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Guinan Su, Li Shen, Lu Yin, Shiwei Liu, Yanwu Yang, Jonas Geiping

Large language models (LLMs) have shown remarkable capabilities in language understanding and generation. However, such impressive capability typically comes with a substantial model size, which presents significant challenges in deployment and inference. While structured pruning of model parameters offers a promising way to reduce computational costs at deployment time, current methods primarily focus on single model pruning. In this work, we develop a novel strategy to compress models by strategically combining or merging layers from finetuned model variants, which preserves the original model's abilities by aggregating capabilities accentuated in different finetunes. We pose the optimal tailoring of these LLMs as a zero-order optimization problem, adopting a search space that supports three different operations: (1) Layer removal, (2) Layer selection from different candidate models, and (3) Layer merging. Our experiments demonstrate that this approach leads to competitive model pruning, for example, for the Llama2-13B model families, our compressed models maintain approximately 97.3\% of the original performance while removing ~25\% of parameters, significantly outperforming previous state-of-the-art methods.

Zhuofeng Li, Haoxiang Zhang, Seungju Han, Sheng Liu, Jianwen Xie, Yu Zhang, Yejin Choi, James Y Zou, Pan Lu

Outcome-driven reinforcement learning has advanced reasoning in large language models (LLMs), but prevailing tool-augmented approaches train a single, monolithic policy that interleaves thoughts and tool calls under full context; this scales poorly with long horizons and diverse tools and generalizes weakly to new scenarios. Agentic systems offer a promising alternative by decomposing work across specialized modules, yet most remain training-free or rely on offline training decoupled from the live dynamics of multi-turn interaction. We introduce AgentFlow, a trainable, *in-the-flow* agentic framework that coordinates four modules (planner, executor, verifier, generator) through an evolving memory and directly optimizes its planner inside the multi-turn loop. To train on-policy in live environments, we propose *Flow-based Group Refined Policy Optimization* (Flow-GRPO), which tackles long-horizon, sparse-reward credit assignment by converting multi-turn optimization into a sequence of tractable single-turn policy updates. It broadcasts a single, verifiable trajectory-level outcome to every turn to align local planner decisions with global success and stabilizes learning with group-normalized advantages. Across ten benchmarks, AgentFlow with a 7B-scale backbone outperforms top-performing baselines with average accuracy gains of 14.9% on search, 14.0% on agentic, 14.5% on mathematical, and 4.1% on scientific tasks, even surpassing larger proprietary models like GPT-4o. Further analyses confirm the benefits of in-the-flow optimization, showing improved planning, enhanced tool-calling reliability, and positive scaling with model size and reasoning turns.

Ben Finkelshtein, Silviu Cucerzan, Sujay Kumar Jauhar, Ryen White

Large language models (LLMs) are increasingly leveraged for text-rich graph machine learning tasks, with node classification standing out due to its high-impact application domains such as fraud detection and recommendation systems. Yet, despite a surge of interest, the field lacks a principled understanding of the capabilities of LLMs in processing graph data. In this work, we conduct a large-scale, controlled evaluation across the key axes of variability: the LLM-graph interaction mode, comparing prompting, tool-use, and code generation; dataset domains, spanning citation, web-link, e-commerce, and social networks; homophilic vs. heterophilic regimes; short- vs. long-text features; LLM sizes and reasoning capabilities. We further analyze dependencies by independently truncating features, deleting edges, and removing labels to quantify reliance on input types. Our findings provide actionable guidance for both research and practice. (1) Code generation mode achieves the strongest overall performance, with especially large gains on long-text or high-degree graphs where prompting quickly exceeds the token budget. (2) All interaction strategies remain effective on heterophilic graphs, challenging the assumption that LLM-based methods collapse under low homophily. (3) Code generation mode is able to flexibly shift its reliance to the most informative input type, whether that be structure, features, or labels. Together, these results establish a clear picture of the strengths and limitations of current LLM–graph interaction modes and point to design principles for future methods.

