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Reinforcement Learning · Everything Else

Christian Walder, Deep Tejas Karkhanis

Reinforcement Learning algorithms commonly sample multiple ($n>1$) solution attempts for each problem and reward them independently. This optimizes for pass@1 performance and prioritizes individual sample performance over the diversity and collective utility of a set of samples. Such algorithms under-utilize the sampling capacity, limiting exploration and eventual improvement on harder examples. As a fix, we propose Pass-at-$k$ Policy Optimization (PKPO), a multivariate transformation on batches of rewards which leads to direct optimization of \passk\ performance, thus optimizing for sets of samples that feature a large maximum reward when considered jointly. Our primary contribution is to derive novel low variance unbiased estimators for the pass@k and its gradient, in both the binary and continuous reward settings. We show that optimizing with these estimators reduces to reinforcement learning with (batches of) rewards that have been jointly transformed by a function that is stable and efficient to compute. While previous efforts propose transformations for $k=n$, our transformations are the first to enable robust optimization of the pass@k for any arbitrary $k \leq n$. Rather than simply trading off pass@1 performance for pass@k gains, our method allows annealing $k$ during training, optimizing both metrics and often achieving strong pass@1 performance alongside significant pass@k gains. We validate our transformations on illustrative toy experiments, which reveal the variance reducing properties of our formulations. We also include real-world examples using the open-source models Gemma and Llama . We find that our transformation effectively optimizes for the target $k$. Furthermore, higher $k$ values enable solving more and harder problems, while annealing $k$ boosts both the pass@1 and pass@k. Crucially, for challenging task sets where conventional pass@1 optimization stalls, our pass@k approach unblocks learning, likely by improving exploration through the prioritization of joint utility over the utility of individual samples

Applications · Neuroscience, Cognitive Science

Tianhao Chu, Yuling Wu, Neil Burgess, Zilong Ji, Si Wu

Path integration is essential for spatial navigation. Experimental studies have identified neural correlates for path integration, but exactly how the neural system accomplishes this computation remains unresolved. Here, we adopt recurrent neural networks (RNNs) trained to perform a path integration task to explore this issue. After training, we borrow neuroscience prior knowledge and methods to unfold the black box of the trained model, including: clarifying neuron types based on their receptive fields, dissecting information flows between neuron groups by pruning their connections, and analyzing internal dynamics of neuron groups using the attractor framework. Intriguingly, we uncover a hierarchical information processing pathway embedded in the RNN model, along which velocity information of an agent is first forwarded to band cells, band and grid cells then coordinate to carry out path integration, and finally grid cells output the agent location. Inspired by the RNN-based study, we construct a neural circuit model, in which band cells form one-dimensional (1D) continuous attractor neural networks (CANNs) and serve as upstream neurons to support downstream grid cells to carry out path integration in the 2D space. Our study challenges the conventional view of considering grid cells as the principal velocity integrator, and supports a neural circuit model with the hierarchy of band and grid cells.

Computer Vision · Image and Video Generation

Noam Elata, Hyungjin Chung, Jong Chul Ye, Tomer Michaeli, Miki Elad

Diffusion Models have demonstrated remarkable capabilities in handling inverse problems, offering high-quality posterior-sampling-based solutions. Despite significant advances, a fundamental trade-off persists regarding the way the conditioned synthesis is employed: Zero-shot approaches can accommodate any linear degradation but rely on approximations that reduce accuracy. In contrast, training-based methods model the posterior correctly, but cannot adapt to the degradation at test-time. Here we introduce InvFusion, the first training-based degradation-aware posterior sampler. InvFusion combines the best of both worlds - the strong performance of supervised approaches and the flexibility of zero-shot methods. This is achieved through a novel architectural design that seamlessly integrates the degradation operator directly into the diffusion denoiser. We compare InvFusion against existing general-purpose posterior samplers, both degradation-aware zero-shot techniques and blind training-based methods. Experiments on the FFHQ and ImageNet datasets demonstrate state-of-the-art performance. Beyond posterior sampling, we further demonstrate the applicability of our architecture, operating as a general Minimum Mean Square Error predictor, and as a Neural Posterior Principal Component estimator.

