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Apratim Bhattacharyya, Bicheng Xu, Sanjay Haresh, Reza Pourreza, Litian Liu, Sunny Panchal, Leonid Sigal, Roland Memisevic

Multi-modal Large Language Models (LLM) have advanced conversational abilities but struggle with providing live, interactive step-by-step guidance, a key capability for future AI assistants. Effective guidance requires not only delivering instructions but also detecting their successful execution, as well as identifying and alerting users to mistakes, all of which has to happen in real-time. This requires models that are not turn-based, but that can react asynchronously to a video stream, as well as video data showing users performing tasks including mistakes and their corrections. To this end, we introduce Qualcomm Interactive Cooking, a new benchmark and dataset built upon CaptainCook4D, which contains user mistakes during task execution. Our dataset and benchmark features densely annotated, timed instructions and feedback messages, specifically including mistake alerts precisely timestamped to their visual occurrence in the video. We evaluate state-of-the-art multi-modal LLMs on the Qualcomm Interactive Cooking benchmark and introduce LiveMamba, a streaming multi-modal LLM designed for interactive instructional guidance. This work provides the first dedicated benchmark and a strong baseline for developing and evaluating on live, situated coaching.

Social Aspects · Accountability, Transparency and Interpretability

Minh Hieu Vu, Tan Nguyen

Controlling specific behaviors in large language models while preserving their general capabilities is a central challenge for safe and reliable artificial intelligence deployment. Current steering methods, such as vector addition and directional ablation, are constrained within a two-dimensional subspace defined by the activation and feature direction, making them sensitive to chosen parameters and potentially affecting unrelated features due to unintended interactions in activation space. We introduce Angular Steering, a novel and flexible method for behavior modulation that operates by rotating activations within a fixed two-dimensional subspace. By formulating steering as a geometric rotation toward or away from a target behavior direction, Angular Steering provides continuous, fine-grained control over behaviors such as refusal and compliance. We demonstrate this method using refusal steering emotion steering as use cases. Additionally, we propose Adaptive Angular Steering, a selective variant that rotates only activations aligned with the target feature, further enhancing stability and coherence. Angular Steering generalizes existing addition and orthogonalization techniques under a unified geometric rotation framework, simplifying parameter selection and maintaining model stability across a broader range of adjustments. Experiments across multiple model families and sizes show that Angular Steering achieves robust behavioral control while maintaining general language modeling performance, underscoring its flexibility, generalization, and robustness compared to prior approaches. Code and artifacts are available at \url{https://github.com/lone17/angular-steering/}.

Deep Learning · Generative Models and Autoencoders

Litu Rout, Constantine Caramanis, Sanjay Shakkottai

Diffusion Language Models (DLMs) promise parallel generation and bidirectional context, yet they underperform autoregressive (AR) models in both *likelihood modeling* and *generated text quality*. We identify that this performance gap arises when important tokens (e.g., key words or low-frequency words that anchor a sentence) are masked early in the forward process, limiting contextual information for accurate reconstruction. To address this, we introduce the *Anchored Diffusion Language Model (ADLM)*, a novel two-stage framework that first predicts distributions over important tokens via an anchor network, and then predicts the likelihoods of missing tokens conditioned on the anchored predictions. ADLM significantly improves test perplexity on LM1B and OpenWebText, achieving up to 25.4\% gains over prior DLMs, and narrows the gap with strong AR baselines. It also achieves state-of-the-art zero-shot generalization across seven benchmarks and surpasses AR models in MAUVE score, which marks the first time a DLM generates better human-like text than an AR model. Theoretically, we derive an Anchored Negative Evidence Lower Bound (ANELBO) objective and show that anchoring improves sample complexity and likelihood modeling. Beyond diffusion, anchoring boosts performance in AR models and enhances reasoning in math and logic tasks, outperforming existing chain-of-thought approaches. Please see our project page: [anchored-diffusion-llm.github.io](https://anchored-diffusion-llm.github.io/) for code and demo.

