacts. To address this limitation, we propose SemanticControl, a training-free method for effectively leveraging misaligned but semantically relevant visual conditions. Our approach adaptively suppresses the influence of the visual condition where it conflicts with the prompt, while strengthening guidance from the text. The key idea is to first run an auxiliary denoising process using a surrogate prompt aligned with the visual condition (e.g., "a human playing guitar" for a human pose condition) to extract informative attention masks, and then utilize these masks during the denoising of the actual target prompt (e.g., cat playing guitar). Experimental results demonstrate that our method improves performance under loosely aligned conditions across various conditions, including depth maps, edge maps, and human skeletons, outperforming existing baselines. Our code is available at https://mung3477.github.io/semantic-control.

Conditional computation is a popular strategy to make Transformers more efficient. Existing methods often target individual modules (e.g., mixture-of-experts layers) or skip layers independently of one another. However, interpretability research has demonstrated that the middle layers of Transformers exhibit greater redundancy, and that early layers aggregate information into token positions. Guided by these insights, we propose a novel architecture that dynamically skips a variable number of layers from the middle outward. In particular, a learned gating mechanism determines whether to bypass a symmetric span of central blocks based on the input, and a gated attention mechanism prevents subsequent tokens from attending to skipped token positions. Residual norms are controlled with a 'sandwich' or 'perilayernorm' scheme and gate sparsity with an adaptive regularization loss. We had aimed to reduce compute requirements for 'simpler' tokens and potentially foster an emergent multi-level representational hierarchy but, at the scales investigated, our approach does not achieve improvements in the trade-off between validation cross-entropy and estimated FLOPs compared to dense baselines with fewer layers. We release our code at https://github.com/tim-lawson/skip-middle.

Deep reinforcement learning agents often exhibit erratic, high-frequency control behaviors that hinder real-world deployment due to excessive energy consumption and mechanical wear. We systematically investigate action smoothness regularization through higher-order derivative penalties, progressing from theoretical understanding in continuous control benchmarks to practical validation in building energy management. Our comprehensive evaluation across four continuous control environments demonstrates that third-order derivative penalties (jerk minimization) consistently achieve superior smoothness while maintaining competitive performance. We extend these findings to HVAC control systems where smooth policies reduce equipment switching by 60%, translating to significant operational benefits. Our work establishes higher-order action regularization as an effective bridge between RL optimization and operational constraints in energy-critical applications.

We propose a society-first theory of normative appropriateness where individuals, modeled as pre-trained actors with cognitive architectures analogous to Large Language Models (LLMs), generate behavior via predictive pattern completion. Our theory posits that individuals act by completing distributed symbolic patterns based on context, answering questions such as "What does a person such as I do in a situation such as this?". This sense-making mechanism provides a parsimonious account of the key features of human norms: their context-dependence, arbitrariness, automaticity, dynamism, and their support from social sanctioning. It challenges rational-choice theories of social norms by accounting for their key features without needing to exogenously posit scalar rewards or preference relations. By distinguishing between explicit norms, which we associate with in-context adaptation, and implicit norms, which we associate with long-term memory, the theory reconceptualizes several foundational ideas in cognitive science. In particular, it gives an alternative account to the data traditionally seen as supporting dual-process models, and it flips the role of rationality, allowing us to construe it as adherence to culturally-contingent justification standards.

Unrestricted adversarial attacks aim to fool computer vision models without being constrained by ell_p-norm bounds to remain imperceptible to humans, for example, by changing an object's color. This allows attackers to circumvent traditional, norm-bounded defense strategies such as adversarial training or certified defense strategies. However, due to their unrestricted nature, there are also no guarantees of norm-based imperceptibility, necessitating human evaluations to verify just how authentic these adversarial examples look. While some related work assesses this vital quality of adversarial attacks, none provide statistically significant insights. This issue necessitates a unified framework that supports and streamlines such an assessment for evaluating and comparing unrestricted attacks. To close this gap, we introduce SCOOTER - an open-source, statistically powered framework for evaluating unrestricted adversarial examples. Our contributions are: (i) best-practice guidelines for crowd-study power, compensation, and Likert equivalence bounds to measure imperceptibility; (ii) the first large-scale human vs. model comparison across 346 human participants showing that three color-space attacks and three diffusion-based attacks fail to produce imperceptible images. Furthermore, we found that GPT-4o can serve as a preliminary test for imperceptibility, but it only consistently detects adversarial examples for four out of six tested attacks; (iii) open-source software tools, including a browser-based task template to collect annotations and analysis scripts in Python and R; (iv) an ImageNet-derived benchmark dataset containing 3K real images, 7K adversarial examples, and over 34K human ratings. Our findings demonstrate that automated vision systems do not align with human perception, reinforcing the need for a ground-truth SCOOTER benchmark.

