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Emre Adabag, Marcus Greiff, John Subosits, Thomas Lew

Differentiable model predictive control (MPC) offers a powerful framework for combining learning and control. However, its adoption has been limited by the inherently sequential nature of traditional optimization algorithms, which are challenging to parallelize on modern computing hardware like GPUs. In this work, we tackle this bottleneck by introducing a GPU-accelerated differentiable optimization tool for MPC. This solver leverages sequential quadratic programming and a custom preconditioned conjugate gradient (PCG) routine with tridiagonal preconditioning to exploit the problem's structure and enable efficient parallelization. We demonstrate substantial speedups over CPU- and GPU-based baselines, significantly improving upon state-of-the-art training times on benchmark reinforcement learning and imitation learning tasks. Finally, we showcase the method on the challenging task of reinforcement learning for driving at the limits of handling, where it enables robust drifting of a Toyota Supra through water puddles.

Applications · Everything Else

Minsoo Kim, seung-won hwang

LLM-based agents have seen promising advances, yet are still limited in hard-exploration tasks which require agents to perform sustained exploration under sparse feedback. We present GLoW, a novel approach leveraging a dual-scale textual world memory, maintaining a trajectory frontier of high-value discoveries at the global scale, while learning from local trial-and-error in exploration through a Multi-path Advantage Reflection mechanism which infers advantage-based progress signals to guide exploration. To evaluate our framework for hard-exploration, we tackle the Jericho benchmark suite of text-based games, where GLoW achieves a new state-of-the-art performance for LLM-based approaches. Compared to state-of-the-art RL-based methods, our approach achieves comparable performance while requiring 100-800× fewer environment interactions. When scaled to stronger LLMs, GLoW surpasses all prior methods on 4 out of 6 difficult and extreme Jericho games.

Computer Vision · Vision Models & Multimodal

Yasser HAMIDULLAH, Koel Dutta Chowdhury, Yusser Al Ghussin, Shakib Yazdani, Cennet Oguz, Josef Genabith, Cristina España-Bonet

Hallucination, where models generate fluent text unsupported by visual evidence, remains a major flaw in vision–language models and is particularly critical in sign language translation (SLT). In SLT, meaning depends on precise grounding in video, and gloss-free models are especially vulnerable because they map continuous signer movements directly into natural language without intermediate gloss supervision that serves as alignment. We argue that hallucinations arise when models rely on language priors rather than visual input. To capture this, we propose a token-level reliability measure that quantifies how much the decoder uses visual information. Our method combines feature-based sensitivity, which measures internal changes when video is masked, with counterfactual signals, which capture probability differences between clean and altered video inputs. These signals are aggregated into a sentence-level reliability score, providing a compact and interpretable measure of visual grounding. We evaluate the proposed measure on two SLT benchmarks (PHOENIX-2014T and CSL-Daily) with both gloss-based and gloss-free models. Our results show that reliability predicts hallucination rates, generalizes across datasets and architectures, and decreases under visual degradations. Beyond these quantitative trends, we also find that reliability distinguishes grounded tokens from guessed ones, allowing risk estimation without references; when combined with text-based signals (confidence, perplexity, or entropy), it further improves hallucination risk estimation. Qualitative analysis highlights why gloss-free models are more susceptible to hallucinations. Taken together, our findings establish reliability as a practical and reusable tool for diagnosing hallucinations in SLT, and lay the groundwork for more robust hallucination detection in multimodal generation.

Optimization · Large Scale, Parallel and Distributed

Xinwei Qiang, Hongmin chen, Shixuan Sun, Jingwen Leng, Xin Liu, Minyi Guo

Determinism is indispensable for reproducibility in large language model (LLM) training, yet it often exacts a steep performance cost. In widely used attention implementations such as FlashAttention-3, the deterministic backward pass can incur up to a 37.9% throughput reduction relative to its non‑deterministic counterpart, primarily because gradient accumulation operations must be serialized to guarantee numerical consistency. This performance loss stems from suboptimal scheduling of compute and gradient‑reduction phases, leading to significant hardware underutilization. To address this challenge, we formulate the backward pass of deterministic attention as a scheduling problem on a Directed Acyclic Graph (DAG) and derive schedules that minimize the critical path length. Building on this formulation, we present DASH (Deterministic Attention Scheduling for High-Throughput), which encapsulates two complementary scheduling strategies: (i) Descending Q‑Tile Iteration, a reversed query‑block traversal that shrinks pipeline stalls in causal attention, and (ii) Shift Scheduling, a theoretically optimal schedule within our DAG model that reduces pipeline stalls for both full and causal masks. Our empirical evaluations on NVIDIA H800 GPUs demonstrate that DASH narrows the performance gap of deterministic attention. The proposed strategies improve the throughput of the attention backward pass by up to 1.28$\times$ compared to the baseline, significantly advancing the efficiency of reproducible LLM training. Our code is open-sourced at https://github.com/SJTU-Liquid/deterministic-FA3.

