论文检索

Applications · Genetics, Cell Biology, etc

Qihao Duan, Bingding Huang, Zhenqiao Song, Irina Lehmann, Lei Gu, Roland Eils, Benjamin Wild

Large language models (LLMs) have revolutionized natural language processing and are increasingly applied to other sequential data types, including genetic sequences. However, adapting LLMs to genetics presents significant challenges. Capturing complex genomic interactions requires modeling long-range global dependencies within DNA sequences, where interactions often span over 10,000 base pairs, even within a single gene. This poses substantial computational demands under conventional model architectures and training paradigms. Additionally, traditional LLM training approaches are suboptimal for DNA sequences: autoregressive training, while efficient for training, only supports unidirectional sequence understanding. However, DNA is inherently bidirectional. For instance, bidirectional promoters regulate gene expression in both directions and govern approximately 11% of human gene expression. Masked language models (MLMs) enable bidirectional understanding. However, they are inefficient since only masked tokens contribute to loss calculations at each training step. To address these limitations, we introduce JanusDNA, the first bidirectional DNA foundation model built upon a novel pretraining paradigm, integrating the optimization efficiency of autoregressive modeling with the bidirectional comprehension capability of masked modeling. JanusDNA's architecture leverages a Mamba-Attention Mixture-of-Experts (MoE) design, combining the global, high-resolution context awareness of attention mechanisms with the efficient sequential representation learning capabilities of Mamba. The MoE layers further enhance the model's capacity through sparse parameter scaling, while maintaining manageable computational costs. Notably, JanusDNA can process up to 1 million base pairs at single-nucleotide resolution on a single 80GB GPU using its hybrid architecture. Extensive experiments and ablation studies demonstrate that JanusDNA achieves new state-of-the-art performance on three genomic representation benchmarks. Remarkably, JanusDNA surpasses models with 250x more activated parameters, underscoring its efficiency and effectiveness. Code available at https://anonymous.4open.science/r/JanusDNA/.

Computer Vision · Image and Video Generation

Huimin Wu, Xiaojian (Shawn) Ma, Haozhe Zhao, Yanpeng Zhao, Qing Li

Text-guided image editing involves modifying a source image based on a language instruction and, typically, requires changes to only small local regions. However, existing approaches generate the entire target image rather than selectively regenerate only the intended editing areas. This results in (1) unnecessary computational costs and (2) a bias toward reconstructing non-editing regions, which compromises the quality of the intended edits. To resolve these limitations, we propose to formulate image editing as $\textbf{N}$ext $\textbf{E}$diting-token $\textbf{P}$rediction (NEP) based on autoregressive image generation, where only regions that need to be edited are regenerated, thus avoiding unintended modification to the non-editing areas. To enable any-region editing, we propose to pre-train an any-order autoregressive text-to-image (T2I) model. Once trained, it is capable of zero-shot image editing and can be easily adapted to NEP for image editing, which achieves a new state-of-the-art on widely used image editing benchmarks. Moreover, our model naturally supports test-time scaling (TTS) through iteratively refining its generation in a zero-shot manner.

Dionysis Arvanitakis, Vaidehi Srinivas, Aravindan Vijayaraghavan

Tensor decomposition is a canonical non-convex optimization problem that is computationally challenging, and yet important due to applications in factor analysis and parameter estimation of latent variable models. In practice, scalable iterative methods, particularly Alternating Least Squares (ALS), remain the workhorse for tensor decomposition despite the lack of global convergence guarantees. A popular approach to tackle challenging non-convex optimization problems is overparameterization--- on input an $n \times n \times n$ tensor of rank $r$, the algorithm can output a decomposition of potentially rank $k$ (potentially larger than $r$). On the theoretical side, overparameterization for iterative methods is challenging to reason about and requires new techniques. The work of Wang et al., (NeurIPS 2020) makes progress by showing that a variant of gradient descent globally converges when overparameterized to $k=O(r^{7.5} \log n)$. Our main result shows that overparameterization provably enables global convergence of ALS: on input a third order $n \times n \times n$ tensor with a decomposition of rank $r \ll n$, ALS overparameterized with rank $k=O(r^2)$ achieves global convergence with high probability under random initialization. Moreover our analysis also gives guarantees for the more general low-rank approximation problem. The analysis introduces new techniques for understanding iterative methods in the overparameterized regime based on new matrix anticoncentration arguments.

