Daily Papers

Low-Rank Adaptation (LoRA) merging can efficiently combine diverse generative capabilities from multiple trained LoRAs for a diffusion model. However, existing LoRA merging techniques often suffer from severe parameter interference, causing destructive collisions in the shared parameter space. To address this, we propose Subspace Signal Routing (SSR), which resolves interference by routing internal signals instead of performing parameter-space merge. Specifically, SSR first constructs a unified subspace by concatenating candidate LoRAs along the rank dimension. Next, SSR employs an inverse correlation matrix to decorrelate mixed signals within this space. Finally, a directional guide matrix steers these purified signals into their respective task-specific subspaces. We provide a rigorous theoretical analysis proving that SSR aligns with the Ordinary Least Squares (OLS) solution, thereby ensuring mathematical optimality. We utilize the additivity of sufficient statistics to design a streaming algorithm. This enables on-the-fly updates that significantly reduce memory overhead and computation time. Extensive experiments validate that SSR significantly outperforms state-of-the-art methods while maintaining comparable efficiency. Code is available at https://github.com/nagara214/SSR-Merge.

Graph neural networks have recently achieved great successes in predicting quantum mechanical properties of molecules. These models represent a molecule as a graph using only the distance between atoms (nodes). They do not, however, consider the spatial direction from one atom to another, despite directional information playing a central role in empirical potentials for molecules, e.g. in angular potentials. To alleviate this limitation we propose directional message passing, in which we embed the messages passed between atoms instead of the atoms themselves. Each message is associated with a direction in coordinate space. These directional message embeddings are rotationally equivariant since the associated directions rotate with the molecule. We propose a message passing scheme analogous to belief propagation, which uses the directional information by transforming messages based on the angle between them. Additionally, we use spherical Bessel functions and spherical harmonics to construct theoretically well-founded, orthogonal representations that achieve better performance than the currently prevalent Gaussian radial basis representations while using fewer than 1/4 of the parameters. We leverage these innovations to construct the directional message passing neural network (DimeNet). DimeNet outperforms previous GNNs on average by 76% on MD17 and by 31% on QM9. Our implementation is available online.

Diffusion models are among the most effective methods for image generation. This is in particular because, unlike GANs, they can be easily conditioned during training to produce elements with desired class or properties. However, guiding a pre-trained diffusion model to generate elements from previously unlabeled data is significantly more challenging. One of the possible solutions was given by the ADM-G guiding approach. Although ADM-G successfully generates elements from the given class, there is a significant quality gap compared to a model originally conditioned on this class. In particular, the FID score obtained by the ADM-G-guided diffusion model is nearly three times lower than the class-conditioned guidance. We demonstrate that this issue is partly due to ADM-G providing minimal guidance during the final stage of the denoising process. To address this problem, we propose GeoGuide, a guidance model based on tracing the distance of the diffusion model's trajectory from the data manifold. The main idea of GeoGuide is to produce normalized adjustments during the backward denoising process. As shown in the experiments, GeoGuide surpasses the probabilistic approach ADM-G with respect to both the FID scores and the quality of the generated images.

Low-precision number formats are widely used in modern machine learning systems due to their efficiency. Accurate direction representation is key to the accuracy of vector operations. This work precisely explores the extent to which the direction of a vector can be represented by selecting its scalar elements from a common finite alphabet of a given size. This is standard practice in machine learning, where low-precision significands may be narrow-width floating-point or integer values. A geometric framework is introduced for analyzing the directional coverage of such product-structured codes. This work analytically quantifies the suboptimality gap between such product-structured codes and spherical codes for the vector as a whole, in both low and asymptotically high dimensions. Furthermore, within the product code class, it is proven that the standard formats of two's complement, fixed-point, and floating-point are suboptimal, again with quantified gap, pointing to the potential to develop new scalar number formats. Such scalar alphabets are numerically optimized across multiple block dimensions for directional coverage, including the dimension used in NVIDIA's NVFP4 format. Experimental results are presented comparing the performance of standard formats and the optimized alphabet. We find that for four bits, NVIDIA's choice of E2M1 closely approximates the optimized alphabet, providing a geometric explanation for its strong performance in low-precision machine learning workloads and an analytical understanding of the link between that superiority and block size. We provide open-source formal proofs in Lean for the theorems in this work, along with the experimental code and the optimized alphabets obtained.

We require decomposition methods for the ABCD-matrix formulation in rotationally symmetric paraxial geometric optics when designing a multi-component optical system from a given single paraxial specification (represented by an ABCD matrix) to optimize non-paraxial specifications (e.g., optical aberrations). In this study, we propose two kinds of three-matrix decomposition of ABCD matrices by focusing on the fact that the ABCD matrices have three real-number degrees of freedom. In addition, we formulate a transformation between the two kinds of decomposition for a single matrix, which can increase or decrease the number of refraction surfaces in the optical configuration while keeping the paraxial specifications fixed. This nature is useful for the optical design of multi-component systems with optimized non-paraxial characteristics.

Transformers were originally proposed as a sequence-to-sequence model for text but have become vital for a wide range of modalities, including images, audio, video, and undirected graphs. However, transformers for directed graphs are a surprisingly underexplored topic, despite their applicability to ubiquitous domains including source code and logic circuits. In this work, we propose two direction- and structure-aware positional encodings for directed graphs: (1) the eigenvectors of the Magnetic Laplacian - a direction-aware generalization of the combinatorial Laplacian; (2) directional random walk encodings. Empirically, we show that the extra directionality information is useful in various downstream tasks, including correctness testing of sorting networks and source code understanding. Together with a data-flow-centric graph construction, our model outperforms the prior state of the art on the Open Graph Benchmark Code2 relatively by 14.7%.

Backward Filtering Forward Guiding (BFFG) is a bidirectional algorithm proposed in Mider et al. [2021] and studied more in depth in a general setting in Van der Meulen and Schauer [2022]. In category theory, optics have been proposed for modelling systems with bidirectional data flow. We connect BFFG with optics and prove that different ways of composing the building blocks of BFFG correspond to equivalent optics.

Node clustering is a powerful tool in the analysis of networks. We introduce a graph neural network framework, named DIGRAC, to obtain node embeddings for directed networks in a self-supervised manner, including a novel probabilistic imbalance loss, which can be used for network clustering. Here, we propose directed flow imbalance measures, which are tightly related to directionality, to reveal clusters in the network even when there is no density difference between clusters. In contrast to standard approaches in the literature, in this paper, directionality is not treated as a nuisance, but rather contains the main signal. DIGRAC optimizes directed flow imbalance for clustering without requiring label supervision, unlike existing graph neural network methods, and can naturally incorporate node features, unlike existing spectral methods. Extensive experimental results on synthetic data, in the form of directed stochastic block models, and real-world data at different scales, demonstrate that our method, based on flow imbalance, attains state-of-the-art results on directed graph clustering when compared against 10 state-of-the-art methods from the literature, for a wide range of noise and sparsity levels, graph structures, and topologies, and even outperforms supervised methods.

Guidance is a crucial technique for extracting the best performance out of image-generating diffusion models. Traditionally, a constant guidance weight has been applied throughout the sampling chain of an image. We show that guidance is clearly harmful toward the beginning of the chain (high noise levels), largely unnecessary toward the end (low noise levels), and only beneficial in the middle. We thus restrict it to a specific range of noise levels, improving both the inference speed and result quality. This limited guidance interval improves the record FID in ImageNet-512 significantly, from 1.81 to 1.40. We show that it is quantitatively and qualitatively beneficial across different sampler parameters, network architectures, and datasets, including the large-scale setting of Stable Diffusion XL. We thus suggest exposing the guidance interval as a hyperparameter in all diffusion models that use guidance.

Text-to-image diffusion models excel at generating photorealistic images, but commonly struggle to render accurate spatial relationships described in text prompts. We identify two core issues underlying this common failure: 1) the ambiguous nature of spatial-related data in existing datasets, and 2) the inability of current text encoders to accurately interpret the spatial semantics of input descriptions. We address these issues with CoMPaSS, a versatile training framework that enhances spatial understanding of any T2I diffusion model. CoMPaSS solves the ambiguity of spatial-related data with the Spatial Constraints-Oriented Pairing (SCOP) data engine, which curates spatially-accurate training data through a set of principled spatial constraints. To better exploit the curated high-quality spatial priors, CoMPaSS further introduces a Token ENcoding ORdering (TENOR) module to allow better exploitation of high-quality spatial priors, effectively compensating for the shortcoming of text encoders. Extensive experiments on four popular open-weight T2I diffusion models covering both UNet- and MMDiT-based architectures demonstrate the effectiveness of CoMPaSS by setting new state-of-the-arts with substantial relative gains across well-known benchmarks on spatial relationships generation, including VISOR (+98%), T2I-CompBench Spatial (+67%), and GenEval Position (+131%). Code will be available at https://github.com/blurgyy/CoMPaSS.

Recent texture generation methods achieve impressive results due to the powerful generative prior they leverage from large-scale text-to-image diffusion models. However, abstract textual prompts are limited in providing global textural or shape information, which results in the texture generation methods producing blurry or inconsistent patterns. To tackle this, we present FlexiTex, embedding rich information via visual guidance to generate a high-quality texture. The core of FlexiTex is the Visual Guidance Enhancement module, which incorporates more specific information from visual guidance to reduce ambiguity in the text prompt and preserve high-frequency details. To further enhance the visual guidance, we introduce a Direction-Aware Adaptation module that automatically designs direction prompts based on different camera poses, avoiding the Janus problem and maintaining semantically global consistency. Benefiting from the visual guidance, FlexiTex produces quantitatively and qualitatively sound results, demonstrating its potential to advance texture generation for real-world applications.

Prompt highlighting steers a large language model to prioritize user-specified text spans during generation. A key challenge is extracting steering directions that capture the difference between relevant and irrelevant contexts, rather than shared structural patterns common to both. We propose PRISM-Δ (Projection-based Relevance-Informed Steering Method), which decomposes the difference between positive and negative cross-covariance matrices to maximize discriminative energy while eliminating shared directions. Each attention head receives a continuous softplus importance weight, letting weak-but-useful heads contribute at reduced strength. The framework extends naturally to Value representations, capturing content-channel signal that Key-only methods leave unused. Across four benchmarks and five models, PRISM-Δ matches or exceeds the best existing method on 19 of 20 configurations, with relative gains up to +10.6%, while halving the fluency cost of steering. PRISM-Δ also scales to long-context retrieval, outperforming the best existing method by up to +4.8% relative gain. PRISM-Δ is compatible with FlashAttention and adds negligible memory overhead.

This article presents an in-depth review of the topic of path following for autonomous robotic vehicles, with a specific focus on vehicle motion in two dimensional space (2D). From a control system standpoint, path following can be formulated as the problem of stabilizing a path following error system that describes the dynamics of position and possibly orientation errors of a vehicle with respect to a path, with the errors defined in an appropriate reference frame. In spite of the large variety of path following methods described in the literature we show that, in principle, most of them can be categorized in two groups: stabilization of the path following error system expressed either in the vehicle's body frame or in a frame attached to a "reference point" moving along the path, such as a Frenet-Serret (F-S) frame or a Parallel Transport (P-T) frame. With this observation, we provide a unified formulation that is simple but general enough to cover many methods available in the literature. We then discuss the advantages and disadvantages of each method, comparing them from the design and implementation standpoint. We further show experimental results of the path following methods obtained from field trials testing with under-actuated and fully-actuated autonomous marine vehicles. In addition, we introduce open-source Matlab and Gazebo/ROS simulation toolboxes that are helpful in testing path following methods prior to their integration in the combined guidance, navigation, and control systems of autonomous vehicles.

The raster-ordered image token sequence exhibits a significant Euclidean distance between index-adjacent tokens at line breaks, making it unsuitable for autoregressive generation. To address this issue, this paper proposes Direction-Aware Diagonal Autoregressive Image Generation (DAR) method, which generates image tokens following a diagonal scanning order. The proposed diagonal scanning order ensures that tokens with adjacent indices remain in close proximity while enabling causal attention to gather information from a broader range of directions. Additionally, two direction-aware modules: 4D-RoPE and direction embeddings are introduced, enhancing the model's capability to handle frequent changes in generation direction. To leverage the representational capacity of the image tokenizer, we use its codebook as the image token embeddings. We propose models of varying scales, ranging from 485M to 2.0B. On the 256times256 ImageNet benchmark, our DAR-XL (2.0B) outperforms all previous autoregressive image generators, achieving a state-of-the-art FID score of 1.37.

Steering vectors work for some concepts and layers but fail for others, and practitioners have no way to predict which setting applies before running an intervention. We introduce the Linear Accessibility Profile (LAP), a per-layer diagnostic that repurposes the logit lens as a predictor of steering vector effectiveness. The key measure, A_{lin}, applies the model's unembedding matrix to intermediate hidden states, requiring no training. Across 24 controlled binary concept families on five models (Pythia-2.8B to Llama-8B), peak A_{lin} predicts steering effectiveness at ρ= +0.86 to +0.91 and layer selection at ρ= +0.63 to +0.92. A three-regime framework explains when difference-of-means steering works, when nonlinear methods are needed, and when no method can work. An entity-steering demo confirms the prediction end-to-end: steering at the LAP-recommended layer redirects completions on Gemma-2-2B and OLMo-2-1B-Instruct, while the middle layer (the standard heuristic) has no effect on either model.

Denoising diffusion models have shown great promise in human motion synthesis conditioned on natural language descriptions. However, integrating spatial constraints, such as pre-defined motion trajectories and obstacles, remains a challenge despite being essential for bridging the gap between isolated human motion and its surrounding environment. To address this issue, we propose Guided Motion Diffusion (GMD), a method that incorporates spatial constraints into the motion generation process. Specifically, we propose an effective feature projection scheme that manipulates motion representation to enhance the coherency between spatial information and local poses. Together with a new imputation formulation, the generated motion can reliably conform to spatial constraints such as global motion trajectories. Furthermore, given sparse spatial constraints (e.g. sparse keyframes), we introduce a new dense guidance approach to turn a sparse signal, which is susceptible to being ignored during the reverse steps, into denser signals to guide the generated motion to the given constraints. Our extensive experiments justify the development of GMD, which achieves a significant improvement over state-of-the-art methods in text-based motion generation while allowing control of the synthesized motions with spatial constraints.