Despite significant progress in text-to-image diffusion models, achieving precise spatial control over generated outputs remains challenging. ControlNet addresses this by introducing an auxiliary conditioning module, while ControlNet++ further refines alignment through a cycle consistency loss applied only to the final denoising steps. However, this approach neglects intermediate generation stages, limiting its effectiveness. We propose InnerControl, a training strategy that enforces spatial consistency across all diffusion steps. Our method trains lightweight convolutional probes to reconstruct input control signals (e.g., edges, depth) from intermediate UNet features at every denoising step. These probes efficiently extract signals even from highly noisy latents, enabling pseudo ground truth controls for training. By minimizing the discrepancy between predicted and target conditions throughout the entire diffusion process, our alignment loss improves both control fidelity and generation quality. Combined with established techniques like ControlNet++, InnerControl achieves state-of-the-art performance across diverse conditioning methods (e.g., edges, depth).

Representation rank is an important concept for understanding the role of Neural Networks (NNs) in Deep Reinforcement learning (DRL), which measures the expressive capacity of value networks. Existing studies focus on unboundedly maximizing this rank; nevertheless, that approach would introduce overly complex models in the learning, thus undermining performance. Hence, fine-tuning representation rank presents a challenging and crucial optimization problem. To address this issue, we find a guiding principle for adaptive control of the representation rank. We employ the Bellman equation as a theoretical foundation and derive an upper bound on the cosine similarity of consecutive state-action pairs representations of value networks. We then leverage this upper bound to propose a novel regularizer, namely BEllman Equation-based automatic rank Regularizer (BEER). This regularizer adaptively regularizes the representation rank, thus improving the DRL agent's performance. We first validate the effectiveness of automatic control of rank on illustrative experiments. Then, we scale up BEER to complex continuous control tasks by combining it with the deterministic policy gradient method. Among 12 challenging DeepMind control tasks, BEER outperforms the baselines by a large margin. Besides, BEER demonstrates significant advantages in Q-value approximation. Our code is available at https://github.com/sweetice/BEER-ICLR2024.

Score-based generative modeling, informally referred to as diffusion models, continue to grow in popularity across several important domains and tasks. While they provide high-quality and diverse samples from empirical distributions, important questions remain on the reliability and trustworthiness of these sampling procedures for their responsible use in critical scenarios. Conformal prediction is a modern tool to construct finite-sample, distribution-free uncertainty guarantees for any black-box predictor. In this work, we focus on image-to-image regression tasks and we present a generalization of the Risk-Controlling Prediction Sets (RCPS) procedure, that we term K-RCPS, which allows to (i) provide entrywise calibrated intervals for future samples of any diffusion model, and (ii) control a certain notion of risk with respect to a ground truth image with minimal mean interval length. Differently from existing conformal risk control procedures, ours relies on a novel convex optimization approach that allows for multidimensional risk control while provably minimizing the mean interval length. We illustrate our approach on two real-world image denoising problems: on natural images of faces as well as on computed tomography (CT) scans of the abdomen, demonstrating state of the art performance.

The massive overactuation in the human musculoskeletal system makes it challenging to train musculoskeletal models to generate human-like motion via reinforcement learning, primarily because exploration in the resulting high-dimensional and redundant action space is extremely inefficient. To address this problem, we propose the λ-hold controller, inspired by the equilibrium-point (EP) hypothesis, which has been widely supported by extensive evidence from human motor control studies. The policy's control variable is the per-muscle EP threshold length λ, from which a stretch-reflex recruitment law computes the muscle excitations automatically. Holding each λ over an interval of the gait phase also sharply reduces the frequency at which the policy must be queried. Consequently, the controller, to our knowledge for the first time, enables a muscle-actuated skeletal model to learn human-like sprinting using only a minimal reward within an hour of training. The efficient exploration through the proposed λ-hold controller is not merely an engineering trick but an approach grounded in physiology, bringing together the EP hypothesis, intermittent control, and optimal feedback control. Beyond encapsulating human-like behavior in predictive simulation, this achievement contributes to developing a learnable model of the human motor controller.

We consider an improper reinforcement learning setting where a learner is given M base controllers for an unknown Markov decision process, and wishes to combine them optimally to produce a potentially new controller that can outperform each of the base ones. This can be useful in tuning across controllers, learnt possibly in mismatched or simulated environments, to obtain a good controller for a given target environment with relatively few trials. Towards this, we propose two algorithms: (1) a Policy Gradient-based approach; and (2) an algorithm that can switch between a simple Actor-Critic (AC) based scheme and a Natural Actor-Critic (NAC) scheme depending on the available information. Both algorithms operate over a class of improper mixtures of the given controllers. For the first case, we derive convergence rate guarantees assuming access to a gradient oracle. For the AC-based approach we provide convergence rate guarantees to a stationary point in the basic AC case and to a global optimum in the NAC case. Numerical results on (i) the standard control theoretic benchmark of stabilizing an cartpole; and (ii) a constrained queueing task show that our improper policy optimization algorithm can stabilize the system even when the base policies at its disposal are unstable.

