The study of population dynamics originated with early sociological works but has since extended into many fields, including biology, epidemiology, evolutionary game theory, and economics. Most studies on population dynamics focus on the problem of prediction rather than control. Existing mathematical models for population control are often restricted to specific, noise-free dynamics, while real-world population changes can be complex and adversarial. To address this gap, we propose a new framework based on the paradigm of online control. We first characterize a set of linear dynamical systems that can naturally model evolving populations. We then give an efficient gradient-based controller for these systems, with near-optimal regret bounds with respect to a broad class of linear policies. Our empirical evaluations demonstrate the effectiveness of the proposed algorithm for population control even in non-linear models such as SIR and replicator dynamics.

Latent Dirichlet Allocation (LDA) is a very popular model for topic modeling as well as many other problems with latent groups. It is both simple and effective. When the number of topics (or latent groups) is unknown, the Hierarchical Dirichlet Process (HDP) provides an elegant non-parametric extension; however, it is a complex model and it is difficult to incorporate prior knowledge since the distribution over topics is implicit. We propose two new models that extend LDA in a simple and intuitive fashion by directly expressing a distribution over the number of topics. We also propose a new online Bayesian moment matching technique to learn the parameters and the number of topics of those models based on streaming data. The approach achieves higher log-likelihood than batch and online HDP with fixed hyperparameters on several corpora. The code is publicly available at https://github.com/whsu/bmm.

Recent work demonstrates that, post-training large language models with opendomain instruction following data have achieved colossal success. Simultaneously, human Chatbot Arena has emerged as one of the most reasonable benchmarks for model evaluation and developmental guidance. However, the processes of manually curating high-quality training data and utilizing online human evaluation platforms are both expensive and limited. To mitigate the manual and temporal costs associated with post-training, this paper introduces a Simulated Chatbot Arena named WizardArena, which is fully based on and powered by open-source LLMs. For evaluation scenario, WizardArena can efficiently predict accurate performance rankings among different models based on offline test set. For the training scenario, we propose Arena Learning, an innovative offline strategy that simulates iterative arena battles among various state-of-the-art models on a large scale of instruction data using AI-driven annotations to evaluate and leverage battle results, thus continuously enhancing the weaknesses of the target model through both supervised fine-tuning and reinforcement learning. Experimental results demonstrate that our WizardArena aligns closely with the online human arena rankings, and our models, trained on extensive offline battle data through Arena Learning, demonstrate marked improvements in performance across the SFT, DPO, and PPO stages.

We will release our trained model together with code as suggested.

While a lot of progress has been made by making networks deeper, filters at each layer independently generate responses given the input and do not communicate with each other. In this paper, we introduce a novel network unit called Cross-channel Communication (C3) block, a simple yet effective module to encourage the communication across filters within the same layer. The C3 block enables filters to exchange information through a micro neural network, which consists of a feature encoder, a message passer, and a feature decoder, before sending the information to the next layer. With C3 block, each channel response is modulated by accounting for the responses at other channels. Extensive experiments on multiple vision tasks show that our proposed block brings improvements for different CNN architectures, and learns more diverse and complementary representations.

We thank the reviewers for the comments. All reviewers think the paper is clearly written and easy to read. We address reviewers' concerns below. We will include these statistics in the paper. All these suggest that the improvement is not simply due to the increased model size.

Prediction-powered inference (PPI) is a method that improves statistical estimates based on limited human-labeled data. PPI achieves this by combining small amounts of human-labeled data with larger amounts of data labeled by a reasonably accurate--but potentially biased--automatic system, in a way that results in tighter confidence intervals for certain parameters of interest (e.g., the mean performance of a language model). In this paper, we propose a method called Stratified Prediction-Powered Inference (StratPPI), in which we show that the basic PPI estimates can be considerably improved by employing simple data stratification strategies. Without making any assumptions on the underlying automatic labeling system or data distribution, we derive an algorithm for computing provably valid confidence intervals for population parameters (such as averages) that is based on stratified sampling. In particular, we show both theoretically and empirically that, with appropriate choices of stratification and sample allocation, our approach can provide substantially tighter confidence intervals than unstratified approaches. Specifically, StratPPI is expected to improve in cases where the performance of the autorater varies across different conditional distributions of the target data.

It is largely agreed that social network links are formed due to either homophily or social influence. Inspired by this, we aim at understanding the generation of links via providing a novel embedding-based graph formation model. Different from existing graph representation learning, where link generation probabilities are defined as a simple function of the corresponding node embeddings, we model the link generation as a mixture model of the two factors. In addition, we model the homophily factor in spherical space and the influence factor in hyperbolic space to accommodate the fact that (1) homophily results in cycles and (2) influence results in hierarchies in networks. We also design a special projection to align these two spaces. We call this model Non-Euclidean Mixture Model, i.e., NMM.

We ran this experiment only to demonstrate scalability.

Extracting and predicting object structure and dynamics from videos without supervision is a major challenge in machine learning. To address this challenge, we adopt a keypoint-based image representation and learn a stochastic dynamics model of the keypoints. Future frames are reconstructed from the keypoints and a reference frame. By modeling dynamics in the keypoint coordinate space, we achieve stable learning and avoid compounding of errors in pixel space. Our method improves upon unstructured representations both for pixel-level video prediction and for downstream tasks requiring object-level understanding of motion dynamics. We evaluate our model on diverse datasets: a multi-agent sports dataset, the Human3.6M