An autonomous first-order algebraic q-difference equation is a difference equation of the form \(f\bigl (y,\sigma _q(y)\bigr)=0\), where f ∈ K[u, v] is a bivariate polynomial over a field K of characteristic zero, q ∈ K∖{0} is not a root of unity, and σq denotes the q-shift operator. In this paper, we develop an algorithm that decides whether such an equation admits a nonconstant rational solution and, when it does, computes such a solution. The corresponding problem for the additive shift operator has been completely resolved by a reduction to a second-order autonomous difference equation, together with an effective upper bound on polynomial solutions of the latter equation. In contrast, no such upper bound exists in the q-shift setting, and the methods for the additive shift case therefore do not apply. To address this obstacle, we introduce a direct approach grounded in an algebraic–geometric viewpoint.

Text-to-speech (TTS) systems have seen significant advancements in recent years, driven by improvements in deep learning and neural network architectures. Viewing the output speech as a data distribution, previous approaches often employ traditional speech representations, such as waveforms or spectrograms, within the Flow Matching framework. However, these methods have limitations, including overlooking various speech attributes and incurring high computational costs due to additional constraints introduced during training. To address these challenges, we introduce OZSpeech, the first TTS method to explore optimal transport conditional flow matching with one-step sampling and a learned prior as the condition, effectively disregarding preceding states and reducing the number of sampling steps. Our approach operates on disentangled, factorized components of speech in token format, enabling accurate modeling of each speech attribute, which enhances the TTS system’s ability to precisely clone the prompt speech. Experimental results show that our method achieves promising performance over existing methods in content accuracy, naturalness, prosody generation, and speaker style preservation. Audio samples are available at our demo page https://ozspeech.github.io/OZSpeech_Web/.

Multi-label learning is a challenging computer vision task that requires assigning multiple categories to each image. However, fully annotating large-scale datasets is often impractical due to high costs and effort, motivating the study of learning from partially annotated data. In the extreme case of Single Positive Multi-Label Learning (SPML), each image is provided with only one positive label, while all other labels remain unannotated. Traditional SPML methods that treat missing labels as unknown or negative tend to yield inaccuracies and false negatives, and integrating various pseudo-labeling strategies can introduce additional noise. To address these challenges, we propose the Generalized Pseudo-Label Robust Loss (GPR Loss), a novel loss function that effectively learns from diverse pseudo-labels while mitigating noise. Complementing this, we introduce a simple yet effective Dynamic Augmented Multi-focus Pseudo-labeling (DAMP) technique. Together, these contributions form the Adaptive and Efficient Vision-Language Pseudo-Labeling (AEVLP) framework. Extensive experiments on four benchmark datasets demonstrate that our framework significantly advances multi-label classification, achieving state-of-the-art results.

This paper systematically explores neural functional networks (NFN) for transformer architectures. NFN are specialized neural networks that treat the weights, gradients, or sparsity patterns of a deep neural network (DNN) as input data and have proven valuable for tasks such as learnable optimizers, implicit data representations, and weight editing. While NFN have been extensively developed for MLP and CNN, no prior work has addressed their design for transformers, despite the importance of transformers in modern deep learning. This paper aims to address this gap by providing a systematic study of NFN for transformers. We first determine the maximal symmetric group of the weights in a multi-head attention module as well as a necessary and sufficient condition under which two sets of hyperparameters of the multi-head attention module define the same function. We then define the weight space of transformer architectures and its associated group action, which leads to the design principles for NFN in transformers. Based on these, we introduce Transformer-NFN, an NFN that is equivariant under this group action. Additionally, we release a dataset of more than 125,000 Transformers model checkpoints trained on two datasets with two different tasks, providing a benchmark for evaluating Transformer-NFN and encouraging further research on transformer training and performance.