Social Aspects · Trustworthy Machine Learning

Liang Yan, Shengzhong Zhang, Bisheng Li, Menglin Yang, Chen Yang, Min Zhou, Weiyang Ding, Yutong Xie, zengfeng Huang

Class imbalance in graph data presents a significant challenge for effective node classification, particularly in semi-supervised scenarios. In this work, we formally introduce the concept of geometric imbalance, which captures how message passing on class-imbalanced graphs leads to geometric ambiguity among minority-class nodes in the riemannian manifold embedding space. We provide a rigorous theoretical analysis of geometric imbalance on the riemannian manifold and propose a unified framework that explicitly mitigates it through pseudo-label alignment, node reordering, and ambiguity filtering. Extensive experiments on diverse benchmarks show that our approach consistently outperforms existing methods, especially under severe class imbalance. Our findings offer new theoretical insights and practical tools for robust semi-supervised node classification.

Applications · Climate

Rishabh Mondal, Jeet Parab, Heer Kubadia, Shataxi Dubey, Shardul Junagade, Zeel Bharatkumar Patel, Nipun Batra

Air pollution was responsible for 2.6 million deaths across South Asia in 2021 alone, with brick manufacturing contributing significantly to this burden. In particular, the Indo-Gangetic Plain; a densely populated and highly polluted region spanning northern India, Pakistan, Bangladesh, and parts of Afghanistan sees brick kilns contributing 8–14% of ambient air pollution. Traditional monitoring approaches, such as field surveys and manual annotation using tools like Google Earth Pro, are time and labor-intensive. Prior ML-based efforts for automated detection have relied on costly high-resolution commercial imagery and non-public datasets, limiting reproducibility and scalability. In this work, we introduce SENTINELKILNDB, a publicly available, hand-validated benchmark of 62,671 brick kilns spanning threekiln types Fixed Chimney Bull’s Trench Kiln (FCBK), Circular FCBK (CFCBK), and Zigzag kilns - annotated with oriented bounding boxes (OBBs) across 2.8 million km2 using free and globally accessible Sentinel-2 imagery. We benchmark state-of-the-art oriented object detection models and evaluate generalization across in-region, out-of-region, and super-resolution settings. SENTINELKILNDB enables rigorous evaluation of geospatial generalization and robustness for low-resolution object detection, and provides a new testbed for ML models addressing real-world environmental and remote sensing challenges at a continental scale. Datasets and code are available in SentinelKilnDB Dataset and SentinelKilnDB Bench-mark, under the Creative Commons Attribution–NonCommercial 4.0 International License.

Applications

Raghu Vamshi Hemadri, Jitendra Bhandari, Andre Nakkab, Johann Knechtel, Badri Gopalan, Ramesh Narayanaswamy, Ramesh Karri, Siddharth Garg

Modern chip design is complex, and there is a crucial need for early-stage prediction of key design-quality metrics like timing and routing congestion directly from Verilog code (a commonly used programming language for hardware design). It is especially important yet complex to predict individual lines of code that cause timing violations or downstream routing congestion. Prior works have tried approaches like converting Verilog into an intermediate graph representation and using LLM embeddings alongside other features to predict module-level quality, but did not consider line-level quality prediction. We propose VeriLoC, the first method that predicts design quality directly from Verilog at both the line- and module-level. To this end, VeriLoC leverages recent Verilog code-generation LLMs to extract local line-level and module-level embeddings, and trains downstream classifiers/regressors on concatenations of these embeddings. VeriLoC achieves high F1-scores of 0.86-0.95 for line-level congestion and timing prediction, and reduces the mean average percentage error from 14%-18% for SOTA methods down to only 4%. We believe that VeriLoC embeddings and insights from our work will also be of value for other predictive and optimization tasks for complex hardware design.

