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1,217篇论文匹配“Discrete Optimization”
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Computer Vision · 3D Rendering & Reconstruction

Diego de Oliveira Hitzges, Suman Ghosh, Guillermo Gallego

Event cameras offer a promising avenue for multi-view stereo depth estimation and Simultaneous Localization And Mapping (SLAM) due to their ability to detect blur-free 3D edges at high-speed and over broad illumination conditions. However, traditional deep learning frameworks designed for conventional cameras struggle with the asynchronous, stream-like nature of event data, as their architectures are optimized for discrete, image-like inputs. We propose a scalable, flexible and adaptable framework for pixel-wise depth estimation with event cameras in both monocular and stereo setups. The 3D scene structure is encoded into disparity space images (DSIs), representing spatial densities of rays obtained by back-projecting events into space via known camera poses. Our neural network processes local subregions of the DSIs combining 3D convolutions and a recurrent structure to recognize valuable patterns for depth prediction. Local processing enables fast inference with full parallelization and ensures constant ultra-low model complexity and memory costs, regardless of camera resolution. Experiments on standard benchmarks (MVSEC and DSEC datasets) demonstrate unprecedented effectiveness: (i) using purely monocular data, our method achieves comparable results to existing stereo methods; (ii) when applied to stereo data, it strongly outperforms all state-of-the-art (SOTA) approaches, reducing the mean absolute error by at least 42\%; (iii) our method also allows for increases in depth completeness by more than 3-fold while still yielding a reduction in median absolute error of at least 30\%. Given its remarkable performance and effective processing of event-data, our framework holds strong potential to become a standard approach for using deep learning for event-based depth estimation and SLAM.

Eshaan Agarwal, Raghav Magazine, Joykirat Singh, Vivek Dani, Tanuja Ganu, Akshay Nambi

Large language models (LLMs) have transformed AI across diverse domains, with prompting being central to their success in guiding model outputs. However, manual prompt engineering is both labor-intensive and domain-specific, necessitating the need for automated solutions. We introduce PromptWizard, a novel, fully automated framework for discrete prompt optimization, utilizing a self-evolving, self-adapting mechanism. Through a feedback-driven critique and synthesis process, PromptWizard achieves an effective balance between exploration and exploitation, iteratively refining both prompt instructions and in-context examples to generate human-readable, task-specific prompts. This guided approach systematically improves prompt quality, resulting in superior performance across 45 tasks. PromptWizard excels even with limited training data, smaller LLMs, and various LLM architectures. Additionally, our cost analysis reveals a substantial reduction in API calls, token usage, and overall cost, demonstrating PromptWizard’s efficiency, scalability, and advantages over existing prompt optimization strategies.

Hongming Yang, Shi Lin, Jun Shao, Changting Lin, Donghai Zhu, Meng Han, Qinglei Kong

Lightweight Large Language Models (LwLLMs) are reduced-parameter, optimized models designed to run efficiently on consumer-grade hardware, offering significant advantages in resource efficiency, cost-effectiveness, and data privacy. However, these models often struggle with limited inference and reasoning capabilities, which restrict their performance on complex tasks and limit their practical applicability. Moreover, existing prompt optimization methods typically rely on extensive manual effort or the meta-cognitive abilities of state-of-the-art LLMs, making them less effective for LwLLMs.To address these challenges, we introduce DeBoP, a new Direct Behavior Optimization Paradigm, original from the Chain-of-Thought (CoT) prompting technique. Unlike CoT Prompting, DeBoP is an automatic optimization method, which focuses on the optimization directly on the behavior of LwLLMs. In particular, DeBoP transforms the optimization of complex prompts into the optimization of discrete, quantifiable execution sequences using a gradient-free Monte Carlo Tree Search. We evaluate DeBoP on seven challenging tasks where state-of-the-art LLMs excel but LwLLMs generally underperform. Experimental results demonstrate that DeBoP significantly outperforms recent prompt optimization methods on most tasks. In particular, DeBoP-optimized LwLLMs surpass GPT-3.5 on most tasks while reducing computational time by approximately 60% compared to other automatic prompt optimization methods.