AI control is a family of techniques to prevent an AI with malicious goals from subverting its operator's intent. AI Control usually studies a single agent in one trajectory, but real deployments run many agents over shared infrastructure, and the most severe risks (model-weight exfiltration, training-run poisoning) plausibly need several agents acting in concert. We initiate the empirical study of multi-agent AI control, formalising distributed attacks in which several agents jointly aim for a malicious goal. We develop FakeLab: a synthetic AI-lab codebase (9 services, 86 benign tasks, 4 attack objectives). We evaluate single agent monitoring against distributed attacks, varying the number of agents, their coordination, model capabilities and precise monitoring configuration. Our central finding is the fragmentation effect: as more agents coordinate to attack, per-agent monitoring becomes less likely to catch any of the attackers. Secondly, this is not driven by the ratio of benign to malicious code -- we argue this is likely dependent on model capability. Third, an explicit planner amplifies the fragmentation effect, raises the rate of completing the attack up to sevenfold, and mildly sharpens executors' poor monitor-theory-of-mind. Finally: a weak "trusted" monitor misses most attacks, while a stronger one cuts undetected success by more than an order of magnitude but remains imperfect. We are happy to share FakeLab, our control setting, with safety researchers on request.

Control barrier functions are an effective model-based tool to formally certify the safety of a system. However, transferring their theoretical guarantees to real-world robotics systems requires high model fidelity. For example, payloads or wind disturbances can cause significant model perturbations to an aerial vehicle, leading to safety compromises. In this work, we propose a certifiable online learning-enhanced robust adaptive control barrier function, which adapts to disturbances using a Neural ODE and quantifies its adaptation uncertainty with conformal prediction. Our approach guarantees safety at all time under unknown time-varying model disturbances. It adopts a conservative strategy when the adaptation uncertainty is high; and efficiently adapts to reduce controller conservativeness as it receives more data. Our approach provides a provable safety guarantee with a probability bound under suitable Lipschitz smoothness assumptions on the underlying model and trajectory. These results demonstrate the potential of our method as a practical safety controller for robotics system operating under model perturbations.

For industrial control, developing high-performance controllers with few samples and low technical debt is appealing. Foundation models, possessing rich prior knowledge obtained from pre-training with Internet-scale corpus, have the potential to be a good controller with proper prompts. In this paper, we take HVAC (Heating, Ventilation, and Air Conditioning) building control as an example to examine the ability of GPT-4 (one of the first-tier foundation models) as the controller. To control HVAC, we wrap the task as a language game by providing text including a short description for the task, several selected demonstrations, and the current observation to GPT-4 on each step and execute the actions responded by GPT-4. We conduct series of experiments to answer the following questions: 1)~How well can GPT-4 control HVAC? 2)~How well can GPT-4 generalize to different scenarios for HVAC control? 3) How different parts of the text context affect the performance? In general, we found GPT-4 achieves the performance comparable to RL methods with few samples and low technical debt, indicating the potential of directly applying foundation models to industrial control tasks.

ControlNet offers a powerful way to guide diffusion-based generative models, yet most implementations rely on ad-hoc heuristics to choose which network blocks to control-an approach that varies unpredictably with different tasks. To address this gap, we propose FlexControl, a novel framework that copies all diffusion blocks during training and employs a trainable gating mechanism to dynamically select which blocks to activate at each denoising step. With introducing a computation-aware loss, we can encourage control blocks only to activate when it benefit the generation quality. By eliminating manual block selection, FlexControl enhances adaptability across diverse tasks and streamlines the design pipeline, with computation-aware training loss in an end-to-end training manner. Through comprehensive experiments on both UNet (e.g., SD1.5) and DiT (e.g., SD3.0), we show that our method outperforms existing ControlNet variants in certain key aspects of interest. As evidenced by both quantitative and qualitative evaluations, FlexControl preserves or enhances image fidelity while also reducing computational overhead by selectively activating the most relevant blocks. These results underscore the potential of a flexible, data-driven approach for controlled diffusion and open new avenues for efficient generative model design.