Applications · Language, Speech and Dialog

Junnan Liu, Hongwei Liu, Songyang Zhang, Kai Chen

Recent advancements in large language models (LLMs) have been driven by their emergent reasoning capabilities, particularly through long chain-of-thought (CoT) prompting, which enables thorough exploration and deliberation. Despite these advances, long-CoT LLMs often exhibit suboptimal reasoning behaviors, such as overthinking and excessively protracted reasoning chains, which can impair performance. In this paper, we analyze reasoning processes through an optimization lens, framing CoT as a gradient descent procedure where each reasoning step constitutes an update toward problem resolution. Building on this perspective, we introduce RePro (**Re**ctifying **Pro**cess-level Reward), a novel approach to refine LLM reasoning during post-training. RePro defines a surrogate objective function to assess the optimization process underlying CoT, utilizing a dual scoring mechanism to quantify its intensity and stability. These scores are aggregated into a composite process-level reward, seamlessly integrated into reinforcement learning with verifiable rewards (RLVR) pipelines to optimize LLMs. Extensive experiments across multiple reinforcement learning algorithms and diverse LLMs, evaluated on benchmarks spanning mathematics, science, and coding, demonstrate that RePro consistently enhances reasoning performance and mitigates suboptimal reasoning behaviors.

Reinforcement Learning · Deep RL

Xichen Zhang, Sitong Wu, Yinghao Zhu, Haoru Tan, Shaozuo Yu, Ziyi He, Jiaya Jia

Reinforcement learning from verifiable rewards has emerged as a powerful technique for enhancing the complex reasoning abilities of Large Language Models (LLMs). However, these methods are fundamentally constrained by the ''learning cliff'' phenomenon: when faced with problems far beyond their current capabilities, models consistently fail, yielding a persistent zero-reward signal. In policy optimization algorithms like GRPO, this collapses the advantage calculation to zero, rendering these difficult problems invisible to the learning gradient and stalling progress. To overcome this, we introduce Scaf-GRPO (Scaffolded Group Relative Policy Optimization), a progressive training framework that strategically provides minimal guidance only when a model's independent learning has plateaued. The framework first diagnoses learning stagnation and then intervenes by injecting tiered in-prompt hints, ranging from abstract concepts to concrete steps, enabling the model to construct a valid solution by itself. Extensive experiments on challenging mathematics benchmarks demonstrate Scaf-GRPO's effectiveness, boosting the pass@1 score of the Qwen2.5-Math-7B model on the AIME24 benchmark by a relative 44.3\% over a vanilla GRPO baseline. This result demonstrates our framework provides a robust and effective methodology for unlocking a model's ability to solve problems previously beyond its reach, a critical step towards extending the frontier of autonomous reasoning in LLM.

Reinforcement Learning · Batch/Offline

Yujia Zhang, Lin Li, Wei Wei, Jianguo Wu, Yi Ma, Jiye Liang

Offline reinforcement learning (RL) seeks to learn an optimal policy from a fixed dataset, but distributional shift between the dataset and the learned policy often leads to suboptimal real-world performance. Existing methods typically use behavior policy regularization to constrain the learned policy, but these conservative approaches can limit performance and generalization, especially when the behavior policy is suboptimal. We propose a Peer-Influenced Constraint (PIC) framework with a ``peer review" mechanism. Specifically, we construct a set of similar states and use the corresponding actions as candidates, from which we select the optimal action to constrain the policy. This method helps the policy escape local optima while approximately ensuring the staying within the in-distribution space, boosting both performance and generalization. We also introduce an improved version, Ensemble Peer-Influenced Constraint (EPIC), which combines ensemble methods to achieve strong performance while maintaining high efficiency. Additionally, we uncover the Coupling Effect between PIC and uncertainty estimation, providing valuable insights for offline RL. We evaluate our methods on classic continuous control tasks from the D4RL benchmark, with both PIC and EPIC achieving competitive performance compared to state-of-the-art approaches.

