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Rapidly Mixing Multiple-try Metropolis Algorithms for Model Selection Problems

Neural Information Processing Systems

The multiple-try Metropolis (MTM) algorithm is an extension of the Metropolis-Hastings (MH) algorithm by selecting the proposed state among multiple trials according to some weight function. Although MTM has gained great popularity owing to its faster empirical convergence and mixing than the standard MH algorithm, its theoretical mixing property is rarely studied in the literature due to its complex proposal scheme. We prove that MTM can achieve a mixing time bound smaller than that of MH by a factor of the number of trials under a general setting applicable to high-dimensional model selection problems with discrete state spaces. Our theoretical results motivate a new class of weight functions called locally balanced weight functions and guide the choice of the number of trials, which leads to improved performance over standard MTM algorithms. We support our theoretical results by extensive simulation studies and real data applications with several Bayesian model selection problems.




MTM: A Multi-Scale Token Mixing Transformer for Irregular Multivariate Time Series Classification

Zhong, Shuhan, Zhuo, Weipeng, Song, Sizhe, Li, Guanyao, Yu, Zhongyi, Chan, S. -H. Gary

arXiv.org Artificial Intelligence

Irregular multivariate time series (IMTS) is characterized by the lack of synchronized observations across its different channels. In this paper, we point out that this channel-wise asynchrony can lead to poor channel-wise modeling of existing deep learning methods. To overcome this limitation, we propose MTM, a multi-scale token mixing transformer for the classification of IMTS. We find that the channel-wise asynchrony can be alleviated by down-sampling the time series to coarser timescales, and propose to incorporate a masked concat pooling in MTM that gradually down-samples IMTS to enhance the channel-wise attention modules. Meanwhile, we propose a novel channel-wise token mixing mechanism which proactively chooses important tokens from one channel and mixes them with other channels, to further boost the channel-wise learning of our model. Through extensive experiments on real-world datasets and comparison with state-of-the-art methods, we demonstrate that MTM consistently achieves the best performance on all the benchmarks, with improvements of up to 3.8% in AUPRC for classification.


Rapidly Mixing Multiple-try Metropolis Algorithms for Model Selection Problems

Neural Information Processing Systems

The multiple-try Metropolis (MTM) algorithm is an extension of the Metropolis-Hastings (MH) algorithm by selecting the proposed state among multiple trials according to some weight function. Although MTM has gained great popularity owing to its faster empirical convergence and mixing than the standard MH algorithm, its theoretical mixing property is rarely studied in the literature due to its complex proposal scheme.


Model Directions, Not Words: Mechanistic Topic Models Using Sparse Autoencoders

Zheng, Carolina, Beltran-Velez, Nicolas, Karlekar, Sweta, Shi, Claudia, Nazaret, Achille, Mallik, Asif, Feder, Amir, Blei, David M.

arXiv.org Artificial Intelligence

Traditional topic models are effective at uncovering latent themes in large text collections. However, due to their reliance on bag-of-words representations, they struggle to capture semantically abstract features. While some neural variants use richer representations, they are similarly constrained by expressing topics as word lists, which limits their ability to articulate complex topics. We introduce Mechanistic Topic Models (MTMs), a class of topic models that operate on interpretable features learned by sparse autoencoders (SAEs). By defining topics over this semantically rich space, MTMs can reveal deeper conceptual themes with expressive feature descriptions. Moreover, uniquely among topic models, MTMs enable controllable text generation using topic-based steering vectors. To properly evaluate MTM topics against word-list-based approaches, we propose \textit{topic judge}, an LLM-based pairwise comparison evaluation framework. Across five datasets, MTMs match or exceed traditional and neural baselines on coherence metrics, are consistently preferred by topic judge, and enable effective steering of LLM outputs.


Memory OS of AI Agent

Kang, Jiazheng, Ji, Mingming, Zhao, Zhe, Bai, Ting

arXiv.org Artificial Intelligence

Large Language Models (LLMs) face a crucial challenge from fixed context windows and inadequate memory management, leading to a severe shortage of long-term memory capabilities and limited personalization in the interactive experience with AI agents. To overcome this challenge, we innovatively propose a Memory Operating System, i.e., MemoryOS, to achieve comprehensive and efficient memory management for AI agents. Inspired by the memory management principles in operating systems, MemoryOS designs a hierarchical storage architecture and consists of four key modules: Memory Storage, Updating, Retrieval, and Generation. Specifically, the architecture comprises three levels of storage units: short-term memory, mid-term memory, and long-term personal memory. Key operations within MemoryOS include dynamic updates between storage units: short-term to mid-term updates follow a dialogue-chain-based FIFO principle, while mid-term to long-term updates use a segmented page organization strategy. Our pioneering MemoryOS enables hierarchical memory integration and dynamic updating. Extensive experiments on the LoCoMo benchmark show an average improvement of 49.11% on F1 and 46.18% on BLEU-1 over the baselines on GPT-4o-mini, showing contextual coherence and personalized memory retention in long conversations. The implementation code is open-sourced at https://github.com/BAI-LAB/MemoryOS.


Rapidly Mixing Multiple-try Metropolis Algorithms for Model Selection Problems

Neural Information Processing Systems

The multiple-try Metropolis (MTM) algorithm is an extension of the Metropolis-Hastings (MH) algorithm by selecting the proposed state among multiple trials according to some weight function. Although MTM has gained great popularity owing to its faster empirical convergence and mixing than the standard MH algorithm, its theoretical mixing property is rarely studied in the literature due to its complex proposal scheme. We prove that MTM can achieve a mixing time bound smaller than that of MH by a factor of the number of trials under a general setting applicable to high-dimensional model selection problems with discrete state spaces. Our theoretical results motivate a new class of weight functions called locally balanced weight functions and guide the choice of the number of trials, which leads to improved performance over standard MTM algorithms. We support our theoretical results by extensive simulation studies and real data applications with several Bayesian model selection problems.