Xiaofeng Ma, Michael Kirby, Chris Peterson
The shape and orientation of data clouds reflect variability in observations that can confound pattern recognition systems. Subspace methods, utilizing Grassmann manifolds, have been a great aid in dealing with such variability. However, this usefulness begins to falter when the data cloud contains sufficiently many outliers corresponding to stray elements from another class or when the number of data points is larger than the number of features. We illustrate how nested subspace methods, utilizing flag manifolds, can help to deal with such additional confounding factors. Flag manifolds, which are parameter spaces for nested subspaces, are a natural geometric generalization of Grassmann manifolds. To make practical comparisons on a flag manifold, algorithms are proposed for determining the distances between points $[A], [B]$ on a flag manifold, where $A$ and $B$ are arbitrary orthogonal matrix representatives for $[A]$ and $[B]$, and for determining the initial direction of these minimal length geodesics. The approach is illustrated in the context of (hyper) spectral imagery showing the impact of ambient dimension, sample dimension, and flag structure.
Xiaofeng Mao, Zhengkai Jiang, Qilin Wang, Chencan Fu, Jiangning Zhang, Jiafu Wu, Yabiao Wang, Chengjie Wang, Wei Li, Mingmin Chi
Recent advancements in the field of Diffusion Transformers have substantially improved the generation of high-quality 2D images, 3D videos, and 3D shapes. However, the effectiveness of the Transformer architecture in the domain of co-speech gesture generation remains relatively unexplored, as prior methodologies have predominantly employed the Convolutional Neural Network (CNNs) or simple a few transformer layers. In an attempt to bridge this research gap, we introduce a novel Masked Diffusion Transformer for co-speech gesture generation, referred to as MDT-A2G, which directly implements the denoising process on gesture sequences. To enhance the contextual reasoning capability of temporally aligned speech-driven gestures, we incorporate a novel Masked Diffusion Transformer. This model employs a mask modeling scheme specifically designed to strengthen temporal relation learning among sequence gestures, thereby expediting the learning process and leading to coherent and realistic motions. Apart from audio, Our MDT-A2G model also integrates multi-modal information, encompassing text, emotion, and identity. Furthermore, we propose an efficient inference strategy that diminishes the denoising computation by leveraging previously calculated results, thereby achieving a speedup with negligible performance degradation. Experimental results demonstrate that MDT-A2G excels in gesture generation, boasting a learning speed that is over 6$\times$ faster than traditional diffusion transformers and an inference speed that is 5.7$\times$ than the standard diffusion model.
Xiaofeng Mao, Yucheng Xu, Zhaole Sun, Elle Miller, Daniel Layeghi, Michael Mistry
Long-horizon contact-rich tasks are challenging to learn with reinforcement learning, due to ineffective exploration of high-dimensional state spaces with sparse rewards. The learning process often gets stuck in local optimum and demands task-specific reward fine-tuning for complex scenarios. In this work, we propose a structured framework that leverages privileged actions with curriculum learning, enabling the policy to efficiently acquire long-horizon skills without relying on extensive reward engineering or reference trajectories. Specifically, we use privileged actions in simulation with a general training procedure that would be infeasible to implement in real-world scenarios. These privileges include relaxed constraints and virtual forces that enhance interaction and exploration with objects. Our results successfully achieve complex multi-stage long-horizon tasks that naturally combine non-prehensile manipulation with grasping to lift objects from non-graspable poses. We demonstrate generality by maintaining a parsimonious reward structure and showing convergence to diverse and robust behaviors across various environments. Additionally, real-world experiments further confirm that the skills acquired using our approach are transferable to real-world environments, exhibiting robust and intricate performance. Our approach outperforms state-of-the-art methods in these tasks, converging to solutions where others fail.