Generative Adversarial Networks (GANs) have been widely applied in modeling diverse image distributions. However, despite its impressive applications, the structure of the latent space in GANs largely remains as a black-box, leaving its controllable generation an open problem, especially when spurious correlations between different semantic attributes exist in the image distributions. To address this problem, previous methods typically learn linear directions or individual channels that control semantic attributes in the image space. However, they often suffer from imperfect disentanglement, or are unable to obtain multi-directional controls. In this work, in light of the above challenges, we propose a novel approach that discovers nonlinear controls, which enables multi-directional manipulation as well as effective disentanglement, based on gradient information in the learned GAN latent space. More specifically, we first learn interpolation directions by following the gradients from classification networks trained separately on the attributes, and then navigate the latent space by exclusively controlling channels activated for the target attribute in the learned directions. Empirically, with small training data, our approach is able to gain fine-grained controls over a diverse set of bi-directional and multi-directional attributes, and we showcase its ability to achieve disentanglement significantly better than state-of-the-art methods both qualitatively and quantitatively.

Activation steering presupposes that task-relevant behaviors correspond to linear directions in activation space -- directions that should both steer the model and be readable along the unembedding. Function vectors (FVs), extracted as mean differences across ICL demonstrations, are the canonical test case; the prediction: steering and decoding succeed or fail together. Across 12 tasks, 6 models from 3 families, and 4,032 directed cross-template pairs, we find the opposite. FV steering routinely succeeds where the logit lens cannot decode the correct answer at any intermediate layer, while the converse -- decodable without steerable -- is nearly empty (3 of 72). The gap is not representational dialect. A diagonal tuned lens closes 1 of 14 steerable-not-decodable cases; a 2-layer MLP probe with a Hewitt \& Liang control closes 5 of 10 via nonlinearly encoded structure but leaves 5 invisible to every decoder tested. Even at > 0.90 steering accuracy, projecting the FV through the unembedding yields incoherent token distributions: FVs encode computational instructions, not answer directions. A model-family asymmetry sharpens the picture. Mistral FVs rewrite intermediate representations, while Llama and Gemma FVs steer the final output without leaving a logit-lens-visible trace, corroborated by three signals (post-steering deltas, activation-patching recovery, FV norm-transfer correlations). A previously reported negative cosine-transfer correlation dissolves at scale, adding at most ΔR^2 = 0.011 beyond task identity. These results decompose the linear representation hypothesis into linear decodability and linear steerability and show they come apart opposite to intuition, with implications for safety monitoring: vocabulary-projection tools are blind to FV-style interventions on widely deployed model families.

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 demonstrate that architectures which traditionally are considered to be ill-suited for a task can be trained using inductive biases from another architecture. Networks are considered untrainable when they overfit, underfit, or converge to poor results even when tuning their hyperparameters. For example, plain fully connected networks overfit on object recognition while deep convolutional networks without residual connections underfit. The traditional answer is to change the architecture to impose some inductive bias, although what that bias is remains unknown. We introduce guidance, where a guide network guides a target network using a neural distance function. The target is optimized to perform well and to match its internal representations, layer-by-layer, to those of the guide; the guide is unchanged. If the guide is trained, this transfers over part of the architectural prior and knowledge of the guide to the target. If the guide is untrained, this transfers over only part of the architectural prior of the guide. In this manner, we can investigate what kinds of priors different architectures place on untrainable networks such as fully connected networks. We demonstrate that this method overcomes the immediate overfitting of fully connected networks on vision tasks, makes plain CNNs competitive to ResNets, closes much of the gap between plain vanilla RNNs and Transformers, and can even help Transformers learn tasks which RNNs can perform more easily. We also discover evidence that better initializations of fully connected networks likely exist to avoid overfitting. Our method provides a mathematical tool to investigate priors and architectures, and in the long term, may demystify the dark art of architecture creation, even perhaps turning architectures into a continuous optimizable parameter of the network.

In recent years, many large directed networks such as online social networks are collected with the help of powerful data engineering and data storage techniques. Analyses of such networks attract significant attention from both the academics and industries. However, analyses of large directed networks are often time-consuming and expensive because the complexities of a lot of graph algorithms are often polynomial with the size of the graph. Hence, sampling algorithms that can generate graphs preserving properties of original graph are of great importance because they can speed up the analysis process. We propose a promising framework to sample directed graphs: Construct a sample graph with linearly rescaled Joint Degree Matrix (JDM) and Degree Correlation Matrix (DCM). Previous work shows that graphs with the same JDM and DCM will have a range of very similar graph properties. We also conduct experiments on real-world datasets to show that the numbers of non-zero entries in JDM and DCM are quite small compared to the number of edges and nodes. Adopting this framework, we propose a novel graph sampling algorithm that can provably preserves in-degree and out-degree distributions, which are two most fundamental properties of a graph. We also prove the upper bound for deviations in the joint degree distribution and degree correlation distribution, which correspond to JDM and DCM. Besides, we prove that the deviations in these distributions are negatively correlated with the sparsity of the JDM and DCM. Considering that these two matrices are always quite sparse, we believe that proposed algorithm will have a better-than-theory performance on real-world large directed networks.

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

Guidance of generative models is typically achieved by modifying the probability flow vector field through the addition of a guidance field. In this paper, we instead propose the Source-Guided Flow Matching (SGFM) framework, which modifies the source distribution directly while keeping the pre-trained vector field intact. This reduces the guidance problem to a well-defined problem of sampling from the source distribution. We theoretically show that SGFM recovers the desired target distribution exactly. Furthermore, we provide bounds on the Wasserstein error for the generated distribution when using an approximate sampler of the source distribution and an approximate vector field. The key benefit of our approach is that it allows the user to flexibly choose the sampling method depending on their specific problem. To illustrate this, we systematically compare different sampling methods and discuss conditions for asymptotically exact guidance. Moreover, our framework integrates well with optimal flow matching models since the straight transport map generated by the vector field is preserved. Experimental results on synthetic 2D benchmarks, physics-informed generative tasks, and imaging inverse problems demonstrate the effectiveness and flexibility of the proposed framework.

This paper introduces the point-axis representation for oriented object detection, emphasizing its flexibility and geometrically intuitive nature with two key components: points and axes. 1) Points delineate the spatial extent and contours of objects, providing detailed shape descriptions. 2) Axes define the primary directionalities of objects, providing essential orientation cues crucial for precise detection. The point-axis representation decouples location and rotation, addressing the loss discontinuity issues commonly encountered in traditional bounding box-based approaches. For effective optimization without introducing additional annotations, we propose the max-projection loss to supervise point set learning and the cross-axis loss for robust axis representation learning. Further, leveraging this representation, we present the Oriented DETR model, seamlessly integrating the DETR framework for precise point-axis prediction and end-to-end detection. Experimental results demonstrate significant performance improvements in oriented object detection tasks.

Recent diffusion models achieve the state-of-the-art performance in image generation, but often suffer from semantic inconsistencies or hallucinations. While various inference-time guidance methods can enhance generation, they often operate indirectly by relying on external signals or architectural modifications, which introduces additional computational overhead. In this paper, we propose Tangential Amplifying Guidance (TAG), a more efficient and direct guidance method that operates solely on trajectory signals without modifying the underlying diffusion model. TAG leverages an intermediate sample as a projection basis and amplifies the tangential components of the estimated scores with respect to this basis to correct the sampling trajectory. We formalize this guidance process by leveraging a first-order Taylor expansion, which demonstrates that amplifying the tangential component steers the state toward higher-probability regions, thereby reducing inconsistencies and enhancing sample quality. TAG is a plug-and-play, architecture-agnostic module that improves diffusion sampling fidelity with minimal computational addition, offering a new perspective on diffusion guidance.

This thesis is divided into three parts. The first part deals with cylindric plane partitions. The second with lambda-determinants and the third with commutators in semi-circular systems. For more detailed abstract please see inside. Cylindric plane partitions may be thought of as a natural generalization of reverse plane partitions. A generating series for the enumeration of cylindric plane partitions was recently given by Borodin. The first result of section one is a new bijective proof of Borodin's identity which makes use of Fomin's growth diagram framework for generalized RSK correspondences. The second result is a (q,t)-analog of Borodin's identity which extends previous work by Okada in the reverse plane partition case. The third result is an explicit combinatorial interpretation of the Macdonald weight occurring in the (q,t)-analog using the non-intersecting lattice path model for cylindric plane partitions. Alternating sign matrices were discovered by Robbins and Rumsey whilst studying λ-determinants. In the second part of this thesis we prove a multi-parameter generalization of the λ-determinant, generalizing a recent result by di Francesco. Like the original λ-determinant, our formula exhibits the Laurent phenomenon. Semicircular systems were first introduced by Voiculescu as a part of his study of von Neumann algebras. In the third part of this thesis we study certain commutator subalgebras of the semicircular system. We find a projection matrix with an interesting self-similar structure. Making use of our projection formula we given an alternative, elementary proof that the semicircular system is a factor.

We tackle the problem of estimating a Manhattan frame, i.e. three orthogonal vanishing points, and the unknown focal length of the camera, leveraging a prior vertical direction. The direction can come from an Inertial Measurement Unit that is a standard component of recent consumer devices, e.g., smartphones. We provide an exhaustive analysis of minimal line configurations and derive two new 2-line solvers, one of which does not suffer from singularities affecting existing solvers. Additionally, we design a new non-minimal method, running on an arbitrary number of lines, to boost the performance in local optimization. Combining all solvers in a hybrid robust estimator, our method achieves increased accuracy even with a rough prior. Experiments on synthetic and real-world datasets demonstrate the superior accuracy of our method compared to the state of the art, while having comparable runtimes. We further demonstrate the applicability of our solvers for relative rotation estimation. The code is available at https://github.com/cvg/VP-Estimation-with-Prior-Gravity.

Diffusion models are capable of generating impressive images conditioned on text descriptions, and extensions of these models allow users to edit images at a relatively coarse scale. However, the ability to precisely edit the layout, position, pose, and shape of objects in images with diffusion models is still difficult. To this end, we propose motion guidance, a zero-shot technique that allows a user to specify dense, complex motion fields that indicate where each pixel in an image should move. Motion guidance works by steering the diffusion sampling process with the gradients through an off-the-shelf optical flow network. Specifically, we design a guidance loss that encourages the sample to have the desired motion, as estimated by a flow network, while also being visually similar to the source image. By simultaneously sampling from a diffusion model and guiding the sample to have low guidance loss, we can obtain a motion-edited image. We demonstrate that our technique works on complex motions and produces high quality edits of real and generated images.

Training-free guided sampling in diffusion models leverages off-the-shelf pre-trained networks, such as an aesthetic evaluation model, to guide the generation process. Current training-free guided sampling algorithms obtain the guidance energy function based on a one-step estimate of the clean image. However, since the off-the-shelf pre-trained networks are trained on clean images, the one-step estimation procedure of the clean image may be inaccurate, especially in the early stages of the generation process in diffusion models. This causes the guidance in the early time steps to be inaccurate. To overcome this problem, we propose Symplectic Adjoint Guidance (SAG), which calculates the gradient guidance in two inner stages. Firstly, SAG estimates the clean image via n function calls, where n serves as a flexible hyperparameter that can be tailored to meet specific image quality requirements. Secondly, SAG uses the symplectic adjoint method to obtain the gradients accurately and efficiently in terms of the memory requirements. Extensive experiments demonstrate that SAG generates images with higher qualities compared to the baselines in both guided image and video generation tasks.

Typical diffusion models are trained to accept a particular form of conditioning, most commonly text, and cannot be conditioned on other modalities without retraining. In this work, we propose a universal guidance algorithm that enables diffusion models to be controlled by arbitrary guidance modalities without the need to retrain any use-specific components. We show that our algorithm successfully generates quality images with guidance functions including segmentation, face recognition, object detection, and classifier signals. Code is available at https://github.com/arpitbansal297/Universal-Guided-Diffusion.

A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general solution to a longstanding open problem relevant to a wide variety of applications in robotics, tracking, and control systems. The new inverse complements the Drazin inverse (which is consistent with respect to similarity transformations) and the Moore-Penrose inverse (which is consistent with respect to unitary/orthonormal transformations) to complete a trilogy of generalized matrix inverses that exhausts the standard family of analytically-important linear system transformations. Results are generalized to obtain unit-consistent and unit-invariant matrix decompositions and examples of their use are described.

Popular guidance for denoising diffusion probabilistic model (DDPM) linearly combines distinct conditional models together to provide enhanced control over samples. However, this approach overlooks nonlinear effects that become significant when guidance scale is large. To address this issue, we propose characteristic guidance, a guidance method that provides first-principle non-linear correction for classifier-free guidance. Such correction forces the guided DDPMs to respect the Fokker-Planck (FP) equation of diffusion process, in a way that is training-free and compatible with existing sampling methods. Experiments show that characteristic guidance enhances semantic characteristics of prompts and mitigate irregularities in image generation, proving effective in diverse applications ranging from simulating magnet phase transitions to latent space sampling.

Flow matching has emerged as a powerful generative modeling approach with flexible choices of source distribution. While Gaussian distributions are commonly used, the potential for better alternatives in high-dimensional data generation remains largely unexplored. In this paper, we propose a novel 2D simulation that captures high-dimensional geometric properties in an interpretable 2D setting, enabling us to analyze the learning dynamics of flow matching during training. Based on this analysis, we derive several key insights about flow matching behavior: (1) density approximation can paradoxically degrade performance due to mode discrepancy, (2) directional alignment suffers from path entanglement when overly concentrated, (3) Gaussian's omnidirectional coverage ensures robust learning, and (4) norm misalignment incurs substantial learning costs. Building on these insights, we propose a practical framework that combines norm-aligned training with directionally-pruned sampling. This approach maintains the robust omnidirectional supervision essential for stable flow learning, while eliminating initializations in data-sparse regions during inference. Importantly, our pruning strategy can be applied to any flow matching model trained with a Gaussian source, providing immediate performance gains without the need for retraining. Empirical evaluations demonstrate consistent improvements in both generation quality and sampling efficiency. Our findings provide practical insights and guidelines for source distribution design and introduce a readily applicable technique for improving existing flow matching models. Our code is available at https://github.com/kwanseokk/SourceFM.

