Queuing network control determines the allocation of scarce resources to manage congestion, a fundamental problem in manufacturing, communications, and healthcare. Compared to standard RL problems, queueing problems are distinguished by unique challenges: i) a system operating in continuous time, ii) high stochasticity, and iii) long horizons over which the system can become unstable (exploding delays). To spur methodological progress tackling these challenges, we present an open-sourced queueing simulation framework, QGym, that benchmark queueing policies across realistic problem instances. Our modular framework allows the researchers to build on our initial instances, which provide a wide range of environments including parallel servers, criss-cross, tandem, and re-entrant networks, as well as a realistically calibrated hospital queuing system. QGym makes it easy to compare multiple policies, including both model-free RL methods and classical queuing policies. Our testbed complements the traditional focus on evaluating algorithms based on mathematical guarantees in idealized settings, and significantly expands the scope of empirical benchmarking in prior work.

Long-tailed semi-supervised learning poses a significant challenge in training models with limited labeled data exhibiting a long-tailed label distribution. Current state-of-the-art LTSSL approaches heavily rely on high-quality pseudo-labels for large-scale unlabeled data. However, these methods often neglect the impact of representations learned by the neural network and struggle with real-world unlabeled data, which typically follows a different distribution than labeled data. This paper introduces a novel probabilistic framework that unifies various recent proposals in long-tail learning. Our framework derives the class-balanced contrastive loss through Gaussian kernel density estimation. We introduce a continuous contrastive learning method, CCL, extending our framework to unlabeled data using reliable and smoothed pseudo-labels. By progressively estimating the underlying label distribution and optimizing its alignment with model predictions, we tackle the diverse distribution of unlabeled data in real-world scenarios. Extensive experiments across multiple datasets with varying unlabeled data distributions demonstrate that CCL consistently outperforms prior state-of-the-art methods, achieving over 4% improvement on the ImageNet-127 dataset. Our source code is available at https://github.com/zhouzihao11/CCL

Event knowledge graphs (EKG) extend the classical notion of a trace to capture multiple, interacting views of a process execution. In this paper, we tackle the open problem of automating EKG discovery from uncurated data through a principled, probabilistic framing based on the outcome space resulting from featured-derived partial orders on events. From this, we derive an EKG discovery algorithm based upon statistical inference rather than an ad-hoc or heuristic-based strategy, or relying on manual analysis from domain experts. This approach comes at the computational cost of exploring a large, non-convex hypothesis space. In particular, solving the maximum likelihood term involves counting the number of linear extensions of posets, which in general is #P-complete. Fortunately, bound estimates suffice for model comparison, and admit incorporation into a bespoke branch-and-bound algorithm. We show that the posterior probability as defined is antitonic w.r.t. search depth for branching rules that are monotonic w.r.t. model inclusion. This allows pruning of large portions of the search space, which we show experimentally leads to rapid convergence toward optimal solutions that are consistent with manually built EKGs.

We introduce a framework for expanding residual computational graphs using jets, operators that generalize truncated Taylor series. Our method provides a systematic approach to disentangle contributions of different computational paths to model predictions. In contrast to existing techniques such as distillation, probing, or early decoding, our expansions rely solely on the model itself and requires no data, training, or sampling from the model. We demonstrate how our framework grounds and subsumes logit lens, reveals a (super-)exponential path structure in the recursive residual depth and opens up several applications. These include sketching a transformer large language model with n-gram statistics extracted from its computations, and indexing the models' levels of toxicity knowledge. Our approach enables data-free analysis of residual computation for model interpretability, development, and evaluation. The project website can be found here. Machine learning models, particularly large-scale foundation models, have become increasingly prevalent and impactful across a wide range of domains (Wei et al., 2021; Bommasani et al., 2023; Touvron et al., 2023b). While delivering strong results, their black-box nature has led to the development of techniques to assess their behavior and gain insights into their internal mechanisms. In this space, mechanistic interpretability (MI) (see e.g. Bereska & Gavves, 2024; Ferrando et al., 2024, for recent surverys) has emerged as an alternative to more classic local attribution methods such as SHAP (Lundberg, 2017) or integrated gradient (Sundararajan et al., 2017).

Identifying causal relations from purely observational data typically requires additional assumptions on relations and/or noise. Most current methods restrict their analysis to datasets that are assumed to have pure linear or nonlinear relations, which is often not reflective of real-world datasets that contain a combination of both. This paper presents CaPS, an ordering-based causal discovery algorithm that effectively handles linear and nonlinear relations. CaPS introduces a novel identification criterion for topological ordering and incorporates the concept of "parent score" during the post-processing optimization stage. These scores quantify the strength of the average causal effect, helping to accelerate the pruning process and correct inaccurate predictions in the pruning step. Experimental results demonstrate that our proposed solutions outperform state-of-the-art baselines on synthetic data with varying ratios of linear and nonlinear relations. The results obtained from real-world data also support the competitiveness of CaPS. Code and datasets are available at https://github.com/E2real/CaPS.

