We study the optimization landscape of deep linear neural networks with the square loss. It is known that, under weak assumptions, there are no spurious local minima and no local maxima. However, the existence and diversity of non-strict saddle points, which can play a role in first-order algorithms' dynamics, have only been lightly studied. We go a step further with a full analysis of the optimization landscape at order 2. We characterize, among all critical points, which are global minimizers, strict saddle points, and non-strict saddle points. We enumerate all the associated critical values. The characterization is simple, involves conditions on the ranks of partial matrix products, and sheds some light on global convergence or implicit regularization that have been proved or observed when optimizing linear neural networks. In passing, we provide an explicit parameterization of the set of all global minimizers and exhibit large sets of strict and non-strict saddle points.
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This study investigates the robustness of graph embedding methods for community detection in the face of network perturbations, specifically edge deletions. Graph embedding techniques, which represent nodes as low-dimensional vectors, are widely used for various graph machine learning tasks due to their ability to capture structural properties of networks effectively. However, the impact of perturbations on the performance of these methods remains relatively understudied. The research considers state-of-the-art graph embedding methods from two families: matrix factorization (e.g., LE, LLE, HOPE, M-NMF) and random walk-based (e.g., DeepWalk, LINE, node2vec). Through experiments conducted on both synthetic and real-world networks, the study reveals varying degrees of robustness within each family of graph embedding methods. The robustness is found to be influenced by factors such as network size, initial community partition strength, and the type of perturbation. Notably, node2vec and LLE consistently demonstrate higher robustness for community detection across different scenarios, including networks with degree and community size heterogeneity. These findings highlight the importance of selecting an appropriate graph embedding method based on the specific characteristics of the network and the task at hand, particularly in scenarios where robustness to perturbations is crucial.
Computer-generated holography (CGH) is a promising technology for augmented reality displays, such as head-mounted or head-up displays. However, its high computational demand makes it impractical for implementation. Recent efforts to integrate neural networks into CGH have successfully accelerated computing speed, demonstrating the potential to overcome the trade-off between computational cost and image quality. Nevertheless, deploying neural network-based CGH algorithms on computationally limited embedded systems requires more efficient models with lower computational cost, memory footprint, and power consumption. In this study, we developed a lightweight model for complex hologram generation by introducing neural network quantization. Specifically, we built a model based on tensor holography and quantized it from 32-bit floating-point precision (FP32) to 8-bit integer precision (INT8). Our performance evaluation shows that the proposed INT8 model achieves hologram quality comparable to that of the FP32 model while reducing the model size by approximately 70% and increasing the speed fourfold. Additionally, we implemented the INT8 model on a system-on-module to demonstrate its deployability on embedded platforms and high power efficiency.
Process mining gains increasing popularity in business process analysis, also in heavy industry. It requires a specific data format called an event log, with the basic structure including a case identifier (case ID), activity (event) name, and timestamp. In the case of industrial processes, data is very often provided by a monitoring system as time series of low level sensor readings. This data cannot be directly used for process mining since there is no explicit marking of activities in the event log, and sometimes, case ID is not provided. We propose a novel rule-based algorithm for identification patterns, based on the identification of significant changes in short-term mean values of selected variable to detect case ID. We present our solution on the mining use case. We compare computed results (identified patterns) with expert labels of the same dataset. Experiments show that the developed algorithm in the most of the cases correctly detects IDs in datasets with and without outliers reaching F1 score values: 96.8% and 97% respectively. We also evaluate our algorithm on dataset from manufacturing domain reaching value 92.6% for F1 score.
Criminal networks arise from the unique attempt to balance a need of establishing frequent ties among affiliates to facilitate the coordination of illegal activities, with the necessity to sparsify the overall connectivity architecture to hide from law enforcement. This efficiency-security tradeoff is also combined with the creation of groups of redundant criminals that exhibit similar connectivity patterns, thus guaranteeing resilient network architectures. State-of-the-art models for such data are not designed to infer these unique structures. In contrast to such solutions we develop a computationally-tractable Bayesian zero-inflated Poisson stochastic block model (ZIP-SBM), which identifies groups of redundant criminals with similar connectivity patterns, and infers both overt and covert block interactions within and across such groups. This is accomplished by modeling weighted ties (corresponding to counts of interactions among pairs of criminals) via zero-inflated Poisson distributions with block-specific parameters that quantify complex patterns in the excess of zero ties in each block (security) relative to the distribution of the observed weighted ties within that block (efficiency). The performance of ZIP-SBM is illustrated in simulations and in a study of summits co-attendances in a complex Mafia organization, where we unveil efficiency-security structures adopted by the criminal organization that were hidden to previous analyses.
Snoring, an acoustic biomarker commonly observed in individuals with Obstructive Sleep Apnoea Syndrome (OSAS), holds significant potential for diagnosing and monitoring this recognized clinical disorder. Irrespective of snoring types, most snoring instances exhibit identifiable harmonic patterns manifested through distinctive energy distributions over time. In this work, we propose a novel method to differentiate monaural snoring from non-snoring sounds by analyzing the harmonic content of the input sound using harmonic/percussive sound source separation (HPSS). The resulting feature, based on the harmonic spectrogram from HPSS, is employed as input data for conventional neural network architectures, aiming to enhance snoring detection performance even under a limited data learning framework. To evaluate the performance of our proposal, we studied two different scenarios: 1) using a large dataset of snoring and interfering sounds, and 2) using a reduced training set composed of around 1% of the data material. In the former scenario, the proposed HPSS-based feature provides competitive results compared to other input features from the literature. However, the key advantage of the proposed method lies in the superior performance of the harmonic spectrogram derived from HPSS in a limited data learning context. In this particular scenario, using the proposed harmonic feature significantly enhances the performance of all the studied architectures in comparison to the classical input features documented in the existing literature. This finding clearly demonstrates that incorporating harmonic content enables more reliable learning of the essential time-frequency characteristics that are prevalent in most snoring sounds, even in scenarios where the amount of training data is limited.
