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Mar 12

Neural Collapse in Deep Linear Networks: From Balanced to Imbalanced Data

Modern deep neural networks have achieved impressive performance on tasks from image classification to natural language processing. Surprisingly, these complex systems with massive amounts of parameters exhibit the same structural properties in their last-layer features and classifiers across canonical datasets when training until convergence. In particular, it has been observed that the last-layer features collapse to their class-means, and those class-means are the vertices of a simplex Equiangular Tight Frame (ETF). This phenomenon is known as Neural Collapse (NC). Recent papers have theoretically shown that NC emerges in the global minimizers of training problems with the simplified "unconstrained feature model". In this context, we take a step further and prove the NC occurrences in deep linear networks for the popular mean squared error (MSE) and cross entropy (CE) losses, showing that global solutions exhibit NC properties across the linear layers. Furthermore, we extend our study to imbalanced data for MSE loss and present the first geometric analysis of NC under bias-free setting. Our results demonstrate the convergence of the last-layer features and classifiers to a geometry consisting of orthogonal vectors, whose lengths depend on the amount of data in their corresponding classes. Finally, we empirically validate our theoretical analyses on synthetic and practical network architectures with both balanced and imbalanced scenarios.

StoryMaker: Towards Holistic Consistent Characters in Text-to-image Generation

Tuning-free personalized image generation methods have achieved significant success in maintaining facial consistency, i.e., identities, even with multiple characters. However, the lack of holistic consistency in scenes with multiple characters hampers these methods' ability to create a cohesive narrative. In this paper, we introduce StoryMaker, a personalization solution that preserves not only facial consistency but also clothing, hairstyles, and body consistency, thus facilitating the creation of a story through a series of images. StoryMaker incorporates conditions based on face identities and cropped character images, which include clothing, hairstyles, and bodies. Specifically, we integrate the facial identity information with the cropped character images using the Positional-aware Perceiver Resampler (PPR) to obtain distinct character features. To prevent intermingling of multiple characters and the background, we separately constrain the cross-attention impact regions of different characters and the background using MSE loss with segmentation masks. Additionally, we train the generation network conditioned on poses to promote decoupling from poses. A LoRA is also employed to enhance fidelity and quality. Experiments underscore the effectiveness of our approach. StoryMaker supports numerous applications and is compatible with other societal plug-ins. Our source codes and model weights are available at https://github.com/RedAIGC/StoryMaker.

LoLCATs: On Low-Rank Linearizing of Large Language Models

Recent works show we can linearize large language models (LLMs) -- swapping the quadratic attentions of popular Transformer-based LLMs with subquadratic analogs, such as linear attention -- avoiding the expensive pretraining costs. However, linearizing LLMs often significantly degrades model quality, still requires training over billions of tokens, and remains limited to smaller 1.3B to 7B LLMs. We thus propose Low-rank Linear Conversion via Attention Transfer (LoLCATs), a simple two-step method that improves LLM linearizing quality with orders of magnitudes less memory and compute. We base these steps on two findings. First, we can replace an LLM's softmax attentions with closely-approximating linear attentions, simply by training the linear attentions to match their softmax counterparts with an output MSE loss ("attention transfer"). Then, this enables adjusting for approximation errors and recovering LLM quality simply with low-rank adaptation (LoRA). LoLCATs significantly improves linearizing quality, training efficiency, and scalability. We significantly reduce the linearizing quality gap and produce state-of-the-art subquadratic LLMs from Llama 3 8B and Mistral 7B v0.1, leading to 20+ points of improvement on 5-shot MMLU. Furthermore, LoLCATs does so with only 0.2% of past methods' model parameters and 0.4% of their training tokens. Finally, we apply LoLCATs to create the first linearized 70B and 405B LLMs (50x larger than prior work). When compared with prior approaches under the same compute budgets, LoLCATs significantly improves linearizing quality, closing the gap between linearized and original Llama 3.1 70B and 405B LLMs by 77.8% and 78.1% on 5-shot MMLU.