A neural functional network (NFN) is a specialized type of neural network designed to process and learn from entire neural networks as input data. Recent NFNs have been proposed with permutation and scaling equivariance based on either graph-based message-passing mechanisms or parameter-sharing mechanisms. Compared to graph-based models, parameter-sharing-based NFNs built upon equivariant linear layers exhibit lower memory consumption and faster running time. However, their expressivity is limited due to the large size of the symmetric group of the input neural networks. The challenge of designing a permutation and scaling equivariant NFN that maintains low memory consumption and running time while preserving expressivity remains unresolved. In this paper, we propose a novel solution with the development of MAGEP-NFN (**M**onomial m**A**trix **G**roup **E**quivariant **P**olynomial **NFN**). Our approach follows the parameter-sharing mechanism but differs from previous works by constructing a nonlinear equivariant layer represented as a polynomial in the input weights. This polynomial formulation enables us to incorporate additional relationships between weights from different input hidden layers, enhancing the model's expressivity while keeping memory consumption and running time low, thereby addressing the aforementioned challenge. We provide empirical evidence demonstrating that MAGEP-NFN achieves competitive performance and efficiency compared to existing baselines.

Vision language models have played a key role in extracting meaningful features for various robotic applications. Among these, Contrastive Language-Image Pretraining (CLIP) is widely used in robotic tasks that require both vision and natural language understanding. However, CLIP was trained solely on static images paired with text prompts and has not yet been fully adapted for robotic tasks involving dynamic actions. In this paper, we introduce Robotic-CLIP to enhance robotic perception capabilities. We first gather and label large-scale action data, and then build our Robotic-CLIP by fine-tuning CLIP on 309,433 videos (≈ 7.4 million frames) of action data using contrastive learning. By leveraging action data, Robotic-CLIP inherits CLIP's strong image performance while gaining the ability to understand actions in robotic contexts. Intensive experiments show that our Robotic-CLIP outperforms other CLIP-based models across various language-driven robotic tasks. Additionally, we demonstrate the practical effectiveness of Robotic-CLIP in real-world grasping applications.

Language-driven grasp detection has the potential to revolutionize human-robot interaction by allowing robots to understand and execute grasping tasks based on natural language commands. However, existing approaches face two key challenges. First, they often struggle to interpret complex text instructions or operate ineffectively in densely cluttered environments. Second, most methods require a training or fine-tuning step to adapt to new domains, limiting their generation in real-world applications. In this paper, we introduce GraspMAS, a new multi-agent system framework for language-driven grasp detection. GraspMAS is designed to reason through ambiguities and improve decision-making in real-world scenarios. Our framework consists of three specialized agents: Planner, responsible for strategizing complex queries; Coder, which generates and executes source code; and Observer, which evaluates the outcomes and provides feedback. Intensive experiments on two large-scale datasets demonstrate that our GraspMAS significantly outperforms existing baselines. Additionally, robot experiments conducted in both simulation and real-world settings further validate the effectiveness of our approach. Our project page is available at https://zquang2202.github.io/GraspMAS.

Learning human motion based on a time-dependent input signal presents a challenging yet impactful task with various applications. The goal of this task is to generate or estimate human movement that consistently reflects the temporal patterns of conditioning inputs. Existing methods typically rely on cross-attention mechanisms to fuse the condition with motion. However, this approach primarily captures global interactions and struggles to maintain step-by-step temporal alignment. To address this limitation, we introduce Temporally Conditional Mamba, a new mamba-based model for human motion generation. Our approach integrates conditional information into the recurrent dynamics of the Mamba block, enabling better temporally aligned motion. To validate the effectiveness of our method, we evaluate it on a variety of human motion tasks. Extensive experiments demonstrate that our model significantly improves temporal alignment, motion realism, and condition consistency over state-of-the-art approaches. Our project page is available at https://zquang2202.github.io/TCM.

Grasp detection is a persistent and intricate challenge with various industrial applications. Recently, many meth-ods and datasets have been proposed to tackle the grasp detection problem. However, most of them do not consider using natural language as a condition to detect the grasp poses. In this paper, we introduce Grasp-Anything++, a new language-driven grasp detection dataset featuring 1M samples, over 3M objects, and upwards of 10M grasping in-structions. We utilize foundation models to create a large-scale scene corpus with corresponding images and grasp prompts. We approach the language-driven grasp detection task as a conditional generation problem. Drawing on the success of diffusion models in generative tasks and given that language plays a vital role in this task, we propose a new language-driven grasp detection method based on dif-fusion models. Our key contribution is the contrastive training objective, which explicitly contributes to the denoising process to detect the grasp pose given the language instructions. We illustrate that our approach is theoretically sup-portive. The intensive experiments show that our method outperforms state-of-the-art approaches and allows real-world robotic grasping. Finally, we demonstrate our large-scale dataset enables zero-short grasp detection and is a challenging benchmark for future work.

