ICML 2026 论文列表

International Conference on Machine Learning

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6,341篇论文

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主题: 对齐与安全 · 551 篇论文 · 重置筛选

EVMbench: Evaluating AI Agents on Smart Contract Security

Justin Wang, Andreas Bigger, Xiaohai Xu, Justin W Lin, Andy Applebaum, Tejal Patwardhan, Alpin Yukseloglu, Olivia Watkins

展开摘要

Smart contracts on public blockchains now manage large amounts of value, and vulnerabilities in these systems can lead to substantial losses. As AI agents become more capable at reading, writing, and running code, it is natural to ask how well they can already navigate this landscape, both in ways that improve security and in ways that might increase risk. We introduce EVMbench, an evaluation that measures the ability of agents to detect, patch, and exploit smart contract vulnerabilities. EVMbench draws on 117 curated vulnerabilities from 40 repositories and, in the most realistic setting, uses programmatic grading based on tests and blockchain state under a local Ethereum execution environment. We evaluate a range of frontier agents and find that they are capable of discovering and exploiting vulnerabilities end-to-end against live blockchain instances. We release code, tasks, and tooling to support continued measurement of these capabilities and future work on security.

Poster
GIST: Targeted Data Selection for Instruction Tuning via Coupled Optimization Geometry

Guanghui Min, Tianhao Huang, Ke Wan, Chen Chen

展开摘要

Targeted data selection has emerged as a crucial paradigm for efficient instruction tuning, aiming to identify a small yet influential subset of training examples for a specific target task. In practice, influence is often measured through the effect of an example on parameter updates. To make selection scalable, many approaches leverage optimizer statistics (e.g., Adam states) as an axis-aligned surrogate for update geometry (i.e., diagonal precondition), implicitly treating parameters as coordinate-wise independent. We show that this assumption breaks down in parameter-efficient fine-tuning (PEFT) methods such as LoRA. In this setting, the induced optimization geometry exhibits strong cross-parameter coupling with non-trivial off-diagonal interactions, while the task-relevant update directions are confined to a low-dimensional subspace. Motivated by this mismatch, we propose **GIST** (Gradient Isometric Subspace Transformation), a simple yet principled alternative that replaces axis-aligned scaling with robust subspace alignment. **GIST** recovers a task-specific subspace from validation gradients via singular value decomposition (SVD), projects training gradients into this coupled subspace, and scores examples by their alignment with target directions. Extensive experiments have demonstrated that **GIST** matches or outperforms the state-of-the-art baseline with only 0.29% of the storage and 25% of the computational time under the same selection budget.

Poster
MAVRL: Learning Reward Functions from Multiple Feedback Types with Amortized Variational Inference

Raphaël Baur, Yannick Metz, Maria Gkoulta, Mennatallah El-Assady, Giorgia Ramponi, Thomas Kleine Buening

展开摘要

Reward learning typically relies on a single feedback type or combines multiple feedback types using manually weighted loss terms. Currently, it remains unclear how to jointly learn reward functions from heterogeneous feedback types such as demonstrations, comparisons, ratings, rankings, and stops that provide qualitatively different signals. We address this challenge by formulating reward learning from multiple feedback types as Bayesian inference over a shared latent reward function, where each feedback type contributes information through an explicit likelihood. We introduce a scalable amortized variational inference approach that learns a shared reward encoder and feedback-specific likelihood decoders and is trained by optimizing a single evidence lower bound. Our approach avoids reducing feedback to a common intermediate representation and eliminates the need for manual loss balancing. Across discrete and continuous-control benchmarks, we show that jointly inferred reward posteriors outperform single-type baselines, exploit complementary information across feedback types, and yield policies that are more robust to environment perturbations. The inferred reward uncertainty further provides interpretable signals for analyzing model confidence and consistency across feedback types.

