Daily Papers

Retrieval-Augmented Generation (RAG) has emerged as a powerful paradigm for grounding large language models in external knowledge sources, improving the precision of agents responses. However, high-dimensional language model embeddings, often in the range of hundreds to thousands of dimensions, can present scalability challenges in terms of storage and latency, especially when processing massive financial text corpora. This paper investigates the use of Principal Component Analysis (PCA) to reduce embedding dimensionality, thereby mitigating computational bottlenecks without incurring large accuracy losses. We experiment with a real-world dataset and compare different similarity and distance metrics under both full-dimensional and PCA-compressed embeddings. Our results show that reducing vectors from 3,072 to 110 dimensions provides a sizeable (up to 60times) speedup in retrieval operations and a sim 28.6times reduction in index size, with only moderate declines in correlation metrics relative to human-annotated similarity scores. These findings demonstrate that PCA-based compression offers a viable balance between retrieval fidelity and resource efficiency, essential for real-time systems such as Zanista AI's Newswitch platform. Ultimately, our study underscores the practicality of leveraging classical dimensionality reduction techniques to scale RAG architectures for knowledge-intensive applications in finance and trading, where speed, memory efficiency, and accuracy must jointly be optimized.

We present PCA-Bench, a multimodal decision-making benchmark for evaluating the integrated capabilities of Multimodal Large Language Models (MLLMs). Departing from previous benchmarks focusing on simplistic tasks and individual model capability, PCA-Bench introduces three complex scenarios: autonomous driving, domestic robotics, and open-world games. Given task instructions and diverse contexts, the model is required to seamlessly integrate multiple capabilities of Perception, Cognition, and Action in a reasoning chain to make accurate decisions. Moreover, PCA-Bench features error localization capabilities, scrutinizing model inaccuracies in areas such as perception, knowledge, or reasoning. This enhances the reliability of deploying MLLMs. To balance accuracy and efficiency in evaluation, we propose PCA-Eval, an automatic evaluation protocol, and assess 10 prevalent MLLMs. The results reveal significant performance disparities between open-source models and powerful proprietary models like GPT-4 Vision. To address this, we introduce Embodied-Instruction-Evolution (EIE), an automatic framework for synthesizing instruction tuning examples in multimodal embodied environments. EIE generates 7,510 training examples in PCA-Bench and enhances the performance of open-source MLLMs, occasionally surpassing GPT-4 Vision (+3\% in decision accuracy), thereby validating the effectiveness of EIE. Our findings suggest that robust MLLMs like GPT4-Vision show promise for decision-making in embodied agents, opening new avenues for MLLM research.

One technique to visualize the training of neural networks is to perform PCA on the parameters over the course of training and to project to the subspace spanned by the first few PCA components. In this paper we compare this technique to the PCA of a high dimensional random walk. We compute the eigenvalues and eigenvectors of the covariance of the trajectory and prove that in the long trajectory and high dimensional limit most of the variance is in the first few PCA components, and that the projection of the trajectory onto any subspace spanned by PCA components is a Lissajous curve. We generalize these results to a random walk with momentum and to an Ornstein-Uhlenbeck processes (i.e., a random walk in a quadratic potential) and show that in high dimensions the walk is not mean reverting, but will instead be trapped at a fixed distance from the minimum. We finally compare the distribution of PCA variances and the PCA projected training trajectories of a linear model trained on CIFAR-10 and ResNet-50-v2 trained on Imagenet and find that the distribution of PCA variances resembles a random walk with drift.

With the proliferation of the Internet of Things (IoT) and the rising interconnectedness of devices, network security faces significant challenges, especially from anomalous activities. While traditional machine learning-based intrusion detection systems (ML-IDS) effectively employ supervised learning methods, they possess limitations such as the requirement for labeled data and challenges with high dimensionality. Recent unsupervised ML-IDS approaches such as AutoEncoders and Generative Adversarial Networks (GAN) offer alternative solutions but pose challenges in deployment onto resource-constrained IoT devices and in interpretability. To address these concerns, this paper proposes a novel federated unsupervised anomaly detection framework, FedPCA, that leverages Principal Component Analysis (PCA) and the Alternating Directions Method Multipliers (ADMM) to learn common representations of distributed non-i.i.d. datasets. Building on the FedPCA framework, we propose two algorithms, FEDPE in Euclidean space and FEDPG on Grassmann manifolds. Our approach enables real-time threat detection and mitigation at the device level, enhancing network resilience while ensuring privacy. Moreover, the proposed algorithms are accompanied by theoretical convergence rates even under a subsampling scheme, a novel result. Experimental results on the UNSW-NB15 and TON-IoT datasets show that our proposed methods offer performance in anomaly detection comparable to nonlinear baselines, while providing significant improvements in communication and memory efficiency, underscoring their potential for securing IoT networks.

