We present experimental results highlighting two key differences resulting from the choice of training algorithm for two-layer neural networks. The spectral bias of neural networks is well known, while the spectral bias dependence on the choice of training algorithm is less studied. Our experiments demonstrate that an adaptive random Fourier features algorithm (ARFF) can yield a spectral bias closer to zero compared to the stochastic gradient descent optimizer (SGD). Additionally, we train two identically structured classifiers, employing SGD and ARFF, to the same accuracy levels and empirically assess their robustness against adversarial noise attacks.
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Successfully achieving bipedal locomotion remains challenging due to real-world factors such as model uncertainty, random disturbances, and imperfect state estimation. In this work, we propose a novel metric for locomotive robustness -- the estimated size of the hybrid forward invariant set associated with the step-to-step dynamics. Here, the forward invariant set can be loosely interpreted as the region of attraction for the discrete-time dynamics. We illustrate the use of this metric towards synthesizing nominal walking gaits using a simulation-in-the-loop learning approach. Further, we leverage discrete-time barrier functions and a sampling-based approach to approximate sets that are maximally forward invariant. Lastly, we experimentally demonstrate that this approach results in successful locomotion for both flat-foot walking and multi-contact walking on the Atalante lower-body exoskeleton.
Vision-based occupancy prediction, also known as 3D Semantic Scene Completion (SSC), presents a significant challenge in computer vision. Previous methods, confined to onboard processing, struggle with simultaneous geometric and semantic estimation, continuity across varying viewpoints, and single-view occlusion. Our paper introduces OccFiner, a novel offboard framework designed to enhance the accuracy of vision-based occupancy predictions. OccFiner operates in two hybrid phases: 1) a multi-to-multi local propagation network that implicitly aligns and processes multiple local frames for correcting onboard model errors and consistently enhancing occupancy accuracy across all distances. 2) the region-centric global propagation, focuses on refining labels using explicit multi-view geometry and integrating sensor bias, especially to increase the accuracy of distant occupied voxels. Extensive experiments demonstrate that OccFiner improves both geometric and semantic accuracy across various types of coarse occupancy, setting a new state-of-the-art performance on the SemanticKITTI dataset. Notably, OccFiner elevates vision-based SSC models to a level even surpassing that of LiDAR-based onboard SSC models.
We propose the Terminating-Random Experiments (T-Rex) selector, a fast variable selection method for high-dimensional data. The T-Rex selector controls a user-defined target false discovery rate (FDR) while maximizing the number of selected variables. This is achieved by fusing the solutions of multiple early terminated random experiments. The experiments are conducted on a combination of the original predictors and multiple sets of randomly generated dummy predictors. A finite sample proof based on martingale theory for the FDR control property is provided. Numerical simulations confirm that the FDR is controlled at the target level while allowing for high power. We prove that the dummies can be sampled from any univariate probability distribution with finite expectation and variance. The computational complexity of the proposed method is linear in the number of variables. The T-Rex selector outperforms state-of-the-art methods for FDR control in numerical experiments and on a simulated genome-wide association study (GWAS), while its sequential computation time is more than two orders of magnitude lower than that of the strongest benchmark methods. The open source R package TRexSelector containing the implementation of the T-Rex selector is available on CRAN.
We investigate efficient methods for training Large Language Models (LLMs) to possess capabilities in multiple specialized domains, such as coding, math reasoning and world knowledge. Our method, named Branch-Train-MiX (BTX), starts from a seed model, which is branched to train experts in embarrassingly parallel fashion with high throughput and reduced communication cost. After individual experts are asynchronously trained, BTX brings together their feedforward parameters as experts in Mixture-of-Expert (MoE) layers and averages the remaining parameters, followed by an MoE-finetuning stage to learn token-level routing. BTX generalizes two special cases, the Branch-Train-Merge method, which does not have the MoE finetuning stage to learn routing, and sparse upcycling, which omits the stage of training experts asynchronously. Compared to alternative approaches, BTX achieves the best accuracy-efficiency tradeoff.
Medical vision language pre-training (VLP) has emerged as a frontier of research, enabling zero-shot pathological recognition by comparing the query image with the textual descriptions for each disease. Due to the complex semantics of biomedical texts, current methods struggle to align medical images with key pathological findings in unstructured reports. This leads to the misalignment with the target disease's textual representation. In this paper, we introduce a novel VLP framework designed to dissect disease descriptions into their fundamental aspects, leveraging prior knowledge about the visual manifestations of pathologies. This is achieved by consulting a large language model and medical experts. Integrating a Transformer module, our approach aligns an input image with the diverse elements of a disease, generating aspect-centric image representations. By consolidating the matches from each aspect, we improve the compatibility between an image and its associated disease. Additionally, capitalizing on the aspect-oriented representations, we present a dual-head Transformer tailored to process known and unknown diseases, optimizing the comprehensive detection efficacy. Conducting experiments on seven downstream datasets, ours outperforms recent methods by up to 8.07% and 11.23% in AUC scores for seen and novel categories, respectively. Our code is released at \href{//github.com/HieuPhan33/MAVL}{//github.com/HieuPhan33/MAVL}.