Mingxu Chai, Ziyu Shen, Chong Zhang, Yue Zhang, Xiao Wang, Shihan Dou, Jihua Kang, Jiazheng Zhang, Qi Zhang

Document parsing involves layout element detection and recognition, essential for extracting information. However, existing methods often employ multiple models for these tasks, leading to increased system complexity and maintenance overhead. While some models attempt to unify detection and recognition, they often fail to address the intrinsic differences in data representations, thereby limiting performance in document processing. Our research reveals that recognition relies on discrete tokens, whereas detection relies on continuous coordinates, leading to challenges in gradient updates and optimization. To bridge this gap, we propose the Gaussian-Kernel Cross-Entropy Loss (GK-CEL), enabling generative frameworks to handle both tasks simultaneously. Building upon GK-CEL, we propose DocFusion, a unified document parsing model with only 0.28B parameters. Additionally, we construct the DocLatex-1.6M dataset to provide high-quality training support. Experimental results show that DocFusion, equipped with GK-CEL, performs competitively across four core document parsing tasks, validating the effectiveness of our unified approach.

Hai Huang, Yan Xia, Shengpeng Ji, Shulei Wang, Hanting Wang, Minghui Fang, Jieming Zhu, Zhenhua Dong, Sashuai Zhou, Zhou Zhao

To enhance the interpretability of multimodal unified representations, many studies have focused on discrete unified representations. These efforts typically start with contrastive learning and gradually extend to the disentanglement of modal information, achieving solid multimodal discrete unified representations. However, existing research often overlooks two critical issues: 1) The use of Euclidean distance for quantization in discrete representations often overlooks the important distinctions among different dimensions of features, resulting in redundant representations after quantization; 2) Different modalities have unique characteristics, and a uniform alignment approach does not fully exploit these traits. To address these issues, we propose Training-free Optimization of Codebook (TOC) and Fine and Coarse cross-modal Information Disentangling (FCID). These methods refine the unified discrete representations from pretraining and perform fine- and coarse-grained information disentanglement tailored to the specific characteristics of each modality, achieving significant performance improvements over previous state-of-the-art models. The code is available at https://github.com/haihuangcode/CMG.

Mingyu Derek Ma, Yanna Ding, Zijie Huang, Jianxi Gao, Yizhou Sun, Wei Wang

Generative Language Models rely on autoregressive decoding to produce the output sequence token by token. Many tasks such as preference optimization, require the model to produce task-level output consisting of multiple tokens directly by selecting candidates from a pool as predictions. Determining a task-level prediction from candidates using the ordinary token-level decoding mechanism is constrained by time-consuming decoding and interrupted gradients by discrete token selection. Existing works have been using decoding-free candidate selection methods to obtain candidate probability from initial output logits over vocabulary. Though these estimation methods are widely used, they are not systematically evaluated, especially on end tasks. We introduce an evaluation of a comprehensive collection of decoding-free candidate selection approaches on a comprehensive set of tasks, including five multiple-choice QA tasks with a small candidate pool and four clinical decision tasks with a massive amount of candidates, some with 10k+ options. We evaluate the estimation methods paired with a wide spectrum of foundation LMs covering different architectures, sizes and training paradigms. The results and insights from our analysis inform the future model design.