Even if the depth maps captured by RGB-D sensors deployed in real environments are often characterized by large areas missing valid depth measurements, the vast majority of depth completion methods still assumes depth values covering all areas of the scene. To address this limitation, we introduce SteeredMarigold, a training-free, zero-shot depth completion method capable of producing metric dense depth, even for largely incomplete depth maps. SteeredMarigold achieves this by using the available sparse depth points as conditions to steer a denoising diffusion probabilistic model. Our method outperforms relevant top-performing methods on the NYUv2 dataset, in tests where no depth was provided for a large area, achieving state-of-art performance and exhibiting remarkable robustness against depth map incompleteness. Our code will be publicly available.

We consider the problem of estimating (diagonally dominant) M-matrices as precision matrices in Gaussian graphical models. These models exhibit intriguing properties, such as the existence of the maximum likelihood estimator with merely two observations for M-matrices lauritzen2019maximum,slawski2015estimation and even one observation for diagonally dominant M-matrices truell2021maximum. We propose an adaptive multiple-stage estimation method that refines the estimate by solving a weighted ell_1-regularized problem at each stage. Furthermore, we develop a unified framework based on the gradient projection method to solve the regularized problem, incorporating distinct projections to handle the constraints of M-matrices and diagonally dominant M-matrices. A theoretical analysis of the estimation error is provided. Our method outperforms state-of-the-art methods in precision matrix estimation and graph edge identification, as evidenced by synthetic and financial time-series data sets.

We present a novel adaptive optimization algorithm for large-scale machine learning problems. Equipped with a low-cost estimate of local curvature and Lipschitz smoothness, our method dynamically adapts the search direction and step-size. The search direction contains gradient information preconditioned by a well-scaled diagonal preconditioning matrix that captures the local curvature information. Our methodology does not require the tedious task of learning rate tuning, as the learning rate is updated automatically without adding an extra hyperparameter. We provide convergence guarantees on a comprehensive collection of optimization problems, including convex, strongly convex, and nonconvex problems, in both deterministic and stochastic regimes. We also conduct an extensive empirical evaluation on standard machine learning problems, justifying our algorithm's versatility and demonstrating its strong performance compared to other start-of-the-art first-order and second-order methods.

In metrology, Fisher information is an important metric that quantifies the precision that can be achieved in a measurement. For optical measurements using coherent light it has been shown that Fisher information can be expressed simply using the scattering matrix of the system. Fisher information can be maximized over the input modes to achieve maximum information states, which produce optimally precise estimates for a parameter when the system is limited by photon noise. Here, we extend this approach to multiparameter estimation, in which case Fisher information takes the form of a matrix. We consider several scalar functions of the Fisher matrix to optimize the precision in multiple parameters at the same time. We also consider strategies for dealing with nuisance parameters, which can degrade the achievable precision of other parameters but are not of interest to measure. We corroborate our findings numerically using a scattering system of 2D coupled dipoles.

Matrix-based optimizers have attracted growing interest for improving LLM training efficiency, with significant progress centered on orthogonalization/whitening based methods. While yielding substantial performance gains, a fundamental question arises: can we develop new paradigms beyond orthogonalization, pushing the efficiency frontier further? We present Adaptively Rotated Optimization (ARO, a new matrix optimization framework that treats gradient rotation as a first class design principle. ARO accelerates LLM training by performing normed steepest descent in a rotated coordinate system, where the rotation is determined by a novel norm-informed policy. This perspective yields update rules that go beyond existing orthogonalization and whitening optimizers, improving sample efficiency in practice. To make comparisons reliable, we propose a rigorously controlled benchmarking protocol that reduces confounding and bias. Under this protocol, ARO consistently outperforms AdamW (by 1.3 sim1.35times) and orthogonalization methods (by 1.1sim1.15times) in LLM pretraining at up to 8B activated parameters, and up to 8times overtrain budget, without evidence of diminishing returns. Finally, we discuss how ARO can be reformulated as a symmetry-aware optimizer grounded in rotational symmetries of residual streams, motivating advanced designs that enable computationally efficient exploitation of cross-layer/cross module couplings.

We focus on addressing the dense backward propagation issue for training efficiency of N:M fine-grained sparsity that preserves at most N out of M consecutive weights and achieves practical speedups supported by the N:M sparse tensor core. Therefore, we present a novel method of Bi-directional Masks (Bi-Mask) with its two central innovations in: 1) Separate sparse masks in the two directions of forward and backward propagation to obtain training acceleration. It disentangles the forward and backward weight sparsity and overcomes the very dense gradient computation. 2) An efficient weight row permutation method to maintain performance. It picks up the permutation candidate with the most eligible N:M weight blocks in the backward to minimize the gradient gap between traditional uni-directional masks and our bi-directional masks. Compared with existing uni-directional scenario that applies a transposable mask and enables backward acceleration, our Bi-Mask is experimentally demonstrated to be more superior in performance. Also, our Bi-Mask performs on par with or even better than methods that fail to achieve backward acceleration. Project of this paper is available at https://github.com/zyxxmu/Bi-Mask.

Hyperspectral unmixing (HU) plays a fundamental role in a wide range of hyperspectral applications. It is still challenging due to the common presence of outlier channels and the large solution space. To address the above two issues, we propose a novel model by emphasizing both robust representation and learning-based sparsity. Specifically, we apply the ell_{2,1}-norm to measure the representation error, preventing outlier channels from dominating our objective. In this way, the side effects of outlier channels are greatly relieved. Besides, we observe that the mixed level of each pixel varies over image grids. Based on this observation, we exploit a learning-based sparsity method to simultaneously learn the HU results and a sparse guidance map. Via this guidance map, the sparsity constraint in the ell_{p}!left(!0!<! p!leq!1right)-norm is adaptively imposed according to the learnt mixed level of each pixel. Compared with state-of-the-art methods, our model is better suited to the real situation, thus expected to achieve better HU results. The resulted objective is highly non-convex and non-smooth, and so it is hard to optimize. As a profound theoretical contribution, we propose an efficient algorithm to solve it. Meanwhile, the convergence proof and the computational complexity analysis are systematically provided. Extensive evaluations verify that our method is highly promising for the HU task---it achieves very accurate guidance maps and much better HU results compared with state-of-the-art methods.

Training-free guided generation is a widely used and powerful technique that allows the end user to exert further control over the generative process of flow/diffusion models. Generally speaking, two families of techniques have emerged for solving this problem for gradient-based guidance: namely, posterior guidance (i.e., guidance via projecting the current sample to the target distribution via the target prediction model) and end-to-end guidance (i.e., guidance by performing backpropagation throughout the entire ODE solve). In this work, we show that these two seemingly separate families can actually be unified by looking at posterior guidance as a greedy strategy of end-to-end guidance. We explore the theoretical connections between these two families and provide an in-depth theoretical of these two techniques relative to the continuous ideal gradients. Motivated by this analysis we then show a method for interpolating between these two families enabling a trade-off between compute and accuracy of the guidance gradients. We then validate this work on several inverse image problems and property-guided molecular generation.

When a language model asserts that "the capital of Australia is Sydney," does it know this is wrong? We characterize the geometry of correctness representations across 9 models from 5 architecture families. The structure is simple: the discriminative signal occupies 3-8 dimensions, performance degrades with additional dimensions, and no nonlinear classifier improves over linear separation. Centroid distance in the low-dimensional subspace matches trained probe performance (0.90 AUC), enabling few-shot detection: on GPT-2, 25 labeled examples achieve 89% of full-data accuracy. We validate causally through activation steering: the learned direction produces 10.9 percentage point changes in error rates while random directions show no effect. Internal probes achieve 0.80-0.97 AUC; output-based methods (P(True), semantic entropy) achieve only 0.44-0.64 AUC. The correctness signal exists internally but is not expressed in outputs. That centroid distance matches probe performance indicates class separation is a mean shift, making detection geometric rather than learned.

We introduce directional routing, a lightweight mechanism that gives each transformer attention head learned suppression directions controlled by a shared router, at 3.9% parameter cost. We train a 433M-parameter model alongside an identical baseline in a single run, then trace the resulting circuits through mechanistic interpretability. Routing becomes the model's dominant computational pathway. Disabling it collapses factual recall to near-zero probability across all 8 test prompts and drops induction accuracy from 93.4% to 0.0%. Knocking out individual attention heads has negligible effect: the primary mover head's removal actually increases target probability, and induction heads retain 98.6% accuracy without their strongest member. The coordination mechanism is irreplaceable; the components it coordinates are not. The model also self-organizes, without explicit pressure, into two regimes: domain-adaptive routing in early layers and fixed syntactic pruning in late layers, where the least-varying layer is the most critical (+42.6 PPL when disabled). Routing reduces perplexity 31-56% relative to the baseline, though downstream multiple-choice benchmarks do not yet reflect these gains.

Reinforcement learning fine-tuning has proven effective for steering generative diffusion models toward desired properties in image and molecular domains. Graph diffusion models have similarly been applied to combinatorial structure generation, including neural architecture search (NAS). However, neural architectures are directed acyclic graphs (DAGs) where edge direction encodes functional semantics such as data flow-information that existing graph diffusion methods, designed for undirected structures, discard. We propose Directed Graph Policy Optimization (DGPO), which extends reinforcement learning fine-tuning of discrete graph diffusion models to DAGs via topological node ordering and positional encoding. Validated on NAS-Bench-101 and NAS-Bench-201, DGPO matches the benchmark optimum on all three NAS-Bench-201 tasks (91.61%, 73.49%, 46.77%). The central finding is that the model learns transferable structural priors: pretrained on only 7% of the search space, it generates near-oracle architectures after fine-tuning, within 0.32 percentage points of the full-data model and extrapolating 7.3 percentage points beyond its training ceiling. Bidirectional control experiments confirm genuine reward-driven steering, with inverse optimization reaching near random-chance accuracy (9.5%). These results demonstrate that reinforcement learning-steered discrete diffusion, once extended to handle directionality, provides a controllable generative framework for directed combinatorial structures.

We introduce the problem of active causal structure learning with advice. In the typical well-studied setting, the learning algorithm is given the essential graph for the observational distribution and is asked to recover the underlying causal directed acyclic graph (DAG) G^* while minimizing the number of interventions made. In our setting, we are additionally given side information about G^* as advice, e.g. a DAG G purported to be G^*. We ask whether the learning algorithm can benefit from the advice when it is close to being correct, while still having worst-case guarantees even when the advice is arbitrarily bad. Our work is in the same space as the growing body of research on algorithms with predictions. When the advice is a DAG G, we design an adaptive search algorithm to recover G^* whose intervention cost is at most O(max{1, log psi}) times the cost for verifying G^*; here, psi is a distance measure between G and G^* that is upper bounded by the number of variables n, and is exactly 0 when G=G^*. Our approximation factor matches the state-of-the-art for the advice-less setting.

Denoising Diffusion Models (DDMs) have emerged as a strong competitor to Generative Adversarial Networks (GANs). However, despite their widespread use in image synthesis and editing applications, their latent space is still not as well understood. Recently, a semantic latent space for DDMs, coined `h-space', was shown to facilitate semantic image editing in a way reminiscent of GANs. The h-space is comprised of the bottleneck activations in the DDM's denoiser across all timesteps of the diffusion process. In this paper, we explore the properties of h-space and propose several novel methods for finding meaningful semantic directions within it. We start by studying unsupervised methods for revealing interpretable semantic directions in pretrained DDMs. Specifically, we show that global latent directions emerge as the principal components in the latent space. Additionally, we provide a novel method for discovering image-specific semantic directions by spectral analysis of the Jacobian of the denoiser w.r.t. the latent code. Next, we extend the analysis by finding directions in a supervised fashion in unconditional DDMs. We demonstrate how such directions can be found by relying on either a labeled data set of real images or by annotating generated samples with a domain-specific attribute classifier. We further show how to semantically disentangle the found direction by simple linear projection. Our approaches are applicable without requiring any architectural modifications, text-based guidance, CLIP-based optimization, or model fine-tuning.

This paper makes a formal connection between two families of widely used matrix factorization algorithms in numerical linear algebra. One family consists of the Jacobi eigenvalue algorithm and its variants for computing the Hermitian eigendecomposition and singular value decomposition. The other consists of Gaussian elimination and the Gram-Schmidt procedure with various pivoting rules for computing the Cholesky decomposition and QR decomposition respectively. Both families are cast as special cases of a more general class of factorization algorithms. We provide a randomized pivoting rule that applies to this general class (which differs substantially from the usual pivoting rules for Gaussian elimination / Gram-Schmidt) which results in the same linear rate of convergence for each algorithm, irrespective of which factorization it computes. A second important consequence of this randomized pivoting rule is a provable, effective bound on the numerical stability of the Jacobi eigenvalue algorithm, which addresses a longstanding open problem of Demmel and Veseli\'c `92.

Recently, text-to-image generation has exhibited remarkable advancements, with the ability to produce visually impressive results. In contrast, text-to-3D generation has not yet reached a comparable level of quality. Existing methods primarily rely on text-guided score distillation sampling (SDS), and they encounter difficulties in transferring 2D attributes of the generated images to 3D content. In this work, we aim to develop an effective 3D generative model capable of synthesizing high-resolution textured meshes by leveraging both textual and image information. To this end, we introduce Guide3D, a zero-shot text-and-image-guided generative model for 3D avatar generation based on diffusion models. Our model involves (1) generating sparse-view images of a text-consistent character using diffusion models, and (2) jointly optimizing multi-resolution differentiable marching tetrahedral grids with pixel-aligned image features. We further propose a similarity-aware feature fusion strategy for efficiently integrating features from different views. Moreover, we introduce two novel training objectives as an alternative to calculating SDS, significantly enhancing the optimization process. We thoroughly evaluate the performance and components of our framework, which outperforms the current state-of-the-art in producing topologically and structurally correct geometry and high-resolution textures. Guide3D enables the direct transfer of 2D-generated images to the 3D space. Our code will be made publicly available.

An experimental demonstration of directivities exceeding the fundamental Kildal limit, a phenomenon called superdirectivity, is provided for spherical high-index dielectric antennas with an electric dipole excitation. A directivity factor of about 10 with a total efficiency of more than 80\% for an antenna having a size of a third of the wavelength was measured. High directivities are shown to be associated with constructive interference of particular electric and magnetic modes of an open spherical resonator. Both analytic solution for a point dipole and a full-wave rigorous simulation for a realistic dipole antenna were employed for optimization and analysis, yielding an excellent agreement between experimentally measured and numerically predicted directivities. The use of high-index low-loss ceramics can significantly reduce the physical size of such antennas while maintaining their overall high radiation efficiency. Such antennas can be attractive for various high-frequency applications, such as antennas for the Internet of things, smart city systems, 5G network systems, and others. The demonstrated concept can be scaled in frequency.

