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Compared with the remarkable progress made in parallel numerical solvers of partial differential equations,the development of algorithms for generating unstructured triangular/tetrahedral meshes has been relatively sluggish. In this paper, we propose a novel, consistent parallel advancing front technique (CPAFT) by combining the advancing front technique, the domain decomposition method based on space-filling curves, the distributed forest-of-overlapping-trees approach, and the consistent parallel maximal independent set algorithm. The newly proposed CPAFT algorithm can mathematically ensure that the generated unstructured triangular/tetrahedral meshes are independent of the number of processors and the implementation of domain decomposition. Several numerical tests are conducted to validate the parallel consistency and outstanding parallel efficiency of the proposed algorithm, which scales effectively up to two thousand processors. This is, as far as we know, the first parallel unstructured triangular/tetrahedral mesh generator with scalability to O(1,000) CPU processors.

Large language models are usually fine-tuned to align with human preferences. However, fine-tuning a large language model can be challenging. In this work, we introduce $\textit{weak-to-strong search}$, framing the alignment of a large language model as a test-time greedy search to maximize the log-probability difference between small tuned and untuned models while sampling from the frozen large model. This method serves both as (1) a compute-efficient model up-scaling strategy that avoids directly tuning the large model and as (2) an instance of weak-to-strong generalization that enhances a strong model with weak test-time guidance. Empirically, we demonstrate the flexibility of weak-to-strong search across different tasks. In controlled-sentiment generation and summarization, we use tuned and untuned $\texttt{gpt2}$s to improve the alignment of large models without additional training. Crucially, in a more difficult instruction-following benchmark, AlpacaEval 2.0, we show that reusing off-the-shelf small models (e.g., $\texttt{zephyr-7b-beta}$ and its untuned version) can improve the length-controlled win rates of both white-box and black-box large models against $\texttt{gpt-4-turbo}$ (e.g., $34.4\% \rightarrow 37.9\%$ for $\texttt{Llama-3-70B-Instruct}$ and $16.0\% \rightarrow 20.1\%$ for $\texttt{gpt-3.5-turbo-instruct}$), despite the small models' low win rates $\approx 10.0\%$., Comment: NeurIPS 2024

We propose an unsupervised adaptation framework, Self-TAught Recognizer (STAR), which leverages unlabeled data to enhance the robustness of automatic speech recognition (ASR) systems in diverse target domains, such as noise and accents. STAR is developed for prevalent speech foundation models based on Transformer-related architecture with auto-regressive decoding (e.g., Whisper, Canary). Specifically, we propose a novel indicator that empirically integrates step-wise information during decoding to assess the token-level quality of pseudo labels without ground truth, thereby guiding model updates for effective unsupervised adaptation. Experimental results show that STAR achieves an average of 13.5% relative reduction in word error rate across 14 target domains, and it sometimes even approaches the upper-bound performance of supervised adaptation. Surprisingly, we also observe that STAR prevents the adapted model from the common catastrophic forgetting problem without recalling source-domain data. Furthermore, STAR exhibits high data efficiency that only requires less than one-hour unlabeled data, and seamless generality to alternative large speech models and speech translation tasks. Our code aims to open source to the research communities., Comment: 23 pages, Preprint

Solving the Boltzmann-BGK equation with traditional numerical methods suffers from high computational and memory costs due to the curse of dimensionality. In this paper, we propose a novel accuracy-preserved tensor-train (APTT) method to efficiently solve the Boltzmann-BGK equation. A second-order finite difference scheme is applied to discretize the Boltzmann-BGK equation, resulting in a tensor algebraic system at each time step. Based on the low-rank TT representation, the tensor algebraic system is then approximated as a TT-based low-rank system, which is efficiently solved using the TT-modified alternating least-squares (TT-MALS) solver. Thanks to the low-rank TT representation, the APTT method can significantly reduce the computational and memory costs compared to traditional numerical methods. Theoretical analysis demonstrates that the APTT method maintains the same convergence rate as that of the finite difference scheme. The convergence rate and efficiency of the APTT method are validated by several benchmark test cases.