Wendi Cui, Jiaxin Zhang, Zhuohang Li, Hao Sun, Damien Lopez, Kamalika Das, Bradley A. Malin, Sricharan Kumar

Designing optimal prompts for Large Language Models (LLMs) is a complex and resource-intensive task, often requiring substantial human expertise. Existing approaches typically separate the optimization of prompt instructions and in-context learning examples, leading to incohesive, suboptimal results. To overcome this limitation, we propose a novel Cohesive In-Context Prompt Optimization framework that refines both prompt instructions and examples. In our formulation, coherence refers to the degree to which instructions and examples work synergistically to improve task performance—emerging as a byproduct of performance-driven optimization. However, formulating such an optimization in the discrete and high-dimensional space of natural language poses significant challenges in both convergence and computational efficiency. To address these issues, we introduce SEE, a scalable and efficient prompt optimization framework that adopts metaheuristic optimization principles and strategically balances exploration and exploitation to enhance optimization performance and achieve efficient convergence. SEE features a quad-phased design that alternates between global traversal (exploration) and local optimization (exploitation) and adaptively chooses LLM operators during the optimization process. We have conducted a comprehensive evaluation across 35 benchmark tasks, and SEE significantly outperforms state-of-the-art baseline methods by a large margin, achieving an average performance gain of **13.94** while reducing computational costs by **58.67%**.

Wenxuan Zhou, Shujian Zhang, Lingxiao Zhao, Tao Meng

Reinforcement Learning from Human Feedback (RLHF) has been pivotal in enabling Large Language Models (LLMs) to effectively follow instructions and produce meaningful alignment by leveraging human preference data. Traditionally, RLHF involves generating responses to a query and using a separate reward model to assign a score to the entire completion. This approach, however, presents challenges, as it provides a single, sparse reward at the end of a sequence, making optimization difficult for the model, in which both training and generation occur auto-regressively at token levels. While recent methods have attempted to address this by assigning token-level discrete or continuous rewards, these often rely on either a trained credit assignment model or AI annotators, which raises concerns about the quality and reliability of the token-level rewards. In this paper, we propose T-REG, which utilizes both sequence-level and token-level rewards for preference optimization. T-REG employs self-generated token-level rewards, derived through opposite prompting, as a weak supervision signal to guide the model in distributing sequence-level rewards at the token level, thereby achieving more effective token-level credit assignment and improving alignment performance. Experiments on the instruction following benchmarks, including Alpaca Eval 2 and Arena-Hard, show that our method consistently outperforms baseline methods by up to 3.8% and 4.4%, respectively.

Yige Xu, Xu Guo, Zhiwei Zeng, Chunyan Miao

Chain-of-Thought (CoT) reasoning enables Large Language Models (LLMs) to solve complex reasoning tasks by generating intermediate reasoning steps. However, most existing approaches focus on hard token decoding, which constrains reasoning within the discrete vocabulary space and may not always be optimal. While recent efforts explore continuous-space reasoning, they often require full-model fine-tuning and suffer from catastrophic forgetting, limiting their applicability to state-of-the-art LLMs that already perform well in zero-shot settings with a proper instruction. To address this challenge, we propose a novel approach for continuous-space reasoning that does not require modifying the LLM. Specifically, we employ a lightweight fixed assistant model to speculatively generate instance-specific soft thought tokens as the initial chain of thoughts, which are then mapped into the LLM’s representation space via a trainable projection module. Experimental results on five reasoning benchmarks demonstrate that our method enhances LLM reasoning performance through supervised, parameter-efficient fine-tuning. Source code is available at https://github.com/xuyige/SoftCoT.

Yurui Chang, Bochuan Cao, Yujia Wang, Jinghui Chen, Lu Lin

Large Language Models (LLMs) have demonstrated impressive performances in complex text generation tasks. However, the contribution of the input prompt to the generated content still remains obscure to humans, underscoring the necessity of understanding the causality between input and output pairs. Existing works for providing prompt-specific explanation often confine model output to be classification or next-word prediction. Few initial attempts aiming to explain the entire language generation often treat input prompt texts independently, ignoring their combinatorial effects on the follow-up generation. In this study, we introduce a counterfactual explanation framework based on joint prompt attribution, JoPA, which aims to explain how a few prompt texts collaboratively influences the LLM’s complete generation. Particularly, we formulate the task of prompt attribution for generation interpretation as a combinatorial optimization problem, and introduce a probabilistic algorithm to search for the casual input combination in the discrete space. We define and utilize multiple metrics to evaluate the produced explanations, demonstrating both the faithfulness and efficiency of our framework.