We propose the zero-shot Vision-and-Language Navigation with Collision Mitigation (VLN-CM), which takes these considerations. VLN-CM is composed of four modules and predicts the direction and distance of the next movement at each step. We utilize large foundation models for each modules. To select the direction, we use the Attention Spot Predictor (ASP), View Selector (VS), and Progress Monitor (PM). The ASP employs a Large Language Model (e.g. ChatGPT) to split navigation instructions into attention spots, which are objects or scenes at the location to move to (e.g. a yellow door). The VS selects from panorama images provided at 30-degree intervals the one that includes the attention spot, using CLIP similarity. We then choose the angle of the selected image as the direction to move in. The PM uses a rule-based approach to decide which attention spot to focus on next, among multiple spots derived from the instructions. If the similarity between the current attention spot and the visual observations decreases consecutively at each step, the PM determines that the agent has passed the current spot and moves on to the next one. For selecting the distance to move, we employed the Open Map Predictor (OMP). The OMP uses panorama depth information to predict an occupancy mask. We then selected a collision-free distance in the predicted direction based on the occupancy mask. We evaluated our method using the validation data of VLN-CE. Our approach showed better performance than several baseline methods, and the OPM was effective in mitigating collisions for the agent.

We introduce Directional Stimulus Prompting, a novel framework for guiding black-box large language models (LLMs) toward specific desired outputs. Instead of directly adjusting LLMs, our method employs a small tunable policy model (e.g., T5) to generate an auxiliary directional stimulus prompt for each input instance. These directional stimulus prompts act as nuanced, instance-specific hints and clues to guide LLMs in generating desired outcomes, such as including specific keywords in the generated summary. Our approach sidesteps the challenges of direct LLM tuning by optimizing the policy model to explore directional stimulus prompts that align LLMs with desired behaviors. The policy model can be optimized through 1) supervised fine-tuning using labeled data and 2) reinforcement learning from offline or online rewards based on the LLM's output. We assess our method across summarization, dialogue response generation, and chain-of-thought reasoning tasks. Our experiments demonstrate that the framework consistently improves LLMs' (e.g., ChatGPT, Codex, InstructGPT) performance on these supervised tasks using minimal labeled data. Notably, using just 80 dialogues on the MultiWOZ dataset, our approach enhances ChatGPT's performance by an impressive 41.4%, matching or surpassing some fully supervised start-of-the-art models. Additionally, the instance-specific chain-of-thought prompt generated by our approach improves InstructGPT's reasoning accuracy compared to human-crafted or automatically generated prompts. The code and data are publicly available at https://github.com/Leezekun/Directional-Stimulus-Prompting.

The upper 6 GHz (U6G) band with XL-MIMO is a key enabler for sixth-generation wireless systems, yet intelligent radiomap prediction for such systems remains challenging. Existing datasets support only small-scale arrays (up to 8x8) with predominantly isotropic antennas, far from the 1024-element directional arrays envisioned for 6G. Moreover, current methods encode array configurations as scalar parameters, forcing neural networks to extrapolate array-specific radiation patterns, which fails when predicting radiomaps for configurations absent from training data. To jointly address data scarcity and generalization limitations, this paper advances XL-MIMO radiomap prediction from three aspects. To overcome data limitations, we construct the first XL-MIMO radiomap dataset containing 78400 radiomaps across 800 urban scenes, five frequency bands (1.8-6.7 GHz), and nine array configurations up to 32x32 uniform planar arrays with directional elements. To enable systematic evaluation, we establish a comprehensive benchmark framework covering practical scenarios from coverage estimation without field measurements to generalization across unseen configurations and environments. To enable generalization to arbitrary beam configurations without retraining, we propose the beam map, a physics-informed spatial feature that analytically computes array-specific coverage patterns. By decoupling deterministic array radiation from data learned multipath propagation, beam maps shift generalization from neural network extrapolation to physics-based computation. Integrating beam maps into existing architectures reduces mean absolute error by up to 60.0% when generalizing to unseen configurations and up to 50.5% when transferring to unseen environments. The complete dataset and code are publicly available at https://lxj321.github.io/MulticonfigRadiomapDataset/.

Generative Adversarial Networks (GANs), especially the recent style-based generators (StyleGANs), have versatile semantics in the structured latent space. Latent semantics discovery methods emerge to move around the latent code such that only one factor varies during the traversal. Recently, an unsupervised method proposed a promising direction to directly use the eigenvectors of the projection matrix that maps latent codes to features as the interpretable directions. However, one overlooked fact is that the projection matrix is non-orthogonal and the number of eigenvectors is too large. The non-orthogonality would entangle semantic attributes in the top few eigenvectors, and the large dimensionality might result in meaningless variations among the directions even if the matrix is orthogonal. To avoid these issues, we propose Householder Projector, a flexible and general low-rank orthogonal matrix representation based on Householder transformations, to parameterize the projection matrix. The orthogonality guarantees that the eigenvectors correspond to disentangled interpretable semantics, while the low-rank property encourages that each identified direction has meaningful variations. We integrate our projector into pre-trained StyleGAN2/StyleGAN3 and evaluate the models on several benchmarks. Within only 1% of the original training steps for fine-tuning, our projector helps StyleGANs to discover more disentangled and precise semantic attributes without sacrificing image fidelity.

Classifier guidance is a recently introduced method to trade off mode coverage and sample fidelity in conditional diffusion models post training, in the same spirit as low temperature sampling or truncation in other types of generative models. Classifier guidance combines the score estimate of a diffusion model with the gradient of an image classifier and thereby requires training an image classifier separate from the diffusion model. It also raises the question of whether guidance can be performed without a classifier. We show that guidance can be indeed performed by a pure generative model without such a classifier: in what we call classifier-free guidance, we jointly train a conditional and an unconditional diffusion model, and we combine the resulting conditional and unconditional score estimates to attain a trade-off between sample quality and diversity similar to that obtained using classifier guidance.

This work presents a novel online model-predictive trajectory planner for robotic manipulators called BoundMPC. This planner allows the collision-free following of Cartesian reference paths in the end-effector's position and orientation, including via-points, within desired asymmetric bounds of the orthogonal path error. The path parameter synchronizes the position and orientation reference paths. The decomposition of the path error into the tangential direction, describing the path progress, and the orthogonal direction, which represents the deviation from the path, is well known for the position from the path-following control in the literature. This paper extends this idea to the orientation by utilizing the Lie theory of rotations. Moreover, the orthogonal error plane is further decomposed into basis directions to define asymmetric Cartesian error bounds easily. Using piecewise linear position and orientation reference paths with via-points is computationally very efficient and allows replanning the pose trajectories during the robot's motion. This feature makes it possible to use this planner for dynamically changing environments and varying goals. The flexibility and performance of BoundMPC are experimentally demonstrated by two scenarios on a 7-DoF Kuka LBR iiwa 14 R820 robot. The first scenario shows the transfer of a larger object from a start to a goal pose through a confined space where the object must be tilted. The second scenario deals with grasping an object from a table where the grasping point changes during the robot's motion, and collisions with other obstacles in the scene must be avoided.

Recent studies have demonstrated significant progress in aligning text-to-image diffusion models with human preference via Reinforcement Learning from Human Feedback. However, while existing methods achieve high scores on automated reward metrics, they often lead to Preference Mode Collapse (PMC)-a specific form of reward hacking where models converge on narrow, high-scoring outputs (e.g., images with monolithic styles or pervasive overexposure), severely degrading generative diversity. In this work, we introduce and quantify this phenomenon, proposing DivGenBench, a novel benchmark designed to measure the extent of PMC. We posit that this collapse is driven by over-optimization along the reward model's inherent biases. Building on this analysis, we propose Directional Decoupling Alignment (D^2-Align), a novel framework that mitigates PMC by directionally correcting the reward signal. Specifically, our method first learns a directional correction within the reward model's embedding space while keeping the model frozen. This correction is then applied to the reward signal during the optimization process, preventing the model from collapsing into specific modes and thereby maintaining diversity. Our comprehensive evaluation, combining qualitative analysis with quantitative metrics for both quality and diversity, reveals that D^2-Align achieves superior alignment with human preference.

Guidance in conditional diffusion generation is of great importance for sample quality and controllability. However, existing guidance schemes are to be desired. On one hand, mainstream methods such as classifier guidance and classifier-free guidance both require extra training with labeled data, which is time-consuming and unable to adapt to new conditions. On the other hand, training-free methods such as universal guidance, though more flexible, have yet to demonstrate comparable performance. In this work, through a comprehensive investigation into the design space, we show that it is possible to achieve significant performance improvements over existing guidance schemes by leveraging off-the-shelf classifiers in a training-free fashion, enjoying the best of both worlds. Employing calibration as a general guideline, we propose several pre-conditioning techniques to better exploit pretrained off-the-shelf classifiers for guiding diffusion generation. Extensive experiments on ImageNet validate our proposed method, showing that state-of-the-art diffusion models (DDPM, EDM, DiT) can be further improved (up to 20%) using off-the-shelf classifiers with barely any extra computational cost. With the proliferation of publicly available pretrained classifiers, our proposed approach has great potential and can be readily scaled up to text-to-image generation tasks. The code is available at https://github.com/AlexMaOLS/EluCD/tree/main.

The goal of this paper is to provide a new perspective on audio-visual target speaker extraction (AV-TSE) by decoupling the separation and target selection. Conventional AV-TSE systems typically integrate audio and visual features deeply to re-learn the entire separation process, which can act as a fidelity ceiling due to the noisy nature of in-the-wild audio-visual datasets. To address this, we propose Plug-and-Steer, which assigns high-fidelity separation to a frozen audio-only backbone and limits the role of visual modality strictly to target selection. We introduce the Latent Steering Matrix (LSM), a minimalist linear transformation that re-routes latent features within the backbone to anchor the target speaker to a designated channel. Experiments across four representative architectures show that our method effectively preserves the acoustic priors of diverse backbones, achieving perceptual quality comparable to the original backbones. Audio samples are available at: https://plugandsteer.github.io

Intervention-based model steering offers a lightweight and interpretable alternative to prompting and fine-tuning. However, by adapting strong optimization objectives from fine-tuning, current methods are susceptible to overfitting and often underperform, sometimes generating unnatural outputs. We hypothesize that this is because effective steering requires the faithful identification of internal model mechanisms, not the enforcement of external preferences. To this end, we build on the principles of distributed alignment search (DAS), the standard for causal variable localization, to propose a new steering method: Concept DAS (CDAS). While we adopt the core mechanism of DAS, distributed interchange intervention (DII), we introduce a novel distribution matching objective tailored for the steering task by aligning intervened output distributions with counterfactual distributions. CDAS differs from prior work in two main ways: first, it learns interventions via weak-supervised distribution matching rather than probability maximization; second, it uses DIIs that naturally enable bi-directional steering and allow steering factors to be derived from data, reducing the effort required for hyperparameter tuning and resulting in more faithful and stable control. On AxBench, a large-scale model steering benchmark, we show that CDAS does not always outperform preference-optimization methods but may benefit more from increased model scale. In two safety-related case studies, overriding refusal behaviors of safety-aligned models and neutralizing a chain-of-thought backdoor, CDAS achieves systematic steering while maintaining general model utility. These results indicate that CDAS is complementary to preference-optimization approaches and conditionally constitutes a robust approach to intervention-based model steering. Our code is available at https://github.com/colored-dye/concept_das.

Recently, Ainsworth et al. showed that using weight matching (WM) to minimize the L_2 distance in a permutation search of model parameters effectively identifies permutations that satisfy linear mode connectivity (LMC), in which the loss along a linear path between two independently trained models with different seeds remains nearly constant. This paper provides a theoretical analysis of LMC using WM, which is crucial for understanding stochastic gradient descent's effectiveness and its application in areas like model merging. We first experimentally and theoretically show that permutations found by WM do not significantly reduce the L_2 distance between two models and the occurrence of LMC is not merely due to distance reduction by WM in itself. We then provide theoretical insights showing that permutations can change the directions of the singular vectors, but not the singular values, of the weight matrices in each layer. This finding shows that permutations found by WM mainly align the directions of singular vectors associated with large singular values across models. This alignment brings the singular vectors with large singular values, which determine the model functionality, closer between pre-merged and post-merged models, so that the post-merged model retains functionality similar to the pre-merged models, making it easy to satisfy LMC. Finally, we analyze the difference between WM and straight-through estimator (STE), a dataset-dependent permutation search method, and show that WM outperforms STE, especially when merging three or more models.

Despite much progress in training distributed artificial intelligence (AI), building cooperative multi-agent systems with multi-agent reinforcement learning (MARL) faces challenges in sample efficiency, interpretability, and transferability. Unlike traditional learning-based methods that require extensive interaction with the environment, large language models (LLMs) demonstrate remarkable capabilities in zero-shot planning and complex reasoning. However, existing LLM-based approaches heavily rely on text-based observations and struggle with the non-Markovian nature of multi-agent interactions under partial observability. We present COMPASS, a novel multi-agent architecture that integrates vision-language models (VLMs) with a dynamic skill library and structured communication for decentralized closed-loop decision-making. The skill library, bootstrapped from demonstrations, evolves via planner-guided tasks to enable adaptive strategies. COMPASS propagates entity information through multi-hop communication under partial observability. Evaluations on the improved StarCraft Multi-Agent Challenge (SMACv2) demonstrate COMPASS's strong performance against state-of-the-art MARL baselines across both symmetric and asymmetric scenarios. Notably, in the symmetric Protoss 5v5 task, COMPASS achieved a 57\% win rate, representing a 30 percentage point advantage over QMIX (27\%). Project page can be found at https://stellar-entremet-1720bb.netlify.app/.

