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.

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 Representation (INSR) has emerged as an effective representation of spatially-dependent vector fields. This work explores solving time-dependent PDEs with INSR. Classical PDE solvers introduce both temporal and spatial discretizations. Common spatial discretizations include meshes and meshless 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. Keeping the classical temporal discretization unchanged (e.g., explicit/implicit Euler), we explore INSR as an alternative spatial discretization, where spatial information is implicitly stored in the neural network weights. The network weights then evolve over time via time integration. Our approach does not require any training data generated by existing solvers because our approach is the solver itself. We validate our approach on various PDEs with examples involving large elastic deformations, turbulent fluids, and multi-scale phenomena. While slower to compute than traditional representations, our approach exhibits higher accuracy and lower memory consumption. Whereas classical solvers can dynamically adapt their spatial representation only by resorting to complex remeshing algorithms, our INSR approach is intrinsically adaptive. By tapping into the rich literature of classic time integrators, e.g., operator-splitting schemes, our method enables challenging simulations in contact mechanics and turbulent flows where previous neural-physics approaches struggle. Videos and codes are available on the project page: http://www.cs.columbia.edu/cg/INSR-PDE/

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.

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. This material is based upon work supported by the Center for Brains, Minds and Machines (CBMM), funded by NSF STC award CCF-1231216.