In recent years, the researches about solving partial differential equations (PDEs) based on artificial neural network have attracted considerable attention. In these researches, the neural network models are usually designed depend on human experience or trial and error. Despite the emergence of several model searching methods, these methods primarily concentrate on optimizing the hyperparameters of fully connected neural network model based on the framework of physics-informed neural networks (PINNs), and the corresponding search spaces are relatively restricted, thereby limiting the exploration of superior models. This article proposes an evolutionary computation method aimed at discovering the PINNs model with higher approximation accuracy and faster convergence rate. In addition to searching the numbers of layers and neurons per hidden layer, this method concurrently explores the optimal shortcut connections between the layers and the novel parametric activation functions expressed by the binary trees. In evolution, the strategy about dynamic population size and training epochs (DPSTE) is adopted, which significantly increases the number of models to be explored and facilitates the discovery of models with fast convergence rate. In experiments, the performance of different models that are searched through Bayesian optimization, random search and evolution is compared in solving Klein-Gordon, Burgers, and Lam\'e equations. The experimental results affirm that the models discovered by the proposed evolutionary computation method generally exhibit superior approximation accuracy and convergence rate, and these models also show commendable generalization performance with respect to the source term, initial and boundary conditions, equation coefficient and computational domain. The corresponding code is available at https://github.com/MathBon/Discover-PINNs-Model.

Theoretical descriptions of non equilibrium dynamics of quantum many-body systems essentially employ either (i) explicit treatments, relying on truncation of the expansion of the many-body wave function, (ii) compressed representations of the many-body wave function, or (iii) evolution of an effective (downfolded) representation through Green's functions. In this work, we select representative cases of each of the methods and address how these complementary approaches capture the dynamics driven by intense field perturbations to non equilibrium states. Under strong driving, the systems are characterized by strong entanglement of the single particle density matrix and natural populations approaching those of a strongly interacting equilibrium system. We generate a representative set of results that are numerically exact and form a basis for critical comparison of the distinct families of methods. We demonstrate that the compressed formulation based on similarity transformed Hamiltonians (coupled cluster approach) is practically exact in weak fields and, hence, weakly or moderately correlated systems. Coupled cluster, however, struggles for strong driving fields, under which the system exhibits strongly correlated behavior, as measured by the von Neumann entropy of the single particle density matrix. The dynamics predicted by Green's functions in the (widely popular) GW approximation are less accurate by improve significantly upon the mean-field results in the strongly driven regime., Comment: 11 pages, 2 figures in main text. 11 page supplemental information with 6 figures

This work aims to study a scalable state-space model (SSM), Mamba, for the speech enhancement (SE) task. We exploit a Mamba-based regression model to characterize speech signals and build an SE system upon Mamba, termed SEMamba. We explore the properties of Mamba by integrating it as the core model in both basic and advanced SE systems, along with utilizing signal-level distances as well as metric-oriented loss functions. SEMamba demonstrates promising results and attains a PESQ score of 3.55 on the VoiceBank-DEMAND dataset. When combined with the perceptual contrast stretching technique, the proposed SEMamba yields a new state-of-the-art PESQ score of 3.69.

Antiferromagnet is a promising candidate for the next generation spintronic devices, benefiting from its ultrafast dynamics and spontaneous zero stray field. However, the understanding of their ultrafast spin behaviors is lacking due to the challenges of controlling/detecting the quenched net magnetization. Unconventional compensated semiconducting antiferromagnets present strong time-reversal symmetry breaking, spin splitting in the momentum space, and suitable bandgap for optical control/detection. Thus, it is a powerful platform to uncover the ultrafast dynamics of antiferromagnets. Here, we show an exotic wavelength-dependent spin dynamic in the unconventional compensated semiconducting antiferromagnet {\alpha}-MnTe via time-resolved quadratic magneto-optical Kerr effect measurement, where the probing photon energy of the laser matches its bandgap. This direct excitation and detection of distinct magnon modes reveal varying spin behaviors and time characteristics in a broad temperature range. It originates from the spins triggered at different bands of electronic structures and is depicted in an energy transfer model among electrons, phonons, and magnons. Our study of exotic optical properties in this unconventional semiconducting antiferromagnet fulfills the missing information of spin evolution in the time domain and paves the way for its utilization in ultrafast spintronic devices.

