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1,217篇论文匹配“Discrete Optimization”
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Applications · Language, Speech and Dialog

Yen-Ju Lu, Yashesh Gaur, Wei Zhou, Benjamin Muller, Jesus Villalba, Najim Dehak, Luke Zettlemoyer, Gargi Ghosh, Mike Lewis, Srini Iyer 等

Auto-regressive speech–text models pre-trained on interleaved text tokens and discretized speech tokens demonstrate strong speech understanding and generation, yet remain substantially less compute-efficient than text LLMs, partly due to the much longer sequences of speech tokens relative to text. This modality imbalance disproportionately allocates pre-training and inference compute to speech, potentially hindering effective cross-modal alignment and slowing performance scaling by orders of magnitude. We introduce the Latent Speech-Text Transformer (LST), which aggregates speech tokens into latent speech patches that serve as higher-level autoregressive units. This design aligns the sequence-modeling granularity between speech and text while improving computational efficiency. The resulting patches can align with textual units to facilitate cross-modal knowledge transfer and compactly capture recurring acoustic patterns such as silence. Across story-completion benchmarks under both compute-controlled and data-controlled settings, LST consistently improves speech accuracy while also improving text performance, achieving up to +6.5% absolute gain on speech HellaSwag in compute-controlled training (+5.3% in data-controlled training). Under compute-controlled scaling from 420M to 1.8B parameters in a near compute-optimal regime, gains grow with scale, and improvements persist up to 7B parameters under fixed-token budgets. These benefits extend to downstream tasks: LST stabilizes ASR adaptation and reduces the effective autoregressive sequence length during ASR and TTS inference, lowering computational cost without degrading reconstruction quality. The Code is available at https://github.com/facebookresearch/lst.

Di Zhang 0013, Ligang Liu 0001

We present an asymptotic analysis of shell lattice metamaterials based on Ciarlet's shell theory, introducing a new metric—asymptotic directional stiffness (ADS)—to quantify how the geometry of the middle surface governs the effective stiffness. We prove a convergence theorem that rigorously characterizes ADS and establishes its upper bound, along with necessary and sufficient condition for achieving it. As a key result, our theory provides the first rigorous explanation for the high bulk modulus observed in Triply Periodic Minimal Surfaces (TPMS)-based shell lattices. To optimize ADS on general periodic surfaces, we propose a triangular-mesh-based discretization and shape optimization framework. Numerical experiments validate the theoretical findings and demonstrate the effectiveness of the optimization under various design objectives. Our implementation is available at https://github.com/lavenklau/minisurf.

Yue Chang, Otman Benchekroun, Maurizio M. Chiaramonte, Peter Yichen Chen, Eitan Grinspun

Eigenanalysis of differential operators, such as the Laplace operator or elastic energy Hessian, is typically restricted to a single shape and its discretization, limiting reduced order modeling (ROM). We introduce the first eigenanalysis method for continuously parameterized shape families. Given a parametric shape, our method constructs spatial neural fields that represent eigen-functions across the entire shape space. It is agnostic to the specific shape representation, requiring only an inside/outside indicator function that depends on shape parameters. Eigenfunctions are computed by minimizing a variational principle over nested spaces with orthogonality constraints. Since eigenvalues may swap dominance at points of multiplicity, we jointly train multiple eigenfunctions while dynamically reordering them based on their eigenvalues at each step. Through causal gradient filtering, this reordering is reflected in backpropagation. Our method enables applications to operate over shape space, providing a single ROM that encapsulates vibration modes for all shapes, including previously unseen ones. Since our eigenanalysis is differentiable with respect to shape parameters, it facilitates eigenfunction-aware shape optimization. We evaluate our approach on shape optimization for sound synthesis and locomotion, as well as reduced-order modeling for elastodynamic simulation.