Bocheng Li, Zhujin Gao, Linli Xu

Diffusion models have emerged as a promising approach for text generation, with recent works falling into two main categories: discrete and continuous diffusion models. Discrete diffusion models apply token corruption independently using categorical distributions, allowing for different diffusion progress across tokens but lacking fine-grained control. Continuous diffusion models map tokens to continuous spaces and apply fine-grained noise, but the diffusion progress is uniform across tokens, limiting their ability to capture semantic nuances. To address these limitations, we propose Non-simultaneous Continuous Diffusion Models (NeoDiff), a novel diffusion model that integrates the strengths of both discrete and continuous approaches. NeoDiff introduces a Poisson diffusion process for the forward process, enabling a flexible and fine-grained noising paradigm, and employs a time predictor for the reverse process to adaptively modulate the denoising progress based on token semantics. Furthermore, NeoDiff utilizes an optimized schedule for inference to ensure more precise noise control and improved performance. Our approach unifies the theories of discrete and continuous diffusion models, offering a more principled and effective framework for text generation. Experimental results on several text generation tasks demonstrate NeoDiff’s superior performance compared to baselines of non-autoregressive continuous and discrete diffusion models, iterative-based methods and autoregressive diffusion-based methods. These results highlight NeoDiff’s potential as a powerful tool for generating high-quality text and advancing the field of diffusion-based text generation.

Yangkun Wang, Zihan Wang, Jingbo Shang

Prompt optimization for language models faces challenges due to the large discrete search space, the reliance on continuous gradient updates, and the need to round continuous representations into discrete prompts, which causes inflexibility and instability. Existing methods attempt to address these by constraining the search space and adopting greedy, incremental improvements, but they often fail to fully leverage historical gradient information. In this paper, we model the prompt optimization problem by the probability distribution of the prompt and present a novel approach that integrates greedy strategies into optimization with continuous representations. This approach can exploit historical gradient information to address the instability caused by rounding in existing methods. Our study indicates that using continuous representations can improve prompt optimization performance on both text classification and attack tasks, as well as models, including GPT-2, OPT, Vicuna, and LLaMA-2, and also be adaptable to models of different sizes.

Deep Learning · Generative Models and Autoencoders

Peijia Qin, Jianguo Zhang

Deep neural networks incorporating discrete latent variables have shown significant potential in sequence modeling.A notable approach is to leverage vector quantization (VQ) to generate discrete representations within a codebook.However, its discrete nature prevents the use of standard backpropagation, which has led to challenges in efficient codebook training.In this work, we introduce **Meta-Quantization (MQ)**, a novel vector quantization training framework inspired by meta-learning.Our method separates the optimization of the codebook and the auto-encoder into two levels.Furthermore, we introduce a hyper-net to replace the embedding-parameterized codebook, enabling the codebook to be dynamically generated based on the feedback from the auto-encoder.Different from previous VQ objectives, our innovation results in a meta-objective that makes the codebook training task-aware.We validate the effectiveness of MQ with VQVAE and VQGAN architecture on image reconstruction and generation tasks.Experimental results showcase the superior generative performance of MQ, underscoring its potential as a robust alternative to existing VQ methods.

