Stable Principal Component Pursuit

In this paper, we study the problem of recovering a low-rank matrix (the principal components) from a high-dimensional data matrix despite both small entry-wise noise and gross sparse errors. Recently, it has been shown that a convex program, named Principal Component Pursuit (PCP), can recover the low-rank matrix when the data matrix is corrupted by gross sparse errors. We further prove that the solution to a related convex program (a relaxed PCP) gives an estimate of the low-rank matrix that is simultaneously stable to small entrywise noise and robust to gross sparse errors. More precisely, our result shows that the proposed convex program recovers the low-rank matrix even though a positive fraction of its entries are arbitrarily corrupted, with an error bound proportional to the noise level. We present simulation results to support our result and demonstrate that the new convex program accurately recovers the principal components (the low-rank matrix) under quite broad conditions. To our knowledge, this is the first result that shows the classical Principal Component Analysis (PCA), optimal for small i.i.d. noise, can be made robust to gross sparse errors; or the first that shows the newly proposed PCP can be made stable to small entry-wise perturbations.Comment: 5-page paper submitted to ISIT 201

Testing leptogenesis at the LHC and future muon colliders: a Z′Z' scenario

If the masses of at least two generations of right-handed neutrinos (RHNs) are near-degenerate, the scale of leptogenesis can be as low as $\sim$ 100 GeV. In this work, we study probing such resonant leptogenesis in the $B-L$ model at the LHC and future multi-TeV muon colliders via the process $Z'\to NN\to\ell^\pm\ell^\pm+{\rm jets}$, with $Z'$ the $U(1)_{B-L}$ gauge boson and $N$ the RHN. The same-sign dilepton feature of the signal makes it almost background-free, while the event number difference between positive and negative leptons is a hint for $CP$ violation, which is a key ingredient of leptogenesis. We found that resonant leptogenesis can be tested at the HL-LHC for $M_{Z'}$ up to 12 TeV, while at a 10 (30) TeV muon collider the reach can be up to $M_{Z'}\sim28~(100)$ TeV via the off-shell production of $Z'$.Comment: 11 pages + references, 4 figures, 2 tables. To match the PRD versio

Continuously Discovering Novel Strategies via Reward-Switching Policy Optimization

We present Reward-Switching Policy Optimization (RSPO), a paradigm to discover diverse strategies in complex RL environments by iteratively finding novel policies that are both locally optimal and sufficiently different from existing ones. To encourage the learning policy to consistently converge towards a previously undiscovered local optimum, RSPO switches between extrinsic and intrinsic rewards via a trajectory-based novelty measurement during the optimization process. When a sampled trajectory is sufficiently distinct, RSPO performs standard policy optimization with extrinsic rewards. For trajectories with high likelihood under existing policies, RSPO utilizes an intrinsic diversity reward to promote exploration. Experiments show that RSPO is able to discover a wide spectrum of strategies in a variety of domains, ranging from single-agent particle-world tasks and MuJoCo continuous control to multi-agent stag-hunt games and StarCraftII challenges.Comment: 30 pages, 15 figures, published as a conference paper at ICLR 202

An Efficient Threshold-Driven Aggregate-Label Learning Algorithm for Multimodal Information Processing

The aggregate-label learning paradigm tackles the long-standing temporary credit assignment (TCA) problem in neuroscience and machine learning, enabling spiking neural networks to learn multimodal sensory clues with delayed feedback signals. However, the existing aggregate-label learning algorithms only work for single spiking neurons, and with low learning efficiency, which limit their real-world applicability. To address these limitations, we first propose an efficient threshold-driven plasticity algorithm for spiking neurons, namely ETDP. It enables spiking neurons to generate the desired number of spikes that match the magnitude of delayed feedback signals and to learn useful multimodal sensory clues embedded within spontaneous spiking activities. Furthermore, we extend the ETDP algorithm to support multi-layer spiking neural networks (SNNs), which significantly improves the applicability of aggregate-label learning algorithms. We also validate the multi-layer ETDP learning algorithm in a multimodal computation framework for audio-visual pattern recognition. Experimental results on both synthetic and realistic datasets show significant improvements in the learning efficiency and model capacity over the existing aggregate-label learning algorithms. It, therefore, provides many opportunities for solving real-world multimodal pattern recognition tasks with spiking neural networks

BDC-Adapter: Brownian Distance Covariance for Better Vision-Language Reasoning

Large-scale pre-trained Vision-Language Models (VLMs), such as CLIP and ALIGN, have introduced a new paradigm for learning transferable visual representations. Recently, there has been a surge of interest among researchers in developing lightweight fine-tuning techniques to adapt these models to downstream visual tasks. We recognize that current state-of-the-art fine-tuning methods, such as Tip-Adapter, simply consider the covariance between the query image feature and features of support few-shot training samples, which only captures linear relations and potentially instigates a deceptive perception of independence. To address this issue, in this work, we innovatively introduce Brownian Distance Covariance (BDC) to the field of vision-language reasoning. The BDC metric can model all possible relations, providing a robust metric for measuring feature dependence. Based on this, we present a novel method called BDC-Adapter, which integrates BDC prototype similarity reasoning and multi-modal reasoning network prediction to perform classification tasks. Our extensive experimental results show that the proposed BDC-Adapter can freely handle non-linear relations and fully characterize independence, outperforming the current state-of-the-art methods by large margins.Comment: Accepted by BMVC 202

Holistic Video Stitching for Street Panorama

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryIn this paper, we address how to automatically generate a panorama for a street view from a long video sequence. We model the panorama as a low-rank matrix and formulate the problem as one of robust recovery of the low-rank matrix from highly incomplete, corrupted, deformed measurements (the video frames). We leverage powerful high-dimensional convex optimization tools from compressive sensing of sparse signals and low-rank matrices to solve this problem. In particular, we show how the new method can effectively remove severe occlusions or corruptions (caused by trees, cars, or reflections, etc.), and obtain clean, intrinsic street panoramas that are consistent with all frames. We also show how our method can automatically and robustly establish pixel-wise accurate registration among all the video frames. We demonstrate the effectiveness of our method by conducting extensive experimental comparison with other popular video stitching methods such as AutoStitch and Adobe Photoshop.National Science Foundation / NSF IIS 11-1601