Pengbin Tang, Bernhard Thomaszewski, Stelian Coros, Bernd Bickel

We present a computational approach for designing Discrete Interlocking Materials (DIMs) with desired mechanical properties. Unlike conventional elastic materials, DIMs are kinematic materials governed by internal contacts among elements. These contacts induce anisotropic deformation limits that depend on the shape and topology of the elements. To enable gradient-based design optimization of DIMs with desired deformation limits, we introduce an implicit representation of interlocking elements based on unions of tori. Using this low-dimensional representation, we simulate DIMs with smoothly evolving contacts, allowing us to predict changes in deformation limits as a function of shape parameters. With this toolset in hand, we optimize for element shape parameters to design heterogeneous DIMs that best approximate prescribed limits. We demonstrate the effectiveness of our method by designing discrete interlocking materials with diverse limit profiles for in- and out-of-plane deformation and validate our method on fabricated physical prototypes.

Ellie Arar, Yarden Frenkel, Daniel Cohen-Or, Ariel Shamir, Yael Vinker

Recent advancements in large vision-language models have enabled highly expressive and diverse vector sketch generation. However, state-of-the-art methods rely on a time-consuming optimization process involving repeated feedback from a pretrained model to determine stroke placement. Consequently, despite producing impressive sketches, these methods are limited in practical applications. In this work, we introduce SwiftSketch, a diffusion model for image-conditioned vector sketch generation that can produce high-quality sketches in less than a second. SwiftSketch operates by progressively denoising stroke control points sampled from a Gaussian distribution. Its transformer-decoder architecture is designed to effectively handle the discrete nature of vector representation and capture the inherent global dependencies between strokes. To train SwiftSketch, we construct a synthetic dataset of image-sketch pairs, addressing the limitations of existing sketch datasets, which are often created by non-artists and lack professional quality. For generating these synthetic sketches, we introduce ControlSketch, a method that enhances SDS-based techniques by incorporating precise spatial control through a depth-aware ControlNet. We demonstrate that SwiftSketch generalizes across diverse concepts, efficiently producing sketches that combine high fidelity with a natural and visually appealing style.

Jerry Hsu, Tongtong Wang, Kui Wu 0003, Cem Yuksel

Cosserat rods have become an increasingly popular framework for simulating complex bending and twisting in thin elastic rods, used for hair, tree, and yarn-level cloth models. However, traditional approaches often encounter significant challenges in robustly and efficiently solving for valid quaternion orientations, even when employing small time steps or computationally expensive global solvers. We introduce stable Cosserat rods, a new solver that can achieve high accuracy with high stiffness levels and maintain stability under large time steps. It is also inherently suitable for parallelization. Our key contribution is a split position and rotation optimization scheme with a closed-form Gauss-Seidel quasi-static orientation update. This solver significantly improves the numerical stability with Cosserat rods, allowing faster computation and larger time steps. We validate our method across a wide range of applications, including simulations of hair, trees, yarn-level cloth, slingshots, and bridges, demonstrating its ability to handle diverse material behaviors and complex geometries. Furthermore, we show that our method is orders of magnitude faster and more stable than alternative rod solvers, such as extended position-based dynamics and discrete elastic rods.

Anran Qi, Nico Pietroni, Maria Korosteleva, Olga Sorkine-Hornung, Adrien Bousseau

We present the first algorithm to automatically compute sewing patterns for upcycling existing garments into new designs. Our algorithm takes as input two garment designs along with their corresponding sewing patterns and determines how to cut one of them to match the other by following garment reuse principles. Specifically, our algorithm favors the reuse of seams and hems present in the existing garment, thereby preserving the embedded value of these structural components and simplifying the fabrication of the new garment. Finding optimal reused pattern is computationally challenging because it involves both discrete and continuous quantities. Discrete decisions include the choice of existing panels to cut from and the choice of seams and hems to reuse. Continuous variables include the precise placement of the new panels along seams and hems, and potential deformations of these panels to maximize reuse. Our key idea for making this optimization tractable is quantizing the shape of garment panels. This allows us to frame the search for an optimal reused pattern as a discrete assignment problem, which we solve efficiently with an ILP solver. We showcase our proposed pipeline on several reuse examples, including comparisons with reused patterns crafted by a professional garment designer. Additionally, we manufacture a physical reused garment to demonstrate the practical effectiveness of our approach.