Magnetic navigation (MagNav) is a rising alternative to the Global Positioning System (GPS) and has proven useful for aircraft navigation. Traditional aircraft navigation systems, while effective, face limitations in precision and reliability in certain environments and against attacks. Airborne MagNav leverages the Earth's magnetic field to provide accurate positional information. However, external magnetic fields induced by aircraft electronics and Earth's large-scale magnetic fields disrupt the weaker signal of interest. We introduce a physics-informed approach using Tolles-Lawson coefficients for compensation and Liquid Time-Constant Networks (LTCs) to remove complex, noisy signals derived from the aircraft's magnetic sources. Using real flight data with magnetometer measurements and aircraft measurements, we observe up to a 64% reduction in aeromagnetic compensation error (RMSE nT), outperforming conventional models. This significant improvement underscores the potential of a physics-informed, machine learning approach for extracting clean, reliable, and accurate magnetic signals for MagNav positional estimation.

Recent video diffusion models demonstrate strong potential in spatial intelligence tasks due to their rich latent world priors. However, this potential is hindered by their limited controllability and geometric inconsistency, creating a gap between their strong priors and their practical use in 3D/4D tasks. As a result, current approaches often rely on retraining or fine-tuning, which risks degrading pretrained knowledge and incurs high computational costs. To address this, we propose WorldForge, a training-free, inference-time framework composed of three tightly coupled modules. Intra-Step Recursive Refinement introduces a recursive refinement mechanism during inference, which repeatedly optimizes network predictions within each denoising step to enable precise trajectory injection. Flow-Gated Latent Fusion leverages optical flow similarity to decouple motion from appearance in the latent space and selectively inject trajectory guidance into motion-related channels. Dual-Path Self-Corrective Guidance compares guided and unguided denoising paths to adaptively correct trajectory drift caused by noisy or misaligned structural signals. Together, these components inject fine-grained, trajectory-aligned guidance without training, achieving both accurate motion control and photorealistic content generation. Extensive experiments across diverse benchmarks validate our method's superiority in realism, trajectory consistency, and visual fidelity. This work introduces a novel plug-and-play paradigm for controllable video synthesis, offering a new perspective on leveraging generative priors for spatial intelligence.

Indoor navigation remains a critical challenge for people with visual impairments. The current solutions mainly rely on infrastructure-based systems, which limit their ability to navigate safely in dynamic environments. We propose a novel navigation approach that utilizes a foundation model to transform floor plans into navigable knowledge graphs and generate human-readable navigation instructions. Floorplan2Guide integrates a large language model (LLM) to extract spatial information from architectural layouts, reducing the manual preprocessing required by earlier floorplan parsing methods. Experimental results indicate that few-shot learning improves navigation accuracy in comparison to zero-shot learning on simulated and real-world evaluations. Claude 3.7 Sonnet achieves the highest accuracy among the evaluated models, with 92.31%, 76.92%, and 61.54% on the short, medium, and long routes, respectively, under 5-shot prompting of the MP-1 floor plan. The success rate of graph-based spatial structure is 15.4% higher than that of direct visual reasoning among all models, which confirms that graphical representation and in-context learning enhance navigation performance and make our solution more precise for indoor navigation of Blind and Low Vision (BLV) users.

Recent advancements in Text-to-Image (T2I) diffusion models have demonstrated impressive success in generating high-quality images with zero-shot generalization capabilities. Yet, current models struggle to closely adhere to prompt semantics, often misrepresenting or overlooking specific attributes. To address this, we propose a simple, training-free approach that modulates the guidance direction of diffusion models during inference. We first decompose the prompt semantics into a set of concepts, and monitor the guidance trajectory in relation to each concept. Our key observation is that deviations in model's adherence to prompt semantics are highly correlated with divergence of the guidance from one or more of these concepts. Based on this observation, we devise a technique to steer the guidance direction towards any concept from which the model diverges. Extensive experimentation validates that our method improves the semantic alignment of images generated by diffusion models in response to prompts. Project page is available at: https://korguy.github.io/

The primary axes of interest in image-generating diffusion models are image quality, the amount of variation in the results, and how well the results align with a given condition, e.g., a class label or a text prompt. The popular classifier-free guidance approach uses an unconditional model to guide a conditional model, leading to simultaneously better prompt alignment and higher-quality images at the cost of reduced variation. These effects seem inherently entangled, and thus hard to control. We make the surprising observation that it is possible to obtain disentangled control over image quality without compromising the amount of variation by guiding generation using a smaller, less-trained version of the model itself rather than an unconditional model. This leads to significant improvements in ImageNet generation, setting record FIDs of 1.01 for 64x64 and 1.25 for 512x512, using publicly available networks. Furthermore, the method is also applicable to unconditional diffusion models, drastically improving their quality.

Blind image restoration remains a significant challenge in low-level vision tasks. Recently, denoising diffusion models have shown remarkable performance in image synthesis. Guided diffusion models, leveraging the potent generative priors of pre-trained models along with a differential guidance loss, have achieved promising results in blind image restoration. However, these models typically consider data consistency solely in the spatial domain, often resulting in distorted image content. In this paper, we propose a novel frequency-aware guidance loss that can be integrated into various diffusion models in a plug-and-play manner. Our proposed guidance loss, based on 2D discrete wavelet transform, simultaneously enforces content consistency in both the spatial and frequency domains. Experimental results demonstrate the effectiveness of our method in three blind restoration tasks: blind image deblurring, imaging through turbulence, and blind restoration for multiple degradations. Notably, our method achieves a significant improvement in PSNR score, with a remarkable enhancement of 3.72\,dB in image deblurring. Moreover, our method exhibits superior capability in generating images with rich details and reduced distortion, leading to the best visual quality.

Recent advances in large-scale text-to-image diffusion models have heightened concerns about their potential misuse, especially in generating harmful or misleading content. This underscores the urgent need for effective machine unlearning, i.e., removing specific knowledge or concepts from pretrained models without compromising overall performance. One possible approach is Low-Rank Adaptation (LoRA), which offers an efficient means to fine-tune models for targeted unlearning. However, LoRA often inadvertently alters unrelated content, leading to diminished image fidelity and realism. To address this limitation, we introduce UnGuide -- a novel approach which incorporates UnGuidance, a dynamic inference mechanism that leverages Classifier-Free Guidance (CFG) to exert precise control over the unlearning process. UnGuide modulates the guidance scale based on the stability of a few first steps of denoising processes, enabling selective unlearning by LoRA adapter. For prompts containing the erased concept, the LoRA module predominates and is counterbalanced by the base model; for unrelated prompts, the base model governs generation, preserving content fidelity. Empirical results demonstrate that UnGuide achieves controlled concept removal and retains the expressive power of diffusion models, outperforming existing LoRA-based methods in both object erasure and explicit content removal tasks.

LLMs are multilingual by training, yet their lingua franca is often English, reflecting English language dominance in pretraining. Other languages remain in parametric memory but are systematically suppressed. We argue that language defaultness is governed by a sparse, low-rank control circuit, language neurons, that can be mechanistically isolated and safely steered. We introduce Neural FOXP2, that makes a chosen language (Hindi or Spanish) primary in a model by steering language-specific neurons. Neural FOXP2 proceeds in three stages: (i) Localize: We train per-layer SAEs so each activation decomposes into a small set of active feature components. For every feature, we quantify English vs. Hindi/Spanish selectivity overall logit-mass lift toward the target-language token set. Tracing the top-ranked features back to their strongest contributing units yields a compact language-neuron set. (ii) Steering directions: We localize controllable language-shift geometry via a spectral low-rank analysis. For each layer, we build English to target activation-difference matrices and perform layerwise SVD to extract the dominant singular directions governing language change. The eigengap and effective-rank spectra identify a compact steering subspace and an empirically chosen intervention window (where these directions are strongest and most stable). (iii) Steer: We apply a signed, sparse activation shift targeted to the language neurons. Concretely, within low to mid layers we add a positive steering along the target-language dominant directions and a compensating negative shift toward the null space for the English neurons, yielding controllable target-language defaultness.

Symmetric Positive Definite (SPD) matrices are ubiquitous in data analysis under the form of covariance matrices or correlation matrices. Several O(n)-invariant Riemannian metrics were defined on the SPD cone, in particular the kernel metrics introduced by Hiai and Petz. The class of kernel metrics interpolates between many classical O(n)-invariant metrics and it satisfies key results of stability and completeness. However, it does not contain all the classical O(n)-invariant metrics. Therefore in this work, we investigate super-classes of kernel metrics and we study which key results remain true. We also introduce an additional key result called cometric-stability, a crucial property to implement geodesics with a Hamiltonian formulation. Our method to build intermediate embedded classes between O(n)-invariant metrics and kernel metrics is to give a characterization of the whole class of O(n)-invariant metrics on SPD matrices and to specify requirements on metrics one by one until we reach kernel metrics. As a secondary contribution, we synthesize the literature on the main O(n)-invariant metrics, we provide the complete formula of the sectional curvature of the affine-invariant metric and the formula of the geodesic parallel transport between commuting matrices for the Bures-Wasserstein metric.

Radio maps (RMs) serve as a critical foundation for enabling environment-aware wireless communication, as they provide the spatial distribution of wireless channel characteristics. Despite recent progress in RM construction using data-driven approaches, most existing methods focus solely on pathloss prediction in a fixed 2D plane, neglecting key parameters such as direction of arrival (DoA), time of arrival (ToA), and vertical spatial variations. Such a limitation is primarily due to the reliance on static learning paradigms, which hinder generalization beyond the training data distribution. To address these challenges, we propose UrbanRadio3D, a large-scale, high-resolution 3D RM dataset constructed via ray tracing in realistic urban environments. UrbanRadio3D is over 37times3 larger than previous datasets across a 3D space with 3 metrics as pathloss, DoA, and ToA, forming a novel 3Dtimes33D dataset with 7times3 more height layers than prior state-of-the-art (SOTA) dataset. To benchmark 3D RM construction, a UNet with 3D convolutional operators is proposed. Moreover, we further introduce RadioDiff-3D, a diffusion-model-based generative framework utilizing the 3D convolutional architecture. RadioDiff-3D supports both radiation-aware scenarios with known transmitter locations and radiation-unaware settings based on sparse spatial observations. Extensive evaluations on UrbanRadio3D validate that RadioDiff-3D achieves superior performance in constructing rich, high-dimensional radio maps under diverse environmental dynamics. This work provides a foundational dataset and benchmark for future research in 3D environment-aware communication. The dataset is available at https://github.com/UNIC-Lab/UrbanRadio3D.

Classifier-free guidance is a key component for enhancing the performance of conditional generative models across diverse tasks. While it has previously demonstrated remarkable improvements for the sample quality, it has only been exclusively employed for diffusion models. In this paper, we integrate classifier-free guidance into Flow Matching (FM) models, an alternative simulation-free approach that trains Continuous Normalizing Flows (CNFs) based on regressing vector fields. We explore the usage of Guided Flows for a variety of downstream applications. We show that Guided Flows significantly improves the sample quality in conditional image generation and zero-shot text-to-speech synthesis, boasting state-of-the-art performance. Notably, we are the first to apply flow models for plan generation in the offline reinforcement learning setting, showcasing a 10x speedup in computation compared to diffusion models while maintaining comparable performance.

In recent decades, several assistive technologies have been developed for visually impaired and blind (VIB) individuals to improve their ability to navigate independently and safely. At the same time, simultaneous localization and mapping (SLAM) techniques have become sufficiently robust and efficient to be adopted in the development of these assistive technologies. In this paper, we first report the results of an anonymous worldwide survey conducted with VIB people to understand their experiences, needs, and challenges in navigation, differentiating our approach from prior work that often has a limited geographic scope and focuses on specific challenges. We then present a systematic literature review of recent studies on SLAM-based solutions for VIB people. This review explores various SLAM techniques employed in this context. We discuss the advantages and limitations of these techniques for VIB navigation. Moreover, we examined a range of challenging situations addressed in the studies included in this review. We explain how SLAM-based solutions offer potential to improve the ability of visually impaired individuals to navigate effectively. Finally, we present future opportunities and challenges in this domain.

Projection maintenance is one of the core data structure tasks. Efficient data structures for projection maintenance have led to recent breakthroughs in many convex programming algorithms. In this work, we further extend this framework to the Kronecker product structure. Given a constraint matrix {sf A} and a positive semi-definite matrix Win R^{ntimes n} with a sparse eigenbasis, we consider the task of maintaining the projection in the form of {sf B}^top({sf B}{sf B}^top)^{-1}{sf B}, where {sf B}={sf A}(Wotimes I) or {sf B}={sf A}(W^{1/2}otimes W^{1/2}). At each iteration, the weight matrix W receives a low rank change and we receive a new vector h. The goal is to maintain the projection matrix and answer the query {sf B}^top({sf B}{sf B}^top)^{-1}{sf B}h with good approximation guarantees. We design a fast dynamic data structure for this task and it is robust against an adaptive adversary. Following the beautiful and pioneering work of [Beimel, Kaplan, Mansour, Nissim, Saranurak and Stemmer, STOC'22], we use tools from differential privacy to reduce the randomness required by the data structure and further improve the running time.

Diffusion models have demonstrated remarkable progress in image generation quality, especially when guidance is used to control the generative process. However, guidance requires a large amount of image-annotation pairs for training and is thus dependent on their availability, correctness and unbiasedness. In this paper, we eliminate the need for such annotation by instead leveraging the flexibility of self-supervision signals to design a framework for self-guided diffusion models. By leveraging a feature extraction function and a self-annotation function, our method provides guidance signals at various image granularities: from the level of holistic images to object boxes and even segmentation masks. Our experiments on single-label and multi-label image datasets demonstrate that self-labeled guidance always outperforms diffusion models without guidance and may even surpass guidance based on ground-truth labels, especially on unbalanced data. When equipped with self-supervised box or mask proposals, our method further generates visually diverse yet semantically consistent images, without the need for any class, box, or segment label annotation. Self-guided diffusion is simple, flexible and expected to profit from deployment at scale. Source code will be at: https://taohu.me/sgdm/

Classifier guidance -- using the gradients of an image classifier to steer the generations of a diffusion model -- has the potential to dramatically expand the creative control over image generation and editing. However, currently classifier guidance requires either training new noise-aware models to obtain accurate gradients or using a one-step denoising approximation of the final generation, which leads to misaligned gradients and sub-optimal control. We highlight this approximation's shortcomings and propose a novel guidance method: Direct Optimization of Diffusion Latents (DOODL), which enables plug-and-play guidance by optimizing diffusion latents w.r.t. the gradients of a pre-trained classifier on the true generated pixels, using an invertible diffusion process to achieve memory-efficient backpropagation. Showcasing the potential of more precise guidance, DOODL outperforms one-step classifier guidance on computational and human evaluation metrics across different forms of guidance: using CLIP guidance to improve generations of complex prompts from DrawBench, using fine-grained visual classifiers to expand the vocabulary of Stable Diffusion, enabling image-conditioned generation with a CLIP visual encoder, and improving image aesthetics using an aesthetic scoring network. Code at https://github.com/salesforce/DOODL.

