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In-context learning (ICL) refers to a remarkable capability of pretrained large language models, which can learn a new task given a few examples during inference. However, theoretical understanding of ICL is largely under-explored, particularly whether transformers can be trained to generalize to unseen examples in a prompt, which will require the model to acquire contextual knowledge of the prompt for generalization. This paper investigates the training dynamics of transformers by gradient descent through the lens of non-linear regression tasks. The contextual generalization here can be attained via learning the template function for each task in-context, where all template functions lie in a linear space with $m$ basis functions. We analyze the training dynamics of one-layer multi-head transformers to in-contextly predict unlabeled inputs given partially labeled prompts, where the labels contain Gaussian noise and the number of examples in each prompt are not sufficient to determine the template. Under mild assumptions, we show that the training loss for a one-layer multi-head transformer converges linearly to a global minimum. Moreover, the transformer effectively learns to perform ridge regression over the basis functions. To our knowledge, this study is the first provable demonstration that transformers can learn contextual (i.e., template) information to generalize to both unseen examples and tasks when prompts contain only a small number of query-answer pairs.

In this work, we systematically analyse Feynman integrals in the `t Hooft-Veltman scheme. We write an explicit reduction resulting from partial fractioning the high-multiplicity integrands to a finite basis of topologies at any given loop order. We find all of these finite basis topologies at two loops in four external dimensions. Their maximal cut and the leading singularity are expressed in terms of the Gram determinant and Baikov polynomial. By performing an Integration-By-Parts reduction without any cut constraint on a numerical probe for one of these topologies, we show that the computational complexity drops significantly compared to the Conventional Dimensional Regularization scheme. Formally, our work implies an upper bound on the rigidity of special functions appearing in the iterated integral solutions at each loop order in perturbative Quantum Field Theory. Phenomenologically, the integrand-level reduction we present will substantially simplify the task of providing high-precision predictions for future high-multiplicity collider observables., Comment: 10 pages, 2 figures, 2 tables

Building efficient inference framework has gained increasing interests for research community. Early-exit models, a variant of LLMs, improves the inference efficiency of LLMs by skipping rest layers and directly generate output tokens when they are confident enough. However, there is no work of LLM inference framework that takes early-exit models into consideration. This is non-trivial as prior art on LLM inference cannot be directly applied to early-exit models. In this work, we solves two key challenges in building efficient inference framework for early-exit models: (1) batch inference at iteration-level granularity; and (2) KV cache management. For the former, we propose to process the batch until all sequences surpass the early-exit confidence threshold. For the latter, we propose to fill the KV cache of rest layers before the iteration terminates. Our evaluation shows that, compared with the original vLLM operating at full layers, our solution achieves up to 1.25x speed up.

Materials with topological flat bands can serve as a promising platform to investigate strongly interacting phenomena. However, experimental realization of ideal flat bands is mostly limited to artificial lattices or moir\'e systems. Here we report a general way to construct one-dimensional (1D) flat bands in phosphorene nanoribbons (PNRs) with pentagonal nature: penta-hexa-PNRs and penta-dodeca-PNRs, wherein the corresponding flat bands are directly verified by using angle-resolved photoemission spectroscopy. We confirm that the observed 1D flat bands originate from the electronic 1D sawtooth and Lieb lattices, respectively, as revealed by the combination of bond-resolved scanning tunneling microscopy, scanning tunneling spectroscopy, tight-binding models, and first-principles calculations. Our study demonstrates a general way to construct 1D flat bands in 1D solid materials system, which provides a robust platform to explore strongly interacting phases of matter., Comment: 13 pages, 4 figures

The matrix quantization entails representing matrix elements in a more space-efficient form to reduce storage usage, with dequantization restoring the original matrix for use. We formulate the Quantization Error Minimization (QEM) problem as minimizing the distance between a matrix before and after quantization, under the condition that the quantized matrix occupies the same memory space. Matrix quantization is crucial in various applications, including Large Language Models (LLMs) weight quantization, vector databases, KV cache quantization, graph compression, and image compression. Recent advancements in LLMs, such as GPT-4 and BERT, have highlighted the importance of matrix compression due to the large size of parameters and KV cache, which are stored as matrices. We propose Quantum Entanglement Trees (QET) to address the QEM problem by leveraging the local orderliness of matrix elements, involving iterative element swapping to form a locally ordered matrix. This matrix is then grouped and quantized by columns. To enhance QET, we introduce two optimizations: further quantizing residuals to reduce MSE, and using masking and batch processing to accelerate the algorithm. Experimental results demonstrate that QET can effectively reduce MSE to 5.05%, 13.33%, and 11.89% of the current best method on the LLM dataset, K cache, and V cache, respectively. Our contributions include the abstraction of the QEM problem, the design of the QET algorithm, and the proposal of two optimizations to improve accuracy and speed.

