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The use of guidance in diffusion models was originally motivated by the premise that the guidance-modified score is that of the data distribution tilted by a conditional likelihood raised to some power. In this work we clarify this misconception by rigorously proving that guidance fails to sample from the intended tilted distribution. Our main result is to give a fine-grained characterization of the dynamics of guidance in two cases, (1) mixtures of compactly supported distributions and (2) mixtures of Gaussians, which reflect salient properties of guidance that manifest on real-world data. In both cases, we prove that as the guidance parameter increases, the guided model samples more heavily from the boundary of the support of the conditional distribution. We also prove that for any nonzero level of score estimation error, sufficiently large guidance will result in sampling away from the support, theoretically justifying the empirical finding that large guidance results in distorted generations. In addition to verifying these results empirically in synthetic settings, we also show how our theoretical insights can offer useful prescriptions for practical deployment.

The particle filter (PF), also known as the sequential Monte Carlo (SMC), is designed to approximate high-dimensional probability distributions and their normalizing constants in the discrete-time setting. To reduce the variance of the Monte Carlo approximation, several twisted particle filters (TPF) have been proposed by researchers, where one chooses or learns a twisting function that modifies the Markov transition kernel. In this paper, we study the TPF from a continuous-time perspective. Under suitable settings, we show that the discrete-time model converges to a continuous-time limit, which can be solved through a series of well-studied control-based importance sampling algorithms. This discrete-continuous connection allows the design of new TPF algorithms inspired by established continuous-time algorithms. As a concrete example, guided by existing importance sampling algorithms in the continuous-time setting, we propose a novel algorithm called ``Twisted-Path Particle Filter" (TPPF), where the twist function, parameterized by neural networks, minimizes specific KL-divergence between path measures. Some numerical experiments are given to illustrate the capability of the proposed algorithm.

We investigate the dependence of physical observable of open quantum systems with Bosonic bath on the bath correlation function. We provide an error estimate of the difference of physical observable induced by the variation of bath correlation function, based on diagrammatic and combinatorial arguments. This gives a mathematically rigorous justification of the result in [Mascherpa et al, Phys Rev Lett 2017]., Comment: arXiv admin note: text overlap with arXiv:1811.08044

We study a qDRIFT-type randomized method to simulate the Lindblad equations. For Lindblad dynamics generated by an ensemble of Lindbladians $\{\mathcal{L}_a\}_{a \in \mathcal{A}}$, our approach implements a single randomly sampled Lindbladian $\mathcal{L}_a$ at each time step. The only assumption is that each $\mathcal{L}_a$ involves only a single jump operator with an efficient implementation available for the evolution $e^{t \mathcal{L}_a}$. A notable application of the randomized method is for quantum Gibbs sampling, where the Lindblad dynamics is utilized to prepare a specific Gibbs state. Unlike existing deterministic methods that require numerous jump operators to ensure ergodicity, our approach simplifies the implementation by using a single randomly sampled jump operator. As an example, we demonstrate that our method ensures fast thermalization of Hamiltonian systems characterized by random Pauli strings, where the spectral density closely adheres to the semi-circle law., Comment: 23 pages

In this paper, we present our solution for the WSDM2023 Toloka Visual Question Answering Challenge. Inspired by the application of multimodal pre-trained models to various downstream tasks(e.g., visual question answering, visual grounding, and cross-modal retrieval), we approached this competition as a visual grounding task, where the input is an image and a question, guiding the model to answer the question and display the answer as a bounding box on the image. We designed a three-stage solution for this task. Specifically, we used the visual-language pre-trained model OFA as the foundation. In the first stage, we constructed a large-scale synthetic dataset similar to the competition dataset and coarse-tuned the model to learn generalized semantic information. In the second stage, we treated the competition task as a visual grounding task, loaded the weights from the previous stage, and continued to fine-tune the model on the competition dataset, transferring the semantic information learned in the first stage to the competition task. Finally, we designed a bounding box matching and replacing post-processing strategy to correct the model's prediction results. Our team achieved a score of 76.342 on the final leaderboard, ranking second., Comment: Second Place of WSDM2023 Toloka Visual Question Answering Challenge

In this paper, we propose a solution for improving the quality of temporal sound localization. We employ a multimodal fusion approach to combine visual and audio features. High-quality visual features are extracted using a state-of-the-art self-supervised pre-training network, resulting in efficient video feature representations. At the same time, audio features serve as complementary information to help the model better localize the start and end of sounds. The fused features are trained in a multi-scale Transformer for training. In the final test dataset, we achieved a mean average precision (mAP) of 0.33, obtaining the second-best performance in this track.