Poster
IRPM: Intergroup Relative Preference Modeling for Pointwise Generative Reward Models

Haonan Song, Qingchen Xie, Huan Zhu, Feng Xiao, Luxi Xing, Liu Kang, Fuzhen Li, Zhiyong Zheng, Feng Jiang, Ziheng Li, Kun Yan, Qingyi Si, Yanghua Xiao, Hongcheng Guo, Fan Yang

展开摘要

Generative Reward Models (GRMs) have demonstrated strong performance in reward modeling, due to their interpretability and potential for refinement through reinforcement learning (RL). However, widely used pairwise GRMs create a computational bottleneck in reinforcement learning from human feedback (RLHF), when calibrating or aggregating preference signals over $n$ candidates, often incurring $\mathcal{O}(n^2)$ pairwise judgments. To address this issue, we propose **Intergroup Relative Preference Modeling (IRPM)**, an RL-based method that extends the Bradley-Terry preference-learning paradigm via intergroup comparisons to train *pointwise* GRMs from pairwise preference data. IRPM derives a pointwise reward for each response by contrasting groups of chosen vs. rejected samples, enabling pointwise scores comparable across candidate sets and $\mathcal{O}(n)$ reward evaluation for a variable number of candidates during RL training, while preserving interpretability and scalability. Experiments show that IRPM achieves state-of-the-art performance among pointwise GRMs on JudgeBench and RewardBench, and approaches the performance of leading pairwise GRMs. In addition, IRPM achieves substantial gains in post-training evaluations, demonstrating its effectiveness. Our models and code are available at https://github.com/XINGYUN-AI-LAB/IRPM.

Poster
Estimating Tail Risks in Language Model Output Distributions

Rico Angell, Raghav Singhal, Zachary Horvitz, Zhou Yu, Rajesh Ranganath, Kathleen McKeown, He He

展开摘要

Language models are increasingly capable and are being rapidly deployed on a population-level scale. As a result, the safety of these models is increasingly high-stakes. Fortunately, advances in alignment have significantly reduced the likelihood of harmful model outputs. However, when models are queried billions of times in a day, even rare worst-case behaviors will occur. Current safety evaluations focus on capturing the distribution of inputs that yield harmful outputs. These evaluations disregard the probabilistic nature of models and their tail output behavior. To measure this tail risk, we propose a method to efficiently estimate the probability of harmful outputs for any input query. Instead of naive brute-force sampling from the target model, where harmful outputs could be rare, we operationalize importance sampling by creating unsafe versions of the target model. These unsafe versions enable sample-efficient estimation by making harmful outputs more probable. On benchmarks measuring misuse and misalignment, these estimates match brute-force Monte Carlo estimates using 10–20× fewer samples. For example, we can estimate probability of harmful outputs on the order of $10^{−4}$ with just 500 samples. Additionally, we find that these harmfulness estimates can reveal the sensitivity of models to perturbations in model input and predict deployment risks. Our work demonstrates that rare-event estimation is both critical and feasible for safety evaluations.

Spotlight
PICACO: Pluralistic In-Context Value Alignment via Total Correlation Optimization

Han Jiang, Dongyao Zhu, Xiaoyuan Yi, Ziang Xiao, Zhihua Wei, Xing Xie

展开摘要

In-Context Learning has shown great potential for aligning Large Language Models (LLMs) with human values, helping reduce harmful outputs and accommodate diverse preferences without costly post-training, known as *In-Context Alignment* (ICA). However, LLMs' comprehension of input prompts remains agnostic, limiting ICA's ability to address value tensions—human values are inherently *pluralistic*, often imposing conflicting demands, *e.g.*, stimulation vs. tradition. Current ICA methods therefore face the *Instruction Bottleneck* challenge, where LLMs struggle to reconcile multiple intended values within a single prompt, leading to incomplete or biased alignment. To address this, we propose **PICACO**, a novel pluralistic ICA method. Without fine-tuning, PICACO optimizes a meta-instruction that incorporates multiple values to better elicit LLMs' understanding of them and improve alignment. This is achieved by maximizing the total correlation between specified values and LLM responses, which theoretically reinforces value conformity and reduces distractive noise, resulting in more effective instructions. Extensive experiments on five value sets show that PICACO works well with both black-box and open-source LLMs, outperforms several recent strong baselines, and achieves a better balance across up to 8 distinct values.