Computer Vision · Vision Models & Multimodal

Benedetta Liberatori, Alessandro Conti, Lorenzo Vaquero, Yiming Wang, Elisa Ricci, Paolo Rota

What does it mean for two videos to be similar? Videos may appear similar when judged by the actions they depict, yet entirely different if evaluated based on the locations where they were filmed. While humans naturally compare videos by taking different aspects into account, this ability has not been thoroughly studied and presents a challenge for models that often depend on broad global similarity scores. Large Multimodal Models (LMMs) with video understanding capabilities open new opportunities for leveraging natural language in comparative video tasks. We introduce Concept-based Video Similarity estimation (ConViS), a novel task that compares pairs of videos by computing interpretable similarity scores across a predefined set of key semantic concepts. ConViS allows for human-like reasoning about video similarity and enables new applications such as concept-conditioned video retrieval. To support this task, we also introduce ConViS-Bench, a new benchmark comprising carefully annotated video pairs spanning multiple domains. Each pair comes with concept-level similarity scores and textual descriptions of both differences and similarities. Additionally, we benchmark several state-of-the-art models on ConViS, providing insights into their alignment with human judgments. Our results reveal significant performance differences on ConViS, indicating that some concepts present greater challenges for estimating video similarity. We believe that ConViS-Bench will serve as a valuable resource for advancing research in language-driven video understanding.

Applications · Everything Else

Lyle Regenwetter, Yazan Abu Obaideh, Fabien Chiotti, Ioanna Lykourentzou, Faez Ahmed

We introduce BikeBench, an engineering design benchmark for evaluating generative models on problems with multiple real-world objectives and constraints. As generative AI's reach continues to grow, evaluating its capability to understand physical laws, human guidelines, and hard constraints grows increasingly important. Engineering product design lies at the intersection of these difficult tasks, providing new challenges for AI capabilities. BikeBench evaluates AI models' capabilities to generate bicycle designs that not only resemble the dataset, but meet specific performance objectives and constraints. To do so, BikeBench quantifies a variety of human-centered and multiphysics performance characteristics, such as aerodynamics, ergonomics, structural mechanics, human-rated usability, and similarity to subjective text or image prompts. Supporting the benchmark are several datasets of simulation results, a dataset of 10,000 human-rated bicycle assessments, and a synthetically generated dataset of 1.6M designs, each with a parametric, CAD/XML, SVG, and PNG representation. BikeBench is uniquely configured to evaluate tabular generative models, large language models (LLMs), design optimization, and hybrid algorithms side-by-side. Our experiments indicate that LLMs and tabular generative models fall short of hybrid GenAI+optimization algorithms in design quality, constraint satisfaction, and similarity scores, suggesting significant room for improvement. We hope that BikeBench, a first-of-its-kind benchmark, will help catalyze progress in generative AI for constrained multi-objective engineering design problems. We provide code, data, an interactive leaderboard, and other resources at https://github.com/Lyleregenwetter/BikeBench.

Huiyang Shao, Xin Xia, Yuxi Ren, XING WANG, Xuefeng Xiao

Diffusion models have emerged as state‑of‑the‑art in image synthesis.However, it often suffer from semantic instability and slow iterative denoising. We introduce Latent Alignment Framework (LABridge), a novel Text–Image Latent Alignment Framework via an Ornstein–Uhlenbeck (OU) Process, which explicitly preserves and aligns textual and visual semantics in an aligned latent space. LABridge employs a Text-Image Alignment Encoder (TIAE) to encode text prompts into structured priors that are directly aligned with image latents. Instead of a homogeneous Gaussian, Mean-Conditioned OU process smoothly interpolates between these text‑conditioned priors and image latents, improving stability and reducing the number of denoising steps. Extensive experiments on standard text-to-image benchmarks show that LABridge achieves better text–image alignment metric and competitive FID scores compared to leading diffusion baselines. By unifying text and image representations through principled latent alignment, LABridge paves the way for more efficient, semantically consistent, and high‑fidelity text to image generation.

Deep Learning · Algorithms

Wenhong Zhu, Ruobing Xie, Weinan Zhang, Rui Wang

Realignment becomes necessary when a language model (LM) fails to meet expected performance. We propose a flexible realignment framework that supports quantitative control of alignment degree during training and inference. This framework incorporates **Training-time Realignment (TrRa)**, which efficiently realigns the reference model by leveraging the controllable fusion of logits from both the reference and already aligned models. For example, TrRa reduces token usage by **54.63%** on DeepSeek-R1-Distill-Qwen-1.5B without any performance degradation, outperforming DeepScaleR-1.5B’s **33.86%**. To complement TrRa during inference, we introduce a layer adapter that enables **smooth Inference-time Realignment (InRa)**. This adapter is initialized to perform an identity transformation at the bottom layer and is inserted preceding the original layers. During inference, input embeddings are simultaneously processed by the adapter and the original layer, followed by the remaining layers, and then controllably interpolated at the logit level. We upgraded DeepSeek-R1-Distill-Qwen-7B from a slow-thinking model to one that supports both fast and slow thinking, allowing flexible alignment control even **during inference**. By encouraging deeper reasoning, it even surpassed its original performance.