In this paper, we present our champion solution to the Global Artificial Intelligence Technology Innovation Competition Track 1: Medical Imaging Diagnosis Report Generation. We select CPT-BASE as our base model for the text generation task. During the pre-training stage, we delete the mask language modeling task of CPT-BASE and instead reconstruct the vocabulary, adopting a span mask strategy and gradually increasing the number of masking ratios to perform the denoising auto-encoder pre-training task. In the fine-tuning stage, we design iterative retrieval augmentation and noise-aware similarity bucket prompt strategies. The retrieval augmentation constructs a mini-knowledge base, enriching the input information of the model, while the similarity bucket further perceives the noise information within the mini-knowledge base, guiding the model to generate higher-quality diagnostic reports based on the similarity prompts. Surprisingly, our single model has achieved a score of 2.321 on leaderboard A, and the multiple model fusion scores are 2.362 and 2.320 on the A and B leaderboards respectively, securing first place in the rankings., Comment: First Place of 2023 Global Artificial Intelligence Technology Innovation Competition

Thompson sampling (TS) is one of the most popular exploration techniques in reinforcement learning (RL). However, most TS algorithms with theoretical guarantees are difficult to implement and not generalizable to Deep RL. While the emerging approximate sampling-based exploration schemes are promising, most existing algorithms are specific to linear Markov Decision Processes (MDP) with suboptimal regret bounds, or only use the most basic samplers such as Langevin Monte Carlo. In this work, we propose an algorithmic framework that incorporates different approximate sampling methods with the recently proposed Feel-Good Thompson Sampling (FGTS) approach (Zhang, 2022; Dann et al., 2021), which was previously known to be computationally intractable in general. When applied to linear MDPs, our regret analysis yields the best known dependency of regret on dimensionality, surpassing existing randomized algorithms. Additionally, we provide explicit sampling complexity for each employed sampler. Empirically, we show that in tasks where deep exploration is necessary, our proposed algorithms that combine FGTS and approximate sampling perform significantly better compared to other strong baselines. On several challenging games from the Atari 57 suite, our algorithms achieve performance that is either better than or on par with other strong baselines from the deep RL literature., Comment: First two authors contributed equally. Accepted to the Reinforcement Learning Conference (RLC) 2024

We investigate the mixing properties of primitive hypocoercive Lindblad dynamics. By extending the variational framework originally developed for underdamped Langevin dynamics, we derive fully explicit and constructive exponential decay estimates for the convergence in the noncommutative $L^2$-norm. Our analysis relies on establishing a quantum analog of space-time Poincar\'{e} inequalities. To complement these hypocoercive estimates, we also analyze the limiting behavior of the spectral gap for Lindblad dynamics with a large coherent contribution, providing sharper convergence rate estimates in this asymptotic regime. A number of concrete examples are provided as applications of our theoretical results.

The recently unprecedented advancements in Large Language Models (LLMs) have propelled the medical community by establishing advanced medical-domain models. However, due to the limited collection of medical datasets, there are only a few comprehensive benchmarks available to gauge progress in this area. In this paper, we introduce a new medical question-answering (QA) dataset that contains massive manual instruction for solving Traditional Chinese Medicine examination tasks, called TCMD. Specifically, our TCMD collects massive questions across diverse domains with their annotated medical subjects and thus supports us in comprehensively assessing the capability of LLMs in the TCM domain. Extensive evaluation of various general LLMs and medical-domain-specific LLMs is conducted. Moreover, we also analyze the robustness of current LLMs in solving TCM QA tasks by introducing randomness. The inconsistency of the experimental results also reveals the shortcomings of current LLMs in solving QA tasks. We also expect that our dataset can further facilitate the development of LLMs in the TCM area.

The recent introduction of prompt tuning based on pre-trained vision-language models has dramatically improved the performance of multi-label image classification. However, some existing strategies that have been explored still have drawbacks, i.e., either exploiting massive labeled visual data at a high cost or using text data only for text prompt tuning and thus failing to learn the diversity of visual knowledge. Hence, the application scenarios of these methods are limited. In this paper, we propose a pseudo-visual prompt~(PVP) module for implicit visual prompt tuning to address this problem. Specifically, we first learn the pseudo-visual prompt for each category, mining diverse visual knowledge by the well-aligned space of pre-trained vision-language models. Then, a co-learning strategy with a dual-adapter module is designed to transfer visual knowledge from pseudo-visual prompt to text prompt, enhancing their visual representation abilities. Experimental results on VOC2007, MS-COCO, and NUSWIDE datasets demonstrate that our method can surpass state-of-the-art~(SOTA) methods across various settings for multi-label image classification tasks. The code is available at https://github.com/njustkmg/PVP., Comment: Accepted for publication at IJCAI 2024; 13 pages; 11 figures