Poster
Selective Coupling of Decoupled Informative Regions: Masked Attention Alignment for Data-Free Quantization of Vision Transformers

Biao Qian, Yang Wang, Yong Wu, Jungong Han

展开摘要

Data-Free Quantization (DFQ) addresses data security concerns by synthesizing samples, without accessing real data. It has garnered increasing attention in the context of Vision Transformers (ViTs), owing to the superiority of the self-attention mechanism compared to classical convolutional operation. However, previous DFQ arts for ViTs often suffer from a distribution mismatch between synthetic samples and input distribution expected by quantized models $Q$, resulting in the suboptimal performance. In this paper, we propose a novel Masked Attention Alignment approach for Data-Free Quantization of ViTs, named MaskAQ, revealing that: 1) the semantics in the self-attention mechanism is predominantly localized to a sparse subset of patches, called informative regions; 2) the informative regions dominate the mutual information between synthetic samples and $Q$'s outputs. To these ends, we incorporate differential entropy maximum over patch similarity of synthetic samples, to decouple informative regions from noisy background. To couple with varied $Q$, the informative regions are selected to align full-precision models with $Q$ via a masked attention alignment objective, thus yielding high-quality synthetic samples. Furthermore, a periodic sample refreshing strategy comes up to endow MaskAQ with the capacity to continually adapt to the evolving state of $Q$ throughout the training process, to preserve desirable mutual information with synthetic samples. Extensive experiments verify the merits of MaskAQ over state-of-the-art approaches across multiple backbones and downstream tasks. Our code is available at https://github.com/hfutqian/MaskAQ.

Poster
Dissect and Prune: Enhancing Robustness in AI-Generated Image Detection

Dahye Kim, Jaehyun Choi, Hyun Seok Seong, Seongho Kim, Donghun Lee, Sungwon Yi, Jang-Ho Choi, Jang-Ho Choi

展开摘要

While existing AI-generated image detectors report high performance, we identify that this is largely driven by a critical *prediction asymmetry*: a bias toward the real class that severely limits sensitivity to generated content, especially under standard post-processing operations such as compression and resizing. We hypothesize that this stems from the model's reliance on spurious features, distracting signals that obscure true generative artifacts. To address this, we propose DEAR (Dissect and Prune), which leverages inpainted images to identify and prune these interfering components. Specifically, we find that features strongly aligned to either inpainted or non-inpainted regions are less robust to post-processing. By measuring the alignment between channel activations and inpaint masks, DEAR removes features at both extremes, retaining only those that capture genuine generative artifacts. Experimental results demonstrate that our approach significantly enhances robustness against unseen generators and post-processing, effectively mitigating the prediction asymmetry. Our code is available at https://github.com/dahyedahye/dear.

Poster
Divergence Decoding: Inference-Time Unlearning via Auxiliary Models

Humzah Merchant, Bradford Levy

展开摘要

Large Language Models (LLMs) frequently memorize sensitive training data thereby creating significant privacy and copyright risks. Addressing these risks, i.e., removing such knowledge from an existing model checkpoint, has proven challenging as many unlearning methods lead to catastrophic utility loss or are ineffective for complex queries. We introduce **Divergence Decoding (DD)**, a mechanism that uses small auxiliary models to steer the logits of the LLM away from specific data during inference. Training these models is straight forward, i.e., we use standard pre-training and fine-tuning setups. We find the method decisively outperforms state-of-the-art (SOTA) baselines on unlearning benchmarks across a variety of model and training dataset scales consistent with DD being an effective and inexpensive solution to unlearning. We then demonstrate that this steered distribution can be trivially distilled back into the base model. Since the method is generally applicable to any probabilistic model, we explore its efficacy outside of text generation and find evidence of generalization to the domain of images.

Poster
SIPO: Stabilized and Improved Preference Optimization for Aligning Diffusion Models

Xiaomeng Yang, Mengping Yang, Junyan Wang, Zhijian Zhou, Zhiyu Tan, Hao Li

展开摘要

Preference learning has garnered extensive attention as an effective technique for aligning diffusion models with human preferences in visual generation tasks. However, existing alignment approaches such as Diffusion-DPO suffer from two fundamental challenges: training instability caused by high gradient variances at various timesteps and high parameter sensitivities, and off-policy bias arising from the discrepancy between the optimization data and the policy model's distribution. Our first contribution is a systematical analysis of the diffusion trajectories across different timesteps and identify that the instability primarily originates from early timesteps with low importance weights. To address these issues, we propose SIPO, a Stabilized and Improved preference Optimization framework for aligning diffusion models with human preferences. Concretely, a key gradient, \emph{i.e.,} DPO-C&M is introduced to facilitate stabilize training by clipping and masking uninformative timesteps. Followed by a timestep aware importance re-weighting paradigm to fully correct off-policy bias and emphasize informative updates throughout the alignment process. Extensive experiments on various baseline models, including image generation models on SD1.5, SDXL, and video generation models CogVideoX-2B, CogVideoX-5B, and Wan2.1-1.3B, demonstrate that our SIPO consistently promotes stabilized training and outperforms existing alignment methods, with meticulous adjustments on parameters. Overall, these results highlight the importance of timestep-aware alignment and and provide valuable guidelines for improved preference optimization in diffusion models.