Xiaofeng Mao, Yuefeng Chen, Yao Zhu, Da Chen, Hang Su, Rong Zhang, Hui Xue
Practical object detection application can lose its effectiveness on image inputs with natural distribution shifts. This problem leads the research community to pay more attention on the robustness of detectors under Out-Of-Distribution (OOD) inputs. Existing works construct datasets to benchmark the detector's OOD robustness for a specific application scenario, e.g., Autonomous Driving. However, these datasets lack universality and are hard to benchmark general detectors built on common tasks such as COCO. To give a more comprehensive robustness assessment, we introduce COCO-O(ut-of-distribution), a test dataset based on COCO with 6 types of natural distribution shifts. COCO-O has a large distribution gap with training data and results in a significant 55.7% relative performance drop on a Faster R-CNN detector. We leverage COCO-O to conduct experiments on more than 100 modern object detectors to investigate if their improvements are credible or just over-fitting to the COCO test set. Unfortunately, most classic detectors in early years do not exhibit strong OOD generalization. We further study the robustness effect on recent breakthroughs of detector's architecture design, augmentation and pre-training techniques. Some empirical findings are revealed: 1) Compared with detection head or neck, backbone is the most important part for robustness; 2) An end-to-end detection transformer design brings no enhancement, and may even reduce robustness; 3) Large-scale foundation models have made a great leap on robust object detection. We hope our COCO-O could provide a rich testbed for robustness study of object detection. The dataset will be available at https://github.com/alibaba/easyrobust/tree/main/benchmarks/coco_o.
Xiaofeng Mao, Yuefeng Chen, Rong Zhang, Hui Xue, Zhao Li, Hang Su
Deep neural networks (DNNs) has shown great promise in computer vision tasks. However, machine vision achieved by DNNs cannot be as robust as human perception. Adversarial attacks and data distribution shifts have been known as two major scenarios which degrade machine performance and obstacle the wide deployment of machines "in the wild". In order to break these obstructions and facilitate the research of model robustness, we develop EasyRobust, a comprehensive and easy-to-use toolkit for training, evaluation and analysis of robust vision models. EasyRobust targets at two types of robustness: 1) Adversarial robustness enables the model to defense against malicious inputs crafted by worst-case perturbations, also known as adversarial examples; 2) Non-adversarial robustness enhances the model performance on natural test images with corruptions or distribution shifts. Thorough benchmarks on image classification enable EasyRobust to provide an accurate robustness evaluation on vision models. We wish our EasyRobust can help for training practically-robust models and promote academic and industrial progress in closing the gap between human and machine vision. Codes and models of EasyRobust have been open-sourced in https://github.com/alibaba/easyrobust.
Xiaofeng Mao, Zhengkai Jiang, Fu-Yun Wang, Jiangning Zhang, Hao Chen, Mingmin Chi, Yabiao Wang, Wenhan Luo
Video diffusion models have shown great potential in generating high-quality videos, making them an increasingly popular focus. However, their inherent iterative nature leads to substantial computational and time costs. While efforts have been made to accelerate video diffusion by reducing inference steps (through techniques like consistency distillation) and GAN training (these approaches often fall short in either performance or training stability). In this work, we introduce a two-stage training framework that effectively combines consistency distillation with GAN training to address these challenges. Additionally, we propose a novel video discriminator design, which eliminates the need for decoding the video latents and improves the final performance. Our model is capable of producing high-quality videos in merely one-step, with the flexibility to perform multi-step refinement for further performance enhancement. Our quantitative evaluation on the OpenWebVid-1M benchmark shows that our model significantly outperforms existing methods. Notably, our 1-step performance(FVD 171.15) exceeds the 8-step performance of the consistency distillation based method, AnimateLCM (FVD 184.79), and approaches the 25-step performance of advanced Stable Video Diffusion (FVD 156.94).
Xiaofeng Mao, Yuefeng Chen, Xiaojun Jia, Rong Zhang, Hui Xue, Zhao Li
Contrastive Language-Image Pre-trained (CLIP) models have zero-shot ability of classifying an image belonging to "[CLASS]" by using similarity between the image and the prompt sentence "a [CONTEXT] of [CLASS]". Based on exhaustive text cues in "[CONTEXT]", CLIP model is aware of different contexts, e.g. background, style, viewpoint, and exhibits unprecedented robustness against a wide range of distribution shifts. However, recent works find further fine-tuning of CLIP models improves accuracy but sacrifices the robustness on downstream tasks. We conduct an empirical investigation to show fine-tuning will corrupt the context-aware ability of pre-trained CLIP features. To solve this problem, we propose Context-Aware Robust Fine-tuning (CAR-FT). CAR-FT regularizes the model during fine-tuning to capture the context information. Specifically, we use zero-shot prompt weights to get the context distribution contained in the image. By minimizing the Kullback-Leibler Divergence (KLD) between context distributions induced by original/fine-tuned CLIP models, CAR-FT makes the context-aware ability of CLIP inherited into downstream tasks, and achieves both higher In-Distribution (ID) and Out-Of-Distribution (OOD) accuracy. The experimental results show CAR-FT achieves superior robustness on five OOD test datasets of ImageNet, and meanwhile brings accuracy gains on nine downstream tasks. Additionally, CAR-FT surpasses previous Domain Generalization (DG) methods and gets 78.5% averaged accuracy on DomainBed benchmark, building the new state-of-the-art.
