The recently proposed generative flow networks (GFlowNets) are a method of training a policy to sample compositional discrete objects with probabilities proportional to a given reward via a sequence of actions. GFlowNets exploit the sequential nature of the problem, drawing parallels with reinforcement learning (RL). Our work extends the connection between RL and GFlowNets to a general case. We demonstrate how the task of learning a generative flow network can be efficiently redefined as an entropy-regularized RL problem with a specific reward and regularizer structure. Furthermore, we illustrate the practical efficiency of this reformulation by applying standard soft RL algorithms to GFlowNet training across several probabilistic modeling tasks. Contrary to previously reported results, we show that entropic RL approaches can be competitive against established GFlowNet training methods. This perspective opens a direct path for integrating reinforcement learning principles into the realm of generative flow networks.

Model reparametrization, which follows the change-of-variable rule of calculus, is a popular way to improve the training of neural nets. But it can also be problematic since it can induce inconsistencies in, e.g., Hessian-based flatness measures, optimization trajectories, and modes of probability densities. This complicates downstream analyses: e.g. one cannot definitively relate flatness with generalization since arbitrary reparametrization changes their relationship. In this work, we study the invariance of neural nets under reparametrization from the perspective of Riemannian geometry. From this point of view, invariance is an inherent property of any neural net if one explicitly represents the metric and uses the correct associated transformation rules. This is important since although the metric is always present, it is often implicitly assumed as identity, and thus dropped from the notation, then lost under reparametrization. We discuss implications for measuring the flatness of minima, optimization, and for probability-density maximization. Finally, we explore some interesting directions where invariance is useful.

Many resource management problems require sequential decision-making under uncertainty, where the only uncertainty affecting the decision outcomes are exogenous variables outside the control of the decision-maker. We model these problems as Exo-MDPs (Markov Decision Processes with Exogenous Inputs) and design a class of data-efficient algorithms for them termed Hindsight Learning (HL). Our HL algorithms achieve data efficiency by leveraging a key insight: having samples of the exogenous variables, past decisions can be revisited in hindsight to infer counterfactual consequences that can accelerate policy improvements. We compare HL against classic baselines in the multi-secretary and airline revenue management problems. We also scale our algorithms to a business-critical cloud resource management problem -- allocating Virtual Machines (VMs) to physical machines, and simulate their performance with real datasets from a large public cloud provider. We find that HL algorithms outperform domain-specific heuristics, as well as state-of-the-art reinforcement learning methods.

The Hidden Markov Model (HMM) can predict the future value of a time series based on its current and previous values, making it a powerful algorithm for handling various types of time series. Numerous studies have explored the improvement of HMM using advanced techniques, leading to the development of several variations of HMM. Despite these studies indicating the increased competitiveness of HMM compared to other advanced algorithms, few have recognized the significance and impact of incorporating multistep stochastic states into its performance. In this work, we propose a Pyramidal Hidden Markov Model (PHMM) that can capture multiple multistep stochastic states. Initially, a multistep HMM is designed for extracting short multistep stochastic states. Next, a novel time series forecasting structure is proposed based on PHMM, which utilizes pyramid-like stacking to adaptively identify long multistep stochastic states. By employing these two schemes, our model can effectively handle non-stationary and noisy data, while also establishing long-term dependencies for more accurate and comprehensive forecasting. The experimental results on diverse multivariate time series datasets convincingly demonstrate the superior performance of our proposed PHMM compared to its competitive peers in time series forecasting.

Over the past decade, Artificial Intelligence (AI) has had great success recently and is being used in a wide range of academic and industrial fields. More recently, LLMs have made rapid advancements that have propelled AI to a new level, enabling even more diverse applications and industrial domains with intelligence, particularly in areas like software engineering and natural language processing. Nevertheless, a number of emerging trustworthiness concerns and issues exhibited in LLMs have already recently received much attention, without properly solving which the widespread adoption of LLMs could be greatly hindered in practice. The distinctive characteristics of LLMs, such as the self-attention mechanism, extremely large model scale, and autoregressive generation schema, differ from classic AI software based on CNNs and RNNs and present new challenges for quality analysis. Up to the present, it still lacks universal and systematic analysis techniques for LLMs despite the urgent industrial demand. Towards bridging this gap, we initiate an early exploratory study and propose a universal analysis framework for LLMs, LUNA, designed to be general and extensible, to enable versatile analysis of LLMs from multiple quality perspectives in a human-interpretable manner. In particular, we first leverage the data from desired trustworthiness perspectives to construct an abstract model as an auxiliary analysis asset, which is empowered by various abstract model construction methods. To assess the quality of the abstract model, we collect and define a number of evaluation metrics, aiming at both abstract model level and the semantics level. Then, the semantics, which is the degree of satisfaction of the LLM w.r.t. the trustworthiness perspective, is bound to and enriches the abstract model with semantics, which enables more detailed analysis applications for diverse purposes.