Poster
NeuralFLoC: Neural Flow-Based Joint Registration and Clustering of Functional Data

Xinyang Xiong, Siyuan Jiang, Pengcheng Zeng

展开摘要

Clustering functional data in the presence of phase variation is challenging, as temporal misalignment can obscure intrinsic shape differences and degrade clustering performance. Most existing approaches treat registration and clustering as separate tasks or rely on restrictive parametric assumptions. We present **NeuralFLoC**, a fully unsupervised, end-to-end deep learning framework for joint functional registration and clustering based on Neural ODE-driven diffeomorphic flows and spectral clustering. The proposed model learns smooth, invertible warping functions and cluster-specific templates simultaneously, effectively disentangling phase and amplitude variation. We establish universal approximation guarantees and asymptotic consistency for the proposed framework. Experiments on functional benchmarks show state-of-the-art performance in both registration and clustering, with robustness to missing data, irregular sampling, and noise, while maintaining scalability. Code is available at https://github.com/LastQuater/NeuralFLoC.

Poster
FoeGlass: Simple In-Context Learning Is Enough for Red Teaming Audio Deepfake Detectors

Sepehr Dehdashtian, Jacob H Seidman, Vishnu Boddeti, Gaurav Bharaj

展开摘要

Audio deepfake detection (ADD) models are critical for countering the malicious use of text-to-speech (TTS) models. Evaluating and strengthening ADD models requires developing datasets that span the space of generated audio and highlight high-error regions. Existing dataset development strategies face two challenges: (i) manual collection, and (ii) inefficient discovery of blind spots in the ADD models. To address these challenges, we propose FoeGlass, the first black-box automated red-teaming method for ADDs, which effectively discovers ADD failure modes in the space of generated audio underexplored by state-of-the-art deepfake benchmarks. FoeGlass uses the in-context learning capabilities of an LLM to explore the input space of a TTS model, generating audio samples that fool the target ADD using only black-box access to all components. By using a carefully designed context based on diversity measurements, FoeGlass mitigates the common problem of mode collapse in automated red-teaming systems. Empirical evaluations on several open-source ADD and TTS models demonstrate that data generated from FoeGlass substantially improves the false negative rates over unconditional sampling baselines and recent spoofing datasets by up to 94%, while requiring no manual supervision. Furthermore, we show that the attacks generated by FoeGlass are transferable across different target ADDs, demonstrating its broad applicability and ease of use for the automated red teaming of ADD systems. Finally, fine-tuning ADD models on FoeGlass-generated samples notably enhances the robustness of the detectors (up 41%).

Poster
Mind the Gap: Structure-Aware Consistency in Preference Learning

Mehryar Mohri, Yutao Zhong

展开摘要

Aligning Large Language Models (LLMs) with human intent, whether through explicit reward modeling or direct methods such as DPO, fundamentally relies on minimizing a surrogate loss as a proxy for the true pairwise ranking objective. We prove that this reliance is flawed for the standard surrogate losses used: for the equicontinuous hypothesis sets characteristic of neural networks, *no* standard surrogate provides a meaningful consistency guarantee. Minimizing the surrogate loss to zero can leave the true ranking error arbitrarily high. To resolve this, we formulate LLM alignment within a margin-shifted ranking framework and derive $H$-consistency bounds showing that enforcing a confidence margin $\gamma$ is not merely beneficial but *necessary* for consistency. We further introduce Structure-Aware $H$-consistency and a corresponding objective (SA-DPO) that adapts the margin to the semantic distance between responses, preventing instability on near-synonymous pairs. Finally, we analyze the trade-off between the margin required for consistency and the model's finite capacity to satisfy it, revealing a strict hierarchy of surrogate losses: heavy-tailed surrogates (e.g., the Polynomial Hinge family) offer strictly superior consistency guarantees for capacity-bounded models compared to the logistic loss used in DPO. Experiments on UltraFeedback and Argilla DPO-Mix-7k confirm that SA-DPO consistently outperforms DPO and SimPO, with a 58.5\% head-to-head win-rate in downstream generation quality.

