论文检索

Computer Vision · Vision Models & Multimodal

Danial Kamali, Parisa Kordjamshidi

Modern Vision-Language Models (VLMs) have achieved impressive performance in various tasks, yet they often struggle with compositional reasoning, the ability to decompose and recombine concepts to solve novel problems. While neuro-symbolic approaches offer a promising direction, they are typically constrained by crisp logical execution or predefined predicates, which limit flexibility. In this work, we introduce NePTune, a neuro-symbolic framework that overcomes these limitations through a hybrid execution model that integrates the perception capabilities of foundation vision models with the compositional expressiveness of symbolic reasoning. NePTune dynamically translates natural language queries into executable Python programs that blend imperative control flow with soft logic operators capable of reasoning over VLM-generated uncertainty. Operating in a training-free manner, NePTune, with a modular design, decouples perception from reasoning, yet its differentiable composition operations support fine-tuning. We evaluate NePTune on multiple visual reasoning benchmarks and various domains, utilizing adversarial tests, and demonstrate a significant improvement over base models, as well as its effective compositional generalization and adaptation capabilities in novel environments.

Elvis Dohmatob, Mohammad Pezeshki, Reyhane Askari Hemmat

This paper introduces a theoretical framework to resolve a central paradox in modern machine learning: When is it better to use less data? This question has become critical as classical scaling laws suggesting ``more is more'' (Sun et al., 2025) are challenged by methods like LIMO (``less is more'') and s1 (Ye et al., 2025; Muenighoff et al., 2025), which achieve superior performance with small, aggressively curated datasets. Here, we study data curation strategies where an imperfect oracle selects the training examples according to their difficulty and correctness. Our results provide exact scaling law curves for test error under both label-agnostic and label-aware curation rules, revealing when and why keeping only a subset of data can improve generalization. In contrast to classical scaling laws, we show that under certain conditions, small curated datasets can outperform full datasets, and we provide analytical conditions for this by deriving precise phase transition curves tied to data size and quality. We validate these theoretical claims with empirical results on ImageNet, confirming our predictions about when curation improves accuracy and can even mitigate model collapse. Furthermore, our framework provides a principled explanation for the contradictory curation strategies recently observed in LLM mathematical reasoning.

Yichao Fu, Xuewei Wang, Hao Zhang, Yuandong Tian, Jiawei Zhao

Large Language Models (LLMs) have shown great potential in reasoning tasks through test-time scaling methods like self-consistency with majority voting. However, this approach often leads to diminishing returns in accuracy and high computational overhead. To address these challenges, we introduce \textbf{Deep Think with Confidence (DeepConf)}, a simple yet powerful method that enhances both reasoning efficiency and performance at test time. DeepConf leverages model-internal confidence signals to dynamically filter out low-quality reasoning traces during or after generation. It requires no additional model training or hyperparameter tuning and can be seamlessly integrated into existing serving frameworks. We evaluate DeepConf across a variety of tasks and the latest open-source models, including Qwen3 and GPT-OSS series. Notably, on challenging benchmarks such as AIME 2025, DeepConf@512 achieves up to 99.9\% accuracy and reduces generated tokens by up to 84.7\% compared to full parallel thinking. Our code is available at https://github.com/facebookresearch/deepconf

Applications · Health

Yahan Li, Jifan Yao, John Bunyi, Adam Frank, Angel Hwang, Ruishan Liu

Medical question answering (QA) benchmarks often focus on multiple-choice or fact-based tasks, leaving open-ended answers to real patient questions underexplored. This gap is particularly critical in mental health, where patient questions often mix symptoms, treatment concerns, and emotional needs, requiring answers that balance clinical caution with contextual sensitivity. We present CounselBench, a large-scale benchmark developed with 100 mental health professionals to evaluate and stress-test large language models (LLMs) in realistic help-seeking scenarios. The first component, CounselBench-EVAL, contains 2,000 expert evaluations of answers from GPT-4, LLaMA 3, Gemini, and online human therapists on patient questions from the public forum CounselChat. Each answer is rated across six clinically grounded dimensions, with span-level annotations and written rationales. Expert evaluations show that while LLMs achieve high scores on several dimensions, they also exhibit recurring issues, including unconstructive feedback, overgeneralization, and limited personalization or relevance. Responses were frequently flagged for safety risks, most notably unauthorized medical advice. Follow-up experiments show that LLM judges systematically overrate model responses and overlook safety concerns identified by human experts. To probe failure modes more directly, we construct CounselBench-Adv, an adversarial dataset of 120 expert-authored mental health questions designed to trigger specific model issues. Expert evaluation of 1,080 responses from nine LLMs reveals consistent, model-specific failure patterns. Together, CounselBench establishes a clinically grounded framework for benchmarking LLMs in mental health QA.