Acting to complete tasks in stochastic partially observable domains is an important problem in artificial intelligence, and is often formulated as a goal-based POMDP. Goal-based POMDPs can be solved using the RTDP-BEL algorithm, that operates by running forward trajectories from the initial belief to the goal. These trajectories can be guided by a heuristic, and more accurate heuristics can result in significantly faster convergence. In this paper, we develop a heuristic function that leverages the structured representation of domain models. We compute, in a relaxed space, a plan to achieve the goal, while taking into account the value of information, as well as the stochastic effects. We provide experiments showing that while our heuristic is slower to compute, it requires an order of magnitude less trajectories before convergence. Overall, it thus speeds up RTDP-BEL, particularly in problems where significant information gathering is needed.

Their approach involved modeling the problem using a set of processes, each dedicated to searching for a plan, akin to representing search nodes on an open list. Each process is characterized by a probabilistic performance profile, modeled by a random variable indicating the probability of successful termination given processing time, as well as a random variable modeling the deadline corresponding to each partial plan, which is only revealed after planning is concluded. The meta-level problem lies in finding an optimal schedule of processing time across all processes that maximizes the probability that any process delivers a plan before its deadline. A simplified version of this problem, known as "simplified allocating planning effort when actions expire," assumes discrete time intervals and has been proven to be NP-hard. However, under the condition of known deadlines, the problem becomes solvable in pseudo-polynomial time through dynamic programming. Later, this line of work was extended to consider interleaved planning and execution, where partial plans can be executed during the search [62, 63]. While this body of work bears relevance to our research, it primarily concentrates on deriving symbolic plans. In contrast, our focus lies in elaborating existing symbolic plans through motion-level reasoning to make them executable for a robot, optimizing the likelihood of meeting a pre-specified deadline.

Unlike regular models, these very simple models--often referred to as toy models--are not required to be linked to the real world through structural similarity or resemblance relations. They are not meant to be approximations of the target world system, and in some cases, they are not even required to be representational. In semantic terms, they do not accurately map onto their targets. Despite these limitations, they are still useful in understanding theoretical concepts and possible configurations of the target system. Paradigmatic examples of toy models include Boyle's law and the Ising model in physics, the Lotka-Volterra model in population ecology, and the Schelling model in the social sciences (Weisberg, 2013). In recent years, philosophers of science have become interested in toy models (Grüne-Yanoff, 2009; Luczak, 2017; Reutlinger et al., 2018; Frigg & Nguyen, 2017; Nguyen, 2020). The main purpose of this literature is to explore the nature of these models and examine how they perform their epistemic function. Despite lacking the regular descriptive and predictive features of full-scale scientific models, they often offer an elementary understanding of a phenomenon. Their definitions of "toy model" differ as well as their assessment of the importance of representation in modelling generally, but they all agree that toy models play an important epistemic role in scientific research, exploration, and pedagogy.

Real-world data often violates the equal-variance assumption (homoscedasticity), making it essential to account for heteroscedastic noise in causal discovery. In this work, we explore heteroscedastic symmetric noise models (HSNMs), where the effect $Y$ is modeled as $Y = f(X) + \sigma(X)N$, with $X$ as the cause and $N$ as independent noise following a symmetric distribution. We introduce a novel criterion for identifying HSNMs based on the skewness of the score (i.e., the gradient of the log density) of the data distribution. This criterion establishes a computationally tractable measurement that is zero in the causal direction but nonzero in the anticausal direction, enabling the causal direction discovery. We extend this skewness-based criterion to the multivariate setting and propose SkewScore, an algorithm that handles heteroscedastic noise without requiring the extraction of exogenous noise. We also conduct a case study on the robustness of SkewScore in a bivariate model with a latent confounder, providing theoretical insights into its performance. Empirical studies further validate the effectiveness of the proposed method.

Obtaining a reliable estimate of the joint probability mass function (PMF) of a set of random variables from observed data is a significant objective in statistical signal processing and machine learning. Modelling the joint PMF as a tensor that admits a low-rank canonical polyadic decomposition (CPD) has enabled the development of efficient PMF estimation algorithms. However, these algorithms require the rank (model order) of the tensor to be specified beforehand. In real-world applications, the true rank is unknown. Therefore, an appropriate rank is usually selected from a candidate set either by observing validation errors or by computing various likelihood-based information criteria, a procedure which is computationally expensive for large datasets. This paper presents a novel Bayesian framework for estimating the joint PMF and automatically inferring its rank from observed data. We specify a Bayesian PMF estimation model and employ appropriate prior distributions for the model parameters, allowing for tuning-free rank inference via a single training run. We then derive a deterministic solution based on variational inference (VI) to approximate the posterior distributions of various model parameters. Additionally, we develop a scalable version of the VI-based approach by leveraging stochastic variational inference (SVI) to arrive at an efficient algorithm whose complexity scales sublinearly with the size of the dataset. Numerical experiments involving both synthetic data and real movie recommendation data illustrate the advantages of our VI and SVI-based methods in terms of estimation accuracy, automatic rank detection, and computational efficiency.