Variational Quantum Eigensolver (VQE) provides a powerful solution for approximating molecular ground state energies by combining quantum circuits and classical computers. However, estimating probabilistic outcomes on quantum hardware requires repeated measurements (shots), incurring significant costs as accuracy increases. Optimizing shot allocation is thus critical for improving the efficiency of VQE. Current strategies rely heavily on hand-crafted heuristics requiring extensive expert knowledge. This paper proposes a reinforcement learning (RL) based approach that automatically learns shot assignment policies to minimize total measurement shots while achieving convergence to the minimum of the energy expectation in VQE. The RL agent assigns measurement shots across VQE optimization iterations based on the progress of the optimization. This approach reduces VQE's dependence on static heuristics and human expertise. When the RL-enabled VQE is applied to a small molecule, a shot reduction policy is learned. The policy demonstrates transferability across systems and compatibility with other wavefunction ansatzes. In addition to these specific findings, this work highlights the potential of RL for automatically discovering efficient and scalable quantum optimization strategies., Comment: 15 pages, 4 figures

The computational complexity of tiling finite simply connected regions with a fixed set of tiles is studied in this paper. We show that the problem of tiling simply connected regions with a fixed set of $23$ Wang tiles is NP-complete. As a consequence, the problem of tiling simply connected regions with a fixed set of $111$ rectangles is NP-complete. Our results improve that of Igor Pak and Jed Yang by using fewer numbers of tiles. Notably in the case of Wang tiles, the number has decreased by more than one third from $35$ to $23$.

Scale has opened new frontiers in natural language processing, but at a high cost. In response, by learning to only activate a subset of parameters in training and inference, Mixture-of-Experts (MoE) have been proposed as an energy efficient path to even larger and more capable language models and this shift towards a new generation of foundation models is gaining momentum, particularly within the field of Automatic Speech Recognition (ASR). Recent works that incorporating MoE into ASR models have complex designs such as routing frames via supplementary embedding network, improving multilingual ability for the experts, and utilizing dedicated auxiliary losses for either expert load balancing or specific language handling. We found that delicate designs are not necessary, while an embarrassingly simple substitution of MoE layers for all Feed-Forward Network (FFN) layers is competent for the ASR task. To be more specific, we benchmark our proposed model on a large scale inner-source dataset (160k hours), the results show that we can scale our baseline Conformer (Dense-225M) to its MoE counterparts (MoE-1B) and achieve Dense-1B level Word Error Rate (WER) while maintaining a Dense-225M level Real Time Factor (RTF). Furthermore, by applying Unified 2-pass framework with bidirectional attention decoders (U2++), we achieve the streaming and non-streaming decoding modes in a single MoE based model, which we call U2++ MoE. We hope that our study can facilitate the research on scaling speech foundation models without sacrificing deployment efficiency.

Large language models (LLMs) can adapt to new tasks through in-context learning (ICL) based on a few examples presented in dialogue history without any model parameter update. Despite such convenience, the performance of ICL heavily depends on the quality of the in-context examples presented, which makes the in-context example selection approach a critical choice. This paper proposes a novel Bayesian in-Context example Selection method (ByCS) for ICL. Extending the inference probability conditioned on in-context examples based on Bayes' theorem, ByCS focuses on the inverse inference conditioned on test input. Following the assumption that accurate inverse inference probability (likelihood) will result in accurate inference probability (posterior), in-context examples are selected based on their inverse inference results. Diverse and extensive cross-tasking and cross-modality experiments are performed with speech, text, and image examples. Experimental results show the efficacy and robustness of our ByCS method on various models, tasks and modalities., Comment: 17 pages, 6 figures

Given the important role turbulence plays in the settling and growth of dust grains in protoplanetary disks, it is crucial that we determine whether these disks are turbulent and to what extent. Protoplanetary disks are weakly ionized near the mid-plane, which has led to a paradigm in which largely laminar magnetic field structures prevail deeper in the disk, with angular momentum being transported via magnetically launched winds. Yet, there has been little exploration on the precise behavior of the gas within the bulk of the disk. We carry out 3D, local shearing box simulations that include all three low-ionization effects (Ohmic diffusion, ambipolar diffusion, and the Hall effect) to probe the nature of magnetically driven gas dynamics 1-30 AU from the central star. We find that gas turbulence can persist with a generous yet physically motivated ionization prescription (order unity Elsasser numbers). The gas velocity fluctuations range from 0.03-0.09 of the sound speed $c_s$ at the disk mid-plane to $\sim c_s$ near the disk surface, and are dependent on the initial magnetic field strength. However, the turbulent velocities do not appear to be strongly dependent on the field polarity, and thus appear to be insensitive to the Hall effect. The mid-plane turbulence has the potential to drive dust grains to collision velocities exceeding their fragmentation limit, and likely reduces the efficacy of particle clumping in the mid-plane, though it remains to be seen if this level of turbulence persists in disks with lower ionization levels., Comment: 23 pages, 19 figures, 2 tables, submitted to ApJ