Automated cephalometric landmark detection is crucial in real-world orthodontic diagnosis. Current studies mainly focus on only adult subjects, neglecting the clinically crucial scenario presented by adolescents whose landmarks often exhibit significantly different appearances compared to adults. Hence, an open question arises about how to develop a unified and effective detection algorithm across various age groups, including adolescents and adults. In this paper, we propose CeLDA, the first work for Cephalometric Landmark Detection across Ages. Our method leverages a prototypical network for landmark detection by comparing image features with landmark prototypes. To tackle the appearance discrepancy of landmarks between age groups, we design new strategies for CeLDA to improve prototype alignment and obtain a holistic estimation of landmark prototypes from a large set of training images. Moreover, a novel prototype relation mining paradigm is introduced to exploit the anatomical relations between the landmark prototypes. Extensive experiments validate the superiority of CeLDA in detecting cephalometric landmarks on both adult and adolescent subjects. To our knowledge, this is the first effort toward developing a unified solution and dataset for cephalometric landmark detection across age groups. Our code and dataset will be made public on https://github.com/ShanghaiTech-IMPACT/Cephalometric-Landmark-Detection-across-Ages-with-Prototypical-Network, Comment: MICCAI 2024

To approximate sums of values in key-value data streams, sketches are widely used in databases and networking systems. They offer high-confidence approximations for any given key while ensuring low time and space overhead. While existing sketches are proficient in estimating individual keys, they struggle to maintain this high confidence across all keys collectively, an objective that is critically important in both algorithm theory and its practical applications. We propose ReliableSketch, the first to control the error of all keys to less than $\Lambda$ with a small failure probability $\Delta$, requiring only $O(1 + \Delta\ln\ln(\frac{N}{\Lambda}))$ amortized time and $O(\frac{N}{\Lambda} + \ln(\frac{1}{\Delta}))$ space. Furthermore, its simplicity makes it hardware-friendly, and we implement it on CPU servers, FPGAs, and programmable switches. Our experiments show that under the same small space, ReliableSketch not only keeps all keys' errors below $\Lambda$ but also achieves near-optimal throughput, outperforming competitors with thousands of uncontrolled estimations. We have made our source code publicly available.

The challenge of estimating similarity between sets has been a significant concern in data science, finding diverse applications across various domains. However, previous approaches, such as MinHash, have predominantly centered around hashing techniques, which are well-suited for sets but less naturally adaptable to multisets, a common occurrence in scenarios like network streams and text data. Moreover, with the increasing prevalence of data arriving in streaming patterns, many existing methods struggle to handle cases where set items are presented in a continuous stream. Consequently, our focus in this paper is on the challenging scenario of multisets with item streams. To address this, we propose SimiSketch, a sketching algorithm designed to tackle this specific problem. The paper begins by presenting two simpler versions that employ intuitive sketches for similarity estimation. Subsequently, we formally introduce SimiSketch and leverage SALSA to enhance accuracy. To validate our algorithms, we conduct extensive testing on synthetic datasets, real-world network traffic, and text articles. Our experiment shows that compared with the state-of-the-art, SimiSketch can improve the accuracy by up to 42 times, and increase the throughput by up to 360 times. The complete source code is open-sourced and available on GitHub for reference.