Foundation models such as ChatGPT have made significant strides in robotic tasks due to their universal representation of real-world domains. In this paper, we leverage foundation models to tackle grasp detection, a persistent challenge in robotics with broad industrial applications. Despite numerous grasp datasets, their object diversity remains limited compared to real-world figures. Fortunately, foundation models possess an extensive repository of real-world knowledge, including objects we encounter in our daily lives. As a consequence, a promising solution to the limited representation in previous grasp datasets is to harness the universal knowledge embedded in these foundation models. We present Grasp-Anything, a new large-scale grasp dataset synthesized from foundation models to implement this solution. Grasp-Anything excels in diversity and magnitude, boasting 1M samples with text descriptions and more than 3M objects, surpassing prior datasets. Empirically, we show that Grasp-Anything successfully facilitates zero-shot grasp detection on vision-based tasks and real-world robotic experiments. Our dataset and code are available at https://airvlab.github.io/grasp-anything/.

Affordance detection and pose estimation are of great importance in many robotic applications. Their combination helps the robot gain an enhanced manipulation capability, in which the generated pose can facilitate the corresponding affordance task. Previous methods for affodance-pose joint learning are limited to a predefined set of affordances, thus limiting the adaptability of robots in real-world environments. In this paper, we propose a new method for language-conditioned affordance-pose joint learning in 3D point clouds. Given a 3D point cloud object, our method detects the affordance region and generates appropriate 6-DoF poses for any unconstrained affordance label. Our method consists of an open-vocabulary affordance detection branch and a language-guided diffusion model that generates 6-DoF poses based on the affordance text. We also introduce a new high-quality dataset for the task of language-driven affordance-pose joint learning. Intensive experimental results demonstrate that our proposed method works effectively on a wide range of open-vocabulary affordances and outperforms other baselines by a large margin. In addition, we illustrate the usefulness of our method in real-world robotic applications. Our code and dataset are publicly available at https://3DAPNet.github.io.

Affordance detection presents intricate challenges and has a wide range of robotic applications. Previous works have faced limitations such as the complexities of 3D object shapes, the wide range of potential affordances on real-world objects, and the lack of open-vocabulary support for affordance understanding. In this paper, we introduce a new open-vocabulary affordance detection method in 3D point clouds, leveraging knowledge distillation and text-point correlation. Our approach employs pre-trained 3D models through knowledge distillation to enhance feature extraction and semantic understanding in 3D point clouds. We further introduce a new text-point correlation method to learn the semantic links between point cloud features and open-vocabulary labels. The intensive experiments show that our approach outperforms previous works and adapts to new affordance labels and unseen objects. Notably, our method achieves the improvement of 7.96% mIOU score compared to the baselines. Furthermore, it offers real-time inference which is well-suitable for robotic manipulation applications.

Language-driven grasp detection is a fundamental yet challenging task in robotics with various industrial applications. This work presents a new approach for language-driven grasp detection that leverages lightweight diffusion models to achieve fast inference time. By integrating diffusion processes with grasping prompts in natural language, our method can effectively encode visual and textual information, enabling more accurate and versatile grasp positioning that aligns well with the text query. To overcome the long inference time problem in diffusion models, we leverage the image and text features as the condition in the consistency model to reduce the number of denoising timesteps during inference. The intensive experimental results show that our method outperforms other recent grasp detection methods and lightweight diffusion models by a clear margin. We further validate our method in real-world robotic experiments to demonstrate its fast inference time capability.