Changli Tang, Qinfan Xiao, Ke Mei, Tianyi Wang, Fengyun Rao, Chao Zhang

While embeddings from multimodal large language models (LLMs) excel as general-purpose representations, their application to dynamic modalities like audio and video remains underexplored. We introduce WAVE (\textbf{u}nified \& \textbf{v}ersatile \textbf{a}udio-\textbf{v}isual \textbf{e}mbeddings), the first LLM-based embedding that creates a unified representation space for text, audio, and video modalities. WAVE employs a novel hierarchical feature fusion strategy and a joint multi-modal, multi-task training approach to enable two key capabilities: any-to-any cross-modal retrieval and the generation of prompt-aware embeddings tailored to user instructions. Experimentally, WAVE sets a new state-of-the-art on the MMEB-v2 video benchmark and achieves superior results in audio and video-to-audio retrieval. Its prompt-aware nature also yields remarkable performance in multimodal question answering, significantly outperforming existing embedding models. Ablation studies validate our joint training strategy, demonstrating improved performance across all modalities. With a newly introduced benchmark for versatile audio-visual learning, WAVE opens up broad possibilities for cross-modal, any-to-any applications. Our code and checkpoints are released at \href{https://github.com/TCL606/WAVE}{https://github.com/TCL606/WAVE}.

Deep Learning · Graph Neural Networks

Guanjun Wang, Binwu Wang, Jiaming Ma, Zhengyang Zhou, Pengkun Wang, Xu Wang, Yang Wang

Graph Neural Networks (GNNs) have advanced graph classification, yet they remain vulnerable to graph-level imbalance, encompassing class imbalance and topological imbalance. To address both types of imbalance in a unified manner, we propose UniImb, a Unified framework for Imbalanced graph classification. Specifically, UniImb first captures multi-scale topological features and enhances data diversity via learnable personalized graph perturbations. It then employs a dynamic balanced prototype module to learn representative prototypes from graph instances, improving the quality of graph representations. Concurrently, a prototype load-balancing optimization term mitigates dominance by majority samples to equalize sample influence during training. We justify these design choices theoretically using the Information Bottleneck principle. Extensive experiments on 19 datasets-including a large-scale imbalanced air pollution graph dataset AirGraph released by us and 23 baselines demonstrate that UniImb has achieved dominant performance across various imbalanced scenarios. Our code is available at GitHub.

Deep Learning · Everything Else

Zhikai Chen, Han Xie, Jian Zhang, Jiliang Tang, Xiang song, Huzefa Rangwala

Predictive modeling over relational databases (RDBs) powers applications in various domains, yet remains challenging due to the need to capture both cross-table dependencies and complex feature interactions. Recent Relational Deep Learning (RDL) methods automate feature engineering via message passing, while classical approaches like Deep Feature Synthesis (DFS) rely on predefined non-parametric aggregators. Despite promising performance gains, the comparative advantages of RDL over DFS and the design principles for selecting effective architectures remain poorly understood. We present a comprehensive study that unifies RDL and DFS in a shared design space and conducts large-scale architecture-centric searches across diverse RDB tasks. Our analysis yields three key findings: (1) RDL does not consistently outperform DFS, with performance being highly task-dependent; (2) no single architecture dominates across tasks, underscoring the need for task-aware model selection; and (3) validation accuracy is an unreliable guide for architecture choice. This search yields a curated model performance bank that links model architecture configurations to their performance; leveraging this bank, we analyze the drivers of the RDL–DFS performance gap and introduce two task signals—RDB task homophily and an affinity embedding that captures size, path, feature, and temporal structure—whose correlation with the gap enables principled routing. Guided by these signals, we propose Relatron, a task embedding-based meta-selector that first chooses between RDL and DFS and then prunes the within-family search to deliver strong performance. Lightweight loss-landscape metrics further guard against brittle checkpoints by preferring flatter optima. In experiments, Relatron resolves the “more tuning, worse performance” effect and, in joint hyperparameter–architecture optimization, achieves up to 18.5\% improvement over strong baselines with $10\times$ lower computational cost than Fisher information–based alternatives. Our code is available at https://github.com/amazon-science/Automating-Relational-Machine-Learning.