Optimization

Runyu Zhang, Arvind Raghunathan, Jeff Shamma, Na Li

Tools from control and dynamical systems have proven valuable for analyzing and developing optimization methods. In this paper, we establish rigorous theoretical foundations for using feedback linearization—a well-established nonlinear control technique—to solve constrained optimization problems. For equality-constrained optimization, we establish global convergence rates to first-order Karush-Kuhn-Tucker (KKT) points and uncover the close connection between the FL method and the Sequential Quadratic Programming (SQP) algorithm. Building on this relationship, we extend the FL approach to handle inequality-constrained problems. Furthermore, we introduce a momentum-accelerated feedback linearization algorithm and provide a rigorous convergence guarantee.

Theory · Learning Theory

Yuchen Liang, Renxiang Huang, Lifeng LAI, Ness Shroff, Yingbin Liang

Discrete state space diffusion models have shown significant advantages in applications involving discrete data, such as text and image generation. It has also been observed that their performance is highly sensitive to the choice of rate matrices, particularly between uniform and absorbing rate matrices. While empirical results suggest that absorbing rate matrices often yield better generation quality compared to uniform rate matrices, existing theoretical works have largely focused on the uniform rate matrices case. Notably, convergence guarantees and error analyses for absorbing diffusion models are still missing. In this work, we provide the first finite-time error bounds and convergence rate analysis for discrete diffusion models using absorbing rate matrices. We begin by deriving an upper bound on the KL divergence of the forward process, introducing a surrogate initialization distribution to address the challenge posed by the absorbing stationary distribution, which is a singleton and causes the KL divergence to be ill-defined. We then establish the first convergence guarantees for both the $\tau$-leaping and uniformization samplers under absorbing rate matrices, demonstrating improved rates over their counterparts using uniform rate matrices. Furthermore, under suitable assumptions, we provide convergence guarantees without early stopping. Our analysis introduces several new technical tools to address challenges unique to absorbing rate matrices. These include a Jensen-type argument for bounding forward process convergence, novel techniques for bounding absorbing score functions, and a non-divergent upper bound on the score near initialization that removes the need of early-stopping.

General Machine Learning · Everything Else

Tam Le, Truyen Nguyen, Hideitsu Hino, Kenji Fukumizu

We investigate optimal transport (OT) for measures on graph metric spaces with different total masses. To mitigate the limitations of traditional $L^p$ geometry, Orlicz-Wasserstein (OW) and generalized Sobolev transport (GST) employ \emph{Orlicz geometric structure}, leveraging convex functions to capture nuanced geometric relationships and remarkably contribute to advance certain machine learning approaches. However, both OW and GST are restricted to measures with equal total mass, limiting their applicability to real-world scenarios where mass variation is common, and input measures may have noisy supports, or outliers. To address unbalanced measures, OW can either incorporate mass constraints or marginal discrepancy penalization, but this leads to a more complex two-level optimization problem. Additionally, GST provides a scalable yet rigid framework, which poses significant challenges to extend GST to accommodate nonnegative measures. To tackle these challenges, in this work we revisit the entropy partial transport (EPT) problem. By exploiting Caffarelli \& McCann's insights, we develop a novel variant of EPT endowed with Orlicz geometric structure, called \emph{Orlicz-EPT}. We establish theoretical background to solve Orlicz-EPT using a binary search algorithmic approach. Especially, by leveraging the dual EPT and the underlying graph structure, we formulate a novel regularization approach that leads to the proposed \emph{Orlicz-Sobolev transport} (OST). Notably, we demonstrate that OST can be efficiently computed by simply solving a univariate optimization problem, in stark contrast to the intensive computation needed for Orlicz-EPT. Building on this, we derive geometric structures for OST and draw its connections to other transport distances. We empirically illustrate that OST is several-order faster than Orlicz-EPT. Furthermore, we show preliminary evidence on the advantages of OST for measures on a graph in document classification and topological data analysis.

