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1. Trainable Time Warping: Aligning Time-series in the Continuous-time Domain

   https://doi.org/10.1109/icassp.2019.8682322  

   Khorram, Soheil; McInnis, Melvin G; Mower Provost, Emily (May 2019, International Conference on Acoustics, Speech, and Signal Processing (ICASSP))

   DTW calculates the similarity or alignment between two signals, subject to temporal warping. However, its computational complexity grows exponentially with the number of time-series. Although there have been algorithms developed that are linear in the number of time-series, they are generally quadratic in time-series length. The exception is generalized time warping (GTW), which has linear computational cost. Yet, it can only identify simple time warping functions. There is a need for a new fast, high-quality multisequence alignment algorithm. We introduce trainable time warping (TTW), whose complexity is linear in both the number and the length of time-series. TTW performs alignment in the continuoustime domain using a sinc convolutional kernel and a gradient-based optimization technique. We compare TTW and GTW on S5 UCR datasets in time-series averaging and classification. TTW outperforms GTW on 67.1% of the datasets for the averaging tasks, and 61.2% of the datasets for the classification tasks. 

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2. Time series clustering in linear time complexity

   https://doi.org/10.1007/s10618-021-00798-w  

   Li, Xiaosheng; Lin, Jessica; Zhao, Liang (November 2021, Data Mining and Knowledge Discovery)
3. Real-Time LaCAM for Real-Time MAPF

   https://doi.org/10.1609/socs.v18i1.35993  

   Liang, Runzhe; Veerapaneni, Rishi; Harabor, Daniel; Li, Jiaoyang; Likhachev, Maxim (July 2025, Proceedings of the International Symposium on Combinatorial Search)

   The vast majority of Multi-Agent Path Finding (MAPF) methods with completeness guarantees require planning full-horizon paths. However, planning full-horizon paths can take too long and be impractical in real-world applications. Instead, real-time planning and execution, which only allows the planner a finite amount of time before executing and replanning, is more practical for real-world multi-agent systems. Several methods utilize real-time planning schemes but none are provably complete, which leads to livelock or deadlock. Our main contribution is Real-Time LaCAM, the first Real-Time MAPF method with provable completeness guarantees. We do this by leveraging LaCAM in an incremental fashion. Our results show how we can iteratively plan for congested environments with a cutoff time of milliseconds while still maintaining the same success rate as full-horizon LaCAM. We also show how it can be used with a single-step learned MAPF policy. 

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4. Real-Time Time-Dependent Electronic Structure Theory

   https://doi.org/10.1021/acs.chemrev.0c00223  

   Li, Xiaosong; Govind, Niranjan; Isborn, Christine; DePrince, A. Eugene; Lopata, Kenneth (September 2020, Chemical Reviews)

   null (Ed.)
5. Breaking Time Invariance: Assorted-Time Normalization for RNNs

   https://doi.org/10.1007/s11063-024-11442-1  

   Pospisil, Cole; Zadorozhnyy, Vasily; Ye, Qiang (March 2024, Neural Processing Letters)

   Abstract Methods such as Layer Normalization (LN) and Batch Normalization have proven to be effective in improving the training of Recurrent Neural Networks (RNNs). However, existing methods normalize using only the instantaneous information at one particular time step, and the result of the normalization is a preactivation state with a time-independent distribution. This implementation fails to account for certain temporal differences inherent in the inputs and the architecture of RNNs. Since these networks share weights across time steps, it may also be desirable to account for the connections between time steps in the normalization scheme. In this paper, we propose a normalization method called Assorted-Time Normalization (ATN), which preserves information from multiple consecutive time steps and normalizes using them. This setup allows us to introduce longer time dependencies into the traditional normalization methods without introducing any new trainable parameters. We present theoretical derivations for the gradient propagation and prove the weight scaling invariance property. Our experiments applying ATN to LN demonstrate consistent improvement on various tasks, such as Adding, Copying, and Denoise Problems and Language Modeling Problems. 

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