Computer Vision · Image and Video Generation

Bozhou Zhang, Nan Song, jingyu li, Xiatian Zhu, Jiankang Deng, Li Zhang

End-to-end autonomous driving methods aim to directly map raw sensor inputs to future driving actions such as planned trajectories, bypassing traditional modular pipelines. While these approaches have shown promise, they often operate under a one-shot paradigm that relies heavily on the current scene context, potentially underestimating the importance of scene dynamics and their temporal evolution. This limitation restricts the model’s ability to make informed and adaptive decisions in complex driving scenarios. We propose a new perspective: the future trajectory of an autonomous vehicle is closely intertwined with the evolving dynamics of its environment, and conversely, the vehicle’s own future states can influence how the surrounding scene unfolds. Motivated by this bidirectional relationship, we introduce **SeerDrive**, a novel end-to-end framework that jointly models future scene evolution and trajectory planning in a closed-loop manner. Our method first predicts future bird’s-eye view (BEV) representations to anticipate the dynamics of the surrounding scene, then leverages this foresight to generate future-context-aware trajectories. Two key components enable this: (1) future-aware planning, which injects predicted BEV features into the trajectory planner, and (2) iterative scene modeling and vehicle planning, which refines both future scene prediction and trajectory generation through collaborative optimization. Extensive experiments on the NAVSIM and nuScenes benchmarks show that SeerDrive significantly outperforms existing state-of-the-art methods.

Applications · Language, Speech and Dialog

Letian Peng, Jingbo Shang

This paper introduces Codified Profiles for role-playing, a novel approach that represents character logic as structured, executable functions for behavioral decision-making. Converted by large language model (LLM) from textual profiles, each codified profile defines a set of functions parse_by_scene(scene) that output multiple logic-grounded assertions according to scene, using both explicit control structures (e.g., if-then-else) and flexible check_condition(scene, question) functions where each question is a semantically meaningful prompt about the scene (e.g., "Is the character in danger?") discriminated by the role-playing LLM as true, false, or unknown. This explicit representation offers three key advantages over traditional prompt-based textual profiles, which append character descriptions directly into text prompts: (1) Persistence, by enforcing complete and consistent execution of character logic, rather than relying on the model's implicit reasoning; (2) Updatability, through systematic inspection and revision of behavioral logic, which is difficult to track or debug in prompt-only approaches; (3) Controllable Randomness, by supporting stochastic behavior directly within the logic, enabling fine-grained variability that prompting alone struggles to achieve. To validate these advantages, we introduce a new benchmark constructed from 83 characters and 5,141 scenes curated from Fandom, using natural language inference (NLI)-based scoring to compare character responses against ground-truths. Our experiments demonstrate the significant benefits of codified profiles in improving persistence, updatability, and behavioral diversity. Notably, by offloading a significant portion of reasoning to preprocessing, codified profiles enable even 1B-parameter models to perform high-quality role-playing, providing an efficient, lightweight foundation for local deployment of role-play agents.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Neal Mangaokar, Ashish Hooda, Zhuohang Li, Bradley Malin, Kassem Fawaz, Somesh Jha, Atul Prakash, Amrita Roy Chowdhury

Membership inference tests aim to determine whether a particular data point was included in a language model's training set. However, recent works have shown that such tests often fail under the strict definition of membership based on exact matching, and have suggested relaxing this definition to include semantic neighbors as members as well. In this work, we show that membership inference tests are still *unreliable* under this relaxation - it is possible to poison the training dataset in a way that causes the test to produce incorrect predictions for a target point. We theoretically reveal a trade-off between a test’s accuracy and its robustness to poisoning. We also present a concrete instantiation of this poisoning attack and empirically validate its effectiveness. Our results show that it can degrade the performance of existing tests to well below random.

