With the advancement of large language models (LLMs), solving complex reasoning tasks has gained increasing attention. Inference-time computation methods (e.g., Best-of-N, beam search, et al.) are particularly valuable as they can enhance reasoning performance without modifying model parameters or requiring additional training. However, these techniques come with implementation challenges, and most existing methods remain at the proof-of-concept stage with limited practical adoption due to their computational complexity and varying effectiveness across different tasks. In this paper, we investigate and benchmark diverse inference-time computation strategies across reasoning tasks of varying complexity. Since most current methods rely on a proposer-verifier pipeline that first generates candidate solutions (e.g., reasoning solutions) and then selects the best one based on reward signals (e.g., RLHF rewards, process rewards), our research focuses on optimizing both candidate solution generation (e.g., instructing prompts, hyperparameters such as temperature and top-p) and reward mechanisms (e.g., self-evaluation, reward types). Through extensive experiments (more than 20,000 A100-80G GPU hours with over 1,000 experiments) across a variety of models (e.g., Llama, Qwen, and Mistral families) of various sizes, our ablation studies reveal that previously overlooked strategies can significantly enhance performance (e.g., tuning temperature can improve reasoning task performance by up to 5%). Furthermore, we establish a standardized benchmark for inference-time computation by systematically evaluating six representative methods across eight reasoning tasks. These findings provide a stronger foundation for future research. The code is available at https://github.com/usail-hkust/benchmark_inference_time_computation_LLM

The machine learning and data science community has made significant while dispersive progress in accelerating transformer-based large language models (LLMs), and one promising approach is to replace the original causal attention in a generative pre-trained transformer (GPT) with \emph{exponentially decaying causal linear attention}. In this paper, we present LeetDecoding, which is the first Python package that provides a large set of computation routines for this fundamental operator. The launch of LeetDecoding was motivated by the current lack of (1) clear understanding of the complexity regarding this operator, (2) a comprehensive collection of existing computation methods (usually spread in seemingly unrelated fields), and (3) CUDA implementations for fast inference on GPU. LeetDecoding's design is easy to integrate with existing linear-attention LLMs, and allows for researchers to benchmark and evaluate new computation methods for exponentially decaying causal linear attention. The usage of LeetDecoding does not require any knowledge of GPU programming and the underlying complexity analysis, intentionally making LeetDecoding accessible to LLM practitioners. The source code of LeetDecoding is provided at \href{https://github.com/Computational-Machine-Intelligence/LeetDecoding}{this GitHub repository}, and users can simply install LeetDecoding by the command \texttt{pip install leet-decoding}.

Machine learning models trained on data from blockchain-based marketplaces have the potential to create the world's most powerful artificial intelligences. They combine two potent primitives: private machine learning, which allows for training to be done on sensitive private data without revealing it, and blockchain-based incentives, which allow these systems to attract the best data and models to make them smarter. The result is open marketplaces where anyone can sell their data and keep their data private, while developers can use incentives to attract the best data for their algorithms to them. Constructing these systems is challenging and the requisite building blocks are still being created, but simple initial versions look like they are starting to become possible. I believe these marketplaces will transition us out of the current era of Web 2.0 data monopolies into a Web 3.0 era of open competition for data and algorithms, where both are directly monetized.

The smallest eigenvalues and the associated eigenvectors (i.e., eigenpairs) of a graph Laplacian matrix have been widely used in spectral clustering and community detection. However, in real-life applications the number of clusters or communities (say, $K$) is generally unknown a-priori. Consequently, the majority of the existing methods either choose $K$ heuristically or they repeat the clustering method with different choices of $K$ and accept the best clustering result. The first option, more often, yields suboptimal result, while the second option is computationally expensive. In this work, we propose an incremental method for constructing the eigenspectrum of the graph Laplacian matrix. This method leverages the eigenstructure of graph Laplacian matrix to obtain the $K$-th smallest eigenpair of the Laplacian matrix given a collection of all previously computed $K-1$ smallest eigenpairs. Our proposed method adapts the Laplacian matrix such that the batch eigenvalue decomposition problem transforms into an efficient sequential leading eigenpair computation problem. As a practical application, we consider user-guided spectral clustering. Specifically, we demonstrate that users can utilize the proposed incremental method for effective eigenpair computation and for determining the desired number of clusters based on multiple clustering metrics.

The smallest eigenvalues and the associated eigenvectors (i.e., eigenpairs) of a graph Laplacian matrix have been widely used for spectral clustering and community detection. However, in real-life applications the number of clusters or communities (say, $K$) is generally unknown a-priori. Consequently, the majority of the existing methods either choose $K$ heuristically or they repeat the clustering method with different choices of $K$ and accept the best clustering result. The first option, more often, yields suboptimal result, while the second option is computationally expensive. In this work, we propose an incremental method for constructing the eigenspectrum of the graph Laplacian matrix. This method leverages the eigenstructure of graph Laplacian matrix to obtain the $K$-th eigenpairs of the Laplacian matrix given a collection of all the $K-1$ smallest eigenpairs. Our proposed method adapts the Laplacian matrix such that the batch eigenvalue decomposition problem transforms into an efficient sequential leading eigenpair computation problem. As a practical application, we consider user-guided spectral clustering. Specifically, we demonstrate that users can utilize the proposed incremental method for effective eigenpair computation and determining the desired number of clusters based on multiple clustering metrics.