Augmented Lagrangian Methods (ALMs) are widely employed in solving constrained optimizations, and some efficient solvers are developed based on this framework. Under the quadratic growth assumption, it is known that the dual iterates and the Karush-Kuhn-Tucker (KKT) residuals of ALMs applied to conic programs converge linearly. In contrast, the convergence rate of the primal iterates has remained elusive. In this paper, we resolve this challenge by establishing new $\textit{quadratic growth}$ and $\textit{error bound}$ properties for primal and dual conic programs under the standard strict complementarity condition. Our main results reveal that both primal and dual iterates of the ALMs converge linearly contingent solely upon the assumption of strict complementarity and a bounded solution set. This finding provides a positive answer to an open question regarding the asymptotically linear convergence of the primal iterates of ALMs applied to conic optimization.

Large language models (LLMs) have demonstrated strong capabilities in using external tools to address user inquiries. However, most existing evaluations assume tool use in short contexts, offering limited insight into model behavior during realistic long-term interactions. To fill this gap, we introduce ToolHaystack, a benchmark for testing the tool use capabilities in long-term interactions. Each test instance in ToolHaystack includes multiple tasks execution contexts and realistic noise within a continuous conversation, enabling assessment of how well models maintain context and handle various disruptions. By applying this benchmark to 14 state-of-the-art LLMs, we find that while current models perform well in standard multi-turn settings, they often significantly struggle in ToolHaystack, highlighting critical gaps in their long-term robustness not revealed by previous tool benchmarks.

Randomized smoothing has become essential for achieving certified adversarial robustness in machine learning models. However, current methods primarily use isotropic noise distributions that are uniform across all data dimensions, such as image pixels, limiting the effectiveness of robustness certification by ignoring the heterogeneity of inputs and data dimensions. To address this limitation, we propose UCAN: a novel technique that \underline{U}niversally \underline{C}ertifies adversarial robustness with \underline{A}nisotropic \underline{N}oise. UCAN is designed to enhance any existing randomized smoothing method, transforming it from symmetric (isotropic) to asymmetric (anisotropic) noise distributions, thereby offering a more tailored defense against adversarial attacks. Our theoretical framework is versatile, supporting a wide array of noise distributions for certified robustness in different $\ell_p$-norms and applicable to any arbitrary classifier by guaranteeing the classifier's prediction over perturbed inputs with provable robustness bounds through tailored noise injection. Additionally, we develop a novel framework equipped with three exemplary noise parameter generators (NPGs) to optimally fine-tune the anisotropic noise parameters for different data dimensions, allowing for pursuing different levels of robustness enhancements in practice.Empirical evaluations underscore the significant leap in UCAN's performance over existing state-of-the-art methods, demonstrating up to $182.6\%$ improvement in certified accuracy at large certified radii on MNIST, CIFAR10, and ImageNet datasets.\footnote{Code is anonymously available at \href{https://github.com/youbin2014/UCAN/}{https://github.com/youbin2014/UCAN/}}

Under the quadratic growth assumption, it is known that the dual iterates and the Karush-Kuhn-Tucker (KKT) residuals of ALMs applied to semidefi-nite programs (SDPs) converge linearly. In contrast, the convergence rate of the primal iterates has remained elusive.

Audio Language Models (ALMs) have made significant progress recently. These models integrate the audio modality directly into the model, rather than converting speech into text and inputting text to Large Language Models (LLMs). While jailbreak attacks on LLMs have been extensively studied, the security of ALMs with audio modalities remains largely unexplored. Currently, there is a lack of an adversarial audio dataset and a unified framework specifically designed to evaluate and compare attacks and ALMs. In this paper, we present JALMBench, a comprehensive benchmark to assess the safety of ALMs against jailbreak attacks. JALMBench includes a dataset containing 11,316 text samples and 245,355 audio samples with over 1,000 hours. It supports 12 mainstream ALMs, 4 text-transferred and 4 audio-originated attack methods, and 5 defense methods. Using JALMBench, we provide an in-depth analysis of attack efficiency, topic sensitivity, voice diversity, and architecture. Additionally, we explore mitigation strategies for the attacks at both the prompt level and the response level.

