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Neural Cellular Automata (NCA) are a powerful combination of machine learning and mechanistic modelling. We train NCA to learn complex dynamics from time series of images and PDE trajectories. Our method is designed to identify underlying local rules that govern large scale dynamic emergent behaviours. Previous work on NCA focuses on learning rules that give stationary emergent structures. We extend NCA to capture both transient and stable structures within the same system, as well as learning rules that capture the dynamics of Turing pattern formation in nonlinear Partial Differential Equations (PDEs). We demonstrate that NCA can generalise very well beyond their PDE training data, we show how to constrain NCA to respect given symmetries, and we explore the effects of associated hyperparameters on model performance and stability. Being able to learn arbitrary dynamics gives NCA great potential as a data driven modelling framework, especially for modelling biological pattern formation.

The goal of sequential recommendation (SR) is to predict a user's potential interested items based on her/his historical interaction sequences. Most existing sequential recommenders are developed based on ID features, which, despite their widespread use, often underperform with sparse IDs and struggle with the cold-start problem. Besides, inconsistent ID mappings hinder the model's transferability, isolating similar recommendation domains that could have been co-optimized. This paper aims to address these issues by exploring the potential of multi-modal information in learning robust and generalizable sequence representations. We propose MISSRec, a multi-modal pre-training and transfer learning framework for SR. On the user side, we design a Transformer-based encoder-decoder model, where the contextual encoder learns to capture the sequence-level multi-modal user interests while a novel interest-aware decoder is developed to grasp item-modality-interest relations for better sequence representation. On the candidate item side, we adopt a dynamic fusion module to produce user-adaptive item representation, providing more precise matching between users and items. We pre-train the model with contrastive learning objectives and fine-tune it in an efficient manner. Extensive experiments demonstrate the effectiveness and flexibility of MISSRec, promising a practical solution for real-world recommendation scenarios. Data and code are available on \url{//github.com/gimpong/MM23-MISSRec}.

The video-language (VL) pretraining has achieved remarkable improvement in multiple downstream tasks. However, the current VL pretraining framework is hard to extend to multiple modalities (N modalities, N>=3) beyond vision and language. We thus propose LanguageBind, taking the language as the bind across different modalities because the language modality is well-explored and contains rich semantics. Specifically, we freeze the language encoder acquired by VL pretraining, then train encoders for other modalities with contrastive learning. As a result, all modalities are mapped to a shared feature space, implementing multi-modal semantic alignment. While LanguageBind ensures that we can extend VL modalities to N modalities, we also need a high-quality dataset with alignment data pairs centered on language. We thus propose VIDAL-10M with Video, Infrared, Depth, Audio and their corresponding Language, naming as VIDAL-10M. In our VIDAL-10M, all videos are from short video platforms with complete semantics rather than truncated segments from long videos, and all the video, depth, infrared, and audio modalities are aligned to their textual descriptions. After pretraining on VIDAL-10M, we outperform ImageBind by 5.8% R@1 on the MSR-VTT dataset with only 15% of the parameters in the zero-shot video-text retrieval task. Beyond this, our LanguageBind has greatly improved in the zero-shot video, audio, depth, and infrared understanding tasks. For instance, LanguageBind surpassing InterVideo by 1.9% on MSR-VTT, 8.8% on MSVD, 6.3% on DiDeMo, and 4.4% on ActivityNet. On the LLVIP and NYU-D datasets, LanguageBind outperforms ImageBind with 23.8% and 11.1% top-1 accuracy. Code address: //github.com/PKU-YuanGroup/LanguageBind.

Reinforcement Learning algorithms that learn from human feedback (RLHF) need to be efficient in terms of statistical complexity, computational complexity, and query complexity. In this work, we consider the RLHF setting where the feedback is given in the format of preferences over pairs of trajectories. In the linear MDP model, by using randomization in algorithm design, we present an algorithm that is sample efficient (i.e., has near-optimal worst-case regret bounds) and has polynomial running time (i.e., computational complexity is polynomial with respect to relevant parameters). Our algorithm further minimizes the query complexity through a novel randomized active learning procedure. In particular, our algorithm demonstrates a near-optimal tradeoff between the regret bound and the query complexity. To extend the results to more general nonlinear function approximation, we design a model-based randomized algorithm inspired by the idea of Thompson sampling. Our algorithm minimizes Bayesian regret bound and query complexity, again achieving a near-optimal tradeoff between these two quantities. Computation-wise, similar to the prior Thompson sampling algorithms under the regular RL setting, the main computation primitives of our algorithm are Bayesian supervised learning oracles which have been heavily investigated on the empirical side when applying Thompson sampling algorithms to RL benchmark problems.