Applications · Language, Speech and Dialog

Yang Xiao, Jiashuo WANG, Ruifeng Yuan, Chunpu Xu, Kaishuai Xu, Wenjie Li, Pengfei Liu

Large language models (LLMs) have demonstrated remarkable reasoning capabilities through test-time scaling approaches, particularly when fine-tuned with chain-of-thought (CoT) data distilled from more powerful large reasoning models (LRMs). However, these reasoning chains often contain verbose elements that mirror human problem-solving, categorized as progressive reasoning (the essential solution development path) and functional elements (verification processes, alternative solution approaches, and error corrections). While progressive reasoning is crucial, the functional elements significantly increase computational demands during test-time inference. We introduce PIR (Perplexity-based Importance Refinement), a principled framework that quantitatively evaluates the importance of each reasoning step based on its impact on answer prediction confidence. PIR systematically identifies and selectively prunes only low-importance functional steps while preserving all progressive reasoning components, creating optimized training data that maintains the integrity of the core solution path while reducing verbosity. Models fine-tuned on PIR-optimized data exhibit superior test-time scaling properties, generating more concise reasoning chains while achieving improved accuracy (+0.9\% to +6.6\%) with significantly reduced token usage (-3\% to -41\%) across challenging reasoning benchmarks (AIME, AMC, and GPQA Diamond). Our approach demonstrates strong generalizability across different model sizes, data sources, and token budgets, offering a practical solution for deploying reasoning-capable LLMs in scenarios where efficient test-time scaling, response time, and computational efficiency are valuable constraints. Code and dataset are available at the [LIMOPro GitHub repository.](https://github.com/GAIR-NLP/LIMOPro)

General Machine Learning · Everything Else

Maximilien Dreveton, Elaine Liu, Matthias Grossglauser, Patrick Thiran

This paper establishes the theoretical limits of graph clustering under the Popularity-Adjusted Block Model (PABM), addressing limitations of existing models. In contrast to the Stochastic Block Model (SBM), which assumes uniform vertex degrees, and to the Degree-Corrected Block Model (DCBM), which applies uniform degree corrections across clusters, PABM introduces separate popularity parameters for intra- and inter-cluster connections. Our main contribution is the characterization of the optimal error rate for clustering under PABM, which provides novel insights on clustering hardness: we demonstrate that unlike SBM and DCBM, cluster recovery remains possible in PABM even when traditional edge-density signals vanish, provided intra- and inter-cluster popularity coefficients differ. This highlights a dimension of degree heterogeneity captured by PABM but overlooked by DCBM: local differences in connectivity patterns can enhance cluster separability independently of global edge densities. Finally, because PABM exhibits a richer structure, its expected adjacency matrix has rank between $k$ and $k^2$, where $k$ is the number of clusters. As a result, spectral embeddings based on the top $k$ eigenvectors may fail to capture important structural information. Our numerical experiments on both synthetic and real datasets confirm that spectral clustering algorithms incorporating $k^2$ eigenvectors outperform traditional spectral approaches.

Applications · Chemistry and Drug Discovery

Lorenz Vaitl, Leon Klein

Boltzmann Generators have emerged as a promising machine learning tool for generating samples from equilibrium distributions of molecular systems using Normalizing Flows and importance weighting. Recently, Flow Matching has helped speed up Continuous Normalizing Flows (CNFs), scale them to more complex molecular systems, and minimize the length of the flow integration trajectories. We investigate the benefits of using path gradients to fine-tune CNFs initially trained by Flow Matching, in the setting where a target energy is known. Our experiments show that this hybrid approach yields up to a threefold increase in sampling efficiency for molecular systems, all while using the same model, a similar computational budget and without the need for additional sampling. Furthermore, by measuring the length of the flow trajectories during fine-tuning, we show that path gradients largely preserve the learned structure of the flow.

Data-centric AI · Data-centric AI methods and tools

Alex Fang, Hadi Pouransari, Matt Jordan, Alexander Toshev, Vaishaal Shankar, Ludwig Schmidt, Tom Gunter

Data filtering has become a powerful tool for improving model performance while reducing computational cost. However, as large language model compute budgets continue to grow, the limited data volume provided by heavily filtered and deduplicated datasets will become a practical constraint. In efforts to better understand how to proceed, we study model performance at various compute budgets and across multiple pre-training datasets created through data filtering and deduplication. We find that, given appropriate modifications to the training recipe, repeating existing aggressively filtered datasets for up to ten epochs can outperform training on the ten times larger superset for a single epoch across multiple compute budget orders of magnitude. While this finding relies on repeating the dataset for many epochs, we also investigate repeats within these datasets at the document level. We find that not all documents within a dataset are equal, and we can create better datasets relative to a token budget by explicitly manipulating the counts of individual documents. We conclude by arguing that even as large language models scale, data filtering remains an important direction of research.