Junming Yang, Ning Xu, Biao Liu, Shiqi Qiao, Xin Geng

Preference optimization is crucial for aligning large language models (LLMs) with human values and intentions. A significant challenge in this process is the distribution mismatch between pre-collected offline preference data and the evolving model policy. Existing methods attempt to reduce this gap using static heuristics or decoupled online sampling strategies, but they often fail to adapt to the model's dynamic learning state. To bridge this gap, we propose Meta-Weighted Adaptive Preference Optimization (MetaAPO), a novel framework that dynamically couples data generation with model training. MetaAPO employs a lightweight meta-learner, as an "alignment gap estimator", to evaluate the potential benefits of on-policy sampling in relation to offline data. This guides targeted online generation and assigns sample-wise meta-weights to the optimization objective, dynamically balancing the quality and distribution of online and offline data. Experiments on AlpacaEval 2, Arena-Hard and MT-Bench demonstrate that MetaAPO consistently outperforms existing preference optimization approaches across various settings, while reducing 42% in online annotation costs.

Deep Learning · Algorithms

Xiaodong Chen, Mingming Ha, Zhenzhong Lan, Jing Zhang, Jianguo Li

The Mixture-of-Experts (MoE) architecture has become a predominant paradigm for scaling large language models (LLMs). Despite offering strong performance and computational efficiency, large MoE-based LLMs like DeepSeek-V3-0324 and Kimi-K2-Instruct present serious challenges due to substantial memory requirements in deployment. While recent works have explored MoE compression to address this issue, existing methods often suffer from considerable accuracy drops (e.g., 7-14% relatively) even at modest compression rates. This paper introduces a novel Mixture-of-Basis-Experts (MoBE) method that achieves model compression while incurring minimal accuracy drops. Specifically, each up/gate matrix in an expert is decomposed via a rank decomposition as W = AB, where matrix A is unique to each expert. The relatively larger matrix B is further reparameterized as a linear combination of basis matrices {Bi} shared across all experts within a given MoE layer. The factorization is learned by minimizing the reconstruction error relative to the original weight matrices. Experiments demonstrate that MoBE achieves notably lower accuracy drops compared to prior works. For instance, MoBE can reduce the parameter counts of Qwen3-235BA22B-2507, DeepSeek-V3-0324 (671B) and Kimi-K2-Instruct (1T) by 24%-30% with only 1%-2% accuracy drop (about 2% drops when measured relatively).

Qian Li, Yuxiao Hu, Juncheng Liu, Yuntian Chen

Symbolic Regression (SR) tries to reveal the hidden equations behind observed data. However, most methods search within a discrete equation space, where the structural modifications of equations rarely align with their numerical behavior, leaving fitting error feedback too noisy to guide exploration. To address this challenge, we propose GenSR, a generative latent space–based SR framework following the "map construction $\rightarrow$ coarse localization $\rightarrow$ fine search" paradigm. Specifically, GenSR first pretrains a dual-branch Conditional Variational Autoencoder (CVAE) to reparameterize symbolic equations into a generative latent space with symbolic continuity and local numerical smoothness. This space can be regarded as a well-structured "map" of the equation space, providing directional signals for search. At inference, the CVAE coarsely localizes the input data to promising regions in the latent space. Then, a modified CMA-ES refines the candidate region, leveraging smooth latent gradients. From a Bayesian perspective, GenSR reframes SR task as maximizing the conditional distribution $p({\rm Equ.}|{\rm Num.})$, with CVAE training achieving this objective through the Evidence Lower Bound (ELBO). This new perspective provides a theoretical guarantee for the effectiveness of GenSR. Extensive experiments show that GenSR jointly optimizes predictive accuracy, expression simplicity, and computational efficiency, while remaining robust under noise.