Maximilian Kohlbrenner, Marc Alexa

Lie sphere geometry provides a unified representation of points, oriented spheres and hyperplanes in Euclidean d-space as the subset of lines in \( \mathbb {R}^{d+3} \) that are contained in a certain quadric. The natural scalar product in this construction is zero if two elements are in oriented contact. We show how the sign of this product can be used to decide if spheres are disjoint. This allows us to model the space of spheres that are not intersecting a given union of spheres as the intersection of half-spaces (and the quadric). The maximal spheres are on the boundary of this set and can be computed by first constructing the intersection of half-spaces, which is a convex hull problem, and then intersecting edges of the hull against the quadric, which are the roots of a univariate quadratic. We demonstrate the method at the example of contouring a discrete signed distance field: every sample of the signed distance field represents an empty spheres and the zero-level contour has to be disjoint from the union of these spheres. Maximal spheres outside the empty spheres provide samples on the zero-level contour. The quality of this sample set is comparable to existing methods relying on optimization, while being deterministic and faster in practice.

Jingrui Xing, Bin Wang 0069, Mengyu Chu, Baoquan Chen

We present a grid-free fluid solver featuring a novel Gaussian representation. Drawing inspiration from the expressive capabilities of 3D Gaussian Splatting in multi-view image reconstruction, we model the continuous flow velocity as a weighted sum of multiple Gaussian functions. This representation is continuously differentiable, which enables us to derive spatial differentials directly and solve the time-dependent PDE via a custom first‑order optimization tailored to fluid dynamics.Compared to traditional discretizations, which typically adopt Eulerian, Lagrangian, or hybrid perspectives, our approach is inherently memory-efficient and spatially adaptive, enabling it to preserve fine-scale structures and vortices with high fidelity. While these advantages are also sought by implicit neural representations, GSR offers enhanced robustness, accuracy, and generality across diverse fluid phenomena, with improved computational efficiency during temporal evolution.Though our first‑order solver does not yet match the speed of fluid solvers using explicit representations, its continuous nature substantially reduces spatial discretization error and opens a new avenue for high‑fidelity simulation. We evaluate the proposed solver across a broad range of 2D and 3D fluid phenomena, demonstrating its ability to preserve intricate vortex dynamics, accurately capture boundary-induced effects such as Kármán vortex streets, and remain robust across long time horizons—all without additional parameter tuning. Our results suggest that GSR offers a compelling direction for future research in fluid simulation. The source code for our fluid solver is publicly available at https://github.com/xjr01/Gaussian-Fluids-Code.

Du Chen, Liyi Chen, Zhengqiang Zhang, Lei Zhang

Implicit Neural Representations (INR) have been successfully employed for Arbitrary-scale Super-Resolution (ASR). However, INR-based models need to query the multi-layer perceptron module numerous times and render a pixel in each query, resulting in insufficient representation capability and low computational efficiency. Recently, Gaussian Splatting (GS) has shown its advantages over INR in both visual quality and rendering speed in 3D tasks, which motivates us to explore whether GS can be employed for the ASR task. However, directly applying GS to ASR is exceptionally challenging because the original GS is an optimization-based method through overfitting each single scene, while in ASR we aim to learn a single model that can generalize to different images and scaling factors. We overcome these challenges by developing two novel techniques. Firstly, to generalize GS for ASR, we elaborately design an architecture to predict the corresponding image-conditioned Gaussians of the input low-resolution image in a feed-forward manner. Each Gaussian can fit the shape and direction of an area of complex textures, showing powerful representation capability. Secondly, we implement an efficient differentiable 2D GPU/CUDA-based scale-aware rasterization to render super-resolved images by sampling discrete RGB values from the predicted continuous Gaussians. Via end-to-end training, our optimized network, namely GSASR, can perform ASR for any image and unseen scaling factors. Extensive experiments validate the effectiveness of our proposed method. The code and models are available at https://github.com/ChrisDud0257/GSASR.