Computer Vision · Vision Models & Multimodal

Wufei Ma, Yu-Cheng Chou, Qihao Liu, Xingrui Wang, Celso de Melo, Jianwen Xie, Alan Yuille

Despite recent advances on multi-modal models, 3D spatial reasoning remains a challenging task for state-of-the-art open-source and proprietary models. Recent studies explore data-driven approaches and achieve enhanced spatial reasoning performance by fine-tuning models on 3D-related visual question-answering data. However, these methods typically perform spatial reasoning in an implicit manner and often fail on questions that are trivial to humans, even with long chain-of-thought reasoning. In this work, we introduce SpatialReasoner, a novel large vision-language model (LVLM) that addresses 3D spatial reasoning with explicit 3D representations shared between multiple stages--3D perception, computation, and reasoning. Explicit 3D representations provide a coherent interface that supports advanced 3D spatial reasoning and improves the generalization ability to novel question types. Furthermore, by analyzing the explicit 3D representations in multi-step reasoning traces of SpatialReasoner, we study the factual errors and identify key shortcomings of current LVLMs. Results show that our SpatialReasoner achieves improved performance on a variety of spatial reasoning benchmarks, outperforming Gemini 2.0 by 9.2% on 3DSRBench, and generalizes better when evaluating on novel 3D spatial reasoning questions. Our study bridges the 3D parsing capabilities of prior visual foundation models with the powerful reasoning abilities of large language models, opening new directions for 3D spatial reasoning.

Computer Vision · Everything Else

Lishen Qu, Zhihao Liu, Jinshan Pan, Shihao Zhou, Jinglei Shi, Duosheng Chen, Jufeng Yang

Lens flare occurs when shooting towards strong light sources, significantly degrading the visual quality of images. Due to the difficulty in capturing flare-corrupted and flare-free image pairs in the real world, existing datasets are typically synthesized in 2D by overlaying artificial flare templates onto background images. However, the lack of flare diversity in templates and the neglect of physical principles in the synthesis process hinder models trained on these datasets from generalizing well to real-world scenarios. To address these challenges, we propose a new physics-informed method for flare data generation, which consists of three stages: parameterized template creation, the laws of illumination-aware 2D synthesis, and physical engine-based 3D rendering, which finally gives us a mixed flare dataset that incorporates both 2D and 3D perspectives, namely FlareX. This dataset offers 9,500 2D templates derived from 95 flare patterns and 3,000 flare image pairs rendered from 60 3D scenes. Furthermore, we design a masking approach to obtain real-world flare-free images from their corrupted counterparts to measure the performance of the model on real-world images. Extensive experiments demonstrate the effectiveness of our method and dataset.

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

Jiongli Zhu, Parjanya Prashant, Alex Cloninger, Babak Salimi

Data valuation techniques quantify each training example's contribution to model performance, providing a principled basis for data cleaning, acquisition, and selection. Existing valuation methods remain inadequate: \emph{model-based} techniques depend on a single fitted model and inherit its biases, while \emph{algorithm-based} approaches like Data Shapley scale poorly due to their need to train multiple models. Recent work has proposed model-agnostic alternatives based on Wasserstein distance between the training set and a clean reference set, but exact computation is expensive and approximations often misrank examples. We introduce KAIROS, a model-agnostic framework that values examples by their contribution to the Maximum Mean Discrepancy (MMD) between the training set and a clean reference distribution. Unlike Wasserstein methods, MMD admits a closed-form solution that requires no approximations and is scalable to large datasets. Additionally, KAIROS enables efficient online valuation: adding a new batch of $m$ examples requires only $O(mN)$ computation to update all scores, compared to $O(N^2)$ in prior work where $N$ is the training set size. Empirical evaluations on noise, mislabeling, and poisoning benchmarks show that KAIROS consistently outperforms state-of-the-art baselines in both accuracy and runtime. On ImageNet, KAIROS achieves up to 15 $\times$ speedup over the fastest baseline while maintaining superior data valuation quality. Our results demonstrate that model-agnostic methods can match or exceed model-based approaches in performance while scaling to large datasets.