Poster
Removing Sandbagging in LLMs by Training with Weak Supervision

Emil Ryd, Henning Bartsch, Julian Stastny, Joe Benton, Vivek Hebbar

展开摘要

As AI systems begin to automate complex tasks, supervision increasingly relies on weaker models or limited human oversight that cannot fully verify output quality. A model more capable than its supervisors could exploit this gap through sandbagging, producing work that appears acceptable but falls short of its true abilities. Can training elicit a model's best work even without reliable verification? We study this using model organisms trained to sandbag, testing elicitation techniques on problem-solving math, graduate-level science, and competitive coding tasks. We find that training with weak supervision can reliably elicit sandbagging models when supervised fine-tuning (SFT) and reinforcement learning (RL) are combined: SFT on weak demonstrations breaks the sandbagging behavior, enabling RL to then fully elicit performance. Neither method succeeds reliably alone—RL without SFT almost always leads to reward hacking rather than genuine improvement, and SFT without RL fails to elicit full performance when the supervisor is much weaker than the untrusted model. Critically, this relies on training being indistinguishable from deployment; when models can distinguish between training and deployment, they can perform well during training while continuing to sandbag afterward. Our results provide initial evidence that training is a viable mitigation against sandbagging, while highlighting the importance of making training indistinguishable from deployment.

Poster
Blending Neural Control Density Functions for Stabilization and Safety

Sahil Chaudhary, Chaitanya Murti, Chiranjib Bhattacharyya

展开摘要

Recent work on Neural Network-based methods for nonlinear control use Lyapunov Functions to obtain controllers with guarantees of stability. However, Lyapunov-based methods are fundamentally limited: they cannot be used for smooth blending with formal Region of Attraction (RoA) expansion guarantees, and also fail to certify stability when unstable equilibria or saddle points are present. Density functions provide an alternate stability certificate, and address these limitations by certifying almost everywhere stability, and enable smooth blending of controllers. Learning valid density certificates is challenging due to integrability constraints, and the effect of density-based blending controllers on RoAs is not well understood. In this work, we provide the first guarantee that controllers blended with density functions yield RoAs containing the union of the RoAs achieved by the constituent controllers. Then, we propose a novel exponential characterization of density functions that provably satisfies the integrability condition, and introduce Neural Control Density Functions (NCDFs), that leverage this new parameterization. We also extend NCDFs for synthesizing safe-stable controllers by combining NCDFs with control barrier functions (NCDF-CBFs). Our experiments show that blended controllers obtain superior RoAs to state-of-the-art methods like Neural Lyapunov Control and Sum-of-Squares based techniques.

Poster
DMCO: Budget-Aware Co-Optimization of Data Cleaning and AutoML

Xiaoou Ding, Zekai Qian, Siying Chen, Hongbin Hu, Chen Wang, Hongzhi Wang, Jianmin Wang

展开摘要

Data cleaning and automated machine learning (AutoML) are both crucial for reliable learning systems, yet are commonly treated as independent or sequential stages. This separation ignores their strong interaction and leads to inefficient use of limited computational budgets.We propose DMCO, a unified framework that jointly optimizes data cleaning and model construction under a fixed resource budget. DMCO reformulates the traditional two-stage pipeline into a time-sliced process, where data cleaning and AutoML are interleaved and adaptively scheduled. We introduce a gradient-based data cleaning sampling strategy with theoretical guarantees for minimizing gradient estimation variance, and integrates it with loss-driven sampling and progressive AutoML fitting to continuously leverage intermediate data quality improvements.Experiments on six real-world datasets show that DMCO consistently outperforms standalone data cleaning and AutoML baselines on both classification and regression tasks, as measured by F1 score and MSE. Under limited budgets, DMCO achieves up to 82.19% of the performance of full data cleaning with exhaustive AutoML, while remaining robust across different AutoML frameworks.