Yuancheng Wang, Zhenyu Tang, Yun Wang, Arthur Hinsvark, Yingru Liu, Yinghao Li, Kainan Peng, Junyi Ao, Mingbo Ma, Mike Seltzer 等

Speech tokenizers are foundational to speech language models, yet existing approaches face two major challenges: (1) balancing trade-offs between encoding semantics for understanding and acoustics for reconstruction, and (2) achieving low bit rates and low token rates. We propose Speech Diffusion Tokenizer (SiTok), a diffusion autoencoder that jointly learns semantic-rich representations through supervised learning and enables high-fidelity audio reconstruction with diffusion. We scale SiTok to 1.6B parameters and train it on 2 million hours of speech. Experiments show that SiTok outperforms strong baselines on understanding, reconstruction and generation tasks, at an extremely low token rate of 12.5 Hz and a bit-rate of 200 bits-per-second.

Guanhua Zhang, Ricardo Dominguez-Olmedo, Moritz Hardt

Existing language model benchmarks provide contradictory model rankings, even for benchmarks that aim to capture similar skills. This dilemma of conflicting rankings hampers model selection, clouds model comparisons, and adds confusion to a growing ecosystem of competing models. In this paper, we take a different perspective on model comparison: instead of relying on out-of-the-box performance via direct evaluation, we compare model potential by providing each model with identical benchmark-specific fine-tuning before evaluation. We call this approach train-before-test. Our primary contribution is a comprehensive empirical evaluation of model potential across 24 benchmarks and 61 models. First, we demonstrate that model potential rankings obtained through train-before-test exhibit remarkable consistency across all benchmarks. Whereas traditional rankings demonstrate little external validity under direct evaluation, they enjoy a significant degree of external validity when applying train-before-test: model potential rankings transfer gracefully from one benchmark to another. Second, train-before-test restores the connection between perplexity and downstream task performance, lost under direct evaluation. Remarkably, even pre-finetuning perplexity of a base model predicts post-finetuning downstream performance, suggesting that ranking consistency reflects inherent model potential rather than fine-tuning artifacts. Finally, train-before-test reduces the model-score matrix to essentially rank one, indicating that model potential is dominated by one latent factor, uncovered by train-before-test. While direct evaluation remains useful for assessing deployment-ready performance, train-before-test provides a complementary lens for understanding achievable performance of models after adaptation.

Naimeng Ye, Arnav Ahuja, Georgios Liargkovas, Yunan Lu, Kostis Kaffes, Tianyi Peng

AI agents are increasingly deployed in complex, interactive environments, yet their runtime remains a major bottleneck for training, evaluation, and real-world use. Typical agent behavior unfolds sequentially, where each action requires an API call that can incur substantial latency. For example, a game of chess between two state-of-the-art agents can take hours. We introduce speculative actions, a lossless acceleration framework for general agentic systems. Inspired by speculative execution in microprocessors and speculative decoding in LLM inference, our method uses faster models to predict likely future actions and executes them in parallel, committing only when predictions match. We evaluate speculative actions across gaming, e-commerce, and web search environments, and additionally study a lossy extension in an operating systems setting. Across domains, we achieve up to 55% next-action prediction accuracy, translating into substantial latency reductions. Finally, we present a cost–latency analysis that formalizes the tradeoff between speculative breadth and time savings. This analysis enables principled tuning and selective branch launching, to ensure multi-branch speculation delivers practical speedups without prohibitive cost growth.

