The softmax activation function plays a crucial role in the success of large language models (LLMs), particularly in the self-attention mechanism of the widely adopted Transformer architecture. However, the underlying learning dynamics that contribute to the effectiveness of softmax remain largely unexplored. As a step towards better understanding, this paper provides a theoretical study of the optimization and generalization properties of two-layer softmax neural networks, providing theoretical insights into their superior performance as other activation functions, such as ReLU and exponential. Leveraging the Neural Tangent Kernel (NTK) framework, our analysis reveals that the normalization effect of the softmax function leads to a good perturbation property of the induced NTK matrix, resulting in a good convex region of the loss landscape. Consequently, softmax neural networks can learn the target function in the over-parametrization regime. To demonstrate the broad applicability of our theoretical findings, we apply them to the task of learning score estimation functions in diffusion models, a promising approach for generative modeling. Our analysis shows that gradient-based algorithms can learn the score function with a provable accuracy. Our work provides a deeper understanding of the effectiveness of softmax neural networks and their potential in various domains, paving the way for further advancements in natural language processing and beyond.

In the pursuit of advancing holographic display technology, we face a unique yet persistent roadblock: the inflexibility of learned holography in adapting to various hardware configurations. This is due to the variances in the complex optical components and system settings in existing holographic displays. Although the emerging learned approaches have enabled rapid and high-quality hologram generation, any alteration in display hardware still requires a retraining of the model. Our work introduces a configurable learned model that interactively computes 3D holograms from RGB-only 2D images for a variety of holographic displays. The model can be conditioned to predefined hardware parameters of existing holographic displays such as working wavelengths, pixel pitch, propagation distance, and peak brightness without having to retrain. In addition, our model accommodates various hologram types, including conventional single-color and emerging multi-color holograms that simultaneously use multiple color primaries in holographic displays. Notably, we enabled our hologram computations to rely on identifying the correlation between depth estimation and 3D hologram synthesis tasks within the learning domain for the first time in the literature. We employ knowledge distillation via a student-teacher learning strategy to streamline our model for interactive performance. Achieving up to a 2x speed improvement compared to state-of-the-art models while consistently generating high-quality 3D holograms with different hardware configurations.

Cross-encoder (CE) models which compute similarity by jointly encoding a query-item pair perform better than embedding-based models (dual-encoders) at estimating query-item relevance. Existing approaches perform k-NN search with CE by approximating the CE similarity with a vector embedding space fit either with dual-encoders (DE) or CUR matrix factorization. DE-based retrieve-and-rerank approaches suffer from poor recall on new domains and the retrieval with DE is decoupled from the CE. While CUR-based approaches can be more accurate than the DE-based approach, they require a prohibitively large number of CE calls to compute item embeddings, thus making it impractical for deployment at scale. In this paper, we address these shortcomings with our proposed sparse-matrix factorization based method that efficiently computes latent query and item embeddings to approximate CE scores and performs k-NN search with the approximate CE similarity. We compute item embeddings offline by factorizing a sparse matrix containing query-item CE scores for a set of train queries. Our method produces a high-quality approximation while requiring only a fraction of CE calls as compared to CUR-based methods, and allows for leveraging DE to initialize the embedding space while avoiding compute- and resource-intensive finetuning of DE via distillation. At test time, the item embeddings remain fixed and retrieval occurs over rounds, alternating between a) estimating the test query embedding by minimizing error in approximating CE scores of items retrieved thus far, and b) using the updated test query embedding for retrieving more items. Our k-NN search method improves recall by up to 5% (k=1) and 54% (k=100) over DE-based approaches. Additionally, our indexing approach achieves a speedup of up to 100x over CUR-based and 5x over DE distillation methods, while matching or improving k-NN search recall over baselines.

Existing neural field-based SLAM methods typically employ a single monolithic field as their scene representation. This prevents efficient incorporation of loop closure constraints and limits scalability. To address these shortcomings, we propose a neural mapping framework which anchors lightweight neural fields to the pose graph of a sparse visual SLAM system. Our approach shows the ability to integrate large-scale loop closures, while limiting necessary reintegration. Furthermore, we verify the scalability of our approach by demonstrating successful building-scale mapping taking multiple loop closures into account during the optimization, and show that our method outperforms existing state-of-the-art approaches on large scenes in terms of quality and runtime.