To study the fixed parameter undecidability of tiling problem for a set of Wang tiles, Jeandel and Rolin show that the tiling problem for a set of 44 Wang bars is undecidable. In this paper, we improve their result by proving that whether a set of 29 Wang bars can tile the plane is undecidable. As a consequence, the tiling problem for a set of Wang tiles with color deficiency of 25 is also undecidable.

Significant advancements in video question answering (VideoQA) have been made thanks to thriving large image-language pretraining frameworks. Although these image-language models can efficiently represent both video and language branches, they typically employ a goal-free vision perception process and do not interact vision with language well during the answer generation, thus omitting crucial visual cues. In this paper, we are inspired by the human recognition and learning pattern and propose VideoDistill, a framework with language-aware (i.e., goal-driven) behavior in both vision perception and answer generation process. VideoDistill generates answers only from question-related visual embeddings and follows a thinking-observing-answering approach that closely resembles human behavior, distinguishing it from previous research. Specifically, we develop a language-aware gating mechanism to replace the standard cross-attention, avoiding language's direct fusion into visual representations. We incorporate this mechanism into two key components of the entire framework. The first component is a differentiable sparse sampling module, which selects frames containing the necessary dynamics and semantics relevant to the questions. The second component is a vision refinement module that merges existing spatial-temporal attention layers to ensure the extraction of multi-grained visual semantics associated with the questions. We conduct experimental evaluations on various challenging video question-answering benchmarks, and VideoDistill achieves state-of-the-art performance in both general and long-form VideoQA datasets. In Addition, we verify that VideoDistill can effectively alleviate the utilization of language shortcut solutions in the EgoTaskQA dataset., Comment: This paper is accepted by CVPR2024

Existing methods to fine-tune LLMs, like Adapter, Prefix-tuning, and LoRA, which introduce extra modules or additional input sequences to inject new skills or knowledge, may compromise the innate abilities of LLMs. In this paper, we propose LLaMA-Excitor, a lightweight method that stimulates the LLMs' potential to better follow instructions by gradually paying more attention to worthwhile information. Specifically, the LLaMA-Excitor does not directly change the intermediate hidden state during the self-attention calculation of the transformer structure. We designed the Excitor block as a bypass module for the similarity score computation in LLMs' self-attention to reconstruct keys and change the importance of values by learnable prompts. LLaMA-Excitor ensures a self-adaptive allocation of additional attention to input instructions, thus effectively preserving LLMs' pre-trained knowledge when fine-tuning LLMs on low-quality instruction-following datasets. Furthermore, we unify the modeling of multi-modal tuning and language-only tuning, extending LLaMA-Excitor to a powerful visual instruction follower without the need for complex multi-modal alignment. Our proposed approach is evaluated in language-only and multi-modal tuning experimental scenarios. Notably, LLaMA-Excitor is the only method that maintains basic capabilities while achieving a significant improvement (+6%) on the MMLU benchmark. In the visual instruction tuning, we achieve a new state-of-the-art image captioning performance of 157.5 CIDEr on MSCOCO, and a comparable performance (88.39%) on ScienceQA to cutting-edge models with more parameters and extensive vision-language pertaining., Comment: This paper is accepted by CVPR 2024

In this paper, we study a cooperative linear quadratic Gaussian (LQG) control system with a single user and a server. In this system, the user runs a process and employs the server to meet the needs of computation. However, the user regards its state trajectories as privacy. Therefore, we propose a privacy scheme, in which the user sends data to the server intermittently. By this scheme, the server's received information of the user is reduced, and consequently the user's privacy is preserved. In this paper, we consider a periodic transmission scheme. We analyze the performance of privacy preservation and LQG control of different transmission periods. Under the given threshold of the control performance loss, a trade-off optimization problem is proposed. Finally, we give the solution to the optimization problem.