Deep Learning · Algorithms

Di He, Songjun Tu, Ajay Jaiswal, Li Shen, Ganzhao Yuan, Shiwei Liu, Lu Yin

Weight decay is a standard regularization technique for training large language models (LLMs). While it is common to assign a uniform decay rate to every layer, this approach overlooks the structural diversity of LLMs and the varying spectral properties across modules. In this paper, we introduce AlphaDecay, a simple yet effective method that adaptively assigns different weight decay strengths to each module of an LLM. Our approach is guided by Heavy-Tailed Self-Regularization (HT-SR) theory, which analyzes the empirical spectral density (ESD) of weight correlation matrices to quantify “heavy-tailedness.” Modules exhibiting more pronounced heavy-tailed ESDs, reflecting stronger feature learning, are assigned weaker decay, while modules with lighter-tailed spectra receive stronger decay. Our method leverages tailored weight decay assignments to balance the module-wise differences in spectral properties, leading to improved performance. Extensive pre-training tasks with various model sizes from 60M to 1B demonstrate that AlphaDecay achieves better perplexity and generalization than conventional uniform decay and other adaptive decay baselines. The code is available at https://github.com/hed-ucas/AlphaDecay.

Social Aspects · Trustworthy Machine Learning

Harvey Yiyun Fu, Aryan Shrivastava, Jared Moore, Peter West, Chenhao Tan, Ari Holtzman

Large language models (LLMs) are increasingly capable of processing long inputs and locating specific information within them, as evidenced by their performance on the Needle in a Haystack (NIAH) test. However, while models excel at recalling surprising information, they still struggle to identify clearly omitted information. We introduce AbsenceBench to assesses LLMs' capacity to detect missing information across three domains: numerical sequences, poetry, and GitHub pull requests. AbsenceBench asks models to identify which pieces of a document were deliberately removed, given access to both the original and edited contexts. Despite the apparent straightforwardness of these tasks, our experiments reveal that even state-of-the-art models like Claude-3.7-Sonnet achieve only 69.6% F1-score with a modest average context length of 5K tokens. Our analysis suggests this poor performance stems from a fundamental limitation: Transformer attention mechanisms cannot easily attend to "gaps" in documents since these absences don't correspond to any specific keys that can be attended to. Overall, our results and analysis provide a case study of the close proximity of tasks where models are already superhuman (NIAH) and tasks where models breakdown unexpectedly (AbsenceBench).

Theory · Reinforcement Learning and Planning

Idan Barnea, Tal Lancewicki, Yishay Mansour

We study the regret in stochastic Multi-Armed Bandits (MAB) with multiple agents that communicate over an arbitrary connected communication graph. We analyzed a variant of Cooperative Successive Elimination algorithm, $\texttt{Coop-SE}$, and show an individual regret bound of ${O}(\mathcal{R} / m + A^2 + A \sqrt{\log T})$ and a nearly matching lower bound. Here $A$ is the number of actions, $T$ the time horizon, $m$ the number of agents, and $\mathcal{R} = \sum_{\Delta_i > 0}\log(T)/\Delta_i$ is the optimal single agent regret, where $\Delta_i$ is the sub-optimality gap of action $i$. Our work is the first to show an individual regret bound in cooperative stochastic MAB that is independent of the graph's diameter. When considering communication networks there are additional considerations beyond regret, such as message size and number of communication rounds. First, we show that our regret bound holds even if we restrict the messages to be of logarithmic size. Second, for logarithmic number of communication rounds, we obtain a regret bound of ${O}(\mathcal{R} / m+A \log T)$.

Social Aspects · Accountability, Transparency and Interpretability

Sean McGregor, Vassil Tashev, Armstrong Foundjem, Aishwarya Ramasethu, Sadegh AlMahdi Kazemi Zarkouei, Chris Knotz, Kongtao Chen, Alicia Parrish, Anka Reuel-Lamparth, Heather Frase