General Machine Learning · Representation Learning

Lixuan Guo, Yifei Wang, Tiansheng Wen, Yifan Wang, Aosong Feng, Bo Chen, Stefanie Jegelka, Chenyu You

In the era of large foundation models, the quality of embeddings has become a central determinant of downstream task performance and overall system capability. Yet widely used dense embeddings are often extremely high-dimensional (e.g., 4096), incurring substantial costs in storage, memory, and inference latency. To address these, Contrastive Sparse Representation (CSR) is recently proposed as a promising direction, mapping dense embeddings into high-dimensional but $k$-sparse vectors, in contrast to compact dense embeddings such as Matryoshka Representation Learning (MRL). Despite its promise, CSR suffers severe degradation in the ultra-sparse regime (e.g., $k \leq 4$), where over 80\% of neurons remain inactive, leaving much of its efficiency potential unrealized. In this paper, we introduce CSRv2, a principled training approach designed to make ultra-sparse embeddings viable. CSRv2 stabilizes sparsity learning through progressive $k$-annealing, enhances representational quality via supervised contrastive objectives, and ensures end-to-end adaptability with full backbone finetuning. CSRv2 reduces dead neurons from 80\% to 20\% and delivers a 14\% accuracy gain at $k=2$, bringing ultra-sparse embeddings on par with CSR at $k=8$ and MRL at 32 dimensions, all with only two active features. While maintaining comparable performance, CSRv2 delivers a 7$\times$ speedup over MRL, and yields up to 300$\times$ improvements in compute and memory efficiency relative to dense embeddings in e5-mistral-7b-instruct-based text representation. Extensive experiments across text (MTEB, multiple state-of-the-art LLM embeddings (Qwen and e5-Mistral-7B), SPLADEv3, GraphRAG) and vision (ImageNet-1k) demonstrate that CSRv2 makes ultra-sparse embeddings practical without compromising performance, where CSRv2 achieves 7\%/4\% improvement over CSR when $k=4$ and further increases this gap to 14\%/6\% when $k=2$ in text/vision representation. By making extreme sparsity viable, CSRv2 broadens the design space for large-scale, real-time, and edge-deployable AI systems where both embedding quality and efficiency are critical. Code is available at https://github.com/Y-Research-SBU/CSRv2.

Zhaomin Wu, Mingzhe Du, See-Kiong Ng, Bingsheng He

Large Language Models (LLMs) are widely deployed in reasoning, planning, and decision-making tasks, making their trustworthiness critical. A significant and underexplored risk is intentional deception, where an LLM deliberately fabricates or conceals information to serve a hidden objective. Existing studies typically induce deception by explicitly setting a hidden objective through prompting or fine-tuning, which may not reflect real-world human-LLM interactions. Moving beyond such human-induced deception, we investigate LLMs' self-initiated deception on benign prompts. To address the absence of ground truth, we propose a framework based on Contact Searching Questions~(CSQ). This framework introduces two statistical metrics derived from psychological principles to quantify the likelihood of deception. The first, the *Deceptive Intention Score*, measures the model's bias toward a hidden objective. The second, the *Deceptive Behavior Score*, measures the inconsistency between the LLM's internal belief and its expressed output. Evaluating 16 leading LLMs, we find that both metrics rise in parallel and escalate with task difficulty for most models. Moreover, increasing model capacity does not always reduce deception, posing a significant challenge for future LLM development.

Deep Learning · Attention Mechanisms

Yan Xie, Tiansheng Wen, Tang Da Huang, Bo Chen, Chenyu You, Stefanie Jegelka, Yifei Wang