Xiaofeng Mao, Gabriele Giudici, Claudio Coppola, Kaspar Althoefer, Ildar Farkhatdinov, Zhibin Li, Lorenzo Jamone
Effective execution of long-horizon tasks with dexterous robotic hands remains a significant challenge in real-world problems. While learning from human demonstrations have shown encouraging results, they require extensive data collection for training. Hence, decomposing long-horizon tasks into reusable primitive skills is a more efficient approach. To achieve so, we developed DexSkills, a novel supervised learning framework that addresses long-horizon dexterous manipulation tasks using primitive skills. DexSkills is trained to recognize and replicate a select set of skills using human demonstration data, which can then segment a demonstrated long-horizon dexterous manipulation task into a sequence of primitive skills to achieve one-shot execution by the robot directly. Significantly, DexSkills operates solely on proprioceptive and tactile data, i.e., haptic data. Our real-world robotic experiments show that DexSkills can accurately segment skills, thereby enabling autonomous robot execution of a diverse range of tasks.
Xiaofeng Mao, Zhen Li, Chuanhao Li, Xiaojie Xu, Kaining Ying, Tong He, Jiangmiao Pang, Yu Qiao, Kaipeng Zhang
Recent approaches have demonstrated the promise of using diffusion models to generate interactive and explorable worlds. However, most of these methods face critical challenges such as excessively large parameter sizes, reliance on lengthy inference steps, and rapidly growing historical context, which severely limit real-time performance and lack text-controlled generation capabilities. To address these challenges, we propose \method, a novel framework designed to generate realistic, interactive, and continuous worlds from a single image or text prompt. \method achieves this through a carefully designed framework that supports keyboard-based exploration of the generated worlds. The framework comprises three core components: (1) a long-video generation framework integrating unified context compression with linear attention; (2) a real-time streaming acceleration strategy powered by bidirectional attention distillation and an enhanced text embedding scheme; (3) a text-controlled method for generating world events. We have provided the codebase in the supplementary material.
Xiaofeng Mao, Yuefeng Chen, Ranjie Duan, Yao Zhu, Gege Qi, Shaokai Ye, Xiaodan Li, Rong Zhang, Hui Xue
Adversarial Training (AT), which is commonly accepted as one of the most effective approaches defending against adversarial examples, can largely harm the standard performance, thus has limited usefulness on industrial-scale production and applications. Surprisingly, this phenomenon is totally opposite in Natural Language Processing (NLP) task, where AT can even benefit for generalization. We notice the merit of AT in NLP tasks could derive from the discrete and symbolic input space. For borrowing the advantage from NLP-style AT, we propose Discrete Adversarial Training (DAT). DAT leverages VQGAN to reform the image data to discrete text-like inputs, i.e. visual words. Then it minimizes the maximal risk on such discrete images with symbolic adversarial perturbations. We further give an explanation from the perspective of distribution to demonstrate the effectiveness of DAT. As a plug-and-play technique for enhancing the visual representation, DAT achieves significant improvement on multiple tasks including image classification, object detection and self-supervised learning. Especially, the model pre-trained with Masked Auto-Encoding (MAE) and fine-tuned by our DAT without extra data can get 31.40 mCE on ImageNet-C and 32.77% top-1 accuracy on Stylized-ImageNet, building the new state-of-the-art. The code will be available at https://github.com/alibaba/easyrobust.