Cauchy-Schwarz Divergence Information Bottleneck for Regression

The information bottleneck (IB) approach is popular to improve the generalization, robustness and explainability of deep neural networks. Essentially, it aims to find a minimum sufficient representation t by striking a trade-off between a compression term I(x;t) and a prediction term I(y;t), where I(cdot;cdot) refers to the mutual information (MI). MI is for the IB for the most part expressed in terms of the Kullback-Leibler (KL) divergence, which in the regression case corresponds to prediction based on mean squared error (MSE) loss with Gaussian assumption and compression approximated by variational inference. In this paper, we study the IB principle for the regression problem and develop a new way to parameterize the IB with deep neural networks by exploiting favorable properties of the Cauchy-Schwarz (CS) divergence. By doing so, we move away from MSE-based regression and ease estimation by avoiding variational approximations or distributional assumptions. We investigate the improved generalization ability of our proposed CS-IB and demonstrate strong adversarial robustness guarantees. We demonstrate its superior performance on six real-world regression tasks over other popular deep IB approaches. We additionally observe that the solutions discovered by CS-IB always achieve the best trade-off between prediction accuracy and compression ratio in the information plane. The code is available at https://github.com/SJYuCNEL/Cauchy-Schwarz-Information-Bottleneck.

S3IM: Stochastic Structural SIMilarity and Its Unreasonable Effectiveness for Neural Fields

Recently, Neural Radiance Field (NeRF) has shown great success in rendering novel-view images of a given scene by learning an implicit representation with only posed RGB images. NeRF and relevant neural field methods (e.g., neural surface representation) typically optimize a point-wise loss and make point-wise predictions, where one data point corresponds to one pixel. Unfortunately, this line of research failed to use the collective supervision of distant pixels, although it is known that pixels in an image or scene can provide rich structural information. To the best of our knowledge, we are the first to design a nonlocal multiplex training paradigm for NeRF and relevant neural field methods via a novel Stochastic Structural SIMilarity (S3IM) loss that processes multiple data points as a whole set instead of process multiple inputs independently. Our extensive experiments demonstrate the unreasonable effectiveness of S3IM in improving NeRF and neural surface representation for nearly free. The improvements of quality metrics can be particularly significant for those relatively difficult tasks: e.g., the test MSE loss unexpectedly drops by more than 90% for TensoRF and DVGO over eight novel view synthesis tasks; a 198% F-score gain and a 64% Chamfer L_{1} distance reduction for NeuS over eight surface reconstruction tasks. Moreover, S3IM is consistently robust even with sparse inputs, corrupted images, and dynamic scenes.

EDiffSR: An Efficient Diffusion Probabilistic Model for Remote Sensing Image Super-Resolution

Recently, convolutional networks have achieved remarkable development in remote sensing image Super-Resoltuion (SR) by minimizing the regression objectives, e.g., MSE loss. However, despite achieving impressive performance, these methods often suffer from poor visual quality with over-smooth issues. Generative adversarial networks have the potential to infer intricate details, but they are easy to collapse, resulting in undesirable artifacts. To mitigate these issues, in this paper, we first introduce Diffusion Probabilistic Model (DPM) for efficient remote sensing image SR, dubbed EDiffSR. EDiffSR is easy to train and maintains the merits of DPM in generating perceptual-pleasant images. Specifically, different from previous works using heavy UNet for noise prediction, we develop an Efficient Activation Network (EANet) to achieve favorable noise prediction performance by simplified channel attention and simple gate operation, which dramatically reduces the computational budget. Moreover, to introduce more valuable prior knowledge into the proposed EDiffSR, a practical Conditional Prior Enhancement Module (CPEM) is developed to help extract an enriched condition. Unlike most DPM-based SR models that directly generate conditions by amplifying LR images, the proposed CPEM helps to retain more informative cues for accurate SR. Extensive experiments on four remote sensing datasets demonstrate that EDiffSR can restore visual-pleasant images on simulated and real-world remote sensing images, both quantitatively and qualitatively. The code of EDiffSR will be available at https://github.com/XY-boy/EDiffSR

Improving Efficient Neural Ranking Models with Cross-Architecture Knowledge Distillation

Retrieval and ranking models are the backbone of many applications such as web search, open domain QA, or text-based recommender systems. The latency of neural ranking models at query time is largely dependent on the architecture and deliberate choices by their designers to trade-off effectiveness for higher efficiency. This focus on low query latency of a rising number of efficient ranking architectures make them feasible for production deployment. In machine learning an increasingly common approach to close the effectiveness gap of more efficient models is to apply knowledge distillation from a large teacher model to a smaller student model. We find that different ranking architectures tend to produce output scores in different magnitudes. Based on this finding, we propose a cross-architecture training procedure with a margin focused loss (Margin-MSE), that adapts knowledge distillation to the varying score output distributions of different BERT and non-BERT passage ranking architectures. We apply the teachable information as additional fine-grained labels to existing training triples of the MSMARCO-Passage collection. We evaluate our procedure of distilling knowledge from state-of-the-art concatenated BERT models to four different efficient architectures (TK, ColBERT, PreTT, and a BERT CLS dot product model). We show that across our evaluated architectures our Margin-MSE knowledge distillation significantly improves re-ranking effectiveness without compromising their efficiency. Additionally, we show our general distillation method to improve nearest neighbor based index retrieval with the BERT dot product model, offering competitive results with specialized and much more costly training methods. To benefit the community, we publish the teacher-score training files in a ready-to-use package.

