Quynh Nguyen

Lin Bai, Xiaoyang Li, Liqiang Huang et al.

We present a weak to strong generalization methodology for fully automated training of a multi-head extension of the Mask-RCNN method with efficient channel attention for reliable segmentation of overlapping cell nuclei in multiplex cyclic immunofluorescent (IF) whole-slide images (WSI), and present evidence for pseudo-label correction and coverage expansion, the key phenomena underlying weak to strong generalization. This method can learn to segment de novo a new class of images from a new instrument and/or a new imaging protocol without the need for human annotations. We also present metrics for automated self-diagnosis of segmentation quality in production environments, where human visual proofreading of massive WSI images is unaffordable. Our method was benchmarked against five current widely used methods and showed a significant improvement. The code, sample WSI images, and high-resolution segmentation results are provided in open form for community adoption and adaptation.

Quynh Nguyen, Dac H. Nguyen, Son T. Huynh et al.

Many startups and companies worldwide have been using project management software and tools to monitor, track and manage their projects. For software projects, the number of tasks from the beginning to the end is quite a large number that sometimes takes a lot of time and effort to search and link the current task to a group of previous ones for further references. This paper proposes an efficient task dependency recommendation algorithm to suggest tasks dependent on a given task that the user has just created. We present an efficient feature engineering step and construct a deep neural network to this aim. We performed extensive experiments on two different large projects (MDLSITE from moodle.org and FLUME from apache.org) to find the best features in 28 combinations of features and the best performance model using two embedding methods (GloVe and FastText). We consider three types of models (GRU, CNN, LSTM) using Accuracy@K, MRR@K, and Recall@K (where K = 1, 2, 3, and 5) and baseline models using traditional methods: TF-IDF with various matching score calculating such as cosine similarity, Euclidean distance, Manhattan distance, and Chebyshev distance. After many experiments, the GloVe Embedding and CNN model reached the best result in our dataset, so we chose this model as our proposed method. In addition, adding the time filter in the post-processing step can significantly improve the recommendation system's performance. The experimental results show that our proposed method can reach 0.2335 in Accuracy@1 and MRR@1 and 0.2011 in Recall@1 of dataset FLUME. With the MDLSITE dataset, we obtained 0.1258 in Accuracy@1 and MRR@1 and 0.1141 in Recall@1. In the top 5, our model reached 0.3040 in Accuracy@5, 0.2563 MRR@5, and 0.2651 Recall@5 in FLUME. In the MDLSITE dataset, our model got 0.5270 Accuracy@5, 0.2689 MRR@5, and 0.2651 Recall@5.

Anh M. Vu, Khang P. Le, Trang T. K. Vo et al.

Weakly supervised semantic segmentation (WSSS) in histopathology seeks to reduce annotation cost by learning from image-level labels, yet it remains limited by inter-class homogeneity, intra-class heterogeneity, and the region-shrinkage effect of CAM-based supervision. We propose a simple and effective prototype-driven framework that leverages vision-language alignment to improve region discovery under weak supervision. Our method integrates CoOp-style learnable prompt tuning to generate text-based prototypes and combines them with learnable image prototypes, forming a dual-modal prototype bank that captures both semantic and appearance cues. To address oversmoothing in ViT representations, we incorporate a multi-scale pyramid module that enhances spatial precision and improves localization quality. Experiments on the BCSS-WSSS benchmark show that our approach surpasses existing state-of-the-art methods, and detailed analyses demonstrate the benefits of text description diversity, context length, and the complementary behavior of text and image prototypes. These results highlight the effectiveness of jointly leveraging textual semantics and visual prototype learning for WSSS in digital pathology.

Quynh Nguyen, Pierre Brechet, Marco Mondelli

The question of how and why the phenomenon of mode connectivity occurs in training deep neural networks has gained remarkable attention in the research community. From a theoretical perspective, two possible explanations have been proposed: (i) the loss function has connected sublevel sets, and (ii) the solutions found by stochastic gradient descent are dropout stable. While these explanations provide insights into the phenomenon, their assumptions are not always satisfied in practice. In particular, the first approach requires the network to have one layer with order of $N$ neurons ($N$ being the number of training samples), while the second one requires the loss to be almost invariant after removing half of the neurons at each layer (up to some rescaling of the remaining ones). In this work, we improve both conditions by exploiting the quality of the features at every intermediate layer together with a milder over-parameterization condition. More specifically, we show that: (i) under generic assumptions on the features of intermediate layers, it suffices that the last two hidden layers have order of $\sqrt{N}$ neurons, and (ii) if subsets of features at each layer are linearly separable, then no over-parameterization is needed to show the connectivity. Our experiments confirm that the proposed condition ensures the connectivity of solutions found by stochastic gradient descent, even in settings where the previous requirements do not hold.