Sucheng Ren, Qihang Yu, Ju He, Xiaohui Shen, Alan Yuille, Liang-Chieh Chen

Autoregressive (AR) modeling, known for its next-token prediction paradigm, underpins state-of-the-art language and visual generative models. Traditionally, a "token" is treated as the smallest prediction unit, often a discrete symbol in language or a quantized patch in vision. However, the optimal token definition for 2D image structures remains an open question. Moreover, AR models suffer from exposure bias, where teacher forcing during training leads to error accumulation at inference.In this paper, we propose xAR, a generalized AR framework that extends the notion of a token to an entity X, which can represent an individual patch token, a cell (a kxk grouping of neighboring patches), a subsample (a non-local grouping of distant patches), a scale (coarse-to-fine resolution), or even a whole image. Additionally, we reformulate discrete token classification as continuous entity regression, leveraging flow-matching methods at each AR step. This approach conditions training on noisy entities instead of ground truth tokens, leading to Noisy Context Learning, which effectively alleviates exposure bias.As a result, xAR offers two key advantages: (1) it enables flexible prediction units that capture different contextual granularity and spatial structures, and (2) it mitigates exposure bias by avoiding reliance on teacher forcing.On ImageNet-256 generation benchmark, our base model, xAR-B, outperforms DiT-XL/SiT-XL while achieving 20xfaster inference. Meanwhile, xAR-H sets a new state-of-the-art with an FID of 1.24, running 2.2xfaster than the previous best-performing model without relying on vision foundation modules (e.g., DINOv2) or advanced guidance interval sampling. Codes is publicly available at https://oliverrensu.github.io/project/xAR.

Yuanzhi Zhu, Xi Wang, Stéphane Lathuilière, Vicky Kalogeiton

Masked Diffusion Models (MDMs) have emerged as a powerful generative modeling technique. Despite their remarkable results, they typically suffer from slow inference with several steps. In this paper, we propose Di\mathtt [M] O, a novel approach that distills masked diffusion models into a one-step generator.Di\mathtt [M] O addresses two key challenges: (1) the intractability of using intermediate-step information for one-step generation, which we solve through token-level distribution matching that optimizes model output logits by an `on-policy framework' with the help of an auxiliary model; and (2) the lack of entropy in the initial distribution, which we address through a token initialization strategy that injects randomness while maintaining similarity to teacher training distribution. We show Di\mathtt [M] O's effectiveness on both class-conditional and text-conditional image generation, impressively achieving performance competitive to multi-step teacher outputs while drastically reducing inference time. To our knowledge, we are the first to successfully achieve one-step distillation of masked diffusion models and the first to apply discrete distillation to text-to-image generation, opening new paths for efficient generative modeling.

Peng Zheng, Junke Wang, Yi Chang, Yizhou Yu, Rui Ma, Zuxuan Wu

Recent advances in large language models (LLMs) have spurred interests in encoding images as discrete tokens and leveraging autoregressive (AR) frameworks for visual generation. However, the quantization process in AR-based visual generation models inherently introduces information loss that degrades image fidelity. To mitigate this limitation, recent studies have explored to autoregressively predict continuous tokens. Unlike discrete tokens that reside in a structured and bounded space, continuous representations exist in an unbounded, high-dimensional space, making density estimation more challenging and increasing the risk of generating out-of-distribution artifacts. Based on the above findings, this work introduces DisCon (Discrete-Conditioned Continuous Autoregressive Model), a novel framework that reinterprets discrete tokens as conditional signals rather than generation targets. By modeling the conditional probability of continuous representations conditioned on discrete tokens, DisCon circumvents the optimization challenges of continuous token modeling while avoiding the information loss caused by quantization. DisCon achieves a gFID score of 1.38 on ImageNet 256x256 generation, outperforming state-of-the-art autoregressive approaches by a clear margin. Project page: https://pengzheng0707.github.io/DisCon.