Image super-resolution (SR) methods typically model degradation to improve reconstruction accuracy in complex and unknown degradation scenarios. However, extracting degradation information from low-resolution images is challenging, which limits the model performance. To boost image SR performance, one feasible approach is to introduce additional priors. Inspired by advancements in multi-modal methods and text prompt image processing, we introduce text prompts to image SR to provide degradation priors. Specifically, we first design a text-image generation pipeline to integrate text into the SR dataset through the text degradation representation and degradation model. The text representation applies a discretization manner based on the binning method to describe the degradation abstractly. This method maintains the flexibility of the text and is user-friendly. Meanwhile, we propose the PromptSR to realize the text prompt SR. The PromptSR utilizes the pre-trained language model (e.g., T5 or CLIP) to enhance restoration. We train the model on the generated text-image dataset. Extensive experiments indicate that introducing text prompts into SR, yields excellent results on both synthetic and real-world images. Code is available at: //github.com/zhengchen1999/PromptSR.
Multi-agent influence diagrams (MAIDs) are a popular form of graphical model that, for certain classes of games, have been shown to offer key complexity and explainability advantages over traditional extensive form game (EFG) representations. In this paper, we extend previous work on MAIDs by introducing the concept of a MAID subgame, as well as subgame perfect and trembling hand perfect equilibrium refinements. We then prove several equivalence results between MAIDs and EFGs. Finally, we describe an open source implementation for reasoning about MAIDs and computing their equilibria.
The accurate and interpretable prediction of future events in time-series data often requires the capturing of representative patterns (or referred to as states) underpinning the observed data. To this end, most existing studies focus on the representation and recognition of states, but ignore the changing transitional relations among them. In this paper, we present evolutionary state graph, a dynamic graph structure designed to systematically represent the evolving relations (edges) among states (nodes) along time. We conduct analysis on the dynamic graphs constructed from the time-series data and show that changes on the graph structures (e.g., edges connecting certain state nodes) can inform the occurrences of events (i.e., time-series fluctuation). Inspired by this, we propose a novel graph neural network model, Evolutionary State Graph Network (EvoNet), to encode the evolutionary state graph for accurate and interpretable time-series event prediction. Specifically, Evolutionary State Graph Network models both the node-level (state-to-state) and graph-level (segment-to-segment) propagation, and captures the node-graph (state-to-segment) interactions over time. Experimental results based on five real-world datasets show that our approach not only achieves clear improvements compared with 11 baselines, but also provides more insights towards explaining the results of event predictions.
Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization algorithms due to their susceptibility to spurious local minima, simple iterative methods such as gradient descent have been remarkably successful in practice. The theoretical footings, however, had been largely lacking until recently. In this tutorial-style overview, we highlight the important role of statistical models in enabling efficient nonconvex optimization with performance guarantees. We review two contrasting approaches: (1) two-stage algorithms, which consist of a tailored initialization step followed by successive refinement; and (2) global landscape analysis and initialization-free algorithms. Several canonical matrix factorization problems are discussed, including but not limited to matrix sensing, phase retrieval, matrix completion, blind deconvolution, robust principal component analysis, phase synchronization, and joint alignment. Special care is taken to illustrate the key technical insights underlying their analyses. This article serves as a testament that the integrated consideration of optimization and statistics leads to fruitful research findings.
Learning with limited data is a key challenge for visual recognition. Few-shot learning methods address this challenge by learning an instance embedding function from seen classes and apply the function to instances from unseen classes with limited labels. This style of transfer learning is task-agnostic: the embedding function is not learned optimally discriminative with respect to the unseen classes, where discerning among them is the target task. In this paper, we propose a novel approach to adapt the embedding model to the target classification task, yielding embeddings that are task-specific and are discriminative. To this end, we employ a type of self-attention mechanism called Transformer to transform the embeddings from task-agnostic to task-specific by focusing on relating instances from the test instances to the training instances in both seen and unseen classes. Our approach also extends to both transductive and generalized few-shot classification, two important settings that have essential use cases. We verify the effectiveness of our model on two standard benchmark few-shot classification datasets --- MiniImageNet and CUB, where our approach demonstrates state-of-the-art empirical performance.
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