In the era of Internet of Things (IoT), network-wide anomaly detection is a crucial part of monitoring IoT networks due to the inherent security vulnerabilities of most IoT devices. Principal Components Analysis (PCA) has been proposed to separate network traffics into two disjoint subspaces corresponding to normal and malicious behaviors for anomaly detection. However, the privacy concerns and limitations of devices' computing resources compromise the practical effectiveness of PCA. We propose a federated PCA-based Grassmannian optimization framework that coordinates IoT devices to aggregate a joint profile of normal network behaviors for anomaly detection. First, we introduce a privacy-preserving federated PCA framework to simultaneously capture the profile of various IoT devices' traffic. Then, we investigate the alternating direction method of multipliers gradient-based learning on the Grassmann manifold to guarantee fast training and the absence of detecting latency using limited computational resources. Empirical results on the NSL-KDD dataset demonstrate that our method outperforms baseline approaches. Finally, we show that the Grassmann manifold algorithm is highly adapted for IoT anomaly detection, which permits drastically reducing the analysis time of the system. To the best of our knowledge, this is the first federated PCA algorithm for anomaly detection meeting the requirements of IoT networks.

The recent introduction of synthetic correlated diffusion (CDI^s) imaging has demonstrated significant potential in the realm of clinical decision support for prostate cancer (PCa). CDI^s is a new form of magnetic resonance imaging (MRI) designed to characterize tissue characteristics through the joint correlation of diffusion signal attenuation across different Brownian motion sensitivities. Despite the performance improvement, the CDI^s data for PCa has not been previously made publicly available. In our commitment to advance research efforts for PCa, we introduce Cancer-Net PCa-Data, an open-source benchmark dataset of volumetric CDI^s imaging data of PCa patients. Cancer-Net PCa-Data consists of CDI^s volumetric images from a patient cohort of 200 patient cases, along with full annotations (gland masks, tumor masks, and PCa diagnosis for each tumor). We also analyze the demographic and label region diversity of Cancer-Net PCa-Data for potential biases. Cancer-Net PCa-Data is the first-ever public dataset of CDI^s imaging data for PCa, and is a part of the global open-source initiative dedicated to advancement in machine learning and imaging research to aid clinicians in the global fight against cancer.

The goal of this paper is to revisit Kernel Principal Component Analysis (KPCA) through dualization of a difference of convex functions. This allows to naturally extend KPCA to multiple objective functions and leads to efficient gradient-based algorithms avoiding the expensive SVD of the Gram matrix. Particularly, we consider objective functions that can be written as Moreau envelopes, demonstrating how to promote robustness and sparsity within the same framework. The proposed method is evaluated on synthetic and real-world benchmarks, showing significant speedup in KPCA training time as well as highlighting the benefits in terms of robustness and sparsity.

We study principal component analysis (PCA), where given a dataset in R^d from a distribution, the task is to find a unit vector v that approximately maximizes the variance of the distribution after being projected along v. Despite being a classical task, standard estimators fail drastically if the data contains even a small fraction of outliers, motivating the problem of robust PCA. Recent work has developed computationally-efficient algorithms for robust PCA that either take super-linear time or have sub-optimal error guarantees. Our main contribution is to develop a nearly-linear time algorithm for robust PCA with near-optimal error guarantees. We also develop a single-pass streaming algorithm for robust PCA with memory usage nearly-linear in the dimension.

In this article, we develop an asymptotic method for constructing confidence regions for the set of all linear subspaces arising from PCA, from which we derive hypothesis tests on this set. Our method is based on the geometry of Riemannian manifolds with which some sets of linear subspaces are endowed.