Applications · Time Series

Jinghang Yue, Jing Wang, Lu Zhang, Shuo Zhang, Da Li, Zhaoyang Ma, Youfang Lin

Explaining deep models for time-series data is crucial for identifying key patterns in sensitive domains, such as healthcare and finance. However, due to the lack of unified optimization criterion, existing explanation methods often suffer from redundancy and incompleteness, where irrelevant patterns are included or key patterns are missed in explanations. To address this challenge, we propose the Optimal Information Retention Principle, where conditional mutual information defines minimizing redundancy and maximizing completeness as optimization objectives. We then derive the corresponding objective function theoretically. As a practical framework, we introduce an explanation framework ORTE, learning a binary mask to eliminate redundant information while mining temporal patterns of explanations. We decouple the discrete mapping process to ensure the stability of gradient propagation, while employing contrastive learning to achieve precise filtering of explanatory patterns through the mask, thereby realizing a trade-off between low redundancy and high completeness. Extensive quantitative and qualitative experiments on synthetic and real-world datasets demonstrate that the proposed principle significantly improves the accuracy and completeness of explanations compared to baseline methods. The code is available at https://github.com/moon2yue/ORTE_public.

Optimization

Davide Adamo, Marco Corneli, Manon Vuillien, Emmanuelle Vila

Due to its invariance to rigid transformations such as rotations and reflections, Procrustes-Wasserstein (PW) was introduced in the literature as an optimal transport (OT) distance, alternative to Wasserstein and more suited to tasks such as the alignment and comparison of point clouds. Having that application in mind, we carefully build a space of discrete probability measures and show that over that space PW actually *is* a distance. Algorithms to solve the PW problems already exist, however we extend the PW framework by discussing and testing several initialization strategies. We then introduce the notion of PW barycenter and detail an algorithm to estimate it from the data. The result is a new method to compute representative shapes from a collection of point clouds. We benchmark our method against existing OT approaches, demonstrating superior performance in scenarios requiring precise alignment and shape preservation. We finally show the usefulness of the PW barycenters in an archaeological context. Our results highlight the potential of PW in advancing 2D and 3D point cloud analysis for machine learning and computational geometry applications.

Deep Learning · Generative Models and Autoencoders

Chenze Shao, Fandong Meng, Jie Zhou

Conventional wisdom suggests that autoregressive models are used to process discrete data. When applied to continuous modalities such as visual data, Visual AutoRegressive modeling (VAR) typically resorts to quantization-based approaches to cast the data into a discrete space, which can introduce significant information loss. To tackle this issue, we introduce a Continuous VAR framework that enables direct visual autoregressive generation without vector quantization. The underlying theoretical foundation is strictly proper scoring rules, which provide powerful statistical tools capable of evaluating how well a generative model approximates the true distribution. Within this framework, all we need is to select a strictly proper score and set it as the training objective to optimize. We primarily explore a class of training objectives based on the energy score, which is likelihood-free and thus overcomes the difficulty of making probabilistic predictions in the continuous space. Previous efforts on continuous autoregressive generation, such as GIVT and diffusion loss, can also be derived from our framework using other strictly proper scores. Source code: \url{https://github.com/shaochenze/EAR}.

Deep Learning · Theory

Sibylle Marcotte, Rémi Gribonval, Gabriel Peyré

While conservation laws in gradient flow training dynamics are well understood for (mostly shallow) ReLU and linear networks, their study remains largely unexplored for more practical architectures. For this, we first show that basic building blocks such as ReLU (or linear) shallow networks, with or without convolution, have easily expressed conservation laws, and no more than the known ones. In the case of a single attention layer, we also completely describe all conservation laws, and we show that residual blocks have the same conservation laws as the same block without a skip connection. We then introduce the notion of conservation laws that depend only on *a subset* of parameters (corresponding e.g. to a pair of consecutive layers, to a residual block, or to an attention layer). We demonstrate that the characterization of such laws can be reduced to the analysis of the corresponding building block in isolation. Finally, we examine how these newly discovered conservation principles, initially established in the continuous gradient flow regime, persist under discrete optimization dynamics, particularly in the context of Stochastic Gradient Descent (SGD).