Deep neural classifiers tend to rely on spurious correlations between spurious attributes of inputs and targets to make predictions, which could jeopardize their generalization capability. Training classifiers robust to spurious correlations typically relies on annotations of spurious correlations in data, which are often expensive to get. In this paper, we tackle an annotation-free setting and propose a self-guided spurious correlation mitigation framework. Our framework automatically constructs fine-grained training labels tailored for a classifier obtained with empirical risk minimization to improve its robustness against spurious correlations. The fine-grained training labels are formulated with different prediction behaviors of the classifier identified in a novel spuriousness embedding space. We construct the space with automatically detected conceptual attributes and a novel spuriousness metric which measures how likely a class-attribute correlation is exploited for predictions. We demonstrate that training the classifier to distinguish different prediction behaviors reduces its reliance on spurious correlations without knowing them a priori and outperforms prior methods on five real-world datasets.

Sharpness-Aware Minimization (SAM) is most known for achieving state-of the-art performances on natural image and language tasks. However, its most pronounced improvements (of tens of percent) is rather in the presence of label noise. Understanding SAM's label noise robustness requires a departure from characterizing the robustness of minimas lying in "flatter" regions of the loss landscape. In particular, the peak performance under label noise occurs with early stopping, far before the loss converges. We decompose SAM's robustness into two effects: one induced by changes to the logit term and the other induced by changes to the network Jacobian. The first can be observed in linear logistic regression where SAM provably up-weights the gradient contribution from clean examples. Although this explicit up-weighting is also observable in neural networks, when we intervene and modify SAM to remove this effect, surprisingly, we see no visible degradation in performance. We infer that SAM's effect in deeper networks is instead explained entirely by the effect SAM has on the network Jacobian. We theoretically derive the implicit regularization induced by this Jacobian effect in two layer linear networks. Motivated by our analysis, we see that cheaper alternatives to SAM that explicitly induce these regularization effects largely recover the benefits in deep networks trained on real-world datasets.

Large language models have demonstrated strong performance in recent years, but the high cost of training drives the need for efficient methods to compress dataset sizes. We propose TED pruning, a method that addresses the challenge of overfitting under high pruning ratios by quantifying the model's ability to improve performance on pruned data while fitting retained data, known as Internal Generalization (IG). TED uses an optimization objective based on Internal Generalization Distance (IGD), measuring changes in IG before and after pruning to align with true generalization performance and achieve implicit regularization. The IGD optimization objective was verified to allow the model to achieve the smallest upper bound on generalization error. The impact of small mask fluctuations on IG is studied through masks and Taylor approximation, and fast estimation of IGD is enabled. In analyzing continuous training dynamics, the prior effect of IGD is validated, and a progressive pruning strategy is proposed. Experiments on image classification, natural language understanding, and large language model fine-tuning show TED achieves lossless performance with 60-70\% of the data. Upon acceptance, our code will be made publicly available.

This paper introduces a representative-based approach for distributed learning that transforms multiple raw data points into a virtual representation. Unlike traditional distributed learning methods such as Federated Learning, which do not offer human interpretability, our method makes complex machine learning processes accessible and comprehensible. It achieves this by condensing extensive datasets into digestible formats, thus fostering intuitive human-machine interactions. Additionally, this approach maintains privacy and communication efficiency, and it matches the training performance of models using raw data. Simulation results show that our approach is competitive with or outperforms traditional Federated Learning in accuracy and convergence, especially in scenarios with complex models and a higher number of clients. This framework marks a step forward in integrating human intuition with machine intelligence, which potentially enhances human-machine learning interfaces and collaborative efforts.

The current clinical gold standard for evaluating adolescent idiopathic scoliosis (AIS) is X-ray radiography, using Cobb angle measurement. However, the frequent monitoring of the AIS progression using X-rays poses a challenge due to the cumulative radiation exposure. Although 3D ultrasound has been validated as a reliable and radiation-free alternative for scoliosis assessment, the process of measuring spinal curvature is still carried out manually. Consequently, there is a considerable demand for a fully automatic system that can locate bony landmarks and perform angle measurements. To this end, we introduce an estimation model for automatic ultrasound curve angle (UCA) measurement. The model employs a dual-branch network to detect candidate landmarks and perform vertebra segmentation on ultrasound coronal images. An affinity clustering strategy is utilized within the vertebral segmentation area to illustrate the affinity relationship between candidate landmarks. Subsequently, we can efficiently perform line delineation from a clustered affinity map for UCA measurement. As our method is specifically designed for UCA calculation, this method outperforms other state-of-the-art methods for landmark and line detection tasks. The high correlation between the automatic UCA and Cobb angle (R$^2$=0.858) suggests that our proposed method can potentially replace manual UCA measurement in ultrasound scoliosis assessment.

Uncertainty has long been a critical area of study in robotics, particularly when robots are equipped with analytical models. As we move towards the widespread use of deep neural networks in robots, which have demonstrated remarkable performance in research settings, understanding the nuances of uncertainty becomes crucial for their real-world deployment. This guide offers an overview of the importance of uncertainty and provides methods to quantify and evaluate it from an applications perspective.