Theory · Learning Theory

Carlos Misael Madrid Padilla, OSCAR HERNAN MADRID PADILLA, Sabyasachi Chatterjee

This work examines risk bounds for nonparametric distributional regression estimators. For convex-constrained distributional regression, general upper bounds are established for the continuous ranked probability score (CRPS) and the worst-case mean squared error (MSE) across the domain. These theoretical results are applied to isotonic and trend filtering distributional regression, yielding convergence rates consistent with those for mean estimation. Furthermore, a general upper bound is derived for distributional regression under non-convex constraints, with a specific application to neural network-based estimators. Comprehensive experiments on both simulated and real data validate the theoretical contributions, demonstrating their practical effectiveness.

Computer Vision · Image and Video Generation

Zhiying Jiang, Ruhao Yan, Zengxi Zhang, Bowei Zhang, Jinyuan Liu

Image stitching synthesizes images captured from multiple perspectives into a single image with a broader field of view. The significant variations in object depth often lead to large parallax, resulting in ghosting and misalignment in the stitched results. To address this, we propose a depth-consistency-constrained seamless-free image stitching method. First, to tackle the multi-view alignment difficulties caused by parallax, a multi-stage mechanism combined with global depth regularization constraints is developed to enhance the alignment accuracy of the same apparent target across different depth ranges. Second, during the multi-view image fusion process, an optimal stitching seam is determined through graph-based low-cost computation, and a soft-seam region is diffused to precisely locate transition areas, thereby effectively mitigating alignment errors induced by parallax and achieving natural and seamless stitching results. Furthermore, considering the computational overhead in the shift regression process, a reparameterization strategy is incorporated to optimize the structural design, significantly improving algorithm efficiency while maintaining optimal performance. Extensive experiments demonstrate the superior performance of the proposed method against the existing methods. Code is available at https://github.com/DLUT-YRH/DSFN.

Computer Vision · Vision Models & Multimodal

Junhao Shen, Haiteng Zhao, Yuzhe Gu, Songyang Gao, Kuikun Liu, Haian Huang, Jianfei Gao, Dahua Lin, Wenwei Zhang, Kai Chen

Enhancing large vision-language models (LVLMs) with visual slow-thinking reasoning is crucial for solving complex multimodal tasks. However, since LVLMs are mainly trained with vision-language alignment, it is difficult to adopt on-policy reinforcement learning (RL) to develop the slow thinking ability because the rollout space is restricted by its initial abilities. Off-policy RL offers a way to go beyond the current policy, but directly distilling trajectories from external models may cause visual hallucinations due to mismatched visual perception abilities across models. To address these issues, this paper proposes **SOPHIA**, a simple and scalable **S**emi-**O**ff-**P**olicy RL for vision-language slow-t**HI**nking re**A**soning. SOPHIA builds a semi-off-policy behavior model by combining on-policy visual understanding from a trainable LVLM with off-policy slow-thinking reasoning from a language model, assigns outcome-based rewards to reasoning, and propagates visual rewards backward. Then LVLM learns slow-thinking reasoning ability from the obtained reasoning trajectories using propagated rewards via off-policy RL algorithms. Extensive experiments with InternVL2.5 and InternVL3.0 with 8B and 38B sizes show the effectiveness of SOPHIA. Notably, SOPHIA improves InternVL3.0-38B by 8.50\% in average, reaching state-of-the-art performance among open-source LVLMs on multiple multimodal reasoning benchmarks, and even outperforms some closed-source models (e.g., GPT-4.1) on the challenging MathVision and OlympiadBench, achieving 49.08\% and 49.95\% pass@1 accuracy, respectively. Analysis shows SOPHIA outperforms supervised fine-tuning and direct on-policy RL methods, offering a better policy initialization for further on-policy training.