We give a proof of Ollinger's conjecture that the problem of tiling the plane with translated copies of a set of $8$ polyominoes is undecidable. The techniques employed in our proof include a different orientation for simulating the Wang tiles in polyomino and a new method for encoding the colors of Wang tiles.

Imaginary-time response functions of finite-temperature quantum systems are often obtained with methods that exhibit stochastic or systematic errors. Reducing these errors comes at a large computational cost -- in quantum Monte Carlo simulations, the reduction of noise by a factor of two incurs a simulation cost of a factor of four. In this paper, we relate certain imaginary-time response functions to an inner product on the space of linear operators on Fock space. We then show that data with noise typically does not respect the positive definiteness of its associated Gramian. The Gramian has the structure of a Hankel matrix. As a method for denoising noisy data, we introduce an alternating projection algorithm that finds the closest positive definite Hankel matrix consistent with noisy data. We test our methodology at the example of fermion Green's functions for continuous-time quantum Monte Carlo data and show remarkable improvements of the error, reducing noise by a factor of up to 20 in practical examples. We argue that Hankel projections should be used whenever finite-temperature imaginary-time data of response functions with errors is analyzed, be it in the context of quantum Monte Carlo, quantum computing, or in approximate semianalytic methodologies., Comment: 5 figures

In this paper, we study \lambda-biharmonic hypersurfaces in the product space L^{m}\times\mathbb{R}, where L^{m} is an Einstein space and \mathbb{R} is a real line. We prove that \lambda-biharmonic hypersurfaces with constant mean curvature in L^{m}\times\mathbb{R} are either minimal or vertical cylinders, and obtain some classification results for \lambda$-biharmonic hypersurfaces under various constraints. Furthermore, we investigate \lambda-biharmonic hypersurfaces in the product space L^{m}(c)\times\mathbb{R}, where L^{m}(c) is a space form with constant sectional curvature c, and categorize hypersurfaces that are either totally umbilical or semi-parallel.

Constructing a 3D scene capable of accommodating open-ended language queries, is a pivotal pursuit, particularly within the domain of robotics. Such technology facilitates robots in executing object manipulations based on human language directives. To tackle this challenge, some research efforts have been dedicated to the development of language-embedded implicit fields. However, implicit fields (e.g. NeRF) encounter limitations due to the necessity of processing a large number of input views for reconstruction, coupled with their inherent inefficiencies in inference. Thus, we present the GaussianGrasper, which utilizes 3D Gaussian Splatting to explicitly represent the scene as a collection of Gaussian primitives. Our approach takes a limited set of RGB-D views and employs a tile-based splatting technique to create a feature field. In particular, we propose an Efficient Feature Distillation (EFD) module that employs contrastive learning to efficiently and accurately distill language embeddings derived from foundational models. With the reconstructed geometry of the Gaussian field, our method enables the pre-trained grasping model to generate collision-free grasp pose candidates. Furthermore, we propose a normal-guided grasp module to select the best grasp pose. Through comprehensive real-world experiments, we demonstrate that GaussianGrasper enables robots to accurately query and grasp objects with language instructions, providing a new solution for language-guided manipulation tasks. Data and codes can be available at https://github.com/MrSecant/GaussianGrasper.

In this paper, we prove that PMCV (i.e. \Delta\vec{H} is proportional to \vec{H}) hypersurface M^n_r of a non-flat pseudo-Riemannian space form N^{n+1}_s(c) with at most two distinct principal curvatures is minimal or locally isoparametric, and compute the mean curvature for the isoparametric ones. As an application, we give full classification results of such non-minimal Lorentzian hypersurfaces of non-flat Lorentz space forms.

Best rank-one approximation is one of the most fundamental tasks in tensor computation. In order to fully exploit modern multi-core parallel computers, it is necessary to develop decoupling algorithms for computing the best rank-one approximation of higher-order tensors at large scales. In this paper, we first build a bridge between the rank-one approximation of tensors and the eigenvector-dependent nonlinear eigenvalue problem (NEPv), and then develop an efficient decoupling algorithm, namely the higher-order self-consistent field (HOSCF) algorithm, inspired by the famous self-consistent field (SCF) iteration frequently used in computational chemistry. The convergence theory of the HOSCF algorithm and an estimation of the convergence speed are further presented. In addition, we propose an improved HOSCF (iHOSCF) algorithm that incorporates the Rayleigh quotient iteration, which can significantly accelerate the convergence of HOSCF. Numerical experiments show that the proposed algorithms can efficiently converge to the best rank-one approximation of both synthetic and real-world tensors and can scale with high parallel scalability on a modern parallel computer.