Reinforcement learning from human feedback (RLHF) has demonstrated great promise in aligning large language models (LLMs) with human preference. Depending on the availability of preference data, both online and offline RLHF are active areas of investigation. A key bottleneck is understanding how to incorporate uncertainty estimation in the reward function learned from the preference data for RLHF, regardless of how the preference data is collected. While the principles of optimism or pessimism under uncertainty are well-established in standard reinforcement learning (RL), a practically-implementable and theoretically-grounded form amenable to large language models is not yet available, as standard techniques for constructing confidence intervals become intractable under arbitrary policy parameterizations. In this paper, we introduce a unified approach to online and offline RLHF -- value-incentivized preference optimization (VPO) -- which regularizes the maximum-likelihood estimate of the reward function with the corresponding value function, modulated by a $\textit{sign}$ to indicate whether the optimism or pessimism is chosen. VPO also directly optimizes the policy with implicit reward modeling, and therefore shares a simpler RLHF pipeline similar to direct preference optimization. Theoretical guarantees of VPO are provided for both online and offline settings, matching the rates of their standard RL counterparts. Moreover, experiments on text summarization and dialog verify the practicality and effectiveness of VPO.

Continuous normalizing flows (CNFs) learn an ordinary differential equation to transform prior samples into data. Flow matching (FM) has recently emerged as a simulation-free approach for training CNFs by regressing a velocity model towards the conditional velocity field. However, on constrained domains, the learned velocity model may lead to undesirable flows that result in highly unnatural samples, e.g., oversaturated images, due to both flow matching error and simulation error. To address this, we add a boundary constraint term to CNFs, which leads to reflected CNFs that keep trajectories within the constrained domains. We propose reflected flow matching (RFM) to train the velocity model in reflected CNFs by matching the conditional velocity fields in a simulation-free manner, similar to the vanilla FM. Moreover, the analytical form of conditional velocity fields in RFM avoids potentially biased approximations, making it superior to existing score-based generative models on constrained domains. We demonstrate that RFM achieves comparable or better results on standard image benchmarks and produces high-quality class-conditioned samples under high guidance weight., Comment: ICML 2024 camera-ready

Large Language Models (LLMs) have significantly advanced natural language processing tasks such as machine translation, text generation, and sentiment analysis. However, their large size, often consisting of billions of parameters, poses challenges for storage, computation, and deployment, particularly in resource-constrained environments like mobile devices and edge computing platforms. Effective compression and quantization techniques are crucial for addressing these issues, reducing memory footprint and computational requirements without significantly compromising performance. Traditional methods that uniformly map parameters to compressed spaces fail to account for the uneven distribution of parameters, leading to substantial accuracy loss. In this work, we propose Athena, a novel algorithm for efficient block-wise post-training quantization of LLMs. Athena leverages Second-Order Matrix Derivative Information to guide the quantization process using the curvature information of the loss landscape. By grouping parameters by columns or rows and iteratively optimizing the quantization process, Athena updates the model parameters and Hessian matrix to achieve significant compression while maintaining high accuracy. This makes Athena a practical solution for deploying LLMs in various settings.

Graphs play an increasingly important role in various big data applications. However, existing graph data structures cannot simultaneously address the performance bottlenecks caused by the dynamic updates, large scale, and high query complexity of current graphs. This paper proposes a novel data structure for large-scale dynamic graphs called CuckooGraph. It does not require any prior knowledge of the upcoming graphs, and can adaptively resize to the most memory-efficient form while requiring few memory accesses for very fast graph data processing. The key techniques of CuckooGraph include TRANSFORMATION and DENYLIST. TRANSFORMATION fully utilizes the limited memory by designing related data structures that allow flexible space transformations to smoothly expand/tighten the required space depending on the number of incoming items. DENYLIST efficiently handles item insertion failures and further improves processing speed. Our experimental results show that compared with the most competitive solution Spruce, CuckooGraph achieves about $33\times$ higher insertion throughput while requiring only about $68\%$ of the memory space.

We study the diffusion limit of the strong solution to the Vlasov-Maxwell-Boltzmann (VMB) system with initial data near a global Maxwellian. By introducing a new decomposition of the solution to identify the essential components for generating the initial layer, we prove the convergence and establish the opitmal convergence rate of the classical solution to the VMB system to the solution of the Navier-Stokes-Maxwell system based on the spectral analysis.