Reinforcement Learning · Batch/Offline

Shoukai Xu, ZihaoLian, Mingkui Tan, Liu Liu, Zhong Zhang, Peilin Zhao

Offline reinforcement learning is widely applied in multiple fields due to its advantages in efficiency and risk control. However, a major problem it faces is the distribution shift between offline datasets and online environments. This mismatch leads to out-of-distribution (OOD) state-action pairs that fall outside the scope of the training data. Therefore, existing conservative training policies may not provide reliable decisions when the test environment deviates greatly from the offline dataset. In this paper, we propose Test-time Adapted Reinforcement Learning (TARL) to address this problem. TARL constructs unsupervised test-time optimization objectives for discrete and continuous control tasks, using test data without depending on environmental rewards. In discrete control tasks, it minimizes the entropy of predicted action probabilities to decrease uncertainty and avoid OOD state-action pairs. For continuous control tasks, it represents and minimizes action uncertainty based on the normal distribution of policy network outputs. Moreover, to prevent model bias caused by overfitting and error accumulation during the test-time update process, TARL enforces a KL divergence constraint between the fine-tuned policy and the original policy. For efficiency, TARL only updates the layer normalization layer parameters during testing. Extensive experiments on popular Atari game benchmarks and the D4RL dataset demonstrate the superiority of our method. Our method achieved a significant improvement over CQL, with a 13.6% episode return relative increase on the hopper-expert-v2 task.

Applications · Health / Medicine

Qingtian Zhu, Yumin Zheng, Yuling Sang, Yifan Zhan, Ziyan Zhu, Jun Ding, Yinqiang Zheng

Spatial Transcriptomics (ST) is a method that captures gene expression profiles aligned with spatial coordinates. The discrete spatial distribution and the super-high dimensional sequencing results make ST data challenging to be modeled effectively. In this paper, we manage to model ST in a continuous and compact manner by the proposed tool, SUICA, empowered by the great approximation capability of Implicit Neural Representations (INRs) that can enhance both the spatial density and the gene expression. Concretely within the proposed SUICA, we incorporate a graph-augmented Autoencoder to effectively model the context information of the unstructured spots and provide informative embeddings that are structure-aware for spatial mapping. We also tackle the extremely skewed distribution in a regression-by-classification fashion and enforce classification-based loss functions for the optimization of SUICA. By extensive experiments of a wide range of common ST platforms under varying degradations, SUICA outperforms both conventional INR variants and SOTA methods regarding numerical fidelity, statistical correlation, and bio-conservation. The prediction by SUICA also showcases amplified gene signatures that enriches the bio-conservation of the raw data and benefits subsequent analysis.

Optimization · Non-Convex

Kaheon Kim, Rentian Yao, Changbo Zhu, Xiaohui Chen

The optimal transport barycenter (a.k.a. Wasserstein barycenter) is a fundamental notion of averaging that extends from the Euclidean space to the Wasserstein space of probability distributions. Computation of the *unregularized* barycenter for discretized probability distributions on point clouds is a challenging task when the domain dimension $d > 1$. Most practical algorithms for approximating the barycenter problem are based on entropic regularization. In this paper, we introduce a nearly linear time $O(m \log{m})$ and linear space complexity $O(m)$ primal-dual algorithm, the *Wasserstein-Descent $\dot{\mathbb{H}}^1$-Ascent* (WDHA) algorithm, for computing the *exact* barycenter when the input probability density functions are discretized on an $m$-point grid. The key success of the WDHA algorithm hinges on alternating between two different yet closely related Wasserstein and Sobolev optimization geometries for the primal barycenter and dual Kantorovich potential subproblems. Under reasonable assumptions, we establish the convergence rate and iteration complexity of WDHA to its stationary point when the step size is appropriately chosen. Superior computational efficacy, scalability, and accuracy over the existing Sinkhorn-type algorithms are demonstrated on high-resolution (e.g., $1024 \times 1024$ images) 2D synthetic and real data.