Large language model (LLM) benchmarks inform LLM use decisions (e.g., "is this LLM safe to deploy for my use case and context?"). However, benchmarks may be rendered unreliable by various failure modes impacting benchmark bias, variance, coverage, or people's capacity to understand benchmark evidence. Using the National Institute of Standards and Technology's risk management process as a foundation, this research iteratively analyzed 26 popular benchmarks, identifying 57 potential failure modes and 196 corresponding mitigation strategies. The mitigations reduce failure likelihood and/or severity, providing a frame for evaluating "benchmark risk," which is scored to provide a metaevaluation benchmark: BenchRisk. Higher scores indicate benchmark users are less likely to reach an incorrect or unsupported conclusion about an LLM. All 26 scored benchmarks present significant risk within one or more of the five scored dimensions (comprehensiveness, intelligibility, consistency, correctness, and longevity), which points to important open research directions for the field of LLM benchmarking. The BenchRisk workflow allows for comparison between benchmarks; as an open-source tool, it also facilitates the identification and sharing of risks and their mitigations.

Social Aspects

Raad Khraishi, Cristovao Iglesias de Oliveira, Devesh Batra, Peter Gostev, Giulio Pelosio, Ramin Okhrati, Greig Cowan

This position paper argues that real-time generative AI has the potential to become the next wave of addictive digital media, creating a new class of digital content akin to ``digital heroin'' with severe implications for mental health and youth development. By shortening the content-generation feedback loop to mere seconds, these advanced models will soon be able to hyper-personalize outputs on the fly. When paired with misaligned incentives (e.g., maximizing user engagement), this will fuel unprecedented compulsive consumption patterns with far-reaching consequences for mental health, cognitive development, and social stability. Drawing on interdisciplinary research, from clinical observations of social media addiction to neuroscientific studies of dopamine-driven feedback, we illustrate how real-time tailored content generation may erode user autonomy, foment emotional distress, and disproportionately endanger vulnerable groups, such as adolescents. Due to the rapid advancement of generative AI and its potential to induce severe addiction-like effects, we call for strong government oversight akin to existing controls on addictive substances, particularly for minors. We further urge the machine learning community to act proactively by establishing robust design guidelines, collaborating with public health experts, and supporting targeted policy measures to ensure responsible and ethical deployment, rather than paving the way for another wave of unregulated digital dependence.

Josu Eguíluz, Axel Brando, Migle Laukyte, Marc Serra-Vidal

Artificial intelligence (AI) now permeates critical infrastructures and decisionmaking systems where failures produce social, economic, and democratic harm. This position paper challenges the entrenched belief that regulation and innovation are opposites. As evidenced by analogies from aviation, pharmaceuticals, and welfare systems and recent cases of synthetic misinformation, bias and unaccountable decision-making, the absence of well-designed regulation has already created immeasurable damage. Regulation, when thoughtful and adaptive, is not a brake on innovation—it is its foundation. The present position paper examines the EU AI Act as a model of risk-based, responsibility-driven regulation that addresses the Collingridge Dilemma: acting early enough to prevent harm, yet flexibly enough to sustain innovation. Its adaptive mechanisms—regulatory sandboxes, small and medium enterprises (SMEs) support, real-world testing, fundamental rights impact assessment (FRIA)—demonstrate how regulation can accelerate responsibly, rather than delay, technological progress. The position paper summarises how governance tools transform perceived burdens into tangible advantages: legal certainty, consumer trust, and ethical competitiveness. Ultimately, the paper reframes progress: innovation and regulation advance together. By embedding transparency, impact assessments, accountability, and AI literacy into design and deployment, the EU framework defines what responsible innovation truly means—technological ambition disciplined by democratic values and fundamental rights.

Xingchen Zhang, Zixian Zhao

In the era of artificial intelligence (AI), pedestrian privacy is increasingly at risk. In research areas such as autonomous driving, computer vision, and surveillance, large datasets are often collected in public spaces, capturing pedestrians without consent or anonymization. These datasets are used to train systems that can identify, track, and analyze individuals, often without their knowledge. Although various technical methods and regional regulations have been proposed to address this issue, existing solutions are either insufficient to protect privacy or compromise data utility, thereby limiting their effectiveness for research. In this paper, we argue that more effort is needed to protect pedestrian privacy in the era of AI while maintaining data utility. We call on the AI and computer vision communities to take pedestrian privacy seriously and to rethink how pedestrian data are collected and anonymized. Collaboration with experts in law and ethics will also be essential for the responsible development of AI. Without stronger action, it will become increasingly difficult for individuals to protect their privacy, and public trust in AI may decline.