Burke and Teng introduced a two-player combinatorial game Atropos based on Sperner's lemma, and showed that deciding whether one has a winning strategy for Atropos is PSPACE-complete. In the original Atropos game, the players must color a node adjacent to the last colored node. Burke and Teng also mentioned a variant Atropos-k in which each move is at most of distance k of the previous move, and asked a question on determining the computational complexity of this variant. In this paper, we answer this question by showing that for any fixed integer k (k>=2), Atropos-k is PSPACE-complete by reduction from True Quantified Boolean Formula (TQBF).

Language-conditioned robot behavior plays a vital role in executing complex tasks by associating human commands or instructions with perception and actions. The ability to compose long-horizon tasks based on unconstrained language instructions necessitates the acquisition of a diverse set of general-purpose skills. However, acquiring inherent primitive skills in a coupled and long-horizon environment without external rewards or human supervision presents significant challenges. In this paper, we evaluate the relationship between skills and language instructions from a mathematical perspective, employing two forms of mutual information within the framework of language-conditioned policy learning. To maximize the mutual information between language and skills in an unsupervised manner, we propose an end-to-end imitation learning approach known as Language Conditioned Skill Discovery (LCSD). Specifically, we utilize vector quantization to learn discrete latent skills and leverage skill sequences of trajectories to reconstruct high-level semantic instructions. Through extensive experiments on language-conditioned robotic navigation and manipulation tasks, encompassing BabyAI, LORel, and CALVIN, we demonstrate the superiority of our method over prior works. Our approach exhibits enhanced generalization capabilities towards unseen tasks, improved skill interpretability, and notably higher rates of task completion success., Comment: 16 pages

Robotic behavior synthesis, the problem of understanding multimodal inputs and generating precise physical control for robots, is an important part of Embodied AI. Despite successes in applying multimodal large language models for high-level understanding, it remains challenging to translate these conceptual understandings into detailed robotic actions while achieving generalization across various scenarios. In this paper, we propose a tree-structured multimodal code generation framework for generalized robotic behavior synthesis, termed RoboCodeX. RoboCodeX decomposes high-level human instructions into multiple object-centric manipulation units consisting of physical preferences such as affordance and safety constraints, and applies code generation to introduce generalization ability across various robotics platforms. To further enhance the capability to map conceptual and perceptual understanding into control commands, a specialized multimodal reasoning dataset is collected for pre-training and an iterative self-updating methodology is introduced for supervised fine-tuning. Extensive experiments demonstrate that RoboCodeX achieves state-of-the-art performance in both simulators and real robots on four different kinds of manipulation tasks and one navigation task.

Rapid progress in high-level task planning and code generation for open-world robot manipulation has been witnessed in Embodied AI. However, previous studies put much effort into general common sense reasoning and task planning capabilities of large-scale language or multi-modal models, relatively little effort on ensuring the deployability of generated code on real robots, and other fundamental components of autonomous robot systems including robot perception, motion planning, and control. To bridge this ``ideal-to-real'' gap, this paper presents \textbf{RobotScript}, a platform for 1) a deployable robot manipulation pipeline powered by code generation; and 2) a code generation benchmark for robot manipulation tasks in free-form natural language. The RobotScript platform addresses this gap by emphasizing the unified interface with both simulation and real robots, based on abstraction from the Robot Operating System (ROS), ensuring syntax compliance and simulation validation with Gazebo. We demonstrate the adaptability of our code generation framework across multiple robot embodiments, including the Franka and UR5 robot arms, and multiple grippers. Additionally, our benchmark assesses reasoning abilities for physical space and constraints, highlighting the differences between GPT-3.5, GPT-4, and Gemini in handling complex physical interactions. Finally, we present a thorough evaluation on the whole system, exploring how each module in the pipeline: code generation, perception, motion planning, and even object geometric properties, impact the overall performance of the system., Comment: 10 pages of main paper, 4 pages of appendix; 10 figures in main paper, 3 figures in appendix