Uniform random rotations are a useful primitive in applications such as fast Johnson-Lindenstrauss embeddings, kernel approximation, communication-efficient learning, and recent AI compression pipelines, but they are computationally expensive to generate and apply in high dimensions. A common practical replacement is repeated structured random rotations built from Walsh-Hadamard transforms and random sign diagonals. Applying the structured random rotation twice has been shown empirically to be useful, but the supporting theory is still limited. In this paper we study the approximation quality achieved when using this two-block structured Hadamard rotation. Our results are both positive and negative. On the positive side, we prove that every fixed coordinate of the two-block transform converges uniformly, over all inputs, to the corresponding coordinate of a uniformly rotated vector, with an explicit Kolmogorov-distance bound of order d^{-1/5}. On the negative side, we prove an explicit lower bound on the Wasserstein distance between the full vector distributions, showing that the two-block transform is not a globally accurate surrogate for a uniform random rotation in the worst case. For the extremal input used in the lower bound, we also prove a matching asymptotic upper bound, showing that the lower-bound scale is sharp for that input. Taken together, the results identify a clear separation between one-dimensional marginal behavior, where approximation improves with dimension, and full high-dimensional geometry, where a nonvanishing discrepancy remains. This provides a partial theoretical explanation for the empirical success of structured Hadamard rotations in some algorithms, while also clarifying the limitations of treating them as drop-in replacements for true uniform random rotations.

The potential of applying diffusion models (DMs) for multiple antenna communications is discussed. A unified framework of applying DM for multiple antenna tasks is first proposed. Then, the tasks are innovatively divided into two categories, i.e., decision-making tasks and generation tasks, depending on whether an optimization of system parameters is involved. For each category, it is conceived 1) how the framework can be used for each task and 2) why the DM is superior to traditional artificial intelligence (TAI) and conventional optimization tasks. It is highlighted that the DMs are well-suited for scenarios with strong interference and noise, excelling in modeling complex data distribution and exploring better actions. A case study of learning beamforming with a DM is then provided, to demonstrate the superiority of the DMs with simulation results. Finally, the applications of DM for emerging multiple antenna technologies and promising research directions are discussed.

Objective: Electroencephalography signals are recorded as a multidimensional dataset. We propose a new framework based on the augmented covariance extracted from an autoregressive model to improve motor imagery classification. Methods: From the autoregressive model can be derived the Yule-Walker equations, which show the emergence of a symmetric positive definite matrix: the augmented covariance matrix. The state-of the art for classifying covariance matrices is based on Riemannian Geometry. A fairly natural idea is therefore to extend the standard approach using these augmented covariance matrices. The methodology for creating the augmented covariance matrix shows a natural connection with the delay embedding theorem proposed by Takens for dynamical systems. Such an embedding method is based on the knowledge of two parameters: the delay and the embedding dimension, respectively related to the lag and the order of the autoregressive model. This approach provides new methods to compute the hyper-parameters in addition to standard grid search. Results: The augmented covariance matrix performed noticeably better than any state-of-the-art methods. We will test our approach on several datasets and several subjects using the MOABB framework, using both within-session and cross-session evaluation. Conclusion: The improvement in results is due to the fact that the augmented covariance matrix incorporates not only spatial but also temporal information, incorporating nonlinear components of the signal through an embedding procedure, which allows the leveraging of dynamical systems algorithms. Significance: These results extend the concepts and the results of the Riemannian distance based classification algorithm.

Recently, diffusion models have achieved great success in mono-channel audio generation. However, when it comes to stereo audio generation, the soundscapes often have a complex scene of multiple objects and directions. Controlling stereo audio with spatial contexts remains challenging due to high data costs and unstable generative models. To the best of our knowledge, this work represents the first attempt to address these issues. We first construct a large-scale, simulation-based, and GPT-assisted dataset, BEWO-1M, with abundant soundscapes and descriptions even including moving and multiple sources. Beyond text modality, we have also acquired a set of images and rationally paired stereo audios through retrieval to advance multimodal generation. Existing audio generation models tend to generate rather random and indistinct spatial audio. To provide accurate guidance for Latent Diffusion Models, we introduce the SpatialSonic model utilizing spatial-aware encoders and azimuth state matrices to reveal reasonable spatial guidance. By leveraging spatial guidance, our model not only achieves the objective of generating immersive and controllable spatial audio from text but also extends to other modalities as the pioneer attempt. Finally, under fair settings, we conduct subjective and objective evaluations on simulated and real-world data to compare our approach with prevailing methods. The results demonstrate the effectiveness of our method, highlighting its capability to generate spatial audio that adheres to physical rules.

We study the class of location-scale or heteroscedastic noise models (LSNMs), in which the effect Y can be written as a function of the cause X and a noise source N independent of X, which may be scaled by a positive function g over the cause, i.e., Y = f(X) + g(X)N. Despite the generality of the model class, we show the causal direction is identifiable up to some pathological cases. To empirically validate these theoretical findings, we propose two estimators for LSNMs: an estimator based on (non-linear) feature maps, and one based on neural networks. Both model the conditional distribution of Y given X as a Gaussian parameterized by its natural parameters. When the feature maps are correctly specified, we prove that our estimator is jointly concave, and a consistent estimator for the cause-effect identification task. Although the the neural network does not inherit those guarantees, it can fit functions of arbitrary complexity, and reaches state-of-the-art performance across benchmarks.

Explorable 3D world generation from a single image or text prompt forms a cornerstone of spatial intelligence. Recent works utilize video model to achieve wide-scope and generalizable 3D world generation. However, existing approaches often suffer from a limited scope in the generated scenes. In this work, we propose Matrix-3D, a framework that utilize panoramic representation for wide-coverage omnidirectional explorable 3D world generation that combines conditional video generation and panoramic 3D reconstruction. We first train a trajectory-guided panoramic video diffusion model that employs scene mesh renders as condition, to enable high-quality and geometrically consistent scene video generation. To lift the panorama scene video to 3D world, we propose two separate methods: (1) a feed-forward large panorama reconstruction model for rapid 3D scene reconstruction and (2) an optimization-based pipeline for accurate and detailed 3D scene reconstruction. To facilitate effective training, we also introduce the Matrix-Pano dataset, the first large-scale synthetic collection comprising 116K high-quality static panoramic video sequences with depth and trajectory annotations. Extensive experiments demonstrate that our proposed framework achieves state-of-the-art performance in panoramic video generation and 3D world generation. See more in https://matrix-3d.github.io.

Matrix manifolds, such as manifolds of Symmetric Positive Definite (SPD) matrices and Grassmann manifolds, appear in many applications. Recently, by applying the theory of gyrogroups and gyrovector spaces that is a powerful framework for studying hyperbolic geometry, some works have attempted to build principled generalizations of Euclidean neural networks on matrix manifolds. However, due to the lack of many concepts in gyrovector spaces for the considered manifolds, e.g., the inner product and gyroangles, techniques and mathematical tools provided by these works are still limited compared to those developed for studying hyperbolic geometry. In this paper, we generalize some notions in gyrovector spaces for SPD and Grassmann manifolds, and propose new models and layers for building neural networks on these manifolds. We show the effectiveness of our approach in two applications, i.e., human action recognition and knowledge graph completion.

We introduce a method for generating realistic pedestrian trajectories and full-body animations that can be controlled to meet user-defined goals. We draw on recent advances in guided diffusion modeling to achieve test-time controllability of trajectories, which is normally only associated with rule-based systems. Our guided diffusion model allows users to constrain trajectories through target waypoints, speed, and specified social groups while accounting for the surrounding environment context. This trajectory diffusion model is integrated with a novel physics-based humanoid controller to form a closed-loop, full-body pedestrian animation system capable of placing large crowds in a simulated environment with varying terrains. We further propose utilizing the value function learned during RL training of the animation controller to guide diffusion to produce trajectories better suited for particular scenarios such as collision avoidance and traversing uneven terrain. Video results are available on the project page at https://nv-tlabs.github.io/trace-pace .

Recently, neural network (NN)-based image compression studies have actively been made and has shown impressive performance in comparison to traditional methods. However, most of the works have focused on non-scalable image compression (single-layer coding) while spatially scalable image compression has drawn less attention although it has many applications. In this paper, we propose a novel NN-based spatially scalable image compression method, called COMPASS, which supports arbitrary-scale spatial scalability. Our proposed COMPASS has a very flexible structure where the number of layers and their respective scale factors can be arbitrarily determined during inference. To reduce the spatial redundancy between adjacent layers for arbitrary scale factors, our COMPASS adopts an inter-layer arbitrary scale prediction method, called LIFF, based on implicit neural representation. We propose a combined RD loss function to effectively train multiple layers. Experimental results show that our COMPASS achieves BD-rate gain of -58.33% and -47.17% at maximum compared to SHVC and the state-of-the-art NN-based spatially scalable image compression method, respectively, for various combinations of scale factors. Our COMPASS also shows comparable or even better coding efficiency than the single-layer coding for various scale factors.

Emerging from low-level vision theory, steerable filters found their counterpart in prior work on steerable convolutional neural networks equivariant to rigid transformations. In our work, we propose a steerable feed-forward learning-based approach that consists of neurons with spherical decision surfaces and operates on point clouds. Such spherical neurons are obtained by conformal embedding of Euclidean space and have recently been revisited in the context of learning representations of point sets. Focusing on 3D geometry, we exploit the isometry property of spherical neurons and derive a 3D steerability constraint. After training spherical neurons to classify point clouds in a canonical orientation, we use a tetrahedron basis to quadruplicate the neurons and construct rotation-equivariant spherical filter banks. We then apply the derived constraint to interpolate the filter bank outputs and, thus, obtain a rotation-invariant network. Finally, we use a synthetic point set and real-world 3D skeleton data to verify our theoretical findings. The code is available at https://github.com/pavlo-melnyk/steerable-3d-neurons.

Transitioning bidirectional video diffusion models into an autoregressive paradigm improves the interactivity of video world models, but existing causal pipelines need many stages (control fine-tuning, autoregressive training, causal initialization, few-step distillation) and still trail bidirectional models in quality due to error accumulation. Recent world models such as Yume-1.5 and Matrix-Game-3.0 instead adopt a bidirectional autoregressive approach, gaining fidelity and stable long-horizon rollout from self-correcting error propagation, yet open-source frameworks (e.g., minWM) support only causal models. We present BiWM, the first full-stack framework for interactive video world models under the bidirectional autoregressive paradigm, jointly optimizing generation quality and inference speed. From a pretrained video backbone, BiWM injects camera control by fine-tuning, then runs a few-step Distribution Matching Distillation (DMD) stage that turns the backbone into an action/camera-controllable world model: just two training stages instead of four in minWM, converging in a few hundred steps on 8xH200 GPUs. A single recipe spans Wan2.1-1.3B, Wan2.2-5B, HunyuanVideo-1.5-8B, and LTX-2.3-22B, and also supports secondary fine-tuning of existing bidirectional models. BiWM enables real-world camera control where minWM loses controllability, integrates pluggable history compression (FramePack-style and PackForcing-style) for long rollouts, and offers an optional NVFP4 4-bit training/inference pipeline. To counter DMD's mode-seeking degradation, we add GAN and mass-covering forward-KL objectives that preserve scene dynamics. We open-source BiWM for resource-constrained research and high-fidelity environment simulation.

Local guidance has recently proven to be a powerful driver of empirical performance in real-time, suboptimal multi-agent pathfinding (MAPF), improving the scalable configuration-based solver LaCAM. By injecting informative spatiotemporal cues around each agent, local guidance mitigates congestion, reduces waiting, and remains scalable enough even with tight time budgets, yielding state-of-the-art performance for one-shot MAPF. This study asks whether the same benefits can be lifted to the lifelong setting (LMAPF), where tasks arrive continuously and improvements in per-step plans can increase task completion throughput over long horizons. We propose LLLG, a Lifelong version of LaCAM enhanced with Local Guidance, which employs a receding-horizon windowed planning framework and warm-starts guidance from the previous solution at each timestep. Our method scales effectively, maintains high throughput even in compact, dense environments, and surpasses existing planners, thereby pushing the frontier of real-time, lifelong MAPF.

Diffusion models (DMs) have achieved remarkable success in image and video generation. However, they still struggle with (1) physical alignment and (2) out-of-distribution (OOD) instruction following. We argue that these issues stem from the models' failure to learn causal directions and to disentangle causal factors for novel recombination. We introduce the Causal Scene Graph (CSG) and the Physical Alignment Probe (PAP) dataset to enable diagnostic interventions. This analysis yields three key insights. First, DMs struggle with multi-hop reasoning for elements not explicitly determined in the prompt. Second, the prompt embedding contains disentangled representations for texture and physics. Third, visual causal structure is disproportionately established during the initial, computationally limited denoising steps. Based on these findings, we introduce LINA (Learning INterventions Adaptively), a novel framework that learns to predict prompt-specific interventions, which employs (1) targeted guidance in the prompt and visual latent spaces, and (2) a reallocated, causality-aware denoising schedule. Our approach enforces both physical alignment and OOD instruction following in image and video DMs, achieving state-of-the-art performance on challenging causal generation tasks and the Winoground dataset. Our project page is at https://opencausalab.github.io/LINA.

Existing industrial-scale navigation applications contend with massive road networks, typically employing two main categories of approaches for route planning. The first relies on precomputed road costs for optimal routing and heuristic algorithms for generating alternatives, while the second, generative methods, has recently gained significant attention. However, the former struggles with personalization and route diversity, while the latter fails to meet the efficiency requirements of large-scale real-time scenarios. To address these limitations, we propose GenMRP, a generative framework for multi-route planning. To ensure generation efficiency, GenMRP first introduces a skeleton-to-capillary approach that dynamically constructs a relevant sub-network significantly smaller than the full road network. Within this sub-network, routes are generated iteratively. The first iteration identifies the optimal route, while the subsequent ones generate alternatives that balance quality and diversity using the newly proposed correctional boosting approach. Each iteration incorporates road features, user historical sequences, and previously generated routes into a Link Cost Model to update road costs, followed by route generation using the Dijkstra algorithm. Extensive experiments show that GenMRP achieves state-of-the-art performance with high efficiency in both offline and online environments. To facilitate further research, we have publicly released the training and evaluation dataset. GenMRP has been fully deployed in a real-world navigation app, demonstrating its effectiveness and benefits.