Visual perspective taking (VPT) is the ability to perceive and reason about the perspectives of others. It is an essential feature of human intelligence, which develops over the first decade of life and requires an ability to process the 3D structure of visual scenes. A growing number of reports have indicated that deep neural networks (DNNs) become capable of analyzing 3D scenes after training on large image datasets. We investigated if this emergent ability for 3D analysis in DNNs is sufficient for VPT with the 3D perception challenge (3D-PC): a novel benchmark for 3D perception in humans and DNNs. The 3D-PC is comprised of three 3D-analysis tasks posed within natural scene images: 1. a simple test of object depth order, 2. a basic VPT task (VPT-basic), and 3. another version of VPT (VPT-Strategy) designed to limit the effectiveness of "shortcut" visual strategies. We tested human participants (N=33) and linearly probed or text-prompted over 300 DNNs on the challenge and found that nearly all of the DNNs approached or exceeded human accuracy in analyzing object depth order. Surprisingly, DNN accuracy on this task correlated with their object recognition performance. In contrast, there was an extraordinary gap between DNNs and humans on VPT-basic. Humans were nearly perfect, whereas most DNNs were near chance. Fine-tuning DNNs on VPT-basic brought them close to human performance, but they, unlike humans, dropped back to chance when tested on VPT-perturb. Our challenge demonstrates that the training routines and architectures of today's DNNs are well-suited for learning basic 3D properties of scenes and objects but are ill-suited for reasoning about these properties like humans do. We release our 3D-PC datasets and code to help bridge this gap in 3D perception between humans and machines.

The word embedding space in neural models is skewed, and correcting this can improve task performance. We point out that most approaches for modeling, correcting, and measuring the symmetry of an embedding space implicitly assume that the word frequencies are uniform; in reality, word frequencies follow a highly non-uniform distribution, known as Zipf's law. Surprisingly, simply performing PCA whitening weighted by the empirical word frequency that follows Zipf's law significantly improves task performance, surpassing established baselines. From a theoretical perspective, both our approach and existing methods can be clearly categorized: word representations are distributed according to an exponential family with either uniform or Zipfian base measures. By adopting the latter approach, we can naturally emphasize informative low-frequency words in terms of their vector norm, which becomes evident from the information-geometric perspective, and in terms of the loss functions for imbalanced classification. Additionally, our theory corroborates that popular natural language processing methods, such as skip-gram negative sampling, WhiteningBERT, and headless language models, work well just because their word embeddings encode the empirical word frequency into the underlying probabilistic model.

Diffusion Transformers (DiT) excel in video generation but encounter significant computational challenges due to the quadratic complexity of attention. Notably, attention differences between adjacent diffusion steps follow a U-shaped pattern. Current methods leverage this property by caching attention blocks, however, they still struggle with sudden error spikes and large discrepancies. To address these issues, we propose UniCP a unified caching and pruning framework for efficient video generation. UniCP optimizes both temporal and spatial dimensions through. Error Aware Dynamic Cache Window (EDCW): Dynamically adjusts cache window sizes for different blocks at various timesteps, adapting to abrupt error changes. PCA based Slicing (PCAS) and Dynamic Weight Shift (DWS): PCAS prunes redundant attention components, and DWS integrates caching and pruning by enabling dynamic switching between pruned and cached outputs. By adjusting cache windows and pruning redundant components, UniCP enhances computational efficiency and maintains video detail fidelity. Experimental results show that UniCP outperforms existing methods in both performance and efficiency.

In this work, we introduce two types of makeup prior models to extend existing 3D face prior models: PCA-based and StyleGAN2-based priors. The PCA-based prior model is a linear model that is easy to construct and is computationally efficient. However, it retains only low-frequency information. Conversely, the StyleGAN2-based model can represent high-frequency information with relatively higher computational cost than the PCA-based model. Although there is a trade-off between the two models, both are applicable to 3D facial makeup estimation and related applications. By leveraging makeup prior models and designing a makeup consistency module, we effectively address the challenges that previous methods faced in robustly estimating makeup, particularly in the context of handling self-occluded faces. In experiments, we demonstrate that our approach reduces computational costs by several orders of magnitude, achieving speeds up to 180 times faster. In addition, by improving the accuracy of the estimated makeup, we confirm that our methods are highly advantageous for various 3D facial makeup applications such as 3D makeup face reconstruction, user-friendly makeup editing, makeup transfer, and interpolation.