Denoising is a crucial preprocessing step for hyperspectral images (HSIs) due to noise arising from intra-imaging mechanisms and environmental factors. Long-range spatial-spectral correlation modeling is beneficial for HSI denoising but often comes with high computational complexity. Based on the state space model (SSM), Mamba is known for its remarkable long-range dependency modeling capabilities and computational efficiency. Building on this, we introduce a memory-efficient spatial-spectral UMamba (SSUMamba) for HSI denoising, with the spatial-spectral continuous scan (SSCS) Mamba being the core component. SSCS Mamba alternates the row, column, and band in six different orders to generate the sequence and uses the bidirectional SSM to exploit long-range spatial-spectral dependencies. In each order, the images are rearranged between adjacent scans to ensure spatial-spectral continuity. Additionally, 3D convolutions are embedded into the SSCS Mamba to enhance local spatial-spectral modeling. Experiments demonstrate that SSUMamba achieves superior denoising results with lower memory consumption per batch compared to transformer-based methods. The source code is available at https://github.com/lronkitty/SSUMamba.

Although Hierarchical Federated Learning (HFL) utilizes edge servers (ESs) to alleviate communication burdens, its model performance will be degraded by non-IID data and limited communication resources. Current works often assume that data is uniformly distributed, which however contradicts the heterogeneity of IoT. Solutions of additional model training to check the data distribution inevitably increases computational costs and the risk of privacy leakage. The challenges in solving these issues are how to reduce the impact of non-IID data without involving raw data and how to rationalize the communication resource allocation for addressing straggler problem. To tackle these challenges, we propose a novel optimization method based on coaLition formation gamE and grAdient Projection, called LEAP. Specifically, we combine edge data distribution with coalition formation game innovatively to adjust the correlations between clients and ESs dynamically, which ensures optimal correlations. We further capture the client heterogeneity to achieve the rational bandwidth allocation from coalition perception and determine the optimal transmission power within specified delay constraints at client level. Experimental results on four real datasets show that LEAP is able to achieve 20.62% improvement in model accuracy compared to the state-of-the-art baselines. Moreover, LEAP effectively reduce transmission energy consumption by at least about 2.24 times.

Understanding the mixing of open quantum systems is a fundamental problem in physics and quantum information science. Existing approaches for estimating the mixing time often rely on the spectral gap estimation of the Lindbladian generator, which can be challenging to obtain in practice. We propose a novel theoretical framework to estimate the mixing time of open quantum systems that treats the Hamiltonian and dissipative part separately, thus circumventing the need for a priori estimation of the spectral gap of the full Lindbladian generator. The technique is based on the construction of an energy functional inspired by the hypocoercivity of (classical) kinetic theory.

We revisit the unified two-timescale Q-learning algorithm as initially introduced by Angiuli et al. \cite{angiuli2022unified}. This algorithm demonstrates efficacy in solving mean field game (MFG) and mean field control (MFC) problems, simply by tuning the ratio of two learning rates for mean field distribution and the Q-functions respectively. In this paper, we provide a comprehensive theoretical explanation of the algorithm's bifurcated numerical outcomes under fixed learning rates. We achieve this by establishing a diagram that correlates continuous-time mean field problems to their discrete-time Q-function counterparts, forming the basis of the algorithm. Our key contribution lies in the construction of a Lyapunov function integrating both mean field distribution and Q-function iterates. This Lyapunov function facilitates a unified convergence of the algorithm across the entire spectrum of learning rates, thus providing a cohesive framework for analysis., Comment: 34 pages. Updated version for submission. We added more numerical results and fixed several minor mistakes

Deep learning-based face restoration models, increasingly prevalent in smart devices, have become targets for sophisticated backdoor attacks. These attacks, through subtle trigger injection into input face images, can lead to unexpected restoration outcomes. Unlike conventional methods focused on classification tasks, our approach introduces a unique degradation objective tailored for attacking restoration models. Moreover, we propose the Adaptive Selective Frequency Injection Backdoor Attack (AS-FIBA) framework, employing a neural network for input-specific trigger generation in the frequency domain, seamlessly blending triggers with benign images. This results in imperceptible yet effective attacks, guiding restoration predictions towards subtly degraded outputs rather than conspicuous targets. Extensive experiments demonstrate the efficacy of the degradation objective on state-of-the-art face restoration models. Additionally, it is notable that AS-FIBA can insert effective backdoors that are more imperceptible than existing backdoor attack methods, including WaNet, ISSBA, and FIBA.

This paper studies the numerical approximation of the ground state of the Gross-Pitaevskii (GP) eigenvalue problem with a fully discretized Sobolev gradient flow induced by the $H^1$ norm. For the spatial discretization, we consider the finite element method with quadrature using $P^k$ basis on a simplicial mesh and $Q^k$ basis on a rectangular mesh. We prove the global convergence to a critical point of the discrete GP energy, and establish a local exponential convergence to the ground state under the assumption that the linearized discrete Schr\"odinger operator has a positive spectral gap. We also show that for the $P^1$ finite element discretization with quadrature on an unstructured shape regular simplicial mesh, the eigengap satisfies a mesh-independent lower bound, which implies a mesh-independent local convergence rate for the proposed discrete gradient flow. Numerical experiments with discretization by high order $Q^k$ spectral element methods in two and three dimensions are provided to validate the efficiency of the proposed method.