Poster
A Robust Optimization Guided Pruning Framework for Vision and Large Language Models

Gabriel Afriat, Hussein Hazimeh, Dimitris Paparas, Rahul Mazumder

展开摘要

Pruning is a common approach to reduce the memory footprint and inference cost of large vision and language models. As these architectures continue to scale, one-shot pruning methods - i.e. approaches that prune the network without any retraining - have become increasingly attractive. Many popular one-shot pruning methods (e.g., WoodFisher, CAP, SparseGPT, and ALPS) typically optimize a quadratic objective under sparsity constraints. However, in practice, this objective is affected by multiple sources of uncertainty, including noise in the calibration data and variability introduced by algorithmic updates. To address these issues, we introduce RobOP, a robust optimization framework that explicitly accounts for such uncertainties. RobOP is modular and flexible, and can be applied with any existing pruning method through simple modifications motivated by our theoretical framework. We demonstrate that by taking into account uncertainty, RobOP offers improvements over prior pruning approaches. Our framework applies tractably across a range of stylized uncertainty sets, enabling robust one-shot pruning at scale. Our code is available at https://github.com/mazumder-lab/RobOP.

Poster
The Trojan Knowledge: Bypassing Commercial LLM Guardrails via Harmless Prompt Weaving and Adaptive Tree Search

Rongzhe Wei, Peizhi Niu, Xinjie Shen, Tony Tu, Yifan Li, Ruihan Wu, Eli Chien, Pin-Yu Chen, Olgica Milenkovic, Pan Li

展开摘要

Large language models (LLMs) remain vulnerable to jailbreak attacks that bypass safety guardrails. Existing approaches overwhelmingly operate within the prompt-optimization paradigm; the resulting prompts typically retain malicious semantic signals that modern guardrails are primed to detect. In contrast, we identify a deeper vulnerability stemming from the highly interconnected nature of an LLM’s internal knowledge. This structure allows harmful objectives to be realized by weaving together sequences of benign sub-queries, each of which individually evades detection. To exploit this loophole, we introduce the Correlated Knowledge Attack Agent (CKA-Agent), a dynamic framework that reframes jailbreaking as an adaptive, tree-structured exploration of the target model’s knowledge base. The CKA-Agent issues locally innocuous queries, uses model responses to guide exploration across multiple paths, and ultimately assembles the aggregated information to achieve the original harmful objective. Evaluated across SOTA commercial LLMs, CKA-Agent consistently achieves over 95\% success rates even against strong guardrails, underscoring the severity of this vulnerability and the urgent need for defenses against such knowledge-decomposition attacks. Our codes are available at https://github.com/Graph-COM/CKA-Agent.

Poster
Efficient LLM Moderation with Multi-Layer Latent Prototypes

Maciej Chrabaszcz, Filip Szatkowski, Bartosz Wójcik, Jan Dubiński, Tomasz Trzcinski, Sebastian Cygert

展开摘要

Although modern LLMs are aligned with human values during post-training, robust moderation remains essential to prevent harmful outputs at deployment time. Existing approaches suffer from performance-efficiency trade-offs and are difficult to customize to user-specific requirements. Motivated by this gap, we introduce Multi-Layer Prototype Moderator (MLPM), a lightweight and highly customizable input moderation tool. We propose leveraging prototypes of intermediate representations across multiple layers to improve moderation quality while maintaining high efficiency. By design, our method adds negligible overhead to the generation pipeline and can be seamlessly applied to any model. MLPM achieves state-of-the-art performance on diverse moderation benchmarks and demonstrates strong scalability across model families of various sizes. Moreover, we show that it integrates smoothly into end-to-end moderation pipelines and further improves response safety when combined with output moderation techniques. Overall, our work provides a practical and adaptable solution for safe, robust, and efficient LLM deployment.

Poster
Gradient Flow Dynamics and Implicit Bias of Diagonal Linear Networks under Infinitesimal Initialization

Jiajie Zhao, Jianxing Wang, Junjie Yang, Zhiwei Bai, Yaoyu Zhang

展开摘要

We study the gradient flow dynamics of diagonal linear networks for regression tasks under infinitesimal initialization. Extending Theorem 1 from Pesme & Flammarion (2023), we generalize the analysis to both deep diagonal linear networks and a broader class of two-layer diagonal linear networks (as defined in Definition 4.1). Specifically, we demonstrate that the training trajectories of these models can be equivalently characterized by the proposed Algorithm 1. We further prove that this algorithm converges to the solution of a modified $\mathcal{l}_1$ norm minimization problem. As a result, we establish that the implicit bias of both network architectures corresponds to a modified $\mathcal{l}_1$ norm in the regime of infinitesimal initialization. Additionally, we provide insights into the underlying mechanisms governing these dynamics by identifying the Structural Invariant Manifold (SIM) (Zhao et al., 2026) as the key geometric structure that shapes the learning process.

Poster