Quynh Nguyen

We give a simple proof for the global convergence of gradient descent in training deep ReLU networks with the standard square loss, and show some of its improvements over the state-of-the-art. In particular, while prior works require all the hidden layers to be wide with width at least $Ω(N^8)$ ($N$ being the number of training samples), we require a single wide layer of linear, quadratic or cubic width depending on the type of initialization. Unlike many recent proofs based on the Neural Tangent Kernel (NTK), our proof need not track the evolution of the entire NTK matrix, or more generally, any quantities related to the changes of activation patterns during training. Instead, we only need to track the evolution of the output at the last hidden layer, which can be done much more easily thanks to the Lipschitz property of ReLU. Some highlights of our setting: (i) all the layers are trained with standard gradient descent, (ii) the network has standard parameterization as opposed to the NTK one, and (iii) the network has a single wide layer as opposed to having all wide hidden layers as in most of NTK-related results.

Quynh Nguyen

A fully rigorous proof of the derivation of Xavier/He's initialization for ReLU nets is given.

Quynh Nguyen

It is shown that for deep neural networks, a single wide layer of width $N+1$ ($N$ being the number of training samples) suffices to prove the connectivity of sublevel sets of the training loss function. In the two-layer setting, the same property may not hold even if one has just one neuron less (i.e. width $N$ can lead to disconnected sublevel sets).

Quynh Nguyen, Marco Mondelli, Guido Montufar

A recent line of work has analyzed the theoretical properties of deep neural networks via the Neural Tangent Kernel (NTK). In particular, the smallest eigenvalue of the NTK has been related to the memorization capacity, the global convergence of gradient descent algorithms and the generalization of deep nets. However, existing results either provide bounds in the two-layer setting or assume that the spectrum of the NTK matrices is bounded away from 0 for multi-layer networks. In this paper, we provide tight bounds on the smallest eigenvalue of NTK matrices for deep ReLU nets, both in the limiting case of infinite widths and for finite widths. In the finite-width setting, the network architectures we consider are fairly general: we require the existence of a wide layer with roughly order of $N$ neurons, $N$ being the number of data samples; and the scaling of the remaining layer widths is arbitrary (up to logarithmic factors). To obtain our results, we analyze various quantities of independent interest: we give lower bounds on the smallest singular value of hidden feature matrices, and upper bounds on the Lipschitz constant of input-output feature maps.

Quynh Nguyen, Marco Mondelli

Recent works have shown that gradient descent can find a global minimum for over-parameterized neural networks where the widths of all the hidden layers scale polynomially with $N$ ($N$ being the number of training samples). In this paper, we prove that, for deep networks, a single layer of width $N$ following the input layer suffices to ensure a similar guarantee. In particular, all the remaining layers are allowed to have constant widths, and form a pyramidal topology. We show an application of our result to the widely used LeCun's initialization and obtain an over-parameterization requirement for the single wide layer of order $N^2.$

Quynh Nguyen

This paper shows that every sublevel set of the loss function of a class of deep over-parameterized neural nets with piecewise linear activation functions is connected and unbounded. This implies that the loss has no bad local valleys and all of its global minima are connected within a unique and potentially very large global valley.

Quynh Nguyen, Mahesh Chandra Mukkamala, Matthias Hein

We identify a class of over-parameterized deep neural networks with standard activation functions and cross-entropy loss which provably have no bad local valley, in the sense that from any point in parameter space there exists a continuous path on which the cross-entropy loss is non-increasing and gets arbitrarily close to zero. This implies that these networks have no sub-optimal strict local minima.

Quynh Nguyen, Mahesh Chandra Mukkamala, Matthias Hein

In the recent literature the important role of depth in deep learning has been emphasized. In this paper we argue that sufficient width of a feedforward network is equally important by answering the simple question under which conditions the decision regions of a neural network are connected. It turns out that for a class of activation functions including leaky ReLU, neural networks having a pyramidal structure, that is no layer has more hidden units than the input dimension, produce necessarily connected decision regions. This implies that a sufficiently wide hidden layer is necessary to guarantee that the network can produce disconnected decision regions. We discuss the implications of this result for the construction of neural networks, in particular the relation to the problem of adversarial manipulation of classifiers.