Xiaofeng Mao, Yucheng Xu, Ruoshi Wen, Mohammadreza Kasaei, Wanming Yu, Efi Psomopoulou, Nathan F. Lepora, Zhibin Li
Imitation learning for robot dexterous manipulation, especially with a real robot setup, typically requires a large number of demonstrations. In this paper, we present a data-efficient learning from demonstration framework which exploits the use of rich tactile sensing data and achieves fine bimanual pinch grasping. Specifically, we employ a convolutional autoencoder network that can effectively extract and encode high-dimensional tactile information. Further, We develop a framework that achieves efficient multi-sensor fusion for imitation learning, allowing the robot to learn contact-aware sensorimotor skills from demonstrations. Our comparision study against the framework without using encoded tactile features highlighted the effectiveness of incorporating rich contact information, which enabled dexterous bimanual grasping with active contact searching. Extensive experiments demonstrated the robustness of the fine pinch grasp policy directly learned from few-shot demonstration, including grasping of the same object with different initial poses, generalizing to ten unseen new objects, robust and firm grasping against external pushes, as well as contact-aware and reactive re-grasping in case of dropping objects under very large perturbations. Furthermore, the saliency map analysis method is used to describe weight distribution across various modalities during pinch grasping, confirming the effectiveness of our framework at leveraging multimodal information.
Xiaodan Li, Yining Lang, Yuefeng Chen, Xiaofeng Mao, Yuan He, Shuhui Wang, Hui Xue, Quan Lu
With the rapid development of facial manipulation techniques, face forgery has received considerable attention in multimedia and computer vision community due to security concerns. Existing methods are mostly designed for single-frame detection trained with precise image-level labels or for video-level prediction by only modeling the inter-frame inconsistency, leaving potential high risks for DeepFake attackers. In this paper, we introduce a new problem of partial face attack in DeepFake video, where only video-level labels are provided but not all the faces in the fake videos are manipulated. We address this problem by multiple instance learning framework, treating faces and input video as instances and bag respectively. A sharp MIL (S-MIL) is proposed which builds direct mapping from instance embeddings to bag prediction, rather than from instance embeddings to instance prediction and then to bag prediction in traditional MIL. Theoretical analysis proves that the gradient vanishing in traditional MIL is relieved in S-MIL. To generate instances that can accurately incorporate the partially manipulated faces, spatial-temporal encoded instance is designed to fully model the intra-frame and inter-frame inconsistency, which further helps to promote the detection performance. We also construct a new dataset FFPMS for partially attacked DeepFake video detection, which can benefit the evaluation of different methods at both frame and video levels. Experiments on FFPMS and the widely used DFDC dataset verify that S-MIL is superior to other counterparts for partially attacked DeepFake video detection. In addition, S-MIL can also be adapted to traditional DeepFake image detection tasks and achieve state-of-the-art performance on single-frame datasets.
Yinpeng Dong, Qi-An Fu, Xiao Yang, Wenzhao Xiang, Tianyu Pang, Hang Su, Jun Zhu, Jiayu Tang, Yuefeng Chen, XiaoFeng Mao, Yuan He, Hui Xue, Chao Li, Ye Liu, Qilong Zhang, Lianli Gao, Yunrui Yu, Xitong Gao, Zhe Zhao, Daquan Lin, Jiadong Lin, Chuanbiao Song, Zihao Wang, Zhennan Wu, Yang Guo, Jiequan Cui, Xiaogang Xu, Pengguang Chen
Due to the vulnerability of deep neural networks (DNNs) to adversarial examples, a large number of defense techniques have been proposed to alleviate this problem in recent years. However, the progress of building more robust models is usually hampered by the incomplete or incorrect robustness evaluation. To accelerate the research on reliable evaluation of adversarial robustness of the current defense models in image classification, the TSAIL group at Tsinghua University and the Alibaba Security group organized this competition along with a CVPR 2021 workshop on adversarial machine learning (https://aisecure-workshop.github.io/amlcvpr2021/). The purpose of this competition is to motivate novel attack algorithms to evaluate adversarial robustness more effectively and reliably. The participants were encouraged to develop stronger white-box attack algorithms to find the worst-case robustness of different defenses. This competition was conducted on an adversarial robustness evaluation platform -- ARES (https://github.com/thu-ml/ares), and is held on the TianChi platform (https://tianchi.aliyun.com/competition/entrance/531847/introduction) as one of the series of AI Security Challengers Program. After the competition, we summarized the results and established a new adversarial robustness benchmark at https://ml.cs.tsinghua.edu.cn/ares-bench/, which allows users to upload adversarial attack algorithms and defense models for evaluation.
