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   Liu, Xinru; Wang, Liwei; Smith, Aaron; Atchade, Yves (May 2024, AISTATS 2024)

   Dasgupta, Sanjoy; Mandt, Stephan; Li, Yingzhen (Ed.)

   Cyclical MCMC is a novel MCMC framework recently proposed by Zhang et al. (2019) to address the challenge posed by high-dimensional multimodal posterior distributions like those arising in deep learning. The algorithm works by generating a nonhomogeneous Markov chain that tracks -- cyclically in time -- tempered versions of the target distribution. We show in this work that cyclical MCMC converges to the desired limit in settings where the Markov kernels used are fast mixing, and sufficiently long cycles are employed. However in the far more common settings of slow mixing kernels, the algorithm may fail to converge to the correct limit. In particular, in a simple mixture example with unequal variance where powering is known to produce slow mixing kernels, we show by simulation that cyclical MCMC fails to converge to the desired limit. Finally, we show that cyclical MCMC typically estimates well the local shape of the target distribution around each mode, even when we do not have convergence to the target. 

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2. The Cyclical Behavior of the Price‐Cost Markup

   https://doi.org/10.1111/jmcb.12755  

   NEKARDA, CHRISTOPHER J.; RAMEY, VALERIE A. (December 2020, Journal of Money, Credit and Banking)

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3. Max-pressure signal control with cyclical phase structure

   https://doi.org/10.1016/j.trc.2020.102828  

   Levin, Michael W.; Hu, Jeffrey; Odell, Michael (November 2020, Transportation Research Part C: Emerging Technologies)

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4. Provable Super-Convergence With a Large Cyclical Learning Rate

   https://doi.org/10.1109/LSP.2021.3101131  

   Oymak, Samet (January 2021, IEEE signal processing letters)
5. Cognitive Inertia: Cyclical Interactions Between Attention and Memory Shape Learning

   https://doi.org/10.1177/09637214231217989  

   Turner, Brandon_M; Sloutsky, Vladimir_M (January 2024, Current Directions in Psychological Science)

   In explaining how humans selectively attend, common frameworks often focus on how attention is allocated relative to an idealized allocation based on properties of the task. However, these perspectives often ignore different types of constraints that could help explain why attention was allocated in a particular way. For example, many computational models of learning are well equipped to explain how attention should ideally be allocated to minimize errors within the task, but these models often assume all features are perfectly encoded or that the only learning goal is to maximize accuracy. In this article, we argue for a more comprehensive view by using computational modeling to understand the complex interactions that occur between selective attention and memory. Our central thesis is that although selective attention directs attention to relevant dimensions, relevance can be established only through memories of previous experiences. Hence, attention is initially used to encode features and create memories, but thereafter, attention operates selectively on the basis of what is kept in memory. Through this lens, deviations from ideal performance can still be viewed as goal-directed selective attention, but the orientation of attention is subject to the constraints of the individual learner. 

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