We propose an actor-critic framework to solve the time-continuous stochastic optimal control problem. A least square temporal difference method is applied to compute the value function for the critic. The policy gradient method is implemented as policy improvement for the actor. Our key contribution lies in establishing the global convergence property of our proposed actor-critic flow, demonstrating a linear rate of convergence. Theoretical findings are further validated through numerical examples, showing the efficacy of our approach in practical applications., Comment: arXiv admin note: text overlap with arXiv:2302.05816

This study delves into the enhancement of Under-Display Camera (UDC) image restoration models, focusing on their robustness against adversarial attacks. Despite its innovative approach to seamless display integration, UDC technology faces unique image degradation challenges exacerbated by the susceptibility to adversarial perturbations. Our research initially conducts an in-depth robustness evaluation of deep-learning-based UDC image restoration models by employing several white-box and black-box attacking methods. This evaluation is pivotal in understanding the vulnerabilities of current UDC image restoration techniques. Following the assessment, we introduce a defense framework integrating adversarial purification with subsequent fine-tuning processes. First, our approach employs diffusion-based adversarial purification, effectively neutralizing adversarial perturbations. Then, we apply the fine-tuning methodologies to refine the image restoration models further, ensuring that the quality and fidelity of the restored images are maintained. The effectiveness of our proposed approach is validated through extensive experiments, showing marked improvements in resilience against typical adversarial attacks.

We introduce a novel approach for learning memory kernels in Generalized Langevin Equations. This approach initially utilizes a regularized Prony method to estimate correlation functions from trajectory data, followed by regression over a Sobolev norm-based loss function with RKHS regularization. Our method guarantees improved performance within an exponentially weighted L^2 space, with the kernel estimation error controlled by the error in estimated correlation functions. We demonstrate the superiority of our estimator compared to other regression estimators that rely on L^2 loss functions and also an estimator derived from the inverse Laplace transform, using numerical examples that highlight its consistent advantage across various weight parameter selections. Additionally, we provide examples that include the application of force and drift terms in the equation.

Hyperspectral images (HSIs) often suffer from noise arising from both intra-imaging mechanisms and environmental factors. Leveraging domain knowledge specific to HSIs, such as global spectral correlation (GSC) and non-local spatial self-similarity (NSS), is crucial for effective denoising. Existing methods tend to independently utilize each of these knowledge components with multiple blocks, overlooking the inherent 3D nature of HSIs where domain knowledge is strongly interlinked, resulting in suboptimal performance. To address this challenge, this paper introduces a spatial-spectral recurrent transformer U-Net (SSRT-UNet) for HSI denoising. The proposed SSRT-UNet integrates NSS and GSC properties within a single SSRT block. This block consists of a spatial branch and a spectral branch. The spectral branch employs a combination of transformer and recurrent neural network to perform recurrent computations across bands, allowing for GSC exploitation beyond a fixed number of bands. Concurrently, the spatial branch encodes NSS for each band by sharing keys and values with the spectral branch under the guidance of GSC. This interaction between the two branches enables the joint utilization of NSS and GSC, avoiding their independent treatment. Experimental results demonstrate that our method outperforms several alternative approaches. The source code will be available at https://github.com/lronkitty/SSRT.

Data-driven machine learning approaches are being increasingly used to solve partial differential equations (PDEs). They have shown particularly striking successes when training an operator, which takes as input a PDE in some family, and outputs its solution. However, the architectural design space, especially given structural knowledge of the PDE family of interest, is still poorly understood. We seek to remedy this gap by studying the benefits of weight-tied neural network architectures for steady-state PDEs. To achieve this, we first demonstrate that the solution of most steady-state PDEs can be expressed as a fixed point of a non-linear operator. Motivated by this observation, we propose FNO-DEQ, a deep equilibrium variant of the FNO architecture that directly solves for the solution of a steady-state PDE as the infinite-depth fixed point of an implicit operator layer using a black-box root solver and differentiates analytically through this fixed point resulting in $\mathcal{O}(1)$ training memory. Our experiments indicate that FNO-DEQ-based architectures outperform FNO-based baselines with $4\times$ the number of parameters in predicting the solution to steady-state PDEs such as Darcy Flow and steady-state incompressible Navier-Stokes. Finally, we show FNO-DEQ is more robust when trained with datasets with more noisy observations than the FNO-based baselines, demonstrating the benefits of using appropriate inductive biases in architectural design for different neural network based PDE solvers. Further, we show a universal approximation result that demonstrates that FNO-DEQ can approximate the solution to any steady-state PDE that can be written as a fixed point equation., Comment: NeurIPS 2023

This paper concerns the long-standing question of representing (totally) anti-symmetric functions in high dimensions. We propose a new ansatz based on the composition of an odd function with a fixed set of anti-symmetric basis functions. We prove that this ansatz can exactly represent every anti-symmetric and continuous function and the number of basis functions has efficient scaling with respect to dimension (number of particles).