Junyu Lin, Xiaofeng Mao, Yuefeng Chen, Lei Xu, Yuan He, Hui Xue
DETR is the first fully end-to-end detector that predicts a final set of predictions without post-processing. However, it suffers from problems such as low performance and slow convergence. A series of works aim to tackle these issues in different ways, but the computational cost is yet expensive due to the sophisticated encoder-decoder architecture. To alleviate this issue, we propose a decoder-only detector called D^2ETR. In the absence of encoder, the decoder directly attends to the fine-fused feature maps generated by the Transformer backbone with a novel computationally efficient cross-scale attention module. D^2ETR demonstrates low computational complexity and high detection accuracy in evaluations on the COCO benchmark, outperforming DETR and its variants.
Xiaofeng Mao, Yuefeng Chen, Yuhong Li, Yuan He, Hui Xue
Deep Neural Networks (DNNs) are known to be vulnerable to the maliciously generated adversarial examples. To detect these adversarial examples, previous methods use artificially designed metrics to characterize the properties of \textit{adversarial subspaces} where adversarial examples lie. However, we find these methods are not working in practical attack detection scenarios. Because the artificially defined features are lack of robustness and show limitation in discriminative power to detect strong attacks. To solve this problem, we propose a novel adversarial detection method which identifies adversaries by adaptively learning reasonable metrics to characterize adversarial subspaces. As auxiliary context information, \textit{k} nearest neighbors are used to represent the surrounded subspace of the detected sample. We propose an innovative model called Neighbor Context Encoder (NCE) to learn from \textit{k} neighbors context and infer if the detected sample is normal or adversarial. We conduct thorough experiment on CIFAR-10, CIFAR-100 and ImageNet dataset. The results demonstrate that our approach surpasses all existing methods under three settings: \textit{attack-aware black-box detection}, \textit{attack-unaware black-box detection} and \textit{white-box detection}.
Xiaofeng Mao, Yuefeng Chen, Shuhui Wang, Hang Su, Yuan He, Hui Xue
Adversarial attack is a technique for deceiving Machine Learning (ML) models, which provides a way to evaluate the adversarial robustness. In practice, attack algorithms are artificially selected and tuned by human experts to break a ML system. However, manual selection of attackers tends to be sub-optimal, leading to a mistakenly assessment of model security. In this paper, a new procedure called Composite Adversarial Attack (CAA) is proposed for automatically searching the best combination of attack algorithms and their hyper-parameters from a candidate pool of \textbf{32 base attackers}. We design a search space where attack policy is represented as an attacking sequence, i.e., the output of the previous attacker is used as the initialization input for successors. Multi-objective NSGA-II genetic algorithm is adopted for finding the strongest attack policy with minimum complexity. The experimental result shows CAA beats 10 top attackers on 11 diverse defenses with less elapsed time (\textbf{6 $\times$ faster than AutoAttack}), and achieves the new state-of-the-art on $l_{\infty}$, $l_{2}$ and unrestricted adversarial attacks.
Hao Chen, Jiafu Wu, Ying Jin, Jinlong Peng, Xiaofeng Mao, Mingmin Chi, Mufeng Yao, Bo Peng, Jian Li, Yun Cao
Recently, methods like Zero-1-2-3 have focused on single-view based 3D reconstruction and have achieved remarkable success. However, their predictions for unseen areas heavily rely on the inductive bias of large-scale pretrained diffusion models. Although subsequent work, such as DreamComposer, attempts to make predictions more controllable by incorporating additional views, the results remain unrealistic due to feature entanglement in the vanilla latent space, including factors such as lighting, material, and structure. To address these issues, we introduce the Visual Isotropy 3D Reconstruction Model (VI3DRM), a diffusion-based sparse views 3D reconstruction model that operates within an ID consistent and perspective-disentangled 3D latent space. By facilitating the disentanglement of semantic information, color, material properties and lighting, VI3DRM is capable of generating highly realistic images that are indistinguishable from real photographs. By leveraging both real and synthesized images, our approach enables the accurate construction of pointmaps, ultimately producing finely textured meshes or point clouds. On the NVS task, tested on the GSO dataset, VI3DRM significantly outperforms state-of-the-art method DreamComposer, achieving a PSNR of 38.61, an SSIM of 0.929, and an LPIPS of 0.027. Code will be made available upon publication.