Applications · Language, Speech and Dialog

Yuanfan Li, Qi Zhou, Zexuan Xie

Machine-generated text (MGT) detection is critical for safeguarding online content integrity and preventing the spread of misleading information. Although existing detectors achieve high accuracy in monolingual settings, they exhibit severe performance degradation on zero-shot languages and are vulnerable to adversarial attacks. To tackle these challenges, we propose a robust adversarial training framework named **T**ranslation-based **A**ttacker **S**trengthens Mul**T**ilingual Def**E**nder (TASTE). TASTE comprises two core components: an attacker that performs code-switching by querying translation dictionaries to generate adversarial examples, and a detector trained to resist these attacks while generalizing to unseen languages. We further introduce a novel Language-Agnostic Adversarial Loss (LAAL), which encourages the detector to learn language-invariant feature representations and thus enhances zero-shot detection performance and robustness against unseen attacks. Additionally, the attacker and detector are synchronously updated, enabling continuous improvement of defensive capabilities. Experimental results on 9 languages and 8 attack types show that our TASTE surpasses 8 SOTA detectors, improving the average F1 score by **0.064** and reducing the average Attack Success Rate (ASR) by **3.8\%**. Our framework offers a promising approach for building robust, multilingual MGT detectors with strong generalization to real-world adversarial scenarios. Our codes are available in https://github.com/Liyuuuu111/MGT-Eval, and our datasets and pretrained checkpoint are available in https://drive.google.com/file/d/1w1hbdiZMS_JzPntVMWM3qrTQ4KxJf-t6.

Deep Learning · Algorithms

Ningfeng Yang, Tor Aamodt

Quantization-Aware Pre-Training (QAPT) is an effective technique to reduce the compute and memory overhead of Deep Neural Networks while improving their energy efficiency on edge devices. Existing QAPT methods produce models stored in compute-efficient data types (e.g. integers) that are not information theoretically optimal (ITO). On the other hand, existing ITO data types (e.g. Quantile/NormalFloat Quantization) are not compute-efficient. We propose BBQ, the first ITO quantization method that is also compute-efficient. BBQ builds on our key insight that since learning is domain-agnostic, the output of a quantizer does not need to reside in the same domain as its input. BBQ performs ITO quantization in its input domain, and returns its output in a compute-efficient domain where ITO data types are mapped to compute-efficient data types. Without sacrificing compute efficiency, BBQ outperforms prior SOTA QAPT methods by a perplexity reduction of up to 2 points for 4-bit models, up to 4 points for 3-bit models, up to 5 points for 2-bit models, and up to 18 points for 1-bit models. Code is available at https://github.com/1733116199/bbq.

Computer Vision · Vision Models & Multimodal

Sijing Li, Zhongwei Qiu, Jiang Liu, Wenqiao Zhang, Tianwei Lin, Yihan Xie, Jianxiang An, Boxiang Yun, Chenglin Yang, Jun Xiao 等

Accurate tumor analysis is central to clinical radiology and precision oncology, where early detection, reliable lesion characterization, and pathology-level risk assessment directly guide diagnosis, staging, and treatment planning. Chain-of-Thought (CoT) reasoning is particularly critical in this setting, as it enables stepwise interpretation from imaging findings to clinical impressions and pathology-level conclusions, ensuring traceability and reducing diagnostic errors. Here, we target the clinical tumor analysis task and build a large-scale benchmark that operationalizes a multimodal reasoning pipeline, spanning findings, impressions, and pathology predictions. We curate TumorCoT, a large-scale dataset of 1.5M CoT-labeled VQA instructions paired with 3D CT scans, with step-aligned rationales and cross-modal alignments along the “findings → impression → pathology” trajectory, enabling standardized evaluation of both final accuracy and reasoning consistency. We further propose TumorChain, a multimodal interleaved reasoning framework that tightly couples 3D imaging encoders, clinical text understanding, and organ-level vision-language alignment. Through cross-modal alignment and iterative interleaved causal reasoning, TumorChain grounds visual evidence, aggregates conclusions, and issues pathology predictions after multiple rounds of self-refinement, improving traceability and reducing hallucination risk. TumorChain demonstrates consistent gains over strong unimodal and pipeline baselines in lesion detection, impression quality, and pathology classification, and successfully generalizes to the public DeepTumorVQA benchmark. Ablations validate the key contributions of interleaved reasoning and clinical CoT. Clinically, these advances lay the groundwork for reliable, interpretable tumor assessment to support real-world decision-making. To advance safe, explainable, and reproducible multimodal reasoning for high-stakes tumor analysis, detailed information about our project can be found on our project homepage at https://github.com/ZJU4HealthCare/TumorChain.