Applications · Neuroscience, Cognitive Science

William Qian, Cengiz Pehlevan

Training recurrent neural networks (RNNs) to perform neuroscience-style tasks has become a popular way to generate hypotheses for how neural circuits in the brain might perform computations. Recent work has demonstrated that task-trained RNNs possess a strong simplicity bias. In particular, this inductive bias often causes RNNs trained on the same task to collapse on effectively the same solution, typically comprised of fixed-point attractors or other low-dimensional dynamical motifs. While such solutions are readily interpretable, this collapse proves counterproductive for the sake of generating a set of genuinely unique hypotheses for how neural computations might be performed. Here we propose Iterative Neural Similarity Deflation (INSD), a simple method to break this inductive bias. By penalizing linear predictivity of neural activity produced by standard task-trained RNNs, we find an alternative class of solutions to classic neuroscience-style RNN tasks. These solutions appear distinct across a battery of analysis techniques, including representational similarity metrics, dynamical systems analysis, and the linear decodability of task-relevant variables. Moreover, these alternative solutions can sometimes achieve superior performance in difficult or out-of-distribution task regimes. Our findings underscore the importance of moving beyond the simplicity bias to uncover richer and more varied models of neural computation.

Computer Vision · 3D Rendering & Reconstruction

Junhwa Hur, Charles Herrmann, Songyou Peng, Philipp Henzler, Zeyu Ma, Todd Zickler, Deqing Sun

Dense 4D reconstruction from unposed images remains a critical challenge, with current methods relying on slow test-time optimization or fragmented, task-specific feedforward models. We introduce UFO-4D, a unified feedforward framework to reconstruct a dense, explicit 4D representation from just a pair of unposed images. UFO-4D directly estimates dynamic 3D Gaussian Splats, enabling the joint and consistent estimation of 3D geometry, 3D motion, and camera pose in a feedforward manner. Our core insight is that differentiably rendering multiple signals from a single Dynamic 3D Gaussian representation offers major training advantages. This approach enables a self-supervised image synthesis loss while tightly coupling appearance, depth, and motion. Since all modalities share the same geometric primitives, supervising one inherently regularizes and improves the others. This synergy overcomes data scarcity, allowing UFO-4D to outperform prior work by up to 3 times in joint geometry, motion, and camera pose estimation. Our representation also enables high-fidelity 4D interpolation across novel views and time. Please visit our project page for visual results: https://ufo-4d.github.io/

Applications · Language, Speech and Dialog

Tianshu Zhang, Huan Sun

Autonomous science agents, built on large language models (LLMs), are increasingly being investigated to generate hypotheses, design experiments, and produce reports. Prior science agents primarily focus on open-ended scientific problems, where such outputs—hypotheses, experiments, or analyses are inherently subjective and thus difficult to evaluate rigorously. In contrast, existing scientific coding benchmarks provide tasks with clearly defined, executable outputs that enable objective assessment. However, current agent-based approaches to these benchmarks remain engineering-driven pipelines, lacking principled framework design. This mismatch exposes a gap: the absence of end-to-end, principled science agent frameworks for scientific coding tasks. We address this gap by focusing on scientific coding tasks, where evaluation can be made rigorously, and introducing an agent framework SciNav (Scientific Navigator) that enables more effective solution exploration. Our framework is designed to operate efficiently under constrained search budgets, moving beyond reliance on pre-defined success metrics and prolonged search cycles. Inspired by findings that comparative judgments often reveal finer-grained quality differences and therefore provide greater discriminative power than absolute scoring, our framework leverages pairwise relative judgments within a tree search process to select top-K promising solution branches, prune low-potential ones, and progressively narrow down the solution candidates on the selected branches guided by relative comparisons. We demonstrate our agent's effectiveness across different types of tasks on two benchmarks. Experiments show that SciNav significantly outperforms direct prompting and prior agents like OpenHands and Self-Debug across different base models, task types, and difficulty levels, and exceeds different frontier comparators such as random selection and LLM absolute scoring. These results confirm the strength of our agent design and highlight the effectiveness of relative judgment–guided top-K search for high-quality scientific coding, marking a step toward more practical science agents.

Yonghan Jung

In observational settings where treatment and outcome are confounded by unobserved factors but an observed mediator satisfies front-door conditions, estimating heterogeneous treatment effects remains underdeveloped. We introduce two debiased learners for heterogeneous front-door effects: FD-DR-Learner and FD-R-Learner. Both methods are constructed to be robust to nuisance estimation error, and we show they achieve fast quasi-oracle rates even when nuisance functions converge as slowly as $n^{-1/4}$. We provide error analyses that clarify their behavior under overlap and nuisance misspecification. In synthetic experiments varying sample size, nuisance noise, and overlap severity, both learners consistently outperform a plug-in baseline, with FD-R showing stronger stability under weak overlap. In a real-world case study using FARS data on primary seat-belt laws, the methods deliver reliable personalized effect estimates and interpretable heterogeneity patterns. Overall, the proposed learners offer practical and sample-efficient tools for heterogeneous causal estimation under front-door identification.