In this paper, we study the semiclassical behavior of Bloch electrons in the presence of Weyl nodes, which are singular points in the band structure of certain materials. We carry out asymptotic analysis and present a rigorous derivation of the semiclassical asymptotic expansion of the current of Bloch electrons with the presence of Weyl nodes. The analysis shows that the current contains two parts, one independent of the Weyl nodes and the other a contribution from the singular points. This work provides a theoretical foundation towards a rigorous justification of recent scientific discoveries in Weyl semimetals. The main innovation of this paper is a new strategy to deal with the singular points with quantitative estimates, which may have broader applications in multiscale models with singularities.

Flow-based generative models enjoy certain advantages in computing the data generation and the likelihood, and have recently shown competitive empirical performance. Compared to the accumulating theoretical studies on related score-based diffusion models, analysis of flow-based models, which are deterministic in both forward (data-to-noise) and reverse (noise-to-data) directions, remain sparse. In this paper, we provide a theoretical guarantee of generating data distribution by a progressive flow model, the so-called JKO flow model, which implements the Jordan-Kinderleherer-Otto (JKO) scheme in a normalizing flow network. Leveraging the exponential convergence of the proximal gradient descent (GD) in Wasserstein space, we prove the Kullback-Leibler (KL) guarantee of data generation by a JKO flow model to be $O(\varepsilon^2)$ when using $N \lesssim \log (1/\varepsilon)$ many JKO steps ($N$ Residual Blocks in the flow) where $\varepsilon $ is the error in the per-step first-order condition. The assumption on data density is merely a finite second moment, and the theory extends to data distributions without density and when there are inversion errors in the reverse process where we obtain KL-$W_2$ mixed error guarantees. The non-asymptotic convergence rate of the JKO-type $W_2$-proximal GD is proved for a general class of convex objective functionals that includes the KL divergence as a special case, which can be of independent interest. The analysis framework can extend to other first-order Wasserstein optimization schemes applied to flow-based generative models.

We propose a state-averaged orbital optimization scheme for improving the accuracy of excited states of the electronic structure Hamiltonian for use on near-term quantum computers. Instead of parameterizing the orbital rotation operator in the conventional fashion as an exponential of an anti-hermitian matrix, we parameterize the orbital rotation as a general partial unitary matrix. Whereas conventional orbital optimization methods minimize the state-averaged energy using successive Newton steps of the second-order Taylor expansion of the energy, the method presented here optimizes the state-averaged energy using an orthogonally-constrained gradient projection method which does not require any expansion approximations. Through extensive benchmarking of the method on various small molecular systems, we find that the method is capable of producing more accurate results than fixed basis FCI while simultaneously using fewer qubits. In particular, we show that for $\mathrm{H_2}$, the method is capable of matching the accuracy of FCI in the cc-pVTZ basis (56 qubits) while only using 14 qubits.

In this paper, we present our solution to a Multi-modal Algorithmic Reasoning Task: SMART-101 Challenge. Different from the traditional visual question-answering datasets, this challenge evaluates the abstraction, deduction, and generalization abilities of neural networks in solving visuolinguistic puzzles designed specifically for children in the 6-8 age group. We employed a divide-and-conquer approach. At the data level, inspired by the challenge paper, we categorized the whole questions into eight types and utilized the llama-2-chat model to directly generate the type for each question in a zero-shot manner. Additionally, we trained a yolov7 model on the icon45 dataset for object detection and combined it with the OCR method to recognize and locate objects and text within the images. At the model level, we utilized the BLIP-2 model and added eight adapters to the image encoder VIT-G to adaptively extract visual features for different question types. We fed the pre-constructed question templates as input and generated answers using the flan-t5-xxl decoder. Under the puzzle splits configuration, we achieved an accuracy score of 26.5 on the validation set and 24.30 on the private test set.

In this paper, we present our solution to the New frontiers for Zero-shot Image Captioning Challenge. Different from the traditional image captioning datasets, this challenge includes a larger new variety of visual concepts from many domains (such as COVID-19) as well as various image types (photographs, illustrations, graphics). For the data level, we collect external training data from Laion-5B, a large-scale CLIP-filtered image-text dataset. For the model level, we use OFA, a large-scale visual-language pre-training model based on handcrafted templates, to perform the image captioning task. In addition, we introduce contrastive learning to align image-text pairs to learn new visual concepts in the pre-training stage. Then, we propose a similarity-bucket strategy and incorporate this strategy into the template to force the model to generate higher quality and more matching captions. Finally, by retrieval-augmented strategy, we construct a content-rich template, containing the most relevant top-k captions from other image-text pairs, to guide the model in generating semantic-rich captions. Our method ranks first on the leaderboard, achieving 105.17 and 325.72 Cider-Score in the validation and test phase, respectively.