Computer Vision · Vision Models & Multimodal

Walter Simoncini, Michael Dorkenwald, Tijmen Blankevoort, Cees Snoek, Yuki Asano

Vision foundation models achieve remarkable performance but are only available in a limited set of pre-determined sizes, forcing sub-optimal deployment choices under real-world constraints. We introduce SnapViT: single-shot network approximation for pruned Vision Transformers, a new post-pretraining structured pruning method that enables elastic inference across a continuum of compute budgets. Our approach efficiently combines gradient information with cross-network structure correlations, approximated via an evolutionary algorithm, does not require labeled data, generalizes to models without a classification head, and is retraining-free. Experiments on DINO, SigLIPv2, DeIT, and AugReg models demonstrate superior performance over state-of-the-art methods across various sparsities, requiring less than five minutes on a single A100 GPU to generate elastic models that can be adjusted to any computational budget. Our key contributions include an efficient pruning strategy for pretrained Vision Transformers, a novel evolutionary approximation of Hessian off-diagonal structures, and a self-supervised importance scoring mechanism that maintains strong performance without requiring retraining or labels. Code and pruned models are available at: https://elastic.ashita.nl/

Social Aspects · Accountability, Transparency and Interpretability

R. Teal Witter, Yurong Liu, Christopher Musco

With origins in game-theory, probabilistic values like Shapley values, Banzhaf values, and semi-values have emerged as a central tool in explainable AI. They are used for feature attribution, data attribution, data valuation, and more. Since all of these values require exponential time to compute exactly, research has focused on efficient approximation methods using two techniques: Monte Carlo sampling and linear regression formulations. In this work, we present a new way of combining both of these techniques. Our approach is more flexible than prior algorithms, allowing for linear regression to be replaced with any function family whose probabilistic values can be computed efficiently. This allows us to harness the accuracy of tree-based models like XGBoost, while still producing unbiased estimates. From experiments across eight datasets, we find that our methods give state-of-the-art performance for estimating probabilistic values. For Shapley values, the error of our methods is up to $6\times$ lower than Permutation SHAP (the most popular Monte Carlo method), $2.75\times$ lower than Kernel SHAP (the most popular linear regression method), and $1.75\times$ lower than Leverage SHAP (the prior state-of-the-art Shapley value estimator). For more general probabilistic values, we can obtain error up to $60\times$ lower than prior work.

Probabilistic Methods · Monte Carlo and Sampling Methods

David Zoltowski, Skyler Wu, Xavier Gonzalez, Leo Kozachkov, Scott Linderman

Markov chain Monte Carlo (MCMC) methods are foundational algorithms for Bayesian inference and probabilistic modeling. However, most MCMC algorithms are inherently sequential and their time complexity scales linearly with the sequence length. Previous work on adapting MCMC to modern hardware has therefore focused on running many independent chains in parallel. Here, we take an alternative approach: we propose algorithms to evaluate MCMC samplers in parallel across the chain length. To do this, we build on recent methods for parallel evaluation of nonlinear recursions that formulate the state sequence as a solution to a fixed-point problem and solve for the fixed-point using a parallel form of Newton's method. We show how this approach can be used to parallelize Gibbs, Metropolis-adjusted Langevin, and Hamiltonian Monte Carlo sampling across the sequence length. In several examples, we demonstrate the simulation of up to hundreds of thousands of MCMC samples with only tens of parallel Newton iterations. Additionally, we develop two new parallel quasi-Newton methods to evaluate nonlinear recursions with lower memory costs and reduced runtime. We find that the proposed parallel algorithms accelerate MCMC sampling across multiple examples, in some cases by more than an order of magnitude compared to sequential evaluation.