Computer Vision · Vision Models & Multimodal

Ruiping Liu, Junwei Zheng, Yufan Chen, Zirui Wang, Kunyu Peng, Kailun Yang, Jiaming Zhang, Marc Pollefeys, Rainer Stiefelhagen

Physical environments and circumstances are fundamentally dynamic, yet current 3D datasets and evaluation benchmarks tend to concentrate on either dynamic scenarios or dynamic situations in isolation, resulting in incomplete comprehension. To overcome these constraints, we introduce Situat3DChange, an extensive dataset supporting three situation-aware change understanding tasks following the perception-action model: 121K question-answer pairs, 36K change descriptions for perception tasks, and 17K rearrangement instructions for the action task. To construct this large-scale dataset, Situat3DChange leverages 11K human observations of environmental changes to establish shared mental models and shared situational awareness for human-AI collaboration. These observations, enriched with egocentric and allocentric perspectives as well as categorical and coordinate spatial relations, are integrated using an LLM to support understanding of situated changes. To address the challenge of comparing pairs of point clouds from the same scene with minor changes, we propose SCReasoner, an efficient 3D MLLM approach that enables effective point cloud comparison with minimal parameter overhead and no additional tokens required for the language decoder. Comprehensive evaluation on Situat3DChange tasks highlights both the progress and limitations of MLLMs in dynamic scene and situation understanding. Additional experiments on data scaling and cross-domain transfer demonstrate the task-agnostic effectiveness of using Situat3DChange as a training dataset for MLLMs. The established dataset and source code are publicly available at: https://github.com/RuipingL/Situat3DChange.

Applications · Time Series

Long Li, Wanghu Chen, Wencheng Zhang, Shi Yuan, Hongle Guo

Unsupervised anomaly detection of multivariate time series remains challenging in complex nonstationary dynamics, due to the high false-positive rates and limited interpretability. We propose PhysDiff, combining physics-guided decomposition with diffusion-based reconstruction, to address these issues. The physics-guided signal decomposition is introduced to disentangle overlapping dynamics by isolating high frequency oscillations and low frequency trends, which can reduce interference and provide meaningful physical priors. The reconstruction through conditional diffusion modeling captures deviations from learned normal behavior, making anomalies more distinguishable. Notably, PhysDiff introduces an amplitude-sensitive permutation entropy criterion to adaptively determine the optimal decomposition depth, and automatically extract adaptive frequency components used as explicit physics-based constraints for the diffusion process. Furthermore, the proposed conditional diffusion network employs a dual-path conditioning mechanism that integrates high-frequency and low-frequency physical priors, dynamically regulating the denoising process via a novel time frequency energy routing mechanism. By weighting reconstruction errors across frequency bands, our method improves anomaly localization and enhances interpretability. Extensive experiments on five benchmark datasets and two NeurIPS-TS scenarios demonstrate that PhysDiff outperforms 18 state-of-the-art baselines, with average F1-score improvements on both standard and challenging datasets. Experimental results validate the advantages of combining principled signal decomposition with diffusion-based reconstruction for robust, interpretable anomaly detection in complex dynamic systems.

Probabilistic Methods · Bayesian Models and Methods

Lu Xu, Tsai Hor Chan, Lequan Yu, Kwok Lam, Guosheng Yin

Density estimation is essential for generative modeling, particularly with the rise of modern neural networks. While existing methods capture complex data distributions, they often lack interpretability and uncertainty quantification. Bayesian nonparametric methods, especially the \polya tree, offer a robust framework that addresses these issues by accurately capturing function behavior over small intervals. Traditional techniques like Markov chain Monte Carlo (MCMC) face high computational complexity and scalability limitations, hindering the use of Bayesian nonparametric methods in deep learning. To tackle this, we introduce the variational \polya tree (VPT) model, which employs stochastic variational inference to compute posterior distributions. This model provides a flexible, nonparametric Bayesian prior that captures latent densities and works well with stochastic gradient optimization. We also leverage the joint distribution likelihood for a more precise variational posterior approximation than traditional mean-field methods. We evaluate the model performance on both real data and images, and demonstrate its competitiveness with other state-of-the-art deep density estimation methods. We also explore its ability in enhancing interpretability and uncertainty quantification. Code is available at \url{https://github.com/howardchanth/var-polya-tree}.