Aligning Large Language Models (LLMs) with human values has attracted increasing attention since it provides clarity, transparency, and the ability to adapt to evolving scenarios. In this paper, we introduce a Controlled Value Vector Activation (ConVA) method that directly aligns the internal values of LLMs by interpreting how a value is encoded in their latent representations and modifies relevant activations to ensure consistent values in LLMs. To ensure an accurate and unbiased interpretation, we propose a context-controlled value vector identification method. To consistently control values without sacrificing model performance, we introduce a gated value vector activation method for effective and minimum degree of value control. Experiments show that our method achieves the highest control success rate across 10 basic values without hurting LLM performance and fluency, and ensures target values even with opposite and potentially malicious input prompts. Source code and data are available at~ https://github.com/hr-jin/ConVA.

Controlling the evolution of complex physical systems is a fundamental task across science and engineering. Classical techniques suffer from limited applicability or huge computational costs. On the other hand, recent deep learning and reinforcement learning-based approaches often struggle to optimize long-term control sequences under the constraints of system dynamics. In this work, we introduce Diffusion Physical systems Control (DiffPhyCon), a new class of method to address the physical systems control problem. DiffPhyCon excels by simultaneously minimizing both the learned generative energy function and the predefined control objectives across the entire trajectory and control sequence. Thus, it can explore globally and plan near-optimal control sequences. Moreover, we enhance DiffPhyCon with prior reweighting, enabling the discovery of control sequences that significantly deviate from the training distribution. We test our method on three tasks: 1D Burgers' equation, 2D jellyfish movement control, and 2D high-dimensional smoke control, where our generated jellyfish dataset is released as a benchmark for complex physical system control research. Our method outperforms widely applied classical approaches and state-of-the-art deep learning and reinforcement learning methods. Notably, DiffPhyCon unveils an intriguing fast-close-slow-open pattern observed in the jellyfish, aligning with established findings in the field of fluid dynamics. The project website, jellyfish dataset, and code can be found at https://github.com/AI4Science-WestlakeU/diffphycon.

Ensuring safety is of paramount importance in physical human-robot interaction applications. This requires both adherence to safety constraints defined on the system state, as well as guaranteeing compliant behavior of the robot. If the underlying dynamical system is known exactly, the former can be addressed with the help of control barrier functions. The incorporation of elastic actuators in the robot's mechanical design can address the latter requirement. However, this elasticity can increase the complexity of the resulting system, leading to unmodeled dynamics, such that control barrier functions cannot directly ensure safety. In this paper, we mitigate this issue by learning the unknown dynamics using Gaussian process regression. By employing the model in a feedback linearizing control law, the safety conditions resulting from control barrier functions can be robustified to take into account model errors, while remaining feasible. In order to enforce them on-line, we formulate the derived safety conditions in the form of a second-order cone program. We demonstrate our proposed approach with simulations on a two-degree-of-freedom planar robot with elastic joints.

Textual Inversion (TI) is an efficient approach to text-to-image personalization but often fails on complex prompts. We trace these failures to embedding norm inflation: learned tokens drift to out-of-distribution magnitudes, degrading prompt conditioning in pre-norm Transformers. Empirically, we show semantics are primarily encoded by direction in CLIP token space, while inflated norms harm contextualization; theoretically, we analyze how large magnitudes attenuate positional information and hinder residual updates in pre-norm blocks. We propose Directional Textual Inversion (DTI), which fixes the embedding magnitude to an in-distribution scale and optimizes only direction on the unit hypersphere via Riemannian SGD. We cast direction learning as MAP with a von Mises-Fisher prior, yielding a constant-direction prior gradient that is simple and efficient to incorporate. Across personalization tasks, DTI improves text fidelity over TI and TI-variants while maintaining subject similarity. Crucially, DTI's hyperspherical parameterization enables smooth, semantically coherent interpolation between learned concepts (slerp), a capability that is absent in standard TI. Our findings suggest that direction-only optimization is a robust and scalable path for prompt-faithful personalization.

We present a training-free framework for continuous and controllable image editing at test time for text-conditioned generative models. In contrast to prior approaches that rely on additional training or manual user intervention, we find that a simple steering in the text-embedding space is sufficient to produce smooth edit control. Given a target concept (e.g., enhancing photorealism or changing facial expression), we use a large language model to automatically construct a small set of debiased contrastive prompt pairs, from which we compute a steering vector in the generator's text-encoder space. We then add this vector directly to the input prompt representation to control generation along the desired semantic axis. To obtain a continuous control, we propose an elastic range search procedure that automatically identifies an effective interval of steering magnitudes, avoiding both under-steering (no-edit) and over-steering (changing other attributes). Adding the scaled versions of the same vector within this interval yields smooth and continuous edits. Since our method modifies only textual representations, it naturally generalizes across text-conditioned modalities, including image and video generation. To quantify the steering continuity, we introduce a new evaluation metric that measures the uniformity of semantic change across edit strengths. We compare the continuous editing behavior across methods and find that, despite its simplicity and lightweight design, our approach is comparable to training-based alternatives, outperforming other training-free methods.