Reinforcement Learning · Deep RL

Boxuan Zhang, Runqing Wang, Wei Xiao, Weipu Zhang, Jian Sun, Gao Huang, Jie Chen, Gang Wang

A critical bottleneck in deep reinforcement learning (DRL) is sample inefficiency, as training high-performance agents often demands extensive environmental interactions. Model-based reinforcement learning (MBRL) mitigates this by building world models that simulate environmental dynamics and generate synthetic experience, improving sample efficiency. However, conventional world models process observations holistically, failing to decouple dynamic objects and temporal features from static backgrounds. This approach is computationally inefficient, especially for visual tasks where dynamic objects significantly influence rewards and decision-making performance. To address this, we introduce DyMoDreamer, a novel MBRL algorithm that incorporates a dynamic modulation mechanism to improve the extraction of dynamic features and enrich the temporal information. DyMoDreamer employs differential observations derived from a novel inter-frame differencing mask, explicitly encoding object-level motion cues and temporal dynamics. Dynamic modulation is modeled as stochastic categorical distributions and integrated into a recurrent state-space model (RSSM), enhancing the model's focus on reward-relevant dynamics. Experiments demonstrate that DyMoDreamer sets a new state-of-the-art on the Atari $100$k benchmark with a $156.6$\% mean human-normalized score, establishes a new record of $832$ on the DeepMind Visual Control Suite, and gains a $9.5$\% performance improvement after $1$M steps on the Crafter benchmark.

Computer Vision · 3D Rendering & Reconstruction

Haoran Zhou, Gim Hee Lee

Recent advancements in foundation models for 2D vision have substantially improved the analysis of dynamic scenes from monocular videos. However, despite their strong generalization capabilities, these models often lack 3D consistency, a fundamental requirement for understanding scene geometry and motion, thereby causing severe spatial misalignment and temporal flickering in complex 3D environments. In this paper, we present Motion4D, a novel framework that addresses these challenges by integrating 2D priors from foundation models into a unified 4D Gaussian Splatting representation. Our method features a two-part iterative optimization framework: 1) Sequential optimization, which updates motion and semantic fields in consecutive stages to maintain local consistency, and 2) Global optimization, which jointly refines all attributes for long-term coherence. To enhance motion accuracy, we introduce a 3D confidence map that dynamically adjusts the motion priors, and an adaptive resampling process that inserts new Gaussians into under-represented regions based on per-pixel RGB and semantic errors. Furthermore, we enhance semantic coherence through an iterative refinement process that resolves semantic inconsistencies by alternately optimizing the semantic fields and updating prompts of SAM2. Extensive evaluations demonstrate that our Motion4D significantly outperforms both 2D foundation models and existing 3D-based approaches across diverse scene understanding tasks, including point-based tracking, video object segmentation, and novel view synthesis. Our code is available at https://hrzhou2.github.io/motion4d-web/.

Applications

Jiahao Yu, Xian Wu, Hao Liu, Wenbo Guo, Xinyu Xing

We propose BlockScan, a customized Transformer for anomaly detection in blockchain transactions. Unlike existing methods that rely on rule-based systems or directly apply off-the-shelf large language models (LLMs), BlockScan introduces a series of customized designs to effectively model the unique data structure of blockchain transactions. First, a blockchain transaction is multi-modal, containing blockchain-specific tokens, texts, and numbers. We design a novel modularized tokenizer to handle these multi-modal inputs, balancing the information across different modalities. Second, we design a customized masked language modeling mechanism for pretraining the Transformer architecture, incorporating RoPE embedding and FlashAttention for handling longer sequences. Finally, we design a novel anomaly detection method based on the model outputs. We further provide theoretical analysis for the detection method of our system. Extensive evaluations on Ethereum and Solana transactions demonstrate BlockScan's exceptional capability in anomaly detection while maintaining a low false positive rate. Remarkably, BlockScan is the only method that successfully detects anomalous transactions on Solana with high accuracy, whereas all other approaches achieved very low or zero detection recall scores. This work sets a new benchmark for applying Transformer-based approaches in blockchain data analysis.

