اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدGrassmannian Learning: Embedding Geometry Awareness in Shallow and Deep Learning
195
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Modern machine learning algorithms have been adopted in a range of signal-processing applications spanning computer vision, natural language processing, and artificial intelligence. Many relevant problems involve subspace-structured features, orthogonality constrained or low-rank constrained objective functions, or subspace distances. These mathematical characteristics are expressed naturally using the Grassmann manifold. Unfortunately, this fact is not yet explored in many traditional learning algorithms. In the last few years, there have been growing interests in studying Grassmann manifold to tackle new learning problems. Such attempts have been reassured by substantial performance improvements in both classic learning and learning using deep neural networks. We term the former as shallow and the latter deep Grassmannian learning. The aim of this paper is to introduce the emerging area of Grassmannian learning by surveying common mathematical problems and primary solution approaches, and overviewing various applications. We hope to inspire practitioners in different fields to adopt the powerful tool of Grassmannian learning in their research.
قيم البحث
اقرأ أيضاً
Why and how that deep learning works well on different tasks remains a mystery from a theoretical perspective. In this paper we draw a geometric picture of the deep learning system by finding its analogies with two existing geometric structures, the
geometry of quantum computations and the geometry of the diffeomorphic template matching. In this framework, we give the geometric structures of different deep learning systems including convolutional neural networks, residual networks, recursive neural networks, recurrent neural networks and the equilibrium prapagation framework. We can also analysis the relationship between the geometrical structures and their performance of different networks in an algorithmic level so that the geometric framework may guide the design of the structures and algorithms of deep learning systems.
Mining informative negative instances are of central importance to deep metric learning (DML), however this task is intrinsically limited by mini-batch training, where only a mini-batch of instances is accessible at each iteration. In this paper, we
identify a slow drift phenomena by observing that the embedding features drift exceptionally slow even as the model parameters are updating throughout the training process. This suggests that the features of instances computed at preceding iterations can be used to considerably approximate their features extracted by the current model. We propose a cross-batch memory (XBM) mechanism that memorizes the embeddings of past iterations, allowing the model to collect sufficient hard negative pairs across multiple mini-batches - even over the whole dataset. Our XBM can be directly integrated into a general pair-based DML framework, where the XBM augmented DML can boost performance considerably. In particular, without bells and whistles, a simple contrastive loss with our XBM can have large R@1 improvements of 12%-22.5% on three large-scale image retrieval datasets, surpassing the most sophisticated state-of-the-art methods, by a large margin. Our XBM is conceptually simple, easy to implement - using several lines of codes, and is memory efficient - with a negligible 0.2 GB extra GPU memory. Code is available at: https://github.com/MalongTech/research-xbm.
Gradient-based meta-learning techniques are both widely applicable and proficient at solving challenging few-shot learning and fast adaptation problems. However, they have practical difficulties when operating on high-dimensional parameter spaces in
extreme low-data regimes. We show that it is possible to bypass these limitations by learning a data-dependent latent generative representation of model parameters, and performing gradient-based meta-learning in this low-dimensional latent space. The resulting approach, latent embedding optimization (LEO), decouples the gradient-based adaptation procedure from the underlying high-dimensional space of model parameters. Our evaluation shows that LEO can achieve state-of-the-art performance on the competitive miniImageNet and tieredImageNet few-shot classification tasks. Further analysis indicates LEO is able to capture uncertainty in the data, and can perform adaptation more effectively by optimizing in latent space.
In this work, we present a comparison of a shallow and a deep learning architecture for the automated segmentation of white matter lesions in MR images of multiple sclerosis patients. In particular, we train and test both methods on early stage disea
se patients, to verify their performance in challenging conditions, more similar to a clinical setting than what is typically provided in multiple sclerosis segmentation challenges. Furthermore, we evaluate a prototype naive combination of the two methods, which refines the final segmentation. All methods were trained on 32 patients, and the evaluation was performed on a pure test set of 73 cases. Results show low lesion-wise false positives (30%) for the deep learning architecture, whereas the shallow architecture yields the best Dice coefficient (63%) and volume difference (19%). Combining both shallow and deep architectures further improves the lesion-wise metrics (69% and 26% lesion-wise true and false positive rate, respectively).
We argue that the optimization plays a crucial role in generalization of deep learning models through implicit regularization. We do this by demonstrating that generalization ability is not controlled by network size but rather by some other implicit
control. We then demonstrate how changing the empirical optimization procedure can improve generalization, even if actual optimization quality is not affected. We do so by studying the geometry of the parameter space of deep networks, and devising an optimization algorithm attuned to this geometry.
الأسئلة المقترحة
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