Scaling Transformers to ultra-long contexts is bottlenecked by the $O(n^2 d)$ cost of self-attention. Existing methods reduce this cost along the sequence axis through local windows, kernel approximations, or token-level sparsity, but these approaches consistently degrade accuracy. In this paper, we instead explore an orthogonal axis: \emph{feature sparsity}. We propose \textbf{Sparse Feature Attention (SFA)}, where queries and keys are represented as $k$-sparse codes that preserve high-dimensional expressivity while reducing the cost of attention from $\Theta(n^2 d)$ to $\Theta(n^2 k^2/d)$. To make this efficient at scale, we introduce \textbf{FlashSFA}, an IO-aware kernel that extends FlashAttention to operate directly on sparse overlaps without materializing dense score matrices. Across GPT-2 and Qwen3 pretraining, SFA matches dense baselines while improving speed by up to $2.5\times$ and reducing FLOPs and KV-cache by nearly 50\%. On synthetic and downstream benchmarks, SFA preserves retrieval accuracy and robustness at long contexts, outperforming short-embedding baselines that collapse feature diversity. These results establish feature-level sparsity as a complementary and underexplored axis for efficient attention, enabling Transformers to scale to orders-of-magnitude longer contexts with minimal quality loss.

Computer Vision · Everything Else

Marc Benedi San Millan, Angela Dai, Matthias Niessner

Animation of humanoid characters is essential in various graphics applications, but require significant time and cost to create realistic animations. We propose an approach to synthesize 4D animated sequences of input static 3D humanoid meshes, leveraging strong generalized motion priors from generative video models -- as such video models contain powerful motion information covering a wide variety of human motions. From an input static 3D humanoid mesh and a text prompt describing the desired animation, we synthesize a corresponding video conditioned on a rendered image of the 3D mesh. We then employ an underlying SMPL representation to animate the corresponding 3D mesh according to the video-generated motion, based on our motion optimization. This enables a cost-effective and accessible solution to enable the synthesis of diverse and realistic 4D animations

Geon-Hyeong Kim, Yu Jin Kim, Byoungjip Kim, Honglak Lee, Kyunghoon Bae, Youngsoo Jang, Moontae Lee

As Large Language Models (LLMs) are increasingly deployed in real-world applications, balancing helpfulness and safety has become a central challenge. A natural approach is to incorporate safety constraints into Reinforcement Learning from Human Feedback (RLHF), where recent studies have shown promising progress. However, these methods often rely on auxiliary networks or multi-stage pipelines, thereby increasing complexity. In this work, we revisit the original safety alignment objective and show that, under mild assumptions, it admits a closed-form optimal policy. We further derive a provably equivalent and tractable objective, enabling direct optimization. Building on this insight, we propose SafeDPO, a lightweight method that preserves the optimal solution of the underlying safety-constrained objective while requiring only one additional hyperparameter and minimal modifications to existing preference-based training methods. SafeDPO eliminates the need for reward models, cost models, and online sampling, relying only on preference data and safety indicators. Despite its simplicity, SafeDPO achieves competitive safety–helpfulness trade-offs compared to existing safety alignment methods. Experiments on the PKU-SafeRLHF-30K benchmark demonstrate that SafeDPO substantially improves safety while maintaining competitive helpfulness. Ablation studies further show that the additional hyperparameter provides a flexible mechanism to enhance safety while preserving the theoretical optimum, and confirm that SafeDPO scales reliably to LLMs with up to 13B parameters. Overall, our results highlight that a simple, theory-driven objective can provide a lightweight yet effective solution for safety alignment in practice.

Zhehao Huang, Yuhang Liu, Baijiong Lin, Yixin Lou, Zhengbao He, Hanling Tian, Tao Li, Xiaolin Huang