Deep Learning · Algorithms

Shriram M S, Xinyue Hao, Shihao Hou, Yang Lu, Laura Sevilla-Lara, Anurag Arnab, Shreyank Gowda

The success of the machine learning field has reliably depended on training on large datasets. While effective, this trend comes at an extraordinary cost. This is due to two deeply intertwined factors: the size of models and the size of datasets. While promising research efforts focus on reducing the size of models, the other half of the equation remains fairly mysterious. Indeed, it is surprising that the standard approach to training remains to iterate over and over, uniformly sampling the training dataset. In this paper we explore a series of alternative training paradigms that leverage insights from hard-data-mining and dropout, simple enough to implement and use that can become the new training standard. The proposed Progressive Data Dropout reduces the number of effective epochs to as little as 12.4\% of the baseline. This savings actually do not come at any cost for accuracy. Surprisingly, the proposed method improves accuracy by up to 4.82\%. Our approach requires no changes to model architecture or optimizer, and can be applied across standard training pipelines, thus posing an excellent opportunity for wide adoption. Code can be found here: \url{https://github.com/bazyagami/LearningWithRevision}.

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.

Applications · Neuroscience, Cognitive Science

Haozhe Shan, Sun Minni, Lea Duncker

The ability to continually learn new skills, retain, and flexibly deploy them to accomplish goals is a key feature of intelligent and efficient behavior. However, the neural mechanisms facilitating the continual learning and flexible (re-)composition of skills remain elusive. Here, we study continual learning and the compositional reuse of learned computations in recurrent neural network (RNN) models using a novel two-system approach: one system that infers 'what' computation to perform, and one that implements 'how' to perform it. We focus on a set of compositional cognitive tasks commonly studied in neuroscience. To construct the 'what' system, we first show that a large family of tasks can be systematically described by a probabilistic generative model, where compositionality stems from a shared underlying vocabulary of discrete task-epochs. The shared epoch structure makes these tasks inherently compositional. We first show that this compositionality can be systematically described by a probabilistic generative model. Furthermore, we develop an unsupervised online learning approach that can learn this model on a single-trial basis, building its vocabulary incrementally as it is exposed to new tasks, and inferring the latent epoch structure as a time-varying computational context within a trial. We implement the 'how' system as an RNN whose low-rank components are composed according to the context inferred by the 'what' system. The contextual inference facilitates the creation, learning, and reuse of the low-rank RNN components as new tasks are introduced sequentially, enabling continual learning without catastrophic forgetting. Using an example task set, we demonstrate the efficacy and competitive performance of this two-system learning framework, its potential for forward and backward transfer, as well as few-shot learning via re-composition.

Deep Learning · Everything Else

Guy Bar-Shalom, Fabrizio Frasca, Yaniv Galron, Yftah Ziser, Haggai Maron

Detecting hallucinations in Large Language Model-generated text is crucial for their safe deployment. While probing classifiers show promise, they operate on isolated layer–token pairs and are LLM-specific, limiting their effectiveness and hindering cross-LLM applications. In this paper, we introduce a novel approach to address these shortcomings. We build on the natural sequential structure of activation data in both axes (layers $\times$ tokens) and advocate treating full activation tensors akin to images. We design ACT-ViT, a Vision Transformer-inspired model that can be effectively and efficiently applied to activation tensors and supports training on data from multiple LLMs simultaneously. Through comprehensive experiments encompassing diverse LLMs and datasets, we demonstrate that ACT-ViT consistently outperforms traditional probing techniques while remaining extremely efficient for deployment. In particular, we show that our architecture benefits substantially from multi-LLM training, achieves strong zero-shot performance on unseen datasets, and can be transferred effectively to new LLMs through fine-tuning.

Computer Vision · Classification and Understanding

Ilona Demler, Saumya Chauhan, Georgia Gkioxari

We introduce ITTO, a challenging new benchmark suite for evaluating and diagnosing the capabilities and limitations of point tracking methods. Our videos are sourced from existing datasets and egocentric real-world recordings, with high-quality human annotations collected through a multi-stage pipeline. ITTO captures the motion complexity, occlusion patterns, and object diversity characteristic of real-world scenes -- factors that are largely absent in current benchmarks. We conduct a rigorous analysis of state-of-the-art tracking methods on ITTO, breaking down performance along key axes of motion complexity. Our findings reveal that existing trackers struggle with these challenges, particularly in re-identifying points after occlusion, highlighting critical failure modes. These results point to the need for new modeling approaches tailored to real-world dynamics. We envision ITTO as a foundation testbed for advancing point tracking and guiding the development of more robust tracking algorithms.