Reinforcement Learning · Planning

Wenjie Chen, Di Yao, Wenbin Li, Xuying Meng, Chang Gong, Jingping Bi

Tool planning with large language models (LLMs), referring to selecting, organizing, and preparing the tools necessary to complete a user request, bridges the gap between natural language understanding and task execution. However, current works treat different tools as isolated components and fail to leverage the inherent dependencies of tools, leading to invalid planning results. Since tool dependencies are often incomplete, it becomes challenging for LLMs to accurately identify the appropriate tools required by a user request, especially when confronted with a large toolset. To solve this challenge, we propose GTool, which is the first work aiming to enhance the tool planning ability of LLMs under incomplete dependencies. GTool constructs a request-specific tool graph to select tools efficiently and generate the \ which provides sufficient dependency information understandable by LLMs. Moreover, a missing dependency prediction task is designed to improve the reliability of GTool with incomplete dependencies. Without trimming LLMs, GTool can be seamlessly integrated with various LLM backbones without extensive retraining. Extensive experiments show that GTool achieves more than 29.6% performance improvements compared with the state-of-the-art (SOTA) baselines with a light-weight (7B) LLM backbone.

Yang Hu, Jieren Tan, Changliang Zou, Yajie Bao, Haojie Ren

Robust decision-making is crucial in numerous risk-sensitive applications where outcomes are uncertain and the cost of failure is high. Conditional Robust Optimization (CRO) offers a framework for such tasks by constructing prediction sets for the outcome that satisfy predefined coverage requirements and then making decisions based on these sets. Many existing approaches leverage conformal prediction to build prediction sets with guaranteed coverage for CRO. However, since coverage is a *sufficient but not necessary* condition for robustness, enforcing such constraints often leads to overly conservative decisions. To overcome this limitation, we propose a novel framework named Conformal Robustness Control (CRC), that directly optimizes the prediction set construction under explicit robustness constraints, thereby enabling more efficient decisions without compromising robustness. We develop efficient algorithms to solve the CRC optimization problem, and also provide theoretical guarantees on both robustness and optimality. Empirical results show that CRC consistently yields more effective decisions than existing baselines while still meeting the target robustness level.

Aditya Gopalan, Sayak Ray Chowdhury, Debangshu Banerjee

Direct alignment algorithms such as Direct Preference Optimization (DPO) fine-tune models based on preference data, using only supervised learning instead of two-stage reinforcement learning with human feedback (RLHF). We show that DPO encodes a statistical estimation problem over reward functions induced by a parametric policy class. When the true reward function that generates preferences cannot be realized via the policy class, DPO becomes misspecified, resulting in failure modes such as preference order reversal, worsening of policy reward, and high sensitivity to the input preference data distribution. On the other hand, we study the local behavior of two-stage RLHF for a parametric class and relate it to a natural gradient step in policy space. Our fine-grained geometric characterization allows us to propose AuxDPO, which introduces additional auxiliary variables in the DPO loss function to help move towards the RLHF solution in a principled manner and mitigate the misspecification in DPO. We empirically demonstrate the superior performance of AuxDPO on didactic bandit settings as well as LLM alignment tasks.