Applications · Genetics, Cell Biology, etc

Jiayuan Ding, Jianhui Lin, Shiyu Jiang, Yixin Wang, Ziyang Miao, Zhaoyu Fang, Jiliang Tang, Min Li, Xiaojie Qiu

Foundation models (FMs) have shown great promise in single-cell genomics, yet current approaches, such as scGPT, Geneformer, and scFoundation, rely on centralized training and language modeling objectives that overlook the tabular nature of single-cell data and raise significant privacy concerns. We present TABULA, a foundation model designed for single-cell transcriptomics, which integrates a novel tabular modeling objective and federated learning framework to enable privacy-preserving pretraining across decentralized datasets. TABULA directly models the cell-by-gene expression matrix through column-wise gene reconstruction and row-wise cell contrastive learning, capturing both gene-level relationships and cell-level heterogeneity without imposing artificial gene sequence order. Extensive experiments demonstrate the effectiveness of TABULA: despite using only half the pretraining data, TABULA achieves state-of-the-art performance across key tasks, including gene imputation, perturbation prediction, cell type annotation, and multi-omics integration. It is important to note that as public single-cell datasets continue to grow, TABULA provides a scalable and privacy-aware foundation that not only validates the feasibility of federated tabular modeling but also establishes a generalizable framework for training future models under similar privacy-preserving settings.

Computer Vision · Vision Models & Multimodal

Andrea Amaduzzi, Pierluigi Zama Ramirez, Giuseppe Lisanti, Samuele Salti, Luigi Di Stefano

Neural Radiance Fields (NeRFs) are neural networks -- typically multilayer perceptrons (MLPs) -- that represent the geometry and appearance of objects, with applications in vision, graphics, and robotics. Recent works propose understanding NeRFs with natural language using Multimodal Large Language Models (MLLMs) that directly process the weights of a NeRF's MLP. However, these approaches rely on a global representation of the input object, making them unsuitable for spatial reasoning and fine-grained understanding. In contrast, we propose **weights2space**, a self-supervised framework featuring a novel meta-encoder that can compute a sequence of spatial tokens directly from the weights of a NeRF. Leveraging this representation, we build **Spatial LLaNA**, a novel MLLM for NeRFs, capable of understanding details and spatial relationships in objects represented as NeRFs. We evaluate Spatial LLaNA on NeRF captioning and NeRF Q&A tasks, using both existing benchmarks and our novel **Spatial ObjaNeRF** dataset consisting of $100$ manually-curated language annotations for NeRFs. This dataset features 3D models and descriptions that challenge the spatial reasoning capability of MLLMs. Spatial LLaNA outperforms existing approaches across all tasks.

Computer Vision · Segmentation

Yuli Zhou, Yawei Li, Yuqian Fu, Luca Benini, Ender Konukoglu, Guolei Sun

Video camouflaged object segmentation (VCOS), aiming at segmenting camouflaged objects that seamlessly blend into their environment, is a fundamental vision task with various real-world applications. With the release of SAM2, video segmentation has witnessed significant progress. However, SAM2's capability of segmenting camouflaged videos is suboptimal, especially when given simple prompts such as point and box. To address the problem, we propose Camouflaged SAM2 (CamSAM2), which enhances SAM2's ability to handle camouflaged scenes without modifying SAM2's parameters. Specifically, we introduce a decamouflaged token to provide the flexibility of feature adjustment for VCOS. To make full use of fine-grained and high-resolution features from the current frame and previous frames, we propose implicit object-aware fusion (IOF) and explicit object-aware fusion (EOF) modules, respectively. Object prototype generation (OPG) is introduced to abstract and memorize object prototypes with informative details using high-quality features from previous frames. Extensive experiments are conducted to validate the effectiveness of our approach. While CamSAM2 only adds negligible learnable parameters to SAM2, it substantially outperforms SAM2 on three VCOS datasets, especially achieving 12.2 mDice gains with click prompt on MoCA-Mask and 19.6 mDice gains with mask prompt on SUN-SEG-Hard, with Hiera-T as the backbone. The code is available at https://github.com/zhoustan/CamSAM2.

Reinforcement Learning · Batch Offline

Juan Formanek, Omayma Mahjoub, Louay Nessir, Sasha Abramowitz, Ruan John de Kock, Wiem Khlifi, Daniel Rajaonarivonivelomanantsoa, Simon Du Toit, Arnol Fokam, Siddarth Singh 等

A key challenge in offline multi-agent reinforcement learning (MARL) is achieving effective many-agent multi-step coordination in complex environments. In this work, we propose Oryx, a novel algorithm for offline cooperative MARL to directly address this challenge. Oryx adapts the recently proposed retention-based architecture Sable and combines it with a sequential form of implicit constraint Q-learning (ICQ), to develop a novel offline autoregressive policy update scheme. This allows Oryx to solve complex coordination challenges while maintaining temporal coherence over long trajectories. We evaluate Oryx across a diverse set of benchmarks from prior works—SMAC, RWARE, and Multi-Agent MuJoCo—covering tasks of both discrete and continuous control, varying in scale and difficulty. Oryx achieves state-of-the-art performance on more than 80% of the 65 tested datasets, outperforming prior offline MARL methods and demonstrating robust generalisation across domains with many agents and long horizons. Finally, we introduce new datasets to push the limits of many-agent coordination in offline MARL, and demonstrate Oryx's superior ability to scale effectively in such settings.