Quynh Nguyen, Matthias Hein

We analyze the loss landscape and expressiveness of practical deep convolutional neural networks (CNNs) with shared weights and max pooling layers. We show that such CNNs produce linearly independent features at a "wide" layer which has more neurons than the number of training samples. This condition holds e.g. for the VGG network. Furthermore, we provide for such wide CNNs necessary and sufficient conditions for global minima with zero training error. For the case where the wide layer is followed by a fully connected layer we show that almost every critical point of the empirical loss is a global minimum with zero training error. Our analysis suggests that both depth and width are very important in deep learning. While depth brings more representational power and allows the network to learn high level features, width smoothes the optimization landscape of the loss function in the sense that a sufficiently wide network has a well-behaved loss surface with almost no bad local minima.

Quynh Nguyen, Matthias Hein

While the optimization problem behind deep neural networks is highly non-convex, it is frequently observed in practice that training deep networks seems possible without getting stuck in suboptimal points. It has been argued that this is the case as all local minima are close to being globally optimal. We show that this is (almost) true, in fact almost all local minima are globally optimal, for a fully connected network with squared loss and analytic activation function given that the number of hidden units of one layer of the network is larger than the number of training points and the network structure from this layer on is pyramidal.

Antoine Gautier, Quynh Nguyen, Matthias Hein

The optimization problem behind neural networks is highly non-convex. Training with stochastic gradient descent and variants requires careful parameter tuning and provides no guarantee to achieve the global optimum. In contrast we show under quite weak assumptions on the data that a particular class of feedforward neural networks can be trained globally optimal with a linear convergence rate with our nonlinear spectral method. Up to our knowledge this is the first practically feasible method which achieves such a guarantee. While the method can in principle be applied to deep networks, we restrict ourselves for simplicity in this paper to one and two hidden layer networks. Our experiments confirm that these models are rich enough to achieve good performance on a series of real-world datasets.

Yongqin Xian, Zeynep Akata, Gaurav Sharma et al.

We present a novel latent embedding model for learning a compatibility function between image and class embeddings, in the context of zero-shot classification. The proposed method augments the state-of-the-art bilinear compatibility model by incorporating latent variables. Instead of learning a single bilinear map, it learns a collection of maps with the selection, of which map to use, being a latent variable for the current image-class pair. We train the model with a ranking based objective function which penalizes incorrect rankings of the true class for a given image. We empirically demonstrate that our model improves the state-of-the-art for various class embeddings consistently on three challenging publicly available datasets for the zero-shot setting. Moreover, our method leads to visually highly interpretable results with clear clusters of different fine-grained object properties that correspond to different latent variable maps.

Quynh Nguyen, Francesco Tudisco, Antoine Gautier et al.

Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order optimization problem subject to the assignment constraints which turns out to be NP-hard. In recent work, we have proposed an algorithm for hypergraph matching which first lifts the third-order problem to a fourth-order problem and then solves the fourth-order problem via optimization of the corresponding multilinear form. This leads to a tensor block coordinate ascent scheme which has the guarantee of providing monotonic ascent in the original matching score function and leads to state-of-the-art performance both in terms of achieved matching score and accuracy. In this paper we show that the lifting step to a fourth-order problem can be avoided yielding a third-order scheme with the same guarantees and performance but being two times faster. Moreover, we introduce a homotopy type method which further improves the performance.

Quynh Nguyen, Antoine Gautier, Matthias Hein

The estimation of correspondences between two images resp. point sets is a core problem in computer vision. One way to formulate the problem is graph matching leading to the quadratic assignment problem which is NP-hard. Several so called second order methods have been proposed to solve this problem. In recent years hypergraph matching leading to a third order problem became popular as it allows for better integration of geometric information. For most of these third order algorithms no theoretical guarantees are known. In this paper we propose a general framework for tensor block coordinate ascent methods for hypergraph matching. We propose two algorithms which both come along with the guarantee of monotonic ascent in the matching score on the set of discrete assignment matrices. In the experiments we show that our new algorithms outperform previous work both in terms of achieving better matching scores and matching accuracy. This holds in particular for very challenging settings where one has a high number of outliers and other forms of noise.