This paper addresses the problem of estimating the 3-DoF camera pose for a ground-level image with respect to a satellite image that encompasses the local surroundings. We propose a novel end-to-end approach that leverages the learning of dense pixel-wise flow fields in pairs of ground and satellite images to calculate the camera pose. Our approach differs from existing methods by constructing the feature metric at the pixel level, enabling full-image supervision for learning distinctive geometric configurations and visual appearances across views. Specifically, our method employs two distinct convolution networks for ground and satellite feature extraction. Then, we project the ground feature map to the bird's eye view (BEV) using a fixed camera height assumption to achieve preliminary geometric alignment. To further establish content association between the BEV and satellite features, we introduce a residual convolution block to refine the projected BEV feature. Optical flow estimation is performed on the refined BEV feature map and the satellite feature map using flow decoder networks based on RAFT. After obtaining dense flow correspondences, we apply the least square method to filter matching inliers and regress the ground camera pose. Extensive experiments demonstrate significant improvements compared to state-of-the-art methods. Notably, our approach reduces the median localization error by 89%, 19%, 80% and 35% on the KITTI, Ford multi-AV, VIGOR and Oxford RobotCar datasets, respectively.

In this work, we seek to simulate rare transitions between metastable states using score-based generative models. An efficient method for generating high-quality transition paths is valuable for the study of molecular systems since data is often difficult to obtain. We develop two novel methods for path generation in this paper: a chain-based approach and a midpoint-based approach. The first biases the original dynamics to facilitate transitions, while the second mirrors splitting techniques and breaks down the original transition into smaller transitions. Numerical results of generated transition paths for the M\"uller potential and for Alanine dipeptide demonstrate the effectiveness of these approaches in both the data-rich and data-scarce regimes., Comment: 14 pages, 8 figures

We review thermodynamic limits and scaling limits of electronic structure models for condensed matter. We discuss several mathematical ways to implement these limits in three models of increasing chemical complexity and mathematical difficulty: (1) Thomas-Fermi like models; (2) Hartree-Fock like models; and (3) Kohn-Sham density functional theory models.

This paper introduces two explicit schemes to sample matrices from Gibbs distributions on $\mathcal S^{n,p}_+$, the manifold of real positive semi-definite (PSD) matrices of size $n\times n$ and rank $p$. Given an energy function $\mathcal E:\mathcal S^{n,p}_+\to \mathbb{R}$ and certain Riemannian metrics $g$ on $\mathcal S^{n,p}_+$, these schemes rely on an Euler-Maruyama discretization of the Riemannian Langevin equation (RLE) with Brownian motion on the manifold. We present numerical schemes for RLE under two fundamental metrics on $\mathcal S^{n,p}_+$: (a) the metric obtained from the embedding of $\mathcal S^{n,p}_+ \subset \mathbb{R}^{n\times n} $; and (b) the Bures-Wasserstein metric corresponding to quotient geometry. We also provide examples of energy functions with explicit Gibbs distributions that allow numerical validation of these schemes.

In this report, we introduce NICE (New frontiers for zero-shot Image Captioning Evaluation) project and share the results and outcomes of 2023 challenge. This project is designed to challenge the computer vision community to develop robust image captioning models that advance the state-of-the-art both in terms of accuracy and fairness. Through the challenge, the image captioning models were tested using a new evaluation dataset that includes a large variety of visual concepts from many domains. There was no specific training data provided for the challenge, and therefore the challenge entries were required to adapt to new types of image descriptions that had not been seen during training. This report includes information on the newly proposed NICE dataset, evaluation methods, challenge results, and technical details of top-ranking entries. We expect that the outcomes of the challenge will contribute to the improvement of AI models on various vision-language tasks., Comment: Tech report, project page https://nice.lgresearch.ai/

Deep learning based methods have achieved significant success in the task of single image reflection removal (SIRR). However, the majority of these methods are focused on High-Definition/Standard-Definition (HD/SD) images, while ignoring higher resolution images such as Ultra-High-Definition (UHD) images. With the increasing prevalence of UHD images captured by modern devices, in this paper, we aim to address the problem of UHD SIRR. Specifically, we first synthesize two large-scale UHD datasets, UHDRR4K and UHDRR8K. The UHDRR4K dataset consists of $2,999$ and $168$ quadruplets of images for training and testing respectively, and the UHDRR8K dataset contains $1,014$ and $105$ quadruplets. To the best of our knowledge, these two datasets are the first largest-scale UHD datasets for SIRR. Then, we conduct a comprehensive evaluation of six state-of-the-art SIRR methods using the proposed datasets. Based on the results, we provide detailed discussions regarding the strengths and limitations of these methods when applied to UHD images. Finally, we present a transformer-based architecture named RRFormer for reflection removal. RRFormer comprises three modules, namely the Prepossessing Embedding Module, Self-attention Feature Extraction Module, and Multi-scale Spatial Feature Extraction Module. These modules extract hypercolumn features, global and partial attention features, and multi-scale spatial features, respectively. To ensure effective training, we utilize three terms in our loss function: pixel loss, feature loss, and adversarial loss. We demonstrate through experimental results that RRFormer achieves state-of-the-art performance on both the non-UHD dataset and our proposed UHDRR datasets. The code and datasets are publicly available at https://github.com/Liar-zzy/Benchmarking-Ultra-High-Definition-Single-Image-Reflection-Removal.