Pei Wang, Zhaowei Cai, Hao Yang, Davide Modolo, Ashwin Swaminathan

The optimality of using the de facto cross-entropy loss with one-hot target distribution (hard labeling) is questioned when training (Multimodal) Large Language Models (LLMs/MLLMs). Although it is reasonable for language token prediction, which is a typical multi-class classification problem in discrete space, it is suboptimal for task like numerical prediction, which is a typical regression problem in continuous space. However, enabling regression in LLMs/MLLMs will complicate the training and next-token prediction paradigm at inference. Instead, to address this challenge, we propose a novel loss design, called soft labeling, which smooths the target probability distribution, enabling predictions to be penalized according to their distance to the target. This is similar to regression loss, which penalizes more on the further predictions in the continuous space, but will not change the model architecture and the next-token prediction paradigm of LLMs/MLLMs. We demonstrate the efficacy of soft labeling through extensive experiments on visual grounding, object counting, and chart understanding, achieving state-of-the-art performance on multiple benchmarks without bells and whistles. Soft labeling can be applied in any LLM/MLLM.

Zeyu Liu, Zanlin Ni, Yeguo Hua, Xin Deng, Xiao Ma, Cheng Zhong, Gao Huang

Discrete visual tokenizers transform images into a sequence of tokens, enabling token-based visual generation akin to language models. However, this process is inherently challenging, as it requires both compressing visual signals into a compact representation and discretizing them into a fixed set of codes. Traditional discrete tokenizers typically learn the two tasks jointly, often leading to unstable training, low codebook utilization, and limited reconstruction quality. In this paper, we introduce CODA(COntinuous-to-Discrete Adaptation), a framework that decouples compression and discretization. Instead of training discrete tokenizers from scratch, CODA adapts off-the-shelf continuous VAEs---already optimized for perceptual compression---into discrete tokenizers via a carefully designed discretization process. By primarily focusing on discretization, CODA ensures stable and efficient training while retaining the strong visual fidelity of continuous VAEs. Empirically, with 6 xless training budget than standard VQGAN, our approach achieves a remarkable codebook utilization of 100% and notable reconstruction FID (rFID) of 0.43 and 1.34 for 8 xand 16 xcompression on ImageNet 256x256 benchmark.

Weihao Yu, Yuanhao Cai, Ruyi Zha, Zhiwen Fan, Chenxin Li, Yixuan Yuan

Four-dimensional computed tomography (4D CT) reconstruction is crucial for capturing dynamic anatomical changes but faces inherent limitations from conventional phase-binning workflows. Current methods discretize temporal resolution into fixed phases with respiratory gating devices, introducing motion misalignment and restricting clinical practicality. In this paper, We propose X^2-Gaussian, a novel framework that enables continuous-time 4D-CT reconstruction by integrating dynamic radiative Gaussian splatting with self-supervised respiratory motion learning. Our approach models anatomical dynamics through a spatiotemporal encoder-decoder architecture that predicts time-varying Gaussian deformations, eliminating phase discretization. To remove dependency on external gating devices, we introduce a physiology-driven periodic consistency loss that learns patient-specific breathing cycles directly from projections via differentiable optimization. Extensive experiments demonstrate state-of-the-art performance, achieving a 9.93 dB PSNR gain over traditional methods and 2.25 dB improvement against prior Gaussian splatting techniques. By unifying continuous motion modeling with hardware-free period learning, X^2-Gaussian advances high-fidelity 4D CT reconstruction for dynamic clinical imaging. Code will be publicly available at https://github.com/CUHK-AIM-Group/X2-Gaussian.

Haiwen Diao, Xiaotong Li, Yufeng Cui, Yueze Wang, Haoge Deng, Ting Pan, Wenxuan Wang, Huchuan Lu, Xinlong Wang

Existing encoder-free vision-language models (VLMs) are rapidly narrowing the performance gap with their encoder-based counterparts, highlighting the promising potential for unified multimodal systems with structural simplicity and efficient deployment. We systematically clarify the performance gap between VLMs using pre-trained vision encoders, discrete tokenizers, and minimalist visual layers from scratch, deeply excavating the under-examined characteristics of encoder-free VLMs. We develop efficient strategies for encoder-free VLMs that rival mainstream encoder-based ones. After an in-depth investigation, we launch EVEv2.0, a new and improved family of encoder-free VLMs. We show that: (i) Properly decomposing and hierarchically associating vision and language within a unified model reduces interference between modalities. (ii) A well-designed training strategy enables effective optimization for encoder-free VLMs. Through extensive evaluation, our EVEv2.0 represents a thorough study for developing a decoder-only architecture across modalities, demonstrating superior data efficiency and strong vision-reasoning capability. Code is publicly available at: https://github.com/baaivision/EVE.

