Purest Quantum State Identification

Precise identification of quantum states under noise constraints is essential for quantum information processing. In this study, we generalize the classical best arm identification problem to quantum domains, designing methods for identifying the purest one within $K$ unknown $n$-qubit quantum states using $N$ samples. %, with direct applications in quantum computation and quantum communication. We propose two distinct algorithms: (1) an algorithm employing incoherent measurements, achieving error $\exp\left(- \Omega\left(\frac{N H_1}{\log(K) 2^n }\right) \right)$, and (2) an algorithm utilizing coherent measurements, achieving error $\exp\left(- \Omega\left(\frac{N H_2}{\log(K) }\right) \right)$, highlighting the power of quantum memory. Furthermore, we establish a lower bound by proving that all strategies with fixed two-outcome incoherent POVM must suffer error probability exceeding $ \exp\left( - O\left(\frac{NH_1}{2^n}\right)\right)$. This framework provides concrete design principles for overcoming sampling bottlenecks in quantum technologies.

Counterfactual World Modeling for Physical Dynamics Understanding

The ability to understand physical dynamics is essential to learning agents acting in the world. This paper presents Counterfactual World Modeling (CWM), a candidate pure vision foundational model for physical dynamics understanding. CWM consists of three basic concepts. First, we propose a simple and powerful temporally-factored masking policy for masked prediction of video data, which encourages the model to learn disentangled representations of scene appearance and dynamics. Second, as a result of the factoring, CWM is capable of generating counterfactual next-frame predictions by manipulating a few patch embeddings to exert meaningful control over scene dynamics. Third, the counterfactual modeling capability enables the design of counterfactual queries to extract vision structures similar to keypoints, optical flows, and segmentations, which are useful for dynamics understanding. We show that zero-shot readouts of these structures extracted by the counterfactual queries attain competitive performance to prior methods on real-world datasets. Finally, we demonstrate that CWM achieves state-of-the-art performance on the challenging Physion benchmark for evaluating physical dynamics understanding.

Unifying (Machine) Vision via Counterfactual World Modeling

Leading approaches in machine vision employ different architectures for different tasks, trained on costly task-specific labeled datasets. This complexity has held back progress in areas, such as robotics, where robust task-general perception remains a bottleneck. In contrast, "foundation models" of natural language have shown how large pre-trained neural networks can provide zero-shot solutions to a broad spectrum of apparently distinct tasks. Here we introduce Counterfactual World Modeling (CWM), a framework for constructing a visual foundation model: a unified, unsupervised network that can be prompted to perform a wide variety of visual computations. CWM has two key components, which resolve the core issues that have hindered application of the foundation model concept to vision. The first is structured masking, a generalization of masked prediction methods that encourages a prediction model to capture the low-dimensional structure in visual data. The model thereby factors the key physical components of a scene and exposes an interface to them via small sets of visual tokens. This in turn enables CWM's second main idea -- counterfactual prompting -- the observation that many apparently distinct visual representations can be computed, in a zero-shot manner, by comparing the prediction model's output on real inputs versus slightly modified ("counterfactual") inputs. We show that CWM generates high-quality readouts on real-world images and videos for a diversity of tasks, including estimation of keypoints, optical flow, occlusions, object segments, and relative depth. Taken together, our results show that CWM is a promising path to unifying the manifold strands of machine vision in a conceptually simple foundation.

Implicit Neural Spatial Representations for Time-dependent PDEs

Numerically solving partial differential equations (PDEs) often entails spatial and temporal discretizations. Traditional methods (e.g., finite difference, finite element, smoothed-particle hydrodynamics) frequently adopt explicit spatial discretizations, such as grids, meshes, and point clouds, where each degree-of-freedom corresponds to a location in space. While these explicit spatial correspondences are intuitive to model and understand, these representations are not necessarily optimal for accuracy, memory-usage, or adaptivity. In this work, we explore implicit neural representation as an alternative spatial discretization, where spatial information is implicitly stored in the neural network weights. With implicit neural spatial representation, PDE-constrained time-stepping translates into updating neural network weights, which naturally integrates with commonly adopted optimization time integrators. We validate our approach on a variety of classic PDEs with examples involving large elastic deformations, turbulent fluids, and multiscale phenomena. While slower to compute than traditional representations, our approach exhibits higher accuracy, lower memory consumption, and dynamically adaptive allocation of degrees of freedom without complex remeshing.

Unsupervised Segmentation in Real-World Images via Spelke Object Inference

Self-supervised category-agnostic segmentation of real-world images into objects is a challenging open problem in computer vision. Here, we show how to learn static grouping priors from motion self-supervision, building on the cognitive science notion of Spelke Objects: groupings of stuff that move together. We introduce Excitatory-Inhibitory Segment Extraction Network (EISEN), which learns from optical flow estimates to extract pairwise affinity graphs for static scenes. EISEN then produces segments from affinities using a novel graph propagation and competition mechanism. Correlations between independent sources of motion (e.g. robot arms) and objects they move are resolved into separate segments through a bootstrapping training process. We show that EISEN achieves a substantial improvement in the state of the art for self-supervised segmentation on challenging synthetic and real-world robotic image datasets. We also present an ablation analysis illustrating the importance of each element of the EISEN architecture.

Semi-Supervised First-Person Activity Recognition in Body-Worn Video

Body-worn cameras are now commonly used for logging daily life, sports, and law enforcement activities, creating a large volume of archived footage. This paper studies the problem of classifying frames of footage according to the activity of the camera-wearer with an emphasis on application to real-world police body-worn video. Real-world datasets pose a different set of challenges from existing egocentric vision datasets: the amount of footage of different activities is unbalanced, the data contains personally identifiable information, and in practice it is difficult to provide substantial training footage for a supervised approach. We address these challenges by extracting features based exclusively on motion information then segmenting the video footage using a semi-supervised classification algorithm. On publicly available datasets, our method achieves results comparable to, if not better than, supervised and/or deep learning methods using a fraction of the training data. It also shows promising results on real-world police body-worn video.

Biologically-plausible learning algorithms can scale to large datasets

The backpropagation (BP) algorithm is often thought to be biologically implausible in the brain. One of the main reasons is that BP requires symmetric weight matrices in the feedforward and feedback pathways. To address this "weight transport problem" (Grossberg, 1987), two more biologically plausible algorithms, proposed by Liao et al. (2016) and Lillicrap et al. (2016), relax BP's weight symmetry requirements and demonstrate comparable learning capabilities to that of BP on small datasets. However, a recent study by Bartunov et al. (2018) evaluate variants of target-propagation (TP) and feedback alignment (FA) on MINIST, CIFAR, and ImageNet datasets, and find that although many of the proposed algorithms perform well on MNIST and CIFAR, they perform significantly worse than BP on ImageNet. Here, we additionally evaluate the sign-symmetry algorithm (Liao et al., 2016), which differs from both BP and FA in that the feedback and feedforward weights share signs but not magnitudes. We examine the performance of sign-symmetry and feedback alignment on ImageNet and MS COCO datasets using different network architectures (ResNet-18 and AlexNet for ImageNet, RetinaNet for MS COCO). Surprisingly, networks trained with sign-symmetry can attain classification performance approaching that of BP-trained networks. These results complement the study by Bartunov et al. (2018), and establish a new benchmark for future biologically plausible learning algorithms on more difficult datasets and more complex architectures.