General Machine Learning · Transfer, Multitask and Meta-learning

Hongwei Yan, Guanglong Sun, Kanglei Zhou, Qian Li, Liyuan Wang, Yi Zhong

General continual learning (GCL) challenges intelligent systems to learn from single-pass, non-stationary data streams without clear task boundaries. While recent advances in continual parameter-efficient tuning (PET) of pretrained models show promise, they typically rely on multiple training epochs and explicit task cues, limiting their effectiveness in GCL scenarios. Moreover, existing methods often lack targeted design and fail to address two fundamental challenges in continual PET: how to allocate expert parameters to evolving data distributions, and how to improve their representational capacity under limited supervision. Inspired by the fruit fly's hierarchical memory system characterized by sparse expansion and modular ensembles, we propose FlyPrompt, a brain-inspired framework that decomposes GCL into two subproblems: expert routing and expert competence improvement. FlyPrompt introduces a randomly expanded analytic router for instance-level expert activation and a temporal ensemble of output heads to dynamically adapt decision boundaries over time. Extensive theoretical and empirical evaluations demonstrate FlyPrompt's superior performance, achieving up to 11.23%, 12.43%, and 7.62% gains over state-of-the-art baselines on CIFAR-100, ImageNet-R, and CUB-200, respectively. Our source code is available at https://github.com/AnAppleCore/FlyGCL.

Deep Learning · Generative Models and Autoencoders

Tao Zhang, Jia-Shu Pan, Ruiqi Feng, Tailin Wu

Inspired by human SYSTEM 2 thinking, LLMs excel at complex reasoning tasks via extended Chain-of-Thought. However, similar test-time scaling for diffusion models to tackle complex reasoning remains largely unexplored. From existing work, two primary challenges emerge in this setting: (i) the dependence on an external verifier indicating a notable gap from intrinsic reasoning of human intelligence without any external feedback, and (ii) the lack of an efficient search algorithm. In this paper, we introduce the Verifier-free Test-time Scalable Diffusion Model (VFScale) to achieve scalable intrinsic reasoning, which equips number-of-sample test-time scaling with the intrinsic energy function of diffusion models as the verifier. Concretely, VFScale comprises two key innovations to address the aforementioned challenges. On the training side, VFScale consists of a novel MRNCL loss and a KL regularization to improve the energy landscape, ensuring that the learned energy function itself serves as a reliable verifier. On the inference side, VFScale integrates the denoising process with a novel hybrid Monte Carlo Tree Search (hMCTS) to improve search efficiency. On challenging reasoning tasks of Maze and Sudoku, we demonstrate the effectiveness of VFScale's training objective and scalable inference method. In particular, trained with Maze sizes of up to 6×6, our VFScale solves 88\% of Maze problems with much larger sizes of 15×15, while standard diffusion model completely fails. The code can be found at https://github.com/AI4Science-WestlakeU/VFScale.

General Machine Learning · Transfer, Multitask and Meta-learning

Yidi Wang, Ziyue Qiao, Jiawei Gu, Xubin Zheng, Pengyang Wang, pei Xiaobing, Xiao Luo

This paper studies a novel problem of out-of-distribution graph models merging, which aims to construct a generalized model from multiple graph models pre-trained on different domains with distribution discrepancy. This problem is challenging because of the difficulty in learning domain-invariant knowledge implicitly in model parameters and consolidating expertise from potentially heterogeneous GNN backbones. In this work, we propose a graph generation strategy that instantiates the mixture distribution of multiple domains. Then, we merge and fine-tune the pre-trained graph models via a MoE module and a masking mechanism for generalized adaptation. Our framework is architecture-agnostic and can operate without any source/target domain data. Both theoretical analysis and experimental results demonstrate the effectiveness of our approach in addressing the model generalization problem.