Two-dimensional (2D) transition metal dichalcogenides (TMDs) hold great potential for future low-energy optoelectronics owing to their unique electronic, optical, and mechanical properties. Chemical vapor deposition (CVD) is the technique widely used for the synthesis of large-area TMDs. However, due to high sensitivity to the growth environment, reliable synthesis of monolayer TMDs via CVD remains challenging. Here we develop a controllable CVD process for large-area synthesis of monolayer WS2 crystals, films, and in-plane graphene-WS2 heterostructures by cleaning the reaction tube with hydrochloric acid, sulfuric acid and aqua regia. The concise cleaning process can remove the residual contaminates attached to the CVD reaction tube and crucibles, reducing the nucleation density but enhancing the diffusion length of WS2 species. The photoluminescence (PL) mappings of a WS2 single crystal and film reveal that the extraordinary PL around the edges of a triangular single crystal is induced by ambient water intercalation at the WS2-sapphire interface. The extraordinary PL can be controlled by the choice of substrates with different wettabilities.

This paper explores the expressive power of deep neural networks for a diverse range of activation functions. An activation function set $\mathscr{A}$ is defined to encompass the majority of commonly used activation functions, such as $\mathtt{ReLU}$, $\mathtt{LeakyReLU}$, $\mathtt{ReLU}^2$, $\mathtt{ELU}$, $\mathtt{CELU}$, $\mathtt{SELU}$, $\mathtt{Softplus}$, $\mathtt{GELU}$, $\mathtt{SiLU}$, $\mathtt{Swish}$, $\mathtt{Mish}$, $\mathtt{Sigmoid}$, $\mathtt{Tanh}$, $\mathtt{Arctan}$, $\mathtt{Softsign}$, $\mathtt{dSiLU}$, and $\mathtt{SRS}$. We demonstrate that for any activation function $\varrho\in \mathscr{A}$, a $\mathtt{ReLU}$ network of width $N$ and depth $L$ can be approximated to arbitrary precision by a $\varrho$-activated network of width $3N$ and depth $2L$ on any bounded set. This finding enables the extension of most approximation results achieved with $\mathtt{ReLU}$ networks to a wide variety of other activation functions, albeit with slightly increased constants. Significantly, we establish that the (width,$\,$depth) scaling factors can be further reduced from $(3,2)$ to $(1,1)$ if $\varrho$ falls within a specific subset of $\mathscr{A}$. This subset includes activation functions such as $\mathtt{ELU}$, $\mathtt{CELU}$, $\mathtt{SELU}$, $\mathtt{Softplus}$, $\mathtt{GELU}$, $\mathtt{SiLU}$, $\mathtt{Swish}$, and $\mathtt{Mish}$.

We introduce a sum-of-squares SDP hierarchy approximating the ground-state energy from below for quantum many-body problems, with a natural quantum embedding interpretation. We establish the connections between our approach and other variational methods for lower bounds, including the variational embedding, the RDM method in quantum chemistry, and the Anderson bounds. Additionally, inspired by the quantum information theory, we propose efficient strategies for optimizing cluster selection to tighten SDP relaxations while staying within a computational budget. Numerical experiments are presented to demonstrate the effectiveness of our strategy. As a byproduct of our investigation, we find that quantum entanglement has the potential to capture the underlying graph of the many-body Hamiltonian.

The emergence of text-driven motion synthesis technique provides animators with great potential to create efficiently. However, in most cases, textual expressions only contain general and qualitative motion descriptions, while lack fine depiction and sufficient intensity, leading to the synthesized motions that either (a) semantically compliant but uncontrollable over specific pose details, or (b) even deviates from the provided descriptions, bringing animators with undesired cases. In this paper, we propose DiffKFC, a conditional diffusion model for text-driven motion synthesis with KeyFrames Collaborated, enabling realistic generation with collaborative and efficient dual-level control: coarse guidance at semantic level, with only few keyframes for direct and fine-grained depiction down to body posture level. Unlike existing inference-editing diffusion models that incorporate conditions without training, our conditional diffusion model is explicitly trained and can fully exploit correlations among texts, keyframes and the diffused target frames. To preserve the control capability of discrete and sparse keyframes, we customize dilated mask attention modules where only partial valid tokens participate in local-to-global attention, indicated by the dilated keyframe mask. Additionally, we develop a simple yet effective smoothness prior, which steers the generated frames towards seamless keyframe transitions at inference. Extensive experiments show that our model not only achieves state-of-the-art performance in terms of semantic fidelity, but more importantly, is able to satisfy animator requirements through fine-grained guidance without tedious labor., Comment: AAAI2024