Seyed Mohammad Eshtehardian, Mohammad Hossein Yassaee, Babak HosseinKhalaj

Kolmogorov-Arnold Networks (KANs) have emerged as a promising alternative to traditional neural networks, offering enhanced interpretability based on the Kolmogorov-Arnold representation theorem. While their empirical success is growing, a theoretical understanding of their training dynamics remains nascent. This paper investigates the optimization of a two-layer KAN in the overparameterized regime, focusing on a simplified yet insightful setting where only the first-layer coefficients are trained via gradient descent. Our main result establishes that, provided the network is sufficiently wide, this training method is guaranteed to converge to a global minimum and achieve zero training error. Furthermore, we derive a novel, fine-grained convergence rate that explicitly connects the optimization speed to the structure of the data labels through the eigenspectrum of the KAN Tangent Kernel (KAN-TK). Our analysis reveals a key advantage of this architecture: guaranteed convergence is achieved with a hidden layer width of $m=\mathcal{O}(n^2)$, a significant polynomial improvement over the $m=\mathcal{O}(n^6)$ requirement for classic two-layer neural networks using ReLU activation functions and analyzed within the same Tangent Kernel framework. We validate our theoretical findings with numerical experiments that corroborate our predictions on convergence speed and the impact of label structure.

Shuohao Zhang, Zhilu Zhang, RongJian Xu, Xiaohe Wu, Wangmeng Zuo

High dynamic range (HDR) video can be reconstructed from low dynamic range (LDR) sequences with alternating exposures. However, most existing methods overlook the degradations (e.g., noise and blur) in LDR frames, focusing only on the brightness and position differences between them. To address this gap, we propose DeAltHDR, a novel framework for high-quality HDR video reconstruction from degraded sequences. Our framework addresses two key challenges. First, noisy and blurry content complicate inter-frame alignment. To tackle this, we propose a flow-guided masked attention mechanism that leverages optical flow for a dynamic sparse cross-attention computation, achieving superior performance while maintaining efficiency. Notably, its controllable attention ratio allows for adaptive inference costs. Second, the lack of real-world paired data hinders practical deployment. We overcome this with a two-stage training paradigm: the model is first pre-trained on our newly introduced synthetic paired dataset and subsequently fine-tuned on unlabeled real-world videos via a proposed self-supervised method. Experiments show our method outperforms state-of-the-art ones. Code and data will be available at https://zhang-shuohao.github.io/DeAltHDR/.

Applications · Language, Speech and Dialog

Wei Huang, Anda Cheng, Yinggui Wang

Fine-tuning Large Language Models (LLMs) with downstream data is often considered time-consuming and expensive. Structured pruning methods are primarily employed to improve the inference efficiency of pre-trained models. Meanwhile, they often require additional time and memory for training, knowledge distillation, structure search, and other strategies, making efficient model fine-tuning challenging to achieve. To simultaneously enhance the training and inference efficiency of downstream task fine-tuning, we introduce GradPruner, which can prune layers of LLMs guided by gradients in the early stages of fine-tuning. GradPruner uses the cumulative gradients of each parameter during the initial phase of fine-tuning to compute the Initial Gradient Information Accumulation Matrix (IGIA-Matrix) to assess the importance of layers and perform pruning. We sparsify the pruned layers based on the IGIA-Matrix and merge them with the remaining layers. Only elements with the same sign are merged to reduce interference from sign variations. We conducted extensive experiments on two LLMs across eight well-known datasets in downstream tasks. Including medical, financial, and general benchmark tasks. The results demonstrate that GradPruner has achieved a parameter reduction of 40% with only a 0.99% decrease in accuracy. Our code is available at https://anonymous.4open.science/r/LLM-GradPrune-436D.

Tongfan Guan, Jiaxin Guo, Tianyu Huang, Jinhu Dong, Chen Wang, Yun-Hui Liu

Deep stereo disparity estimation has long been dominated by a \textbf{matching-centric paradigm}, built on constructing cost volumes and iteratively refining local correspondences. Despite its success, this paradigm exhibits an intrinsic vulnerability: visual ambiguities from occlusion or non-Lambertian surfaces invevitably induce errorneous matches that refinement cannot recover. This paper introduces \textbf{DispViT}, a new architecture that establishes a \textbf{regression-centric paradigm}. Instead of explicit matching, DispViT directly regresses disparity from tokenized binocular representations using a single-stream Vision Transformer. This is enabled by a set of lightweight yet critical designs, such as a probability-based disparity parameterization for stable training and an asymmetrically initialized stereo tokenizer for effective view distinction. To better align the two views during stereo tokenization, we introduce a novel shift-embedding mechanism that encodes different disparity shifts into channel groups, preserving geometric cues even under large view displacements. A lightweight refinement module then sharpens the regressed disparity map for fine-grained accuracy. By prioritizing holistic regression over explicit matching, DispViT streamlines the stereo pipeline while improving robustness and efficiency. Experiments on standard benchmarks show that our approach achieves state-of-the-art accuracy, with strong resilience to matching ambiguities and wide disparity ranges. Code will be released.