Applications · Language, Speech and Dialog

Chengsong Huang, Wenhao Yu, Xiaoyang Wang, Hongming Zhang, Zongxia Li, Ruosen Li, Jiaxin Huang, Haitao Mi, Dong Yu

Self-evolving Large Language Models (LLMs) offer a scalable path toward super-intelligence by autonomously generating, refining, and learning from their own experiences. However, existing methods for training such models still rely heavily on vast human-curated tasks and labels, typically via fine-tuning or reinforcement learning, which poses a fundamental bottleneck to advancing AI systems toward capabilities beyond human intelligence. To overcome this limitation, we introduce R-Zero, a fully autonomous framework that generates its own training data from scratch. Starting from a single base LLM, R-Zero initializes two independent models with distinct roles, a Challenger and a Solver. These models are optimized separately and co-evolve through interaction: the Challenger is rewarded for proposing tasks near the edge of the Solver capability, and the Solver is rewarded for solving increasingly challenging tasks posed by the Challenger. This process yields a targeted, self-improving curriculum without any pre-existing tasks and labels. Empirically, R-Zero substantially improves reasoning capability across different backbone LLMs, e.g., boosting the Qwen3-4B-Base by +6.49 on math-reasoning benchmarks and +7.54 on general-domain reasoning benchmarks.

Theory · Probabilistic Methods

Wei Guo, Molei Tao, Yongxin Chen

Given an unnormalized probability density $\pi\propto\mathrm{e}^{-V}$, estimating its normalizing constant $Z=\int_{\mathbb{R}^d}\mathrm{e}^{-V(x)}\mathrm{d}x$ or free energy $F=-\log Z$ is a crucial problem in Bayesian statistics, statistical mechanics, and machine learning. It is challenging especially in high dimensions or when $\pi$ is multimodal. To mitigate the high variance of conventional importance sampling estimators, annealing-based methods such as Jarzynski equality and annealed importance sampling are commonly adopted, yet their quantitative complexity guarantees remain largely unexplored. We take a first step toward a non-asymptotic analysis of annealed importance sampling. In particular, we derive an oracle complexity of $\widetilde{O}\left(\frac{d\beta^2{\mathcal{A}}^2}{\varepsilon^4}\right)$ for estimating $Z$ within $\varepsilon$ relative error with high probability, where $\beta$ is the smoothness of $V$ and $\mathcal{A}$ denotes the action of a curve of probability measures interpolating $\pi$ and a tractable reference distribution. Our analysis, leveraging Girsanov's theorem and optimal transport, does not explicitly require isoperimetric assumptions on the target distribution. Finally, to tackle the large action of the widely used geometric interpolation, we propose a new algorithm based on reverse diffusion samplers, establish a framework for analyzing its complexity, and empirically demonstrate its efficiency in tackling multimodality.

Deep Learning · Theory

Jie Hui, Zhenxiang Zhang, Wenyu Mi, Jianji Wang

Despite the importance of global contextual modeling in visual tasks, a rigorous mathematical definition remains absent, and the concept is still largely described in heuristic or empirical terms. Existing methods either rely on computationally expensive attention mechanisms or are constrained by the recursive modeling nature of State Space Models (SSMs), making it challenging to achieve both efficiency and true global perception. To address this, we first propose a mathematical definition of global modeling for visual images, providing a theoretical foundation for designing globally-aware and interpretable models. Based on in-depth analysis of SSMs and frequency-domain modeling principles, we construct a complete theoretical framework that overcomes the limitations imposed by SSMs' recursive modeling mechanism from a frequency perspective, thereby adapting SSMs for global perception in image modeling. Guided by this framework, we design the Global-aware SSM (GSSM) module and formally prove that it satisfies definitional requirements of global image modeling. GSSM leverages a Discrete Fourier Transform (DFT)-based modulation mechanism, providing precise front-end control over the SSM's modeling behavior, and enabling efficient global image modeling with linear-logarithmic complexity. Building upon GSSM, we develop GMamba, a plug-and-play module that can be seamlessly integrated at any stage of Convolutional Neural Networks (CNNs). Extensive experiments across multiple tasks, including object detection, semantic segmentation, and instance segmentation, across diverse model architectures, demonstrate that GMamba consistently outperforms existing global modeling modules, validating both the effectiveness of our theoretical framework and the rigor of proposed definition. Code is available at \url{https://github.com/Xinmu-Tantai/GMamba-GSSM}

Social Aspects · Accountability, Transparency and Interpretability

Zhengfu He, Junxuan Wang, Rui Lin, Xuyang Ge, Wentao Shu, Qiong Tang, Junping Zhang, Xipeng Qiu