In this work, we introduce Regularity Structures B-series which are used for describing solutions of singular stochastic partial differential equations (SPDEs). We define composition and substitutions of these B-series and as in the context of B-series for ordinary differential equations, these operations can rewritten via products and Hopf algebras which have been used for building up renormalised models. These models provide a suitable topology for solving singular SPDEs. This new construction sheds a new light on these products and open interesting perspectives for the study of singular SPDEs in connection with B-series.

The generalization capacity of Multi-Task Learning (MTL) becomes limited when unrelated tasks negatively impact each other by updating shared parameters with conflicting gradients, resulting in negative transfer and a reduction in MTL accuracy compared to single-task learning (STL). Recently, there has been an increasing focus on the fairness of MTL models, necessitating the optimization of both accuracy and fairness for individual tasks. Similarly to how negative transfer affects accuracy, task-specific fairness considerations can adversely influence the fairness of other tasks when there is a conflict of fairness loss gradients among jointly learned tasks, termed bias transfer. To address both negative and bias transfer in MTL, we introduce a novel method called FairBranch. FairBranch branches the MTL model by assessing the similarity of learned parameters, grouping related tasks to mitigate negative transfer. Additionally, it incorporates fairness loss gradient conflict correction between adjoining task-group branches to address bias transfer within these task groups. Our experiments in tabular and visual MTL problems demonstrate that FairBranch surpasses state-of-the-art MTL methods in terms of both fairness and accuracy.

This article investigates a local discontinuous Galerkin (LDG) method for one-dimensional and two-dimensional singularly perturbed reaction-diffusion problems on a Shishkin mesh. During this process, due to the inability of the energy norm to fully capture the behavior of the boundary layers appearing in the solutions, a balanced norm is introduced. By designing novel numerical fluxes and constructing special interpolations, optimal convergences under the balanced norm are achieved in both 1D and 2D cases. Numerical experiments support the main theoretical conclusions.

We explain the methodology used to create the data submitted to HuMob Challenge, a data analysis competition for human mobility prediction. We adopted a personalized model to predict the individual's movement trajectory from their data, instead of predicting from the overall movement, based on the hypothesis that human movement is unique to each person. We devised the features such as the date and time, activity time, days of the week, time of day, and frequency of visits to POI (Point of Interest). As additional features, we incorporated the movement of other individuals with similar behavior patterns through the employment of clustering. The machine learning model we adopted was the Support Vector Regression (SVR). We performed accuracy through offline assessment and carried out feature selection and parameter tuning. Although overall dataset provided consists of 100,000 users trajectory, our method use only 20,000 target users data, and do not need to use other 80,000 data. Despite the personalized model's traditional feature engineering approach, this model yields reasonably good accuracy with lower computational cost.

Recommender systems play a crucial role in mitigating the problem of information overload by suggesting users' personalized items or services. The vast majority of traditional recommender systems consider the recommendation procedure as a static process and make recommendations following a fixed strategy. In this paper, we propose a novel recommender system with the capability of continuously improving its strategies during the interactions with users. We model the sequential interactions between users and a recommender system as a Markov Decision Process (MDP) and leverage Reinforcement Learning (RL) to automatically learn the optimal strategies via recommending trial-and-error items and receiving reinforcements of these items from users' feedbacks. In particular, we introduce an online user-agent interacting environment simulator, which can pre-train and evaluate model parameters offline before applying the model online. Moreover, we validate the importance of list-wise recommendations during the interactions between users and agent, and develop a novel approach to incorporate them into the proposed framework LIRD for list-wide recommendations. The experimental results based on a real-world e-commerce dataset demonstrate the effectiveness of the proposed framework.