MoE facilitates the development of large models by making the computational complexity of the model no longer scale linearly with increasing parameters. The learning sparse gating network selects a set of experts for each token to be processed; however, this may lead to differences in the number of tokens processed by each expert over several successive iterations, i.e., the expert load fluctuations, which reduces computational parallelization and resource utilization. To this end, we traced and analyzed loads of each expert in the training iterations for several large language models in this work, and defined the transient state with "obvious load fluctuation" and the stable state with "temporal locality". Moreover, given the characteristics of these two states and the computational overhead, we deployed three classical prediction algorithms that achieve accurate expert load prediction results. For the GPT3 350M model, the average error rates for predicting the expert load proportion over the next 1,000 and 2,000 steps are approximately 1.3% and 1.8%, respectively. This work can provide valuable guidance for expert placement or resource allocation for MoE model training. Based on this work, we will propose an expert placement scheme for transient and stable states in our coming work.

We present the analytic calculation of the leading order three-point energy correlator (EEEC) in hadronic Higgs decays, including both gluon-initiated channel $H\rightarrow g g+X$ and quark-initiated channel $H\rightarrow q\bar q+X$. The phase space integration is evaluated directly using Mandelstam variables $s_{ij}=(p_i+p_j)^2$, and the appearing square roots can be rationalized by either conformal ratios or celestial coordinate variables. Throughout the calculation, we observe the same transcendental function space as in $\mathcal{N}=4$ super Yang-Mills (SYM) theory and $e^+e^-\rightarrow \text{ hadrons}$. Different infrared limits are also explored using the full analytic result, offering the fixed-order data for EEEC factorization and resummation. Given its non-trivial shape dependence, the EEEC presents an excellent opportunity to explore the dynamics of gluon jets originating from the $H \to gg$ decay channel at future lepton colliders., Comment: 18 pages, 9 figures, ancillary files with results

We study the hyperbolic version of the Prandtl system derived from the hyperbolic Navier-Stokes system with no-slip boundary condition. Compared to the classical Prandtl system, the quasi-linear terms in the hyperbolic Prandtl equation leads to an additional instability mechanism. To overcome the loss of derivatives in all directions in the quasi-linear term, we introduce a new auxiliary function for the well-posedness of the system in an anisotropic Gevrey space which is Gevrey class $\frac 32$ in the tangential variable and is analytic in the normal variable.

We present a novel framework for 3D object-centric representation learning. Our approach effectively decomposes complex scenes into individual objects from a single image in an unsupervised fashion. This method, called slot-guided Volumetric Object Radiance Fields (sVORF), composes volumetric object radiance fields with object slots as a guidance to implement unsupervised 3D scene decomposition. Specifically, sVORF obtains object slots from a single image via a transformer module, maps these slots to volumetric object radiance fields with a hypernetwork and composes object radiance fields with the guidance of object slots at a 3D location. Moreover, sVORF significantly reduces memory requirement due to small-sized pixel rendering during training. We demonstrate the effectiveness of our approach by showing top results in scene decomposition and generation tasks of complex synthetic datasets (e.g., Room-Diverse). Furthermore, we also confirm the potential of sVORF to segment objects in real-world scenes (e.g., the LLFF dataset). We hope our approach can provide preliminary understanding of the physical world and help ease future research in 3D object-centric representation learning., Comment: NeurIPS 2023

In the pursuit of advanced photoelectric devices, researchers have uncovered near room-temperature metal-insulator transitions (MIT) in non-volatile VO2. Although theoretical investigations propose that polaron dynamics mediate the MIT, direct experimental evidence remains scarce. In this study, we present direct evidence of the polaron state in insulating VO2 through high-resolution spectroscopic ellipsometry measurements and first-principles calculations. We demonstrate that polaron dynamics play a complementary role in facilitating Peierls and Mott transitions to contribute to the MIT processes. Moreover, our observations and characterizations of conventional metallic and correlated plasmons in the respective phases of the VO2 film provide valuable insights into their electron structures. This study provides an understanding of the MIT mechanism in correlated systems and highlights how polarons, lattice distortions and electron correlations facilitate the phase transition processes in strongly-correlated systems, while further inspiring the development of new device functionalities., Comment: 24 pages,4 figures,research article