Diffusion language models (DLMs) have strong theoretical efficiency but are limited by fixed-length decoding and incompatibility with key-value (KV) caches. Block diffusion mitigates these issues, yet still enforces a fixed block size and requires expensive training. We introduce Next Sequence Prediction (NSP), which unifies next-token and next-block prediction, enabling the model to adaptively determine the generation length at each step. When the length is fixed to 1, NSP reduces to standard next-token prediction. Building on NSP, we propose Sequential Diffusion Language Model (SDLM), which can retrofit pre-trained autoregressive language models (ALMs) at minimal cost. Specifically, SDLM performs diffusion inference within fixed-size mask blocks, but dynamically decodes consecutive subsequences based on model confidence, thereby preserving KV-cache compatibility and improving robustness to varying uncertainty and semantics across the sequence. Experiments show that SDLM matches or surpasses strong autoregressive baselines using only 3.5M training samples, while achieving 2.1 higher throughput than Qwen-2.5. Notably, the SDLM-32B model delivers even more pronounced efficiency gains, demonstrating the strong scalability potential of our modeling paradigm. Project page and codes: https://github.com/OpenGVLab/SDLM

Audio editing plays a central role in VR/AR immersion, virtual conferencing, sound design, and other interactive media. However, recent generative audio editing models depend on template-like instruction formats and are restricted to mono-channel audio. These models fail to deal with declarative audio editing, where the user declares what the desired outcome should be, while leaving the details of editing operations to the system. We introduce SmartDJ, a novel framework for stereo audio editing that combines the reasoning capability of audio language models with the generative power of latent diffusion. Given a high-level instruction, SmartDJ decomposes it into a sequence of atomic edit operations, such as adding, removing, or spatially relocating events. These operations are then executed by a diffusion model trained to manipulate stereo audio. To support this, we design a data synthesis pipeline that produces paired examples of high-level instructions, atomic edit operations, and audios before and after each edit operation. Experiments demonstrate that SmartDJ achieves superior perceptual quality, spatial realism, and semantic alignment compared to prior audio editing methods. Demos are available at https://zitonglan.github.io/project/smartdj/smartdj.html.

Evaluations of audio-language models (ALMs) -- multimodal models that take interleaved audio and text as input and output text -- are hindered by the lack of standardized benchmarks; most benchmarks measure only one or two capabilities and omit evaluative aspects such as fairness or safety. Furthermore, comparison across models is difficult as separate evaluations test a limited number of models and use different prompting methods and inference parameters. To address these shortfalls, we introduce AHELM, a benchmark that aggregates various datasets -- including 2 new synthetic audio-text datasets called PARADE, which evaluates the ALMs on avoiding stereotypes, and CoRe-Bench, which measures reasoning over conversational audio through inferential multi-turn question answering -- to holistically measure the performance of ALMs across 10 aspects we have identified as important to the development and usage of ALMs: audio perception, knowledge, reasoning, emotion detection, bias, fairness, multilinguality, robustness, toxicity, and safety. We also standardize the prompts, inference parameters, and evaluation metrics to ensure equitable comparisons across models. We test 14 open-weight and closed-API ALMs from 3 developers and 3 additional simple baseline systems each consisting of an automatic speech recognizer and a language model. Our results show that while Gemini 2.5 Pro ranks top in 5 out of 10 aspects, it exhibits group unfairness ($p=0.01$) on ASR tasks whereas most of the other models do not. We also find that the baseline systems perform reasonably well on AHELM, with one ranking 6th overall despite having only speech-to-text capabilities. For transparency, all raw prompts, model generations, and outputs are available on our website at https://crfm.stanford.edu/helm/audio/v1.0.0. AHELM is intended to be a living benchmark and new datasets and models will be added over time.

Chain-of-thought reasoning has demonstrated significant improvements in large language models and vision language models, yet its potential for audio language models remains largely unexplored. In this technical report, we take a preliminary step towards closing this gap. For better assessment of sound reasoning, we propose AF-Reasoning-Eval, a benchmark targeting common-sense reasoning and the ability to discriminate among closely related choices. To prepare training corpus for sound reasoning abilities, we propose automatic pipelines that transform existing audio question answering and classification data into explicit reasoning chains, yielding AF-CoT-Train with 1.24M samples. We study the effect of finetuning Audio Flamingo series on AF-CoT-Train and observe considerable improvements on several reasoning benchmarks, validating the effectiveness of chain-of-thought finetuning on advanced sound understanding.