Bayesian brain theory suggests that the brain employs generative models to understand the external world. The sampling-based perspective posits that the brain infers the posterior distribution through samples of stochastic neuronal responses. Additionally, the brain continually updates its generative model to approach the true distribution of the external world. In this study, we introduce the Hierarchical Exponential-family Energy-based (HEE) model, which captures the dynamics of inference and learning. In the HEE model, we decompose the partition function into individual layers and leverage a group of neurons with shorter time constants to sample the gradient of the decomposed normalization term. This allows our model to estimate the partition function and perform inference simultaneously, circumventing the negative phase encountered in conventional energy-based models (EBMs). As a result, the learning process is localized both in time and space, and the model is easy to converge. To match the brain's rapid computation, we demonstrate that neural adaptation can serve as a momentum term, significantly accelerating the inference process. On natural image datasets, our model exhibits representations akin to those observed in the biological visual system. Furthermore, for the machine learning community, our model can generate observations through joint or marginal generation. We show that marginal generation outperforms joint generation and achieves performance on par with other EBMs.

Object recognition is a crucial step in perception systems for autonomous and intelligent vehicles, as evidenced by the numerous research works in the topic. In this paper, object recognition is explored by using multisensory and multimodality approaches, with the intention of reducing the false positive rate (FPR). The reduction of the FPR becomes increasingly important in perception systems since the misclassification of an object can potentially cause accidents. In particular, this work presents a strategy through Bayesian inference to reduce the FPR considering the likelihood function as a cumulative distribution function from Gaussian kernel density estimations, and the prior probabilities as cumulative functions of normalized histograms. The validation of the proposed methodology is performed on the KITTI dataset using deep networks (DenseNet, NasNet, and EfficientNet), and recent 3D point cloud networks (PointNet, and PintNet++), by considering three object-categories (cars, cyclists, pedestrians) and the RGB and LiDAR sensor modalities.

We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be formulated as a sign-constrained log-determinant program. Current algorithms are designed using the block coordinate descent method or the proximal point algorithm, which becomes computationally challenging in high-dimensional cases due to the requirement to solve numerous nonnegative quadratic programs or large-scale linear systems. To address this issue, we propose a novel algorithm based on the two-metric projection method, incorporating a carefully designed search direction and variable partitioning scheme. Our algorithm substantially reduces computational complexity, and its theoretical convergence is established. Experimental results on synthetic and real-world datasets demonstrate that our proposed algorithm provides a significant improvement in computational efficiency compared to the state-of-the-art methods.

In this paper we consider the problem of obtaining sharp bounds for the performance of temporal difference (TD) methods with linear functional approximation for policy evaluation in discounted Markov Decision Processes. We show that a simple algorithm with a universal and instance-independent step size together with Polyak-Ruppert tail averaging is sufficient to obtain near-optimal variance and bias terms. We also provide the respective sample complexity bounds. Our proof technique is based on refined error bounds for linear stochastic approximation together with the novel stability result for the product of random matrices that arise from the TD-type recurrence.

Mixture-of-experts (MoE) model incorporates the power of multiple submodels via gating functions to achieve greater performance in numerous regression and classification applications. From a theoretical perspective, while there have been previous attempts to comprehend the behavior of that model under the regression settings through the convergence analysis of maximum likelihood estimation in the Gaussian MoE model, such analysis under the setting of a classification problem has remained missing in the literature. We close this gap by establishing the convergence rates of density estimation and parameter estimation in the softmax gating multinomial logistic MoE model. Notably, when part of the expert parameters vanish, these rates are shown to be slower than polynomial rates owing to an inherent interaction between the softmax gating and expert functions via partial differential equations. To address this issue, we propose using a novel class of modified softmax gating functions which transform the input value before delivering them to the gating functions. As a result, the previous interaction disappears and the parameter estimation rates are significantly improved.