Recently, the growing memory demands of embedding tables in Deep Learning Recommendation Models (DLRMs) pose great challenges for model training and deployment. Existing embedding compression solutions cannot simultaneously meet three key design requirements: memory efficiency, low latency, and adaptability to dynamic data distribution. This paper presents CAFE, a Compact, Adaptive, and Fast Embedding compression framework that addresses the above requirements. The design philosophy of CAFE is to dynamically allocate more memory resources to important features (called hot features), and allocate less memory to unimportant ones. In CAFE, we propose a fast and lightweight sketch data structure, named HotSketch, to capture feature importance and report hot features in real time. For each reported hot feature, we assign it a unique embedding. For the non-hot features, we allow multiple features to share one embedding by using hash embedding technique. Guided by our design philosophy, we further propose a multi-level hash embedding framework to optimize the embedding tables of non-hot features. We theoretically analyze the accuracy of HotSketch, and analyze the model convergence against deviation. Extensive experiments show that CAFE significantly outperforms existing embedding compression methods, yielding 3.92% and 3.68% superior testing AUC on Criteo Kaggle dataset and CriteoTB dataset at a compression ratio of 10000x. The source codes of CAFE are available at GitHub.

Over recent years, diffusion models have facilitated significant advancements in video generation. Yet, the creation of face-related videos still confronts issues such as low facial fidelity, lack of frame consistency, limited editability and uncontrollable human poses. To address these challenges, we introduce a facial animation generation method that enhances both face identity fidelity and editing capabilities while ensuring frame consistency. This approach incorporates the concept of an anchor frame to counteract the degradation of generative ability in original text-to-image models when incorporating a motion module. We propose two strategies towards this objective: training-free and training-based anchor frame methods. Our method's efficacy has been validated on multiple representative DreamBooth and LoRA models, delivering substantial improvements over the original outcomes in terms of facial fidelity, text-to-image editability, and video motion. Moreover, we introduce conditional control using a 3D parametric face model to capture accurate facial movements and expressions. This solution augments the creative possibilities for facial animation generation through the integration of multiple control signals. For additional samples, please visit https://paper-faac.github.io/.

Learnable embedding vector is one of the most important applications in machine learning, and is widely used in various database-related domains. However, the high dimensionality of sparse data in recommendation tasks and the huge volume of corpus in retrieval-related tasks lead to a large memory consumption of the embedding table, which poses a great challenge to the training and deployment of models. Recent research has proposed various methods to compress the embeddings at the cost of a slight decrease in model quality or the introduction of other overheads. Nevertheless, the relative performance of these methods remains unclear. Existing experimental comparisons only cover a subset of these methods and focus on limited metrics. In this paper, we perform a comprehensive comparative analysis and experimental evaluation of embedding compression. We introduce a new taxonomy that categorizes these techniques based on their characteristics and methodologies, and further develop a modular benchmarking framework that integrates 14 representative methods. Under a uniform test environment, our benchmark fairly evaluates each approach, presents their strengths and weaknesses under different memory budgets, and recommends the best method based on the use case. In addition to providing useful guidelines, our study also uncovers the limitations of current methods and suggests potential directions for future research.

Federated reinforcement learning (RL) enables collaborative decision making of multiple distributed agents without sharing local data trajectories. In this work, we consider a multi-task setting, in which each agent has its own private reward function corresponding to different tasks, while sharing the same transition kernel of the environment. Focusing on infinite-horizon Markov decision processes, the goal is to learn a globally optimal policy that maximizes the sum of the discounted total rewards of all the agents in a decentralized manner, where each agent only communicates with its neighbors over some prescribed graph topology. We develop federated vanilla and entropy-regularized natural policy gradient (NPG) methods in the tabular setting under softmax parameterization, where gradient tracking is applied to estimate the global Q-function to mitigate the impact of imperfect information sharing. We establish non-asymptotic global convergence guarantees under exact policy evaluation, where the rates are nearly independent of the size of the state-action space and illuminate the impacts of network size and connectivity. To the best of our knowledge, this is the first time that near dimension-free global convergence is established for federated multi-task RL using policy optimization. We further go beyond the tabular setting by proposing a federated natural actor critic (NAC) method for multi-task RL with function approximation, and establish its finite-time sample complexity taking the errors of function approximation into account.