We propose Low-Rank Sparse Attention (Lorsa), a sparse replacement model of Transformer attention layers to disentangle original Multi Head Self Attention (MHSA) into individually comprehensible components. Lorsa is designed to address the challenge of \textit{attention superposition} to understand attention-mediated interaction between features in different token positions. Lorsa helps find cleaner and finer-grained versions of previously discovered MHSA behaviors like induction heads, successor heads, attention sink, and a comprehensive family of arithmetic-specific Lorsa heads. Interestingly, we identify a novel head type called \emph{subtoken induction heads} that function at character level rather than token level. Automated interpretability analysis indicates that Lorsa achieves parity with SAE in interpretability while Lorsa exhibits superior circuit discovery properties. We also conduct extensive experiments on architectural design ablation, correlation to original MHSA heads and error analysis. Our early attempt to fully sparsify a toy Transformer succeeds to reveal clean global circuits. Eventually, we hope Lorsa would help us greatly understand attention computation and enable full sparsification of model computation along with its MLP counterparts. Lorsa is open-sourced at https://anonymous.4open.science/r/Lorsa-5686/.

Deep Learning · Everything Else

Hong Huang, 吴 德成, Rui Cen, Guanghua Yu, Zonghang Li, Kai Liu, Jianchen Zhu, Peng Chen, Xue Liu, Dapeng Wu

Quantization techniques are essential for the deployment of Large Language Models (LLMs) on edge devices. However, prevailing methods often rely on mixed-precision multiplication that lacks efficient hardware support, making it not feasible. Ternary weight quantization addresses this by constraining weights to {-1, 0, 1}, replacing expensive multiplications with hardware-efficient additions. However, such aggressive compression leads to significant accuracy degradation, even after costly quantization-aware training with massive data. We identify the core issue as _**deadzone trapping**: a large number of weights are trapped at the deadzone boundary._ This occurs because these weights receive only noisy, less informative gradients, preventing stable escape from the deadzone and severely impeding model capacity and optimization. To address this issue, we propose **Tequila**, a trapping-free quantization optimization method that reactivates deadzone-trapped weights by repurposing them as dynamic biases. This allows the repurposed weights to provide a continuous signal in the forward pass and, critically, receive direct, meaningful gradient signals during backpropagation, thereby enhancing model capacity and optimization with nearly _zero_ inference overhead. Extensive evaluations demonstrate that Tequila outperforms state-of-the-art (SOTA) ternary quantization methods across five benchmarks. Specifically, on the ARC benchmark, it achieves $>4$% accuracy gain over the SOTA baseline, nearly matching full-precision performance (within $<1$% gap) with an $3.0\times$ inference speedup. Consequently, Tequila offers a highly practical and efficient implementation for the deployment of advanced LLMs in resource-constrained environments. The code is available at https://github.com/Tencent/AngelSlim/tree/tequila/TernaryQuant .

General Machine Learning · Representation Learning

Jim Zhao, Tin Sum Cheng, Wojciech Masarczyk, Aurelien Lucchi

Neural Collapse (NC) refers to the emergence of highly symmetric geometric structures in the representations of deep neural networks during the terminal phase of training. Despite its prevalence, the theoretical understanding of NC remains limited. Existing analyses largely ignore the role of the optimizer, thereby suggesting that NC is universal across optimization methods. In this work, we challenge this assumption and demonstrate that the choice of optimizer plays a critical role in the emergence of NC. The phenomenon is typically quantified through NC metrics, which, however, are difficult to track and analyze theoretically. To overcome this limitation, we introduce a novel diagnostic metric, NC0, whose convergence to zero is a necessary condition for NC. Using NC0, we provide theoretical evidence that NC cannot emerge under decoupled weight decay in adaptive optimizers, as implemented in AdamW. Concretely, we prove that SGD, SignGD with coupled weight decay (a special case of Adam), and SignGD with decoupled weight decay (a special case of AdamW) exhibit qualitatively different NC0 dynamics. Also, we show the accelerating effect of momentum on NC (beyond convergence of train loss) when trained with SGD, being the first result concerning momentum in the context of NC. Finally, we conduct extensive empirical experiments consisting of 3,900 training runs across various datasets, architectures, optimizers, and hyperparameters, confirming our theoretical results. This work provides the first theoretical explanation for optimizer-dependent emergence of NC and highlights the overlooked role of weight decay coupling in implicit biases of optimizers.