Yi Liu, Shengqian Li, Zuzeng Lin, Feng Wang, Si Liu

The current conditional autoregressive image generation methods have shown promising results, yet their potential remains largely unexplored in the practical unsupervised image translation domain, which operates without explicit cross-domain correspondences.A critical limitation stems from the discrete quantization inherent in traditional Vector Quantization-based frameworks, which disrupts gradient flow between the Variational Autoencoder decoder and causal Transformer, impeding end-to-end optimization during adversarial training in image space.To tackle this issue, we propose using Softmax Relaxed Quantization, a novel approach that reformulates codebook selection as a continuous probability mixing process via Softmax, thereby preserving gradient propagation. Building upon this differentiable foundation, we introduce CycleVAR, which reformulates image-to-image translation as image-conditional visual autoregressivegeneration by injecting multi-scale source image tokens as contextual prompts, analogous to prefix-based conditioning in language models.CycleVAR exploits two modes to generate the target image tokens, including (1) serial multi-step generation enabling iterative refinement across scales and (2) parallel one-step generation synthesizing all resolution outputs in a single forward pass.Experimental findings indicate that the parallel one-step generation mode attains superior translation quality with quicker inference speed than the serial multi-step mode in unsupervised scenarios.Furthermore, both quantitativeand qualitative results indicate that CycleVAR surpasses previous state-of-the-artunsupervised image translation models, e.g., CycleGAN-Turbo.

Valter Piedade, Chitturi Sidhartha, José Gaspar, Venu Madhav Govindu, Pedro Miraldo

Outliers are ubiquitous in geometric vision contexts such as pose estimation and mapping, leading to inaccurate estimates. While robust loss functions can tackle outliers, it is challenging to make the estimation robust to the choice of initialization and to estimate the appropriate robust loss shape parameter that allows distinguishing inliers from outliers. Graduated non-convexity (GNC) often mitigates these issues. However, typical GNC uses a fixed annealing factor to update the shape parameter, which can lead to low-quality or inefficient estimates. This paper proposes a novel approach to adaptively anneal the shape parameter within a GNC framework. We developed a search strategy that incorporates a sampling of annealing choices and model scorings to select the most promising shape parameter at each GNC iteration. Additionally, we propose new stopping criteria and an initialization technique that improves performance for diverse data, and we show the benefits of combining discrete and continuous robust estimation strategies. We evaluate our method using synthetic and real-world data in two problems: 3D registration and pose graph optimization in SLAM sequences. Our results demonstrate greater efficiency and robustness compared to previous GNC schemes. Code and other resources are available at https://www.merl.com/research/highlights/sac-gnc.

Jiahao Zhang, Anoop Cherian, Cristian Rodriguez, Weijian Deng, Stephen Gould

Assembling furniture amounts to solving the discrete-continuous optimization task of selecting the furniture parts to assemble and estimating their connecting poses in a physically realistic manner. The problem is hampered by its combinatorially large yet sparse solution space thus making learning to assemble a challenging task for current machine learning models. In this paper, we attempt to solve this task by leveraging the assembly instructions provided in diagrammatic manuals that typically accompany the furniture parts. Our key insight is to use the cues in these diagrams to split the problem into discrete and continuous phases. Specifically, we present Manual-PA, a transformer-based instruction Manual-guided 3D Part Assembly framework that learns to semantically align 3D parts with their illustrations in the manuals using a contrastive learning backbone towards predicting the assembly order and infers the 6D pose of each part via relating it to the final furniture depicted in the manual. To validate the efficacy of our method, we conduct experiments on the benchmark PartNet dataset. Our results show that using the diagrams and the order of the parts lead to significant improvements in assembly performance against the state of the art. Further, Manual-PA demonstrates strong generalization to real-world IKEA furniture assembly on the IKEA-Manual dataset.