Semi-implicit variational inference (SIVI) has been introduced to expand the analytical variational families by defining expressive semi-implicit distributions in a hierarchical manner. However, the single-layer architecture commonly used in current SIVI methods can be insufficient when the target posterior has complicated structures. In this paper, we propose hierarchical semi-implicit variational inference, called HSIVI, which generalizes SIVI to allow more expressive multi-layer construction of semi-implicit distributions. By introducing auxiliary distributions that interpolate between a simple base distribution and the target distribution, the conditional layers can be trained by progressively matching these auxiliary distributions one layer after another. Moreover, given pre-trained score networks, HSIVI can be used to accelerate the sampling process of diffusion models with the score matching objective. We show that HSIVI significantly enhances the expressiveness of SIVI on several Bayesian inference problems with complicated target distributions. When used for diffusion model acceleration, we show that HSIVI can produce high quality samples comparable to or better than the existing fast diffusion model based samplers with a small number of function evaluations on various datasets., Comment: 25 pages, 13 figures, NeurIPS 2023

We report a new result for the $N_f \,C_F^3$ contribution to the four-loop anomalous dimensions of non-singlet, twist-two operators in Quantum Chromodynamics. This result is obtained through computations of off-shell operator matrix elements. Employing integration-by-parts reductions and differential equations with respect to a tracing parameter allowed us to derive analytic results valid for arbitrary Mellin moment $n$., Comment: 13 pages, 1 figure, ancillary file with result, journal version

With the impressive progress in diffusion-based text-to-image generation, extending such powerful generative ability to text-to-video raises enormous attention. Existing methods either require large-scale text-video pairs and a large number of training resources or learn motions that are precisely aligned with template videos. It is non-trivial to balance a trade-off between the degree of generation freedom and the resource costs for video generation. In our study, we present a few-shot-based tuning framework, LAMP, which enables text-to-image diffusion model Learn A specific Motion Pattern with 8~16 videos on a single GPU. Specifically, we design a first-frame-conditioned pipeline that uses an off-the-shelf text-to-image model for content generation so that our tuned video diffusion model mainly focuses on motion learning. The well-developed text-to-image techniques can provide visually pleasing and diverse content as generation conditions, which highly improves video quality and generation freedom. To capture the features of temporal dimension, we expand the pretrained 2D convolution layers of the T2I model to our novel temporal-spatial motion learning layers and modify the attention blocks to the temporal level. Additionally, we develop an effective inference trick, shared-noise sampling, which can improve the stability of videos with computational costs. Our method can also be flexibly applied to other tasks, e.g. real-world image animation and video editing. Extensive experiments demonstrate that LAMP can effectively learn the motion pattern on limited data and generate high-quality videos. The code and models are available at https://rq-wu.github.io/projects/LAMP., Comment: Project Page: https://rq-wu.github.io/projects/LAMP

The soft theorem states that scattering amplitude in gauge theory with a soft gauge-boson emission can be factorized into a hard scattering amplitude and a soft factor. In this paper, we present calculations of the soft factor for processes involving two hard colored partons, up to three loops in QCD. To accomplish this, we developed a systematic method for recursively calculating relevant Feynman integrals using the Feynman-Parameter representation. Our results constitute an important ingredient for the subtraction of infrared singularities at N$^4$LO in perturbative QCD. Using the principle of leading transcendentality between QCD and ${\cal N}=4$ super Yang-Mills theory, we determine the soft factor in the latter case to three loops with full-color dependence. As a by-product, we also obtain the finite constant $f_2^{(3)}$ in the Bern-Dixon-Smirnov ansatz analytically, which was previously known numerically only., Comment: 31 pages, ancillary files provided, matches published version

A novel mechanism to derive self-entanglement-free (SEF) path for tethered differential-driven robots is proposed in this work. The problem is tailored to the deployment of tethered differential-driven robots in situations where an omni-directional tether re-tractor is not available. This is frequently encountered when it is impractical to concurrently equip an omni-directional tether retracting mechanism with other geometrically intricate devices, such as a manipulator, which is notably relevant in applications like disaster recovery, spatial exploration, etc. Without specific attention to the spatial relation between the shape of the tether and the pose of the mobile unit, the issue of self-entanglement arises when the robot moves, resulting in unsafe robot movements and the risk of damaging the tether. In this paper, the SEF constraint is first formulated as the boundedness of a relative angle function which characterises the angular difference between the tether stretching direction and the robot's heading direction. Then, a constrained searching-based path planning algorithm is proposed which produces a path that is sub-optimal whilst ensuring the avoidance of tether self-entanglement. Finally, the algorithmic efficiency of the proposed path planner is further enhanced by proving the conditioned sparsity of the primitive path validity checking module. The effectiveness of the proposed algorithm is assessed through case studies, comparing its performance against untethered differential-driven planners in challenging planning scenarios. A comparative analysis is further conducted between the normal node expansion module and the improved node expansion module which incorporates sparse waypoint validity checking. Real-world tests are also conducted to validate the algorithm's performance. An open-source implementation has also made available for the benefit of the robotics community., Comment: This is a generalised version of the authors' ICRA23 conference paper