A popular approach to post-training control of large language models (LLMs) is the steering of intermediate latent representations. Namely, identify a well-chosen direction depending on the task at hand and perturbs representations along this direction at inference time. While many propositions exist to pick this direction, considerably less is understood about how to choose the magnitude of the move, whereas its importance is clear: too little and the intended behavior does not emerge, too much and the model's performance degrades beyond repair. In this work, we propose the first theoretical analysis of steering strength. We characterize its effect on next token probability, presence of a concept, and cross-entropy, deriving precise qualitative laws governing these quantities. Our analysis reveals surprising behaviors, including non-monotonic effects of steering strength. We validate our theoretical predictions empirically on eleven language models, ranging from a small GPT architecture to modern models.

We introduce a learning-guided motion planning framework that generates seed trajectories using a diffusion model for trajectory optimization. Given a workspace, our method approximates the configuration space (C-space) obstacles through an environment representation consisting of a sparse set of task-related key configurations, which is then used as a conditioning input to the diffusion model. The diffusion model integrates regularization terms that encourage smooth, collision-free trajectories during training, and trajectory optimization refines the generated seed trajectories to correct any colliding segments. Our experimental results demonstrate that high-quality trajectory priors, learned through our C-space-grounded diffusion model, enable the efficient generation of collision-free trajectories in narrow-passage environments, outperforming previous learning- and planning-based baselines. Videos and additional materials can be found on the project page: https://kiwi-sherbet.github.io/PRESTO.

While researchers are finding concepts represented as linear directions in language models, a bag of linear directions fails to capture relational structure. To better understand this dichotomy, we study a model with known linear representations, but trained in a highly structured domain -- the board game Othello. While the model's internal board-state representation is linearly decodable, we find additional structure in the form of tensor product representations (TPRs). We train TPR probes to recover shared structure amongst the linear probes, yielding a factorization into square-embeddings, color-embeddings, and a binding matrix that composes them to construct the model's board-state representation. We find geometric signatures within the weights of our TPR probe that align with the structure of the board, but perhaps more importantly, that the linear probes can be recovered directly from the parameters of our TPR probe. Our findings suggest that directional representations may be projections of more structured underlying representations.

A new class of affine scaling matrices for the interior point Newton-type methods is considered to solve the nonlinear systems with simple bounds. We review the essential properties of a scaling matrix and consider several well-known scaling matrices proposed in the literature. We define a new scaling matrix that is the convex combination of these matrices. The proposed scaling matrix inherits those interesting properties of the individual matrices and satisfies additional desired requirements. The numerical experiments demonstrate the superiority of the new scaling matrix in solving several important test problems.

Existing motion planning methods often struggle with rapid-motion obstacles due to an insufficient understanding of environmental changes. To address this, we propose integrating motion planners with Doppler LiDARs, which provide not only ranging measurements but also instantaneous point velocities. However, this integration is nontrivial due to the requirements of high accuracy and high frequency. To this end, we introduce Doppler Planning Network (DPNet), which tracks and reacts to rapid obstacles via Doppler model-based learning. We first propose a Doppler Kalman neural network (D-KalmanNet) to track obstacle states under a partially observable Gaussian state space model. We then leverage the predicted motions of obstacles to construct a Doppler-tuned model predictive control (DT-MPC) framework for ego-motion planning, enabling runtime auto-tuning of controller parameters. These two modules allow DPNet to learn fast environmental changes from minimal data while remaining lightweight, achieving high frequency and high accuracy in both tracking and planning. Experiments on high-fidelity simulator and real-world datasets demonstrate the superiority of DPNet over extensive benchmark schemes. Code available at https://github.com/UUwei-zuo/DPNet

Deploying large, complex policies in the real world requires the ability to steer them to fit the needs of a situation. Most common steering approaches, like goal-conditioning, require training the robot policy with a distribution of test-time objectives in mind. To overcome this limitation, we present DynaGuide, a steering method for diffusion policies using guidance from an external dynamics model during the diffusion denoising process. DynaGuide separates the dynamics model from the base policy, which gives it multiple advantages, including the ability to steer towards multiple objectives, enhance underrepresented base policy behaviors, and maintain robustness on low-quality objectives. The separate guidance signal also allows DynaGuide to work with off-the-shelf pretrained diffusion policies. We demonstrate the performance and features of DynaGuide against other steering approaches in a series of simulated and real experiments, showing an average steering success of 70% on a set of articulated CALVIN tasks and outperforming goal-conditioning by 5.4x when steered with low-quality objectives. We also successfully steer an off-the-shelf real robot policy to express preference for particular objects and even create novel behavior. Videos and more can be found on the project website: https://dynaguide.github.io

Prompt learning has emerged as a powerful paradigm for adapting vision-language models such as CLIP to downstream tasks. However, existing methods often overfit to seen data, leading to significant performance degradation when generalizing to novel classes or unseen domains. To address this limitation, we propose DiSa, a Directional Saliency-Aware Prompt Learning framework that integrates two complementary regularization strategies to enhance generalization. First, our Cross-Interactive Regularization (CIR) fosters cross-modal alignment by enabling cooperative learning between prompted and frozen encoders. Within CIR, a saliency-aware masking strategy guides the image encoder to prioritize semantically critical image regions, reducing reliance on less informative patches. Second, we introduce a directional regularization strategy that aligns visual embeddings with class-wise prototype features in a directional manner to prioritize consistency in feature orientation over strict proximity. This approach ensures robust generalization by leveraging stable prototype directions derived from class-mean statistics. Extensive evaluations on 11 diverse image classification benchmarks demonstrate that DiSa consistently outperforms state-of-the-art prompt learning methods across various settings, including base-to-novel generalization, cross-dataset transfer, domain generalization, and few-shot learning.

Super-directive antenna arrays have faced challenges in achieving high realized gains ever since their introduction in the academic literature. The primary challenges are high impedance mismatches and resistive losses, which become increasingly more dominant as the number of elements increases. Consequently, a critical limitation arises in determining the maximum number of elements that should be utilized to achieve super-directivity, particularly within dense array configurations. This paper addresses precisely this issue through an optimization study to design a super-directive antenna array with a maximum number of elements. An iterative approach is employed to increase the array of elements while sustaining a satisfactory realized gain using the differential evolution (DE) algorithm. Thus, it is observed that super-directivity can be obtained in an array with a maximum of five elements. Our results indicate that the obtained unit array has a 67.20% higher realized gain than a uniform linear array with conventional excitation. For these reasons, these results make the proposed architecture a strong candidate for applications that require densely packed arrays, particularly in the context of massive multiple-input multiple-output (MIMO).

This paper gives three formulas for the pseudoinverse of a matrix product A = CR. The first is sometimes correct, the second is always correct, and the third is almost never correct. But that third randomized pseudoinverse A^+_r may be very useful when A is a very large matrix. 1. A^+ = R^+C^+ when A = CR and C has independent columns and R has independent rows. 2. A^+ = (C^+CR)^+(CRR^+)^+ is always correct. 3. A^+_r = (P^TCR)^+P^TCRQ(CRQ)^+ = A^+ only when rank(P^TA) = rank(AQ) = rank(A) with A = CR.

Recent progress in image-to-3D has opened up immense possibilities for design, AR/VR, and robotics. However, to use AI-generated 3D assets in real applications, a critical requirement is the capability to edit them easily. We present a feedforward method, Steer3D, to add text steerability to image-to-3D models, which enables editing of generated 3D assets with language. Our approach is inspired by ControlNet, which we adapt to image-to-3D generation to enable text steering directly in a forward pass. We build a scalable data engine for automatic data generation, and develop a two-stage training recipe based on flow-matching training and Direct Preference Optimization (DPO). Compared to competing methods, Steer3D more faithfully follows the language instruction and maintains better consistency with the original 3D asset, while being 2.4x to 28.5x faster. Steer3D demonstrates that it is possible to add a new modality (text) to steer the generation of pretrained image-to-3D generative models with 100k data. Project website: https://glab-caltech.github.io/steer3d/

Discovering meaningful directions in the latent space of GANs to manipulate semantic attributes typically requires large amounts of labeled data. Recent work aims to overcome this limitation by leveraging the power of Contrastive Language-Image Pre-training (CLIP), a joint text-image model. While promising, these methods require several hours of preprocessing or training to achieve the desired manipulations. In this paper, we present StyleMC, a fast and efficient method for text-driven image generation and manipulation. StyleMC uses a CLIP-based loss and an identity loss to manipulate images via a single text prompt without significantly affecting other attributes. Unlike prior work, StyleMC requires only a few seconds of training per text prompt to find stable global directions, does not require prompt engineering and can be used with any pre-trained StyleGAN2 model. We demonstrate the effectiveness of our method and compare it to state-of-the-art methods. Our code can be found at http://catlab-team.github.io/stylemc.

Forward Gradients - the idea of using directional derivatives in forward differentiation mode - have recently been shown to be utilizable for neural network training while avoiding problems generally associated with backpropagation gradient computation, such as locking and memorization requirements. The cost is the requirement to guess the step direction, which is hard in high dimensions. While current solutions rely on weighted averages over isotropic guess vector distributions, we propose to strongly bias our gradient guesses in directions that are much more promising, such as feedback obtained from small, local auxiliary networks. For a standard computer vision neural network, we conduct a rigorous study systematically covering a variety of combinations of gradient targets and gradient guesses, including those previously presented in the literature. We find that using gradients obtained from a local loss as a candidate direction drastically improves on random noise in Forward Gradient methods.

With the rapid expansion of low-altitude economy (LAE) services and the growing demand for integrated sensing and communication (ISAC) in air-ground networks, reliable direction-of-arrival (DOA) estimation has become essential for both directional communication and sensing functions. DOA underpins beam alignment, spatial-reuse scheduling, and ISAC-critical tasks such as airspace situational awareness and multi-target monitoring. Hybrid analog-digital (HAD) architectures have emerged as a practical solution for large-aperture directional operation under stringent radio frequency (RF), analog-to-digital converter (ADC), and size, weight, and power (SWaP) constraints. However, HAD compresses antenna-domain observations through analog combining, fundamentally reshaping the measurement model and introducing new algorithmic and system-level challenges for DOA estimation. This article first reviews the principles and representative architectures of HAD, highlighting their advantages for scalable beam-centric and ISAC-oriented operation in LAE scenarios. We then provide a structured overview of HAD-enabled DOA estimation methodologies, including spatial covariance matrix (SCM) reconstruction, multi-combiner scan-based acquisition, and pilot-aided estimation, along with key design tradeoffs. Finally, we discuss open challenges and outline reliability-driven research directions toward robust, deployable HAD-enabled DOA solutions for practical ISAC-enabled low-altitude environments.

Radio interferometric imaging aims to estimate an unknown sky intensity image from degraded observations, acquired through an antenna array. In the theoretical case of a perfectly calibrated array, it has been shown that solving the corresponding imaging problem by iterative algorithms based on convex optimization and compressive sensing theory can be competitive with classical algorithms such as CLEAN. However, in practice, antenna-based gains are unknown and have to be calibrated. Future radio telescopes, such as the SKA, aim at improving imaging resolution and sensitivity by orders of magnitude. At this precision level, the direction-dependency of the gains must be accounted for, and radio interferometric imaging can be understood as a blind deconvolution problem. In this context, the underlying minimization problem is non-convex, and adapted techniques have to be designed. In this work, leveraging recent developments in non-convex optimization, we propose the first joint calibration and imaging method in radio interferometry, with proven convergence guarantees. Our approach, based on a block-coordinate forward-backward algorithm, jointly accounts for visibilities and suitable priors on both the image and the direction-dependent effects (DDEs). As demonstrated in recent works, sparsity remains the prior of choice for the image, while DDEs are modelled as smooth functions of the sky, i.e. spatially band-limited. Finally, we show through simulations the efficiency of our method, for the reconstruction of both images of point sources and complex extended sources. MATLAB code is available on GitHub.

We present Submatrix-wise Vector Embedding Learner (Swivel), a method for generating low-dimensional feature embeddings from a feature co-occurrence matrix. Swivel performs approximate factorization of the point-wise mutual information matrix via stochastic gradient descent. It uses a piecewise loss with special handling for unobserved co-occurrences, and thus makes use of all the information in the matrix. While this requires computation proportional to the size of the entire matrix, we make use of vectorized multiplication to process thousands of rows and columns at once to compute millions of predicted values. Furthermore, we partition the matrix into shards in order to parallelize the computation across many nodes. This approach results in more accurate embeddings than can be achieved with methods that consider only observed co-occurrences, and can scale to much larger corpora than can be handled with sampling methods.

Diffusion models, despite their impressive demos, often produce hallucinatory samples with structural inconsistencies that lie outside of the support of the true data distribution. Such hallucinations can be attributed to excessive smoothing between modes of the data distribution. However, semantic interpolations are often desirable and can lead to generation diversity, thus we believe a more nuanced solution is required. In this work, we introduce Dynamic Guidance, which tackles this issue. Dynamic Guidance mitigates hallucinations by selectively sharpening the score function only along the pre-determined directions known to cause artifacts, while preserving valid semantic variations. To our knowledge, this is the first approach that addresses hallucinations at generation time rather than through post-hoc filtering. Dynamic Guidance substantially reduces hallucinations on both controlled and natural image datasets, significantly outperforming baselines.