Posterior-Mean Rectified Flow: Towards Minimum MSE Photo-Realistic Image Restoration

Photo-realistic image restoration algorithms are typically evaluated by distortion measures (e.g., PSNR, SSIM) and by perceptual quality measures (e.g., FID, NIQE), where the desire is to attain the lowest possible distortion without compromising on perceptual quality. To achieve this goal, current methods typically attempt to sample from the posterior distribution, or to optimize a weighted sum of a distortion loss (e.g., MSE) and a perceptual quality loss (e.g., GAN). Unlike previous works, this paper is concerned specifically with the optimal estimator that minimizes the MSE under a constraint of perfect perceptual index, namely where the distribution of the reconstructed images is equal to that of the ground-truth ones. A recent theoretical result shows that such an estimator can be constructed by optimally transporting the posterior mean prediction (MMSE estimate) to the distribution of the ground-truth images. Inspired by this result, we introduce Posterior-Mean Rectified Flow (PMRF), a simple yet highly effective algorithm that approximates this optimal estimator. In particular, PMRF first predicts the posterior mean, and then transports the result to a high-quality image using a rectified flow model that approximates the desired optimal transport map. We investigate the theoretical utility of PMRF and demonstrate that it consistently outperforms previous methods on a variety of image restoration tasks.

iSeeBetter: Spatio-temporal video super-resolution using recurrent generative back-projection networks

Recently, learning-based models have enhanced the performance of single-image super-resolution (SISR). However, applying SISR successively to each video frame leads to a lack of temporal coherency. Convolutional neural networks (CNNs) outperform traditional approaches in terms of image quality metrics such as peak signal to noise ratio (PSNR) and structural similarity (SSIM). However, generative adversarial networks (GANs) offer a competitive advantage by being able to mitigate the issue of a lack of finer texture details, usually seen with CNNs when super-resolving at large upscaling factors. We present iSeeBetter, a novel GAN-based spatio-temporal approach to video super-resolution (VSR) that renders temporally consistent super-resolution videos. iSeeBetter extracts spatial and temporal information from the current and neighboring frames using the concept of recurrent back-projection networks as its generator. Furthermore, to improve the "naturality" of the super-resolved image while eliminating artifacts seen with traditional algorithms, we utilize the discriminator from super-resolution generative adversarial network (SRGAN). Although mean squared error (MSE) as a primary loss-minimization objective improves PSNR/SSIM, these metrics may not capture fine details in the image resulting in misrepresentation of perceptual quality. To address this, we use a four-fold (MSE, perceptual, adversarial, and total-variation (TV)) loss function. Our results demonstrate that iSeeBetter offers superior VSR fidelity and surpasses state-of-the-art performance.

SkyReconNet: A Cross-Resolution Contextual Integration Framework for Inpainting with Application to Enhanced CMB Map Reconstruction

We introduce a novel neural network, SkyReconNet, which combines the expanded receptive fields of dilated convolutional layers along with standard convolutions, to capture both the global and local features for reconstructing the missing information in an image. We implement our network to inpaint the masked regions in a full-sky Cosmic Microwave Background (CMB) map. Inpainting CMB maps is a particularly formidable challenge when dealing with extensive and irregular masks, such as galactic masks which can obscure substantial fractions of the sky. The hybrid design of SkyReconNet leverages the strengths of standard and dilated convolutions to accurately predict CMB fluctuations in the masked regions, by effectively utilizing the information from surrounding unmasked areas. During training, the network optimizes its weights by minimizing a composite loss function that combines the Structural Similarity Index Measure (SSIM) and mean squared error (MSE). SSIM preserves the essential structural features of the CMB, ensuring an accurate and coherent reconstruction of the missing CMB fluctuations, while MSE minimizes the pixel-wise deviations, enhancing the overall accuracy of the predictions. The predicted CMB maps and their corresponding angular power spectra align closely with the targets, achieving the performance limited only by the fundamental uncertainty of cosmic variance. The network's generic architecture enables application to other physics-based challenges involving data with missing or defective pixels, systematic artefacts etc. Our results demonstrate its effectiveness in addressing the challenges posed by large irregular masks, offering a significant inpainting tool not only for CMB analyses but also for image-based experiments across disciplines where such data imperfections are prevalent.