We provide the first polynomial-time convergence guarantees for the probability flow ODE implementation (together with a corrector step) of score-based generative modeling. Our analysis is carried out in the wake of recent results obtaining such guarantees for the SDE-based implementation (i.e., denoising diffusion probabilistic modeling or DDPM), but requires the development of novel techniques for studying deterministic dynamics without contractivity. Through the use of a specially chosen corrector step based on the underdamped Langevin diffusion, we obtain better dimension dependence than prior works on DDPM ($O(\sqrt{d})$ vs. $O(d)$, assuming smoothness of the data distribution), highlighting potential advantages of the ODE framework., Comment: 23 pages, 2 figures

Sampling a probability distribution with known likelihood is a fundamental task in computational science and engineering. Aiming at multimodality, we propose a new sampling method that takes advantage of both birth-death process and exploration component. The main idea of this method is \textit{look before you leap}. We keep two sets of samplers, one at warmer temperature and one at original temperature. The former one serves as pioneer in exploring new modes and passing useful information to the other, while the latter one samples the target distribution after receiving the information. We derive a mean-field limit and show how the exploration process determines sampling efficiency. Moreover, we prove exponential asymptotic convergence under mild assumption. Finally, we test on experiments from previous literature and compared our methodology to previous ones., Comment: 23 pages, 10 figures

An efficient excited state method, named xCDFCI, in the configuration interaction framework, is proposed. xCDFCI extends the unconstrained nonconvex optimization problem in coordinate descent full configuration interaction~(CDFCI) to a multicolumn version, for low-lying excited states computation. The optimization problem is addressed via a tailored coordinate descent method. In each iteration, a determinant is selected based on an approximated gradient, and coefficients of all states associated with the selected determinant are updated. A deterministic compression is applied to limit memory usage. We test xCDFCI applied to H2O and N2 molecules under the cc-pVDZ basis set. For both systems, five low-lying excited states in the same symmetry sector are calculated together with the ground state. xCDFCI also produces accurate binding curves of carbon dimer in the cc-pVDZ basis with chemical accuracy, where the ground state and four excited states in the same symmetry sector are benchmarked.

We use the score-based transport modeling method to solve the mean-field Fokker-Planck equations, which we call MSBTM. We establish an upper bound on the time derivative of the Kullback-Leibler (KL) divergence to MSBTM numerical estimation from the exact solution, thus validates the MSBTM approach. Besides, we provide an error analysis for the algorithm. In numerical experiments, we study two types of mean-field Fokker-Planck equation and their corresponding dynamics of particles in interacting systems. The MSBTM algorithm is numerically validated through qualitative and quantitative comparison between the MSBTM solutions, the results of integrating the associated stochastic differential equation and the analytical solutions if available.

We study the convergence of stochastic gradient descent (SGD) for non-convex objective functions. We establish the local convergence with positive probability under the local \L{}ojasiewicz condition introduced by Chatterjee in \cite{chatterjee2022convergence} and an additional local structural assumption of the loss function landscape. A key component of our proof is to ensure that the whole trajectories of SGD stay inside the local region with a positive probability. We also provide examples of neural networks with finite widths such that our assumptions hold., Comment: v2 fixed several mistakes. Some parts have been rewritten

Predicting high-fidelity future human poses, from a historically observed sequence, is decisive for intelligent robots to interact with humans. Deep end-to-end learning approaches, which typically train a generic pre-trained model on external datasets and then directly apply it to all test samples, emerge as the dominant solution to solve this issue. Despite encouraging progress, they remain non-optimal, as the unique properties (e.g., motion style, rhythm) of a specific sequence cannot be adapted. More generally, at test-time, once encountering unseen motion categories (out-of-distribution), the predicted poses tend to be unreliable. Motivated by this observation, we propose a novel test-time adaptation framework that leverages two self-supervised auxiliary tasks to help the primary forecasting network adapt to the test sequence. In the testing phase, our model can adjust the model parameters by several gradient updates to improve the generation quality. However, due to catastrophic forgetting, both auxiliary tasks typically tend to the low ability to automatically present the desired positive incentives for the final prediction performance. For this reason, we also propose a meta-auxiliary learning scheme for better adaptation. In terms of general setup, our approach obtains higher accuracy, and under two new experimental designs for out-of-distribution data (unseen subjects and categories), achieves significant improvements., Comment: 10 pages, 6 figures, AAAI 2023 accepted