Accurate 3D medical image segmentation requires both long-range volumetric context and fine boundary preservation. CNN-based methods have limited global dependency modeling, while Transformer-based models are often computationally expensive for dense 3D inputs. Recent Mamba-based methods provide an efficient alternative, but existing volumetric designs still depend on repeated high-resolution scanning, forward-only sequential modeling, and fixed directional summation, causing high cost, scan-order bias, and suboptimal directional aggregation. We propose BiSegMamba, an efficient bidirectional tri-oriented Mamba network for 3D medical image segmentation. BiSegMamba follows a compact-to-detail design, where a progressive compacting stem (PCS) enables efficient latent-space reasoning while retaining shallow high-resolution features for reconstruction. A multi-scale spatial mixer (MSSM) captures local anatomical patterns in early stages, and the proposed bidirectional tri-oriented Ortho Mamba (Bi-ToOM) block models long-range dependencies from multiple orthogonal views using jointly processed forward and backward scan sequences. Adaptive directional fusion (ADF) learns input-dependent channel-wise weights across scan orientations, replacing fixed summation with orientation-aware fusion. Experiments on a collected carotid CTA dataset and three public benchmarks, BraTS2023, ACDC, and AMOS-CT, show that BiSegMamba generalizes well across vascular, cardiac, brain tumor, and abdominal multi-organ segmentation tasks. Compared with SegMamba-V2, BiSegMamba achieves slightly better performance on BraTS2023 and clear improvements on ACDC and the carotid dataset, while reducing computational cost by up to 77.9% FLOPs, demonstrating a strong accuracy-efficiency balance for general 3D medical image segmentation.

Visually Impaired Assistance (VIA) aims to automatically help the visually impaired (VI) handle daily activities. The advancement of VIA primarily depends on developments in Computer Vision (CV) and Natural Language Processing (NLP), both of which exhibit cutting-edge paradigms with large models (LMs). Furthermore, LMs have shown exceptional multimodal abilities to tackle challenging physically-grounded tasks such as embodied robots. To investigate the potential and limitations of state-of-the-art (SOTA) LMs' capabilities in VIA applications, we present an extensive study for the task of VIA with LMs (VIALM). In this task, given an image illustrating the physical environments and a linguistic request from a VI user, VIALM aims to output step-by-step guidance to assist the VI user in fulfilling the request grounded in the environment. The study consists of a survey reviewing recent LM research and benchmark experiments examining selected LMs' capabilities in VIA. The results indicate that while LMs can potentially benefit VIA, their output cannot be well environment-grounded (i.e., 25.7% GPT-4's responses) and lacks fine-grained guidance (i.e., 32.1% GPT-4's responses).

Flow-based generative models have become a strong framework for high-quality generative modeling, yet pretrained models are rarely used in their vanilla conditional form: conditional samples without guidance often appear diffuse and lack fine-grained detail due to the smoothing effects of neural networks. Existing guidance techniques such as classifier-free guidance (CFG) improve fidelity but double the inference cost and typically reduce sample diversity. We introduce Momentum Guidance (MG), a new dimension of guidance that leverages the ODE trajectory itself. MG extrapolates the current velocity using an exponential moving average of past velocities and preserves the standard one-evaluation-per-step cost. It matches the effect of standard guidance without extra computation and can further improve quality when combined with CFG. Experiments demonstrate MG's effectiveness across benchmarks. Specifically, on ImageNet-256, MG achieves average improvements in FID of 36.68% without CFG and 25.52% with CFG across various sampling settings, attaining an FID of 1.597 at 64 sampling steps. Evaluations on large flow-based models like Stable Diffusion 3 and FLUX.1-dev further confirm consistent quality enhancements across standard metrics.

Riemannian geometry has been applied to Brain Computer Interface (BCI) for brain signals classification yielding promising results. Studying electroencephalographic (EEG) signals from their associated covariance matrices allows a mitigation of common sources of variability (electronic, electrical, biological) by constructing a representation which is invariant to these perturbations. While working in Euclidean space with covariance matrices is known to be error-prone, one might take advantage of algorithmic advances in information geometry and matrix manifold to implement methods for Symmetric Positive-Definite (SPD) matrices. This paper proposes a comprehensive review of the actual tools of information geometry and how they could be applied on covariance matrices of EEG. In practice, covariance matrices should be estimated, thus a thorough study of all estimators is conducted on real EEG dataset. As a main contribution, this paper proposes an online implementation of a classifier in the Riemannian space and its subsequent assessment in Steady-State Visually Evoked Potential (SSVEP) experimentations.

Recent advances in flow-based generative models have enabled training-free, text-guided image editing by inverting an image into its latent noise and regenerating it under a new target conditional guidance. However, existing methods struggle to preserve source fidelity: higher-order solvers incur additional model inferences, truncated inversion constrains editability, and feature injection methods lack architectural transferability. To address these limitations, we propose SteerFlow, a model-agnostic editing framework with strong theoretical guarantees on source fidelity. In the forward process, we introduce an Amortized Fixed-Point Solver that implicitly straightens the forward trajectory by enforcing velocity consistency across consecutive timesteps, yielding a high-fidelity inverted latent. In the backward process, we introduce Trajectory Interpolation, which adaptively blends target-editing and source-reconstruction velocities to keep the editing trajectory anchored to the source. To further improve background preservation, we introduce an Adaptive Masking mechanism that spatially constrains the editing signal with concept-guided segmentation and source-target velocity differences. Extensive experiments on FLUX.1-dev and Stable Diffusion 3.5 Medium demonstrate that SteerFlow consistently achieves better editing quality than existing methods. Finally, we show that SteerFlow extends naturally to a complex multi-turn editing paradigm without accumulating drift.

Existing approaches to controllable generation typically rely on fine-tuning, auxiliary networks, or test-time search. We show that flow matching admits a different control interface: adaptation through examples. For deterministic interpolants, the velocity field is solely governed by a conditional endpoint mean; shifting this mean shifts the flow itself. This yields a simple principle for controllable generation: steer a pretrained model by changing the reference set it follows. We instantiate this idea in two forms. Reference-Mean Guidance is training-free: it computes a closed-form endpoint-mean correction from a reference bank and applies it to a frozen FLUX.2-klein (4B) model, enabling control of color, identity, style, and structure while keeping the prompt, seed, and weights fixed. Semi-Parametric Guidance amortizes the same idea through an explicit mean anchor and learned residual refiner, matching unconditional DiT-B/4 quality on AFHQv2 while allowing the reference set to be swapped at inference time. These results point to a broader direction: generative models that adapt through data, not parameter updates.

Adapter-based training has emerged as a key mechanism for extending the capabilities of powerful foundation image generators, enabling personalized and stylized text-to-image synthesis. These adapters are typically trained to capture a specific target attribute, such as subject identity, using single-image reconstruction objectives. However, because the input image inevitably contains a mixture of visual factors, adapters are prone to entangle the target attribute with incidental ones, such as pose, expression, and lighting. This spurious correlation problem limits generalization and obstructs the model's ability to adhere to the input text prompt. In this work, we uncover a simple yet effective solution: provide the very shortcuts we wish to eliminate during adapter training. In Shortcut-Rerouted Adapter Training, confounding factors are routed through auxiliary modules, such as ControlNet or LoRA, eliminating the incentive for the adapter to internalize them. The auxiliary modules are then removed during inference. When applied to tasks like facial and full-body identity injection, our approach improves generation quality, diversity, and prompt adherence. These results point to a general design principle in the era of large models: when seeking disentangled representations, the most effective path may be to establish shortcuts for what should NOT be learned.

Inference-time steering methods offer a lightweight alternative to fine-tuning large language models (LLMs) and vision-language models (VLMs) by modifying internal activations at test time without updating model weights. However, most existing approaches rely on fixed, global intervention vectors, overlook the causal influence of individual input tokens, and fail to leverage informative gradients from the model's logits, particularly in multimodal settings where visual and textual inputs contribute unevenly. To address these limitations, we introduce GrAInS, an inference-time steering approach that operates across both language-only and vision-language models and tasks. GrAInS uses contrastive, gradient-based attribution via Integrated Gradients to identify the top-k most influential tokens, both positively and negatively attributed based on their contribution to preferred versus dispreferred outputs. These tokens are then used to construct directional steering vectors that capture semantic shifts from undesirable to desirable behavior. During inference, GrAInS adjusts hidden activations at transformer layers guided by token-level attribution signals, and normalizes activations to preserve representational scale. This enables fine-grained, interpretable, and modular control over model behavior, without retraining or auxiliary supervision. Empirically, GrAInS consistently outperforms both fine-tuning and existing steering baselines: it achieves a 13.22% accuracy gain on TruthfulQA using Llama-3.1-8B, reduces hallucination rates on MMHal-Bench from 0.624 to 0.514 with LLaVA-1.6-7B, and improves alignment win rates on SPA-VL by 8.11%, all while preserving the model's fluency and general capabilities.

Signage is an ubiquitous element of human environments, playing a critical role in both scene understanding and navigation. For autonomous systems to fully interpret human environments, effectively parsing and understanding signs is essential. We introduce the task of navigational sign understanding, aimed at extracting navigational cues from signs that convey symbolic spatial information about the scene. Specifically, we focus on signs capturing directional cues that point toward distant locations and locational cues that identify specific places. To benchmark performance on this task, we curate a comprehensive test set, propose appropriate evaluation metrics, and establish a baseline approach. Our test set consists of over 160 images, capturing signs with varying complexity and design across a wide range of public spaces, such as hospitals, shopping malls, and transportation hubs. Our baseline approach harnesses Vision-Language Models (VLMs) to parse navigational signs under these high degrees of variability. Experiments show that VLMs offer promising performance on this task, potentially motivating downstream applications in robotics. The code and dataset are available on Github.

Path planning is a fundamental capability of autonomous Unmanned Aerial Vehicles (UAVs), enabling them to efficiently navigate toward a target region or explore complex environments while avoiding obstacles. Traditional pathplanning methods, such as Rapidly-exploring Random Trees (RRT), have proven effective but often encounter significant challenges. These include high search space complexity, suboptimal path quality, and slow convergence, issues that are particularly problematic in high-stakes applications like disaster response, where rapid and efficient planning is critical. To address these limitations and enhance path-planning efficiency, we propose Vision Language Model RRT (VLM-RRT), a hybrid approach that integrates the pattern recognition capabilities of Vision Language Models (VLMs) with the path-planning strengths of RRT. By leveraging VLMs to provide initial directional guidance based on environmental snapshots, our method biases sampling toward regions more likely to contain feasible paths, significantly improving sampling efficiency and path quality. Extensive quantitative and qualitative experiments with various state-of-the-art VLMs demonstrate the effectiveness of this proposed approach.

Mobility remains a significant challenge for the 2.2 billion people worldwide affected by blindness and low vision (BLV), with 7% of visually impaired individuals experiencing falls at least once a month. While recent advances in Multimodal Large Language Models (MLLMs) offer promising opportunities for BLV assistance, their development has been hindered by limited datasets. This limitation stems from the fact that BLV-aware annotation requires specialized domain knowledge and intensive labor. To address this gap, we introduce GuideDog, a novel accessibility-aware guide dataset containing 22K image-description pairs (including 2K human-annotated pairs) that capture diverse real-world scenes from a pedestrian's viewpoint. Our approach shifts the annotation burden from generation to verification through a collaborative human-AI framework grounded in established accessibility standards, significantly improving efficiency while maintaining high-quality annotations. We also develop GuideDogQA, a subset of 818 samples featuring multiple-choice questions designed to evaluate fine-grained visual perception capabilities, specifically object recognition and relative depth perception. Our experimental results highlight the importance of accurate spatial understanding for effective BLV guidance. GuideDog and GuideDogQA will advance research in MLLM-based assistive technologies for BLV individuals while contributing to broader applications in understanding egocentric scenes for robotics and augmented reality. The code and dataset will be publicly available.

End-to-end autonomous driving has emerged as a pivotal direction in the field of autonomous systems. Recent works have demonstrated impressive performance by incorporating high-level guidance signals to steer low-level trajectory planners. However, their potential is often constrained by inaccurate high-level guidance and the computational overhead of complex guidance modules. To address these limitations, we propose Mimir, a novel hierarchical dual-system framework capable of generating robust trajectories relying on goal points with uncertainty estimation: (1) Unlike previous approaches that deterministically model, we estimate goal point uncertainty with a Laplace distribution to enhance robustness; (2) To overcome the slow inference speed of the guidance system, we introduce a multi-rate guidance mechanism that predicts extended goal points in advance. Validated on challenging Navhard and Navtest benchmarks, Mimir surpasses previous state-of-the-art methods with a 20% improvement in the driving score EPDMS, while achieving 1.6 times improvement in high-level module inference speed without compromising accuracy. The code and models will be released soon to promote reproducibility and further development. The code is available at https://github.com/ZebinX/Mimir-Uncertainty-Driving

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for partial differential equations. Algorithms for approximating the solution to these systems are often the bottleneck in problems that require their solution, particularly for modern applications that require many millions of unknowns. Indeed, numerical linear algebra techniques have been investigated for many decades to alleviate this computational burden. Recently, data-driven techniques have also shown promise for these problems. Motivated by the conjugate gradients algorithm that iteratively selects search directions for minimizing the matrix norm of the approximation error, we design an approach that utilizes a deep neural network to accelerate convergence via data-driven improvement of the search directions. Our method leverages a carefully chosen convolutional network to approximate the action of the inverse of the linear operator up to an arbitrary constant. We train the network using unsupervised learning with a loss function equal to the L^2 difference between an input and the system matrix times the network evaluation, where the unspecified constant in the approximate inverse is accounted for. We demonstrate the efficacy of our approach on spatially discretized Poisson equations with millions of degrees of freedom arising in computational fluid dynamics applications. Unlike state-of-the-art learning approaches, our algorithm is capable of reducing the linear system residual to a given tolerance in a small number of iterations, independent of the problem size. Moreover, our method generalizes effectively to various systems beyond those encountered during training.

Diffusion Probabilistic Models (DPMs) have recently been employed for image deblurring, formulated as an image-conditioned generation process that maps Gaussian noise to the high-quality image, conditioned on the blurry input. Image-conditioned DPMs (icDPMs) have shown more realistic results than regression-based methods when trained on pairwise in-domain data. However, their robustness in restoring images is unclear when presented with out-of-domain images as they do not impose specific degradation models or intermediate constraints. To this end, we introduce a simple yet effective multiscale structure guidance as an implicit bias that informs the icDPM about the coarse structure of the sharp image at the intermediate layers. This guided formulation leads to a significant improvement of the deblurring results, particularly on unseen domain. The guidance is extracted from the latent space of a regression network trained to predict the clean-sharp target at multiple lower resolutions, thus maintaining the most salient sharp structures. With both the blurry input and multiscale guidance, the icDPM model can better understand the blur and recover the clean image. We evaluate a single-dataset trained model on diverse datasets and demonstrate more robust deblurring results with fewer artifacts on unseen data. Our method outperforms existing baselines, achieving state-of-the-art perceptual quality while keeping competitive distortion metrics.