Large reasoning models (LRMs) excel at a long chain of reasoning but often fail to faithfully follow instructions regarding output format, constraints, or specific requirements. We investigate whether this gap can be closed by integrating an instruction-tuned model (ITM) into an LRM. Analyzing their differences in parameter space, namely task vectors, we find that their principal subspaces are nearly orthogonal across key modules, suggesting a lightweight merging with minimal interference. However, we also demonstrate that naïve merges are fragile because they overlook the output format mismatch between LRMs (with explicit *thinking* and *response* segments) and ITMs (answers-only). We introduce **RAIN-Merging** (Reasoning-Aware Instruction-attention guided Null-space projection Merging), a gradient-free method that integrates instruction following while preserving thinking format and reasoning performance. First, with a small reasoning calibration set, we project the ITM task vector onto the null space of forward features at thinking special tokens, which preserves the LRM's structured reasoning mechanisms. Second, using a small instruction calibration set, we estimate instruction attention to derive module-specific scaling that amplifies instruction-relevant components and suppresses leakage. Across four instruction-following benchmarks and nine reasoning & general capability benchmarks, RAIN-Merging substantially improves instruction adherence while maintaining reasoning quality. The gains are consistent across model scales and architectures, translating to improved performance in agent settings.

General Machine Learning · Representation Learning

Zeeshan Hayder, Ali Cheraghian, Lars Petersson, Mehrtash Harandi, Richard Hartley

Knowledge Distillation (KD) is a widely adopted framework for compressing large models into compact student models by transferring knowledge from a high-capacity teacher. Despite its success, KD presents two persistent challenges: (1) the trade-off between optimizing for the primary task loss and mimicking the teacher's outputs, and (2) the gradient disparity arising from architectural and representational mismatches between teacher and student models. In this work, we propose Dynamic Trade-off Optimization for Knowledge Distillation (DTO-KD), a principled multi-objective optimization formulation of KD that dynamically balances task and distillation losses at the gradient level. Specifically, DTO-KD resolves two critical issues in gradient-based KD optimization: (i) gradient conflict, where task and distillation gradients are directionally misaligned, and (ii) gradient dominance, where one objective suppresses learning progress on the other. Our method adapts per-iteration trade-offs by leveraging gradient projection techniques to ensure balanced and constructive updates. We evaluate DTO-KD on large-scale benchmarks including ImageNet-1K for classification and COCO for object detection. Across both tasks, DTO-KD consistently outperforms prior KD methods, yielding state-of-the-art accuracy and improved convergence behavior. Furthermore, student models trained with DTO-KD exceed the performance of their non-distilled counterparts, demonstrating the efficacy of our multi-objective formulation for KD.

Social Aspects · Fairness, Equity, Justice and Safety

Raghu Arghal, Kevin He, Shirin Saeedi Bidokhti, Saswati Sarkar

Algorithms increasingly serve as information mediators -- from social media feeds and targeted advertising to the increasing ubiquity of LLMs. This engenders a joint process where agents combine private, algorithmically-mediated signals with observational learning from peers to arrive at decisions. To study such settings, we introduce a model of controlled sequential social learning in which an information-mediating planner (e.g., an LLM) controls the information precision of agents while they also learn from the decisions of earlier agents. The planner may seek to improve social welfare (an altruistic planner) or to induce a specific action the planner prefers (a biased planner). Our framework presents a new optimization problem for social learning that combines dynamic programming with decentralized action choices and Bayesian belief updates. In this setting, we prove the convexity of the value function and characterize the optimal policies of altruistic and biased planners, which attain desired tradeoffs between the costs they incur and the payoffs they earn from induced agent choices. The characterization reveals that the optimal planner operates in different modes depending on the range of belief values. The modes include investing the maximum allowed resource, not investing any resource, or the investment increasing or decreasing with increase in the belief. Notably, for some ranges of belief the biased planner even intentionally obfuscates the agents' signals. Even under stringent transparency constraints—information parity with individuals, no lying or cherry‑picking, and full observability—we show that information mediation can substantially shift social welfare in either direction. We complement our theory with simulations in which LLMs act as both planner and agents. Notably, the LLM-based planner in our simulations exhibits emergent strategic behavior in steering public opinion that broadly mirrors the trends predicted, though key deviations suggest the influence of non-Bayesian reasoning—consistent with the cognitive patterns of both human users and LLMs trained on human-like data. Together, we establish our framework as a tractable basis for studying the impact and regulation of LLM information mediators that corresponds to real behavior.