Optimization · Neural Network Optimization

Tong Zhao, Jiacheng Li, Yuanchang Zhou, Guangming Tan, Weile Jia

Finding lower and better-generalizing minima is crucial for deep learning. However, most existing optimizers stop searching the parameter space once they reach a local minimum. Given the complex geometric properties of the loss landscape, it is difficult to guarantee that such a point is the lowest or provides the best generalization. To address this, we propose an adaptor "E" for gradient-based optimizers. The adapted optimizer tends to continue exploring along landscape valleys (areas with low and nearly identical losses) in order to search for potentially better local minima even after reaching a local minimum. This approach increases the likelihood of finding a lower and flatter local minimum, which is often associated with better generalization. We also provide a proof of convergence for the adapted optimizers in both convex and non-convex scenarios for completeness. Finally, we demonstrate their effectiveness in an important but notoriously difficult training scenario, large-minibatch training, where Lamb is the benchmark optimizer. Our testing results show that the adapted Lamb, ALTO, increases the test accuracy (generalization) of the current state-of-the-art optimizer by an average of 2.5\% across a variety of large-batch training tasks. This work potentially opens a new research direction in the design of optimization algorithms.

Reinforcement Learning · Everything Else

Qiyang Li, Zhiyuan (Paul) Zhou, Sergey Levine

We present Q-chunking, a simple yet effective recipe for improving reinforcement learning (RL) algorithms for long-horizon, sparse-reward tasks. Our recipe is designed for the offline-to-online RL setting, where the goal is to leverage an offline prior dataset to maximize the sample-efficiency of online learning. Effective exploration and sample-efficient learning remain central challenges in this setting, as it is not obvious how the offline data should be utilized to acquire a good exploratory policy. Our key insight is that action chunking, a technique popularized in imitation learning where sequences of future actions are predicted rather than a single action at each timestep, can be applied to temporal difference (TD)-based RL methods to mitigate the exploration challenge. Q-chunking adopts action chunking by directly running RL in a *chunked* action space, enabling the agent to (1) leverage temporally consistent behaviors from offline data for more effective online exploration and (2) use unbiased $n$-step backups for more stable and efficient TD learning. Our experimental results demonstrate that Q-chunking exhibits strong offline performance and online sample efficiency, outperforming prior best offline-to-online methods on a range of long-horizon, sparse-reward manipulation tasks.

General Machine Learning · Everything Else

Zhengyao Huang, Daniel Huang, Tiannan Xiao, Dina Ma, Zhenyu Ming, Hao Shi, Yuanhui Wen

Symbolic regression aims to discover concise, interpretable mathematical expressions that satisfy desired objectives, such as fitting data, posing a highly combinatorial optimization problem. While genetic programming has been the dominant approach, recent efforts have explored reinforcement learning methods for improving search efficiency. Monte Carlo Tree Search (MCTS), with its ability to balance exploration and exploitation through guided search, has emerged as a promising technique for symbolic expression discovery. However, its traditional bandit strategies and sequential symbol construction often limit performance. In this work, we propose an improved MCTS framework for symbolic regression that addresses these limitations through two key innovations: (1) an extreme bandit allocation strategy tailored for identifying globally optimal expressions, with finite-time performance guarantees under polynomial reward decay assumptions; and (2) evolution-inspired state-jumping actions such as mutation and crossover, which enable non-local transitions to promising regions of the search space. These state-jumping actions also reshape the reward landscape during the search process, improving both robustness and efficiency. We conduct a thorough numerical study to the impact of these improvements and benchmark our approach against existing symbolic regression methods on a variety of datasets, including both ground-truth and black-box datasets. Our approach achieves competitive performance with state-of-the-art libraries in terms of recovery rate, attains favorable positions on the Pareto frontier of accuracy versus model complexity.