Deep Learning · Graph Neural Networks

Hugh Blayney, Alvaro Arroyo, Xiaowen Dong, Michael Bronstein

Graph Neural Networks (GNNs) leverage the graph structure to transmit information between nodes, typically through the message-passing mechanism. While these models have found a wide variety of applications, they are known to suffer from over-squashing, where information from a large receptive field of node representations is collapsed into a single fixed sized vector, resulting in an information bottleneck. In this paper, we re-examine the over-squashing phenomenon through the lens of model storage and retrieval capacity, which we define as the amount of information that can be stored in a node’s representation for later use. We study some of the limitations of existing tasks used to measure over-squashing and introduce a new synthetic task to demonstrate that an information bottleneck can saturate this capacity. Furthermore, we adapt ideas from the sequence modeling literature on associative memories, fast weight programmers, and the xLSTM model to develop a novel GNN architecture with improved capacity. We demonstrate strong performance of this architecture both on our capacity synthetic task, as well as a range of real-world graph benchmarks.

Applications · Robotics

Kangye Ji, Yuan Meng, Hanyun Cui, Ye Li, Jianbo Zhou, Shengjia Hua, Lei Chen, Zhi Wang

Diffusion Policy has demonstrated strong visuomotor modeling capabilities, but its high computational cost renders it impractical for real-time robotic control. Despite huge redundancy across repetitive denoising steps, existing diffusion acceleration techniques fail to generalize to Diffusion Policy due to fundamental architectural and data divergences. In this paper, we propose **B**lock-wise **A**daptive **C**aching (**BAC**), a method to accelerate Diffusion Policy by caching intermediate action features. BAC achieves lossless action generation acceleration by adaptively updating and reusing cached features at the block level, based on a key observation that feature similarities exhibit non-uniform temporal dynamics and distinct block-specific patterns. To operationalize this insight, we first design an Adaptive Caching Scheduler to identify optimal update timesteps by maximizing the global feature similarities between cached and skipped features. However, applying this scheduler for each block leads to significant error surges due to the inter-block propagation of caching errors, particularly within Feed-Forward Network (FFN) blocks. To mitigate this issue, we develop the Bubbling Union Algorithm, which truncates these errors by updating the upstream blocks with significant caching errors before downstream FFNs. As a training-free plugin, BAC is readily integrable with existing transformer-based Diffusion Policy and vision-language-action models. Extensive experiments on multiple robotic benchmarks demonstrate that BAC achieves up to 3x inference speedup for free. Project page: https://block-wise-adaptive-caching.github.io.

Optimization · Sampling and Optimization

Nishant Jain, Tong Zhang

Diffusion-based generative models have emerged as highly effective methods for synthesizing high-quality samples. Recent works have focused on analyzing the convergence of their generation process with minimal assumptions, either through reverse SDEs or probability flow ODEs. The best known guarantees, without any smoothness assumptions, for the KL divergence so far achieve a linear dependence on the data dimension $d$ and an inverse quadratic dependence on accuracy level $\varepsilon$. In this work, we present a refined analysis for the standard Exponential Integrator discretization that improves the dependence on $\varepsilon$, at the same time maintaining the linear dependence on $d$. Following recent works on higher order/randomized midpoint discretizations, we model the generation process as a composition of two steps: a reverse ODE step followed by a smaller noising step, which leads to better dependence on step size. We then provide a novel analysis which achieves linear dependence on $d$ for the ODE discretization error without any smoothness assumptions. Specifically, we introduce a general ODE-based counterpart of the stochastic localization argument from Benton et al and develop new proof techniques to bound second-order spatial derivatives of the score function -- terms that do not arise in previous diffusion analyses and cannot be handled by existing techniques. Leveraging this framework, we prove that $\tilde{O}\left(\tfrac{d \log^{3/2}(1/\delta)}{\varepsilon}\right)$ steps suffice to approximate the target distribution—corrupted by Gaussian noise of variance $\delta$—to within $O(\varepsilon^2)$ in KL divergence, improving upon the previous best result requiring $\tilde{O}\left(\tfrac{d \log^2(1/\delta)}{\varepsilon^2}\right)$ steps.