Grasp detection is an essential task in robotics with various industrial applications. However, traditional methods often struggle with occlusions and do not utilize language for grasping. Incorporating natural language into grasp detection remains a challenging task and largely unexplored. To address this gap, we propose a new method for language-driven grasp detection with mask-guided attention by utilizing the transformer attention mechanism with semantic segmentation features. Our approach integrates visual data, segmentation mask features, and natural language instructions, significantly improving grasp detection accuracy. Our work introduces a new framework for language-driven grasp detection, paving the way for language-driven robotic applications. Intensive experiments show that our method outperforms other recent baselines by a clear margin, with a 10.0% success score improvement. We further validate our method in real-world robotic experiments, confirming the effectiveness of our approach.

Visual navigation, a foundational aspect of Embodied AI (E-AI) and robotics has been extensively studied in the past few years. While many 3D simulators have been introduced for the visual navigation tasks, scarcely works have combined human dynamics, creating the gap between simulation and real-world applications. Furthermore, current 3D simulators incorporating human dynamics have several limitations, particularly in terms of computational efficiency, which is a promise of modern simulators. To overcome these issues, we introduce HabiCrowd, the new standard benchmark for crowd-aware visual navigation that includes a crowd dynamics model with diverse human settings into photorealistic environments. Empirical evaluations demonstrate that our proposed human dynamics model achieves state-of-the-art performance in collision avoidance while exhibiting superior computational efficiency compared to its counterparts. We leverage HabiCrowd to conduct several comprehensive studies on crowd-aware visual navigation tasks and human-robot interactions. The source code and data can be found at https://habicrowd.github.io/.

Affordance detection is a challenging problem with a wide variety of robotic applications. Traditional affordance detection methods are limited to a predefined set of affordance labels, hence potentially restricting the adaptability of intelligent robots in complex and dynamic environments. In this paper, we present the Open-Vocabulary Affordance Detection (OpenAD) method, which is capable of detecting an unbounded number of affordances in 3D point clouds. By simultaneously learning the affordance text and the point feature, OpenAD successfully exploits the semantic relationships between affordances. Therefore, our proposed method enables zero-shot detection and can be able to detect previously unseen affordances without a single annotation example. Intensive experimental results show that OpenAD works effectively on a wide range of affordance detection setups and outperforms other baselines by a large margin. Additionally, we demonstrate the practicality of the proposed OpenAD in real-world robotic applications with a fast inference speed. Our project is available at https://openad2023.github.io.

Scene synthesis is a challenging problem with several industrial applications. Recently, substantial efforts have been directed to synthesize the scene using human motions, room layouts, or spatial graphs as the input. However, few studies have addressed this problem from multiple modalities, especially combining text prompts. In this paper, we propose a language-driven scene synthesis task, which is a new task that integrates text prompts, human motion, and existing objects for scene synthesis. Unlike other single-condition synthesis tasks, our problem involves multiple conditions and requires a strategy for processing and encoding them into a unified space. To address the challenge, we present a multi-conditional diffusion model, which differs from the implicit unification approach of other diffusion literature by explicitly predicting the guiding points for the original data distribution. We demonstrate that our approach is theoretically supportive. The intensive experiment results illustrate that our method outperforms state-of-the-art benchmarks and enables natural scene editing applications. The source code and dataset can be accessed at https://lang-scene-synth.github.io/.

We propose the Nesterov neural ordinary differential equations (NesterovNODEs), whose layers solve the second-order ordinary differential equations (ODEs) limit of Nesterov's accelerated gradient (NAG) method, and a generalization called GNesterovNODEs. Taking the advantage of the convergence rate $\mathcal{O}(1/k^{2})$ of the NAG scheme, GNesterovNODEs speed up training and inference by reducing the number of function evaluations (NFEs) needed to solve the ODEs. We also prove that the adjoint state of a GNesterovNODEs also satisfies a GNesterovNODEs, thus accelerating both forward and backward ODE solvers and allowing the model to be scaled up for large-scale tasks. We empirically corroborate the advantage of GNesterovNODEs on a wide range of practical applications, including point cloud separation, image classification, and sequence modeling. Compared to NODEs, GNesterovNODEs require a significantly smaller number of NFEs while achieving better accuracy across our experiments.