Performative prediction is a framework accounting for the shift in the data distribution induced by the prediction of a model deployed in the real world. Ensuring rapid convergence to a stable solution where the data distribution remains the same after the model deployment is crucial, especially in evolving environments. This paper extends the Repeated Risk Minimization (RRM) framework by utilizing historical datasets from previous retraining snapshots, yielding a class of algorithms that we call Affine Risk Minimizers and enabling convergence to a performatively stable point for a broader class of problems. We introduce a new upper bound for methods that use only the final iteration of the dataset and prove for the first time the tightness of both this new bound and the previous existing bounds within the same regime. We also prove that utilizing historical datasets can surpass the lower bound for last iterate RRM, and empirically observe faster convergence to the stable point on various perfor-mative prediction benchmarks. We offer at the same time the first lower bound analysis for RRM within the class of Affine Risk Min-imizers, quantifying the potential improvements in convergence speed that could be achieved with other variants in our framework.

Recent work has shown that object-centric representations can greatly help improve the accuracy of learning dynamics while also bringing interpretability. In this work, we take this idea one step further, ask the following question: "can learning disentangled representation further improve the accuracy of visual dynamics prediction in object-centric models?" While there has been some attempt to learn such disentangled representations for the case of static images \citep{nsb}, to the best of our knowledge, ours is the first work which tries to do this in a general setting for video, without making any specific assumptions about the kind of attributes that an object might have. The key building block of our architecture is the notion of a {\em block}, where several blocks together constitute an object. Each block is represented as a linear combination of a given number of learnable concept vectors, which is iteratively refined during the learning process. The blocks in our model are discovered in an unsupervised manner, by attending over object masks, in a style similar to discovery of slots \citep{slot_attention}, for learning a dense object-centric representation. We employ self-attention via transformers over the discovered blocks to predict the next state resulting in discovery of visual dynamics. We perform a series of experiments on several benchmark 2-D, and 3-D datasets demonstrating that our architecture (1) can discover semantically meaningful blocks (2) help improve accuracy of dynamics prediction compared to SOTA object-centric models (3) perform significantly better in OOD setting where the specific attribute combinations are not seen earlier during training. Our experiments highlight the importance discovery of disentangled representation for visual dynamics prediction.