Membership (membership query / membership testing) is a fundamental problem across databases, networks and security. However, previous research has primarily focused on either approximate solutions, such as Bloom Filters, or exact methods, like perfect hashing and dictionaries, without attempting to develop a an integral theory. In this paper, we propose a unified and complete theory, namely chain rule, for general membership problems, which encompasses both approximate and exact membership as extreme cases. Building upon the chain rule, we introduce a straightforward yet versatile algorithm framework, namely ChainedFilter, to combine different elementary filters without losing information. Our evaluation results demonstrate that ChainedFilter performs well in many applications: (1) it requires only 26% additional space over the theoretical lower bound for implicit static dictionary, (2) it requires only 0.22 additional bit per item over the theoretical lower bound for lossless data compression, (3) it reduces up to 31% external memory access than raw Cuckoo Hashing, (4) it reduces up to 36% P99 tail point query latency than Bloom Filter under the same space cost in RocksDB database, and (5) it reduces up to 99.1% filter space than original Learned Bloom Filter., Comment: SIGMOD 2024

The grazing limit of the Boltzmann equation to Landau equation is well-known and has been justified by using cutoff near the grazing angle with some suitable scaling. In this paper, we will provide a new understanding by simply applying a natural scaling on the Boltzmann operator without angular cutoff. The proof is based on a new well-posedness theory on the Boltzmann equation without angular cutoff in the regime with optimal ranges of parameters so that the grazing limit can be justified directly for any $\gamma>-5$ that includes the Coulomb potential corresponding to $\gamma=-3$. With this new understanding, the scaled Boltzmann operator in fact can be decomposed into two components. The first one converges to the Landau operator when the singular parameter $s$ of interaction angle tends to $1^{-}$ and the second one vanishes in this limit., Comment: 56 pages, 2 figures

The scale evolution of parton distributions is determined by universal splitting functions. As a milestone towards the computation of these functions to four-loop order in QCD, we compute all contributions to the pure-singlet quark-quark splitting functions that involve two closed fermion loops. The splitting functions are extracted from the pole terms of off-shell operator matrix elements, and the workflow for their calculation is outlined. We reproduce known results for the non-singlet four-loop splitting functions and validate our new pure-singlet results against fixed Mellin moments., Comment: 26 pages, 2 figures, journal version

Text-Based Person Searching (TBPS) aims to identify the images of pedestrian targets from a large-scale gallery with given textual caption. For cross-modal TBPS task, it is critical to obtain well-distributed representation in the common embedding space to reduce the inter-modal gap. Furthermore, it is also essential to learn detailed image-text correspondence efficiently to discriminate similar targets and enable fine-grained target search. To address these challenges, we present a simple yet effective method that calibrates cross-modal features from these two perspectives. Our method consists of two novel losses to provide fine-grained cross-modal features. The Sew calibration loss takes the quality of textual captions as guidance and aligns features between image and text modalities. On the other hand, the Masking Caption Modeling (MCM) loss leverages a masked captions prediction task to establish detailed and generic relationships between textual and visual parts. The proposed method is cost-effective and can easily retrieve specific persons with textual captions. The architecture has only a dual-encoder without multi-level branches or extra interaction modules, making a high-speed inference. Our method achieves top results on three popular benchmarks with 73.81%, 74.25% and 57.35% Rank1 accuracy on the CUHK-PEDES, ICFG-PEDES, and RSTPReID, respectively. We hope our scalable method will serve as a solid baseline and help ease future research in TBPS. The code will be publicly available.