Marco Bagatella, Matteo Pirotta, Ahmed Touati, Alessandro Lazaric, Andrea Tirinzoni

Latent prediction–where agents learn by predicting their own latents–has emerged as a powerful paradigm for training general representations in machine learning. In reinforcement learning (RL), this approach has been explored to define auxiliary losses for a variety of settings, including reward-based and unsupervised RL, behavior cloning, and world modeling. While existing methods are typically limited to single-task learning, one-step prediction, or on-policy trajectory data, we show that temporal difference (TD) learning enables learning representations predictive of long-term latent dynamics across multiple policies from offline, reward-free transitions. Building on this, we introduce TD-JEPA, which leverages TD-based latent-predictive representations into unsupervised RL. TD-JEPA trains explicit state and task encoders, a policy-conditioned multi-step predictor, and a set of parameterized policies directly in latent space. This enables zero-shot optimization of any reward function at test time. Theoretically, we show that an idealized variant of TD-JEPA avoids collapse with proper initialization, and learns encoders that capture a low-rank factorization of long-term policy dynamics, while the predictor recovers their successor features in latent space. Empirically, TD-JEPA matches or outperforms state-of-the-art baselines on locomotion, navigation, and manipulation tasks across 13 datasets in ExoRL and OGBench, especially in the challenging setting of zero-shot RL from pixels.

Xiaoyuan Cheng, Wenxuan Yuan, Yiming Yang, Yuanzhao Zhang, Sibo Cheng, Yi He, Zhuo Sun

The Koopman operator provides a powerful framework for modeling dynamical systems and has attracted growing interest from the machine learning community. However, its infinite-dimensional nature makes identifying suitable finite-dimensional subspaces challenging, especially for deep architectures. We argue that these difficulties come from suboptimal representation learning, where latent variables fail to balance expressivity and simplicity. This tension is closely related to the information bottleneck (IB) dilemma: constructing compressed representations that are both compact and predictive. Rethinking Koopman learning through this lens, we demonstrate that latent mutual information promotes simplicity, yet an overemphasis on simplicity may cause latent space to collapse onto a few dominant modes. In contrast, expressiveness is sustained by the von Neumann entropy, which prevents such collapse and encourages mode diversity. This insight leads us to propose an information-theoretic Lagrangian formulation that explicitly balances this tradeoff. Furthermore, we propose a new algorithm based on the Lagrangian formulation that encourages both simplicity and expressiveness, leading to a stable and interpretable Koopman representation. Beyond quantitative evaluations, we further visualize the learned manifolds under our representations, observing empirical results consistent with our theoretical predictions. Finally, we validate our approach across a diverse range of dynamical systems, demonstrating improved performance over existing Koopman learning methods.

Zhaomin Wu, Haodong Zhao, Ziyang Wang, Jizhou Guo, Qian Wang, Bingsheng He

The explosive growth of large language models (LLMs) has created a vast but opaque landscape: millions of models exist, yet their evolutionary relationships through fine-tuning, distillation, or adaptation are often undocumented or unclear, complicating LLM management. Existing methods are limited by task specificity, fixed model sets, or strict assumptions about tokenizers or architectures. Inspired by biological DNA, we address these limitations by mathematically defining *LLM DNA* as a low-dimensional, bi-Lipschitz representation of functional behavior. We prove that LLM DNA satisfies *inheritance* and *genetic determinism* and establish its existence. Building on this theory, we derive a general, scalable, training-free pipeline for DNA extraction. In experiments across 305 LLMs, DNA aligns with prior studies on limited subsets and achieves superior or competitive performance on various tasks. Beyond these tasks, DNA comparisons uncover previously undocumented relationships among LLMs. We further construct the evolutionary tree of LLMs using phylogenetic algorithms, which align with shifts from encoder-decoder to decoder-only architectures, reflect temporal progression, and reveal distinct evolutionary speeds across LLM families.