Sun Zhaole, Xiao Gao, Xiaofeng Mao, Jihong Zhu, Aude Billard, Robert B. Fisher
Existing research that addressed cable manipulation relied on two-fingered grippers, which make it difficult to perform similar cable manipulation tasks that humans perform. However, unlike dexterous manipulation of rigid objects, the development of dexterous cable manipulation skills in robotics remains underexplored due to the unique challenges posed by a cable's deformability and inherent uncertainty. In addition, using a dexterous hand introduces specific difficulties in tasks, such as cable grasping, pulling, and in-hand bending, for which no dedicated task definitions, benchmarks, or evaluation metrics exist. Furthermore, we observed that most existing dexterous hands are designed with structures identical to humans', typically featuring only one thumb, which often limits their effectiveness during dexterous cable manipulation. Lastly, existing non-task-specific methods did not have enough generalization ability to solve these cable manipulation tasks or are unsuitable due to the designed hardware. We have three contributions in real-world dexterous cable manipulation in the following steps: (1) We first defined and organized a set of dexterous cable manipulation tasks into a comprehensive taxonomy, covering most short-horizon action primitives and long-horizon tasks for one-handed cable manipulation. This taxonomy revealed that coordination between the thumb and the index finger is critical for cable manipulation, which decomposes long-horizon tasks into simpler primitives. (2) We designed a novel five-fingered hand with 25 degrees of freedom (DoF), featuring two symmetric thumb-index configurations and a rotatable joint on each fingertip, which enables dexterous cable manipulation. (3) We developed a demonstration collection pipeline for this non-anthropomorphic hand, which is difficult to operate by previous motion capture methods.
Xiaohan Yuan, Jinfeng Li, Dongxia Wang, Yuefeng Chen, Xiaofeng Mao, Longtao Huang, Jialuo Chen, Hui Xue, Xiaoxia Liu, Wenhai Wang, Kui Ren, Jingyi Wang
Generative large language models (LLMs) have revolutionized natural language processing with their transformative and emergent capabilities. However, recent evidence indicates that LLMs can produce harmful content that violates social norms, raising significant concerns regarding the safety and ethical ramifications of deploying these advanced models. Thus, it is both critical and imperative to perform a rigorous and comprehensive safety evaluation of LLMs before deployment. Despite this need, owing to the extensiveness of LLM generation space, it still lacks a unified and standardized risk taxonomy to systematically reflect the LLM content safety, as well as automated safety assessment techniques to explore the potential risk efficiently. To bridge the striking gap, we propose S-Eval, a novel LLM-based automated Safety Evaluation framework with a newly defined comprehensive risk taxonomy. S-Eval incorporates two key components, i.e., an expert testing LLM ${M}_t$ and a novel safety critique LLM ${M}_c$. ${M}_t$ is responsible for automatically generating test cases in accordance with the proposed risk taxonomy. ${M}_c$ can provide quantitative and explainable safety evaluations for better risk awareness of LLMs. In contrast to prior works, S-Eval is efficient and effective in test generation and safety evaluation. Moreover, S-Eval can be flexibly configured and adapted to the rapid evolution of LLMs and accompanying new safety threats, test generation methods and safety critique methods thanks to the LLM-based architecture. S-Eval has been deployed in our industrial partner for the automated safety evaluation of multiple LLMs serving millions of users, demonstrating its effectiveness in real-world scenarios. Our benchmark is publicly available at https://github.com/IS2Lab/S-Eval.
Tao Yang, Chuang Liu, Xiaofeng Ma, Weijia Lu, Ning Wu, Bingyang Li, Zhifei Yang, Peng Liu, Lin Sun, Xiaodong Zhang, Can Zhang
Complex continuous or mixed joint distributions (e.g., P(Y | z_1, z_2, ..., z_N)) generally lack closed-form solutions, often necessitating approximations such as MCMC. This paper proposes Indeterminate Probability Theory (IPT), which makes the following contributions: (1) An observer-centered framework in which experimental outcomes are represented as distributions combining ground truth with observation error; (2) The introduction of three independence candidate axioms that enable a two-phase probabilistic inference framework; (3) The derivation of closed-form solutions for arbitrary complex joint distributions under this framework. Both the Indeterminate Probability Neural Network (IPNN) model and the non-neural multivariate time series forecasting application demonstrate IPT's effectiveness in modeling high-dimensional distributions, with successful validation up to 1000 dimensions. Importantly, IPT is consistent with classical probability theory and subsumes the frequentist equation in the limit of vanishing observation error.