We propose a hierarchical training algorithm for standard feed-forward neural networks that adaptively extends the network architecture as soon as the optimization reaches a stationary point. By solving small (low-dimensional) optimization problems, the extended network provably escapes any local minimum or stationary point. Under some assumptions on the approximability of the data with stable neural networks, we show that the algorithm achieves an optimal convergence rate s in the sense that loss is bounded by the number of parameters to the -s. As a byproduct, we obtain computable indicators which judge the optimality of the training state of a given network and derive a new notion of generalization error.
This research explores the interdisciplinary interaction between psychoanalysis and computer science, suggesting a mutually beneficial exchange. Indeed, psychoanalytic concepts can enrich technological applications involving unconscious, elusive aspects of the human factor, such as social media and other interactive digital platforms. Conversely, computer science, especially Artificial Intelligence (AI), can contribute quantitative concepts and methods to psychoanalysis, identifying patterns and emotional cues in human expression. In particular, this research aims to apply computer science methods to establish fundamental relationships between emotions and Lacanian discourses. Such relations are discovered in our approach via empirical investigation and statistical analysis, and are eventually validated in a theoretical (psychoanalytic) way. It is worth noting that, although emotions have been sporadically studied in Lacanian theory, to the best of our knowledge a systematic, detailed investigation of their role is missing. Such fine-grained understanding of the role of emotions can also make the identification of Lacanian discourses more effective and easy in practise. In particular, our methods indicate the emotions with highest differentiation power in terms of corresponding discourses; conversely, we identify for each discourse the most characteristic emotions it admits. As a matter of fact, we develop a method which we call Lacanian Discourse Discovery (LDD), that simplifies (via systematizing) the identification of Lacanian discourses in texts. Although the main contribution of this paper is inherently theoretical (psychoanalytic), it can also facilitate major practical applications in the realm of interactive digital systems. Indeed, our approach can be automated through Artificial Intelligence methods that effectively identify emotions (and corresponding discourses) in texts.
We study stochastic pairwise interaction network systems whereby a finite population of agents, identified with the nodes of a graph, update their states in response to both individual mutations and pairwise interactions with their neighbors. The considered class of systems include the main epidemic models -such as the SIS, SIR, and SIRS models-, certain social dynamics models -such as the voter and anti-voter models-, as well as evolutionary dynamics on graphs. Since these stochastic systems fall into the class of finite-state Markov chains, they always admit stationary distributions. We analyze the asymptotic behavior of these stationary distributions in the limit as the population size grows large while the interaction network maintains certain mixing properties. Our approach relies on the use of Lyapunov-type functions to obtain concentration results on these stationary distributions. Notably, our results are not limited to fully mixed population models, as they do apply to a much broader spectrum of interaction network structures, including, e.g., Erd\"oos-R\'enyi random graphs.
Supervised deep learning has emerged as an effective tool for carrying out power side-channel attacks on cryptographic implementations. While increasingly-powerful deep learning-based attacks are regularly published, comparatively-little work has gone into using deep learning to defend against these attacks. In this work we propose a technique for identifying which timesteps in a power trace are responsible for leaking a cryptographic key, through an adversarial game between a deep learning-based side-channel attacker which seeks to classify a sensitive variable from the power traces recorded during encryption, and a trainable noise generator which seeks to thwart this attack by introducing a minimal amount of noise into the power traces. We demonstrate on synthetic datasets that our method can outperform existing techniques in the presence of common countermeasures such as Boolean masking and trace desynchronization. Results on real datasets are weak because the technique is highly sensitive to hyperparameters and early-stop point, and we lack a holdout dataset with ground truth knowledge of leaking points for model selection. Nonetheless, we believe our work represents an important first step towards deep side-channel leakage localization without relying on strong assumptions about the implementation or the nature of its leakage. An open-source PyTorch implementation of our experiments is provided.
We hypothesize that due to the greedy nature of learning in multi-modal deep neural networks, these models tend to rely on just one modality while under-fitting the other modalities. Such behavior is counter-intuitive and hurts the models' generalization, as we observe empirically. To estimate the model's dependence on each modality, we compute the gain on the accuracy when the model has access to it in addition to another modality. We refer to this gain as the conditional utilization rate. In the experiments, we consistently observe an imbalance in conditional utilization rates between modalities, across multiple tasks and architectures. Since conditional utilization rate cannot be computed efficiently during training, we introduce a proxy for it based on the pace at which the model learns from each modality, which we refer to as the conditional learning speed. We propose an algorithm to balance the conditional learning speeds between modalities during training and demonstrate that it indeed addresses the issue of greedy learning. The proposed algorithm improves the model's generalization on three datasets: Colored MNIST, Princeton ModelNet40, and NVIDIA Dynamic Hand Gesture.
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