Autologous Tissue Repair and Total Face Restoration.

Importance: Total face restoration remains a challenge in modern reconstructive surgery. After 17 years of experiments and preliminary clinical studies, a new concept of face prefabrication was developed for face restoration with autologous tissue. Objective: To evaluate the long-term results of face restoration with autologous tissue and report a finalized and standardized approach of face prefabrication. Design, Setting, and Participants: In this single-center long-term retrospective study, 32 patients who underwent total face restoration between 2005 and 2022 were reviewed. These patients underwent total facial reconstruction, which included flap prefabrication, 3-dimensional printing, tissue expansion, and flap transfer with aid of indocyanine green angiography (IGA). The flap first undergoes prefabrication by transferring vascularized fascia under the skin of the selected chest. A tissue expander is then placed under the fascia to create a large, thin, reliable skin flap after expansion. Once completed, the flap is transferred to the face during the second stage of the reconstruction. Intraoperative IGA is performed to guide the design of subsequent openings for facial fissures. Data were analyzed from July to September 2023. Main Outcomes and Measures: Flap healing, reconstructive outcome, and patient recovery were assessed during follow-up. Three questionnaires, including the 36-Item Short Form Health Survey (SF-36), Aesthetic and Functional Status Score of Facial Soft-Tissue Deformities/Defects, and the EuroQoL Health-Related Quality of Life (EQ-5D-5L), were used to evaluate the quality of life and satisfaction with facial aesthetic and functional status. Results: Of 24 included patients, 14 (58%) were male, and the mean (range) age was 32.9 (8-62) years. The mean (range) follow-up was 5.6 (2-12) years. All patients reported a significant improvement in quality of life (SF-36), especially in mean (SD) social functioning (preoperative score, 53.65 [34.51]; postoperative score, 80.73 [19.10]) and emotional stability (preoperative score, 56.67 [25.55]; postoperative score, 71.17 [18.51]). A total of 22 patients (92%) went back to work. Mean (SD) facial aesthetic status (preoperative score, 4.96 [3.26]; postoperative score, 11.52 [3.49]; P < .001) and functional status (preoperative score, 11.09 [3.51]; postoperative score, 15.78 [3.26]; P < .001) also improved. In addition, there was a significant increase in overall satisfaction and self-reported health status (preoperative score, 8.13 [1.52]; postoperative score, 3.58 [2.31]). Conclusions and Relevance: In this study, 5-year follow-up results suggested that this innovative approach to total face restoration offered a safe and valid option for indicated patients, with acceptable reconstructive and cosmetic outcomes.

A Cas9-fusion proximity-based approach generates an Irak1-Mecp2 tandem duplication mouse model for the study of MeCP2 duplication syndrome.

MECP2 duplication syndrome (MDS) is a neurodevelopmental disorder caused by tandem duplication of the MECP2 locus and its surrounding genes, including IRAK1. Current MDS mouse models involve transgenic expression of MECP2 only, limiting their applicability to the study of the disease. Herein, we show that an efficient and precise CRISPR/Cas9 fusion proximity-based approach can be utilized to generate an Irak1-Mecp2 tandem duplication mouse model ("Mecp2 Dup"). The Mecp2 Dup mouse model recapitulates the genomic landscape of human MDS by harbouring a 160 kb tandem duplication encompassing Mecp2 and Irak1, representing the minimal disease-causing duplication, and the neighbouring genes Opnmw1 and Tex28. The Mecp2 Dup model exhibits neuro-behavioral abnormalities, and an abnormal immune response to infection not previously observed in other mouse models, possibly owing to Irak1 overexpression. The Mecp2 Dup model thus provides a tool to investigate MDS disease mechanisms and develop potential therapies applicable to patients.

Machine Learning Assisted Electronic/Ionic Skin Recognition of Thermal Stimuli and Mechanical Deformation for Soft Robots.

Soft robots have the advantage of adaptability and flexibility in various scenarios and tasks due to their inherent flexibility and mouldability, which makes them highly promising for real-world applications. The development of electronic skin (E-skin) perception systems is crucial for the advancement of soft robots. However, achieving both exteroceptive and proprioceptive capabilities in E-skins, particularly in terms of decoupling and classifying sensing signals, remains a challenge. This study presents an E-skin with mixed electronic and ionic conductivity that can simultaneously achieve exteroceptive and proprioceptive, based on the resistance response of conductive hydrogels. It is integrated with soft robots to enable state perception, with the sensed signals further decoded using the machine learning model of decision trees and random forest algorithms. The results demonstrate that the newly developed hydrogel sensing system can accurately predict attitude changes in soft robots when subjected to varying degrees of pressing, hot pressing, bending, twisting, and stretching. These findings that multifunctional hydrogels combine with machine learning to decode signals may serve as a basis for improving the sensing capabilities of intelligent soft robots in future advancements.

Arid1b haploinsufficiency in pyramidal neurons causes cellular and circuit changes in neocortex but is not sufficient to produce behavioral or seizure phenotypes.

Arid1b is a high confidence risk gene for autism spectrum disorder that encodes a subunit of a chromatin remodeling complex expressed in neuronal progenitors. Haploinsufficiency causes a broad range of social, behavioral, and intellectual disability phenotypes, including Coffin-Siris syndrome. Recent work using transgenic mouse models suggests pathology is due to deficits in proliferation, survival, and synaptic development of cortical neurons. However, there is conflicting evidence regarding the relative roles of excitatory projection neurons and inhibitory interneurons in generating abnormal cognitive and behavioral phenotypes. Here, we conditionally knocked out either one or both copies of Arid1b from excitatory projection neuron progenitors and systematically investigated the effects on intrinsic membrane properties, synaptic physiology, social behavior, and seizure susceptibility. We found that disrupting Arid1b expression in excitatory neurons alters their membrane properties, including hyperpolarizing action potential threshold; however, these changes depend on neuronal subtype. Using paired whole-cell recordings, we found increased synaptic connectivity rate between projection neurons. Furthermore, we found reduced strength of excitatory synapses to parvalbumin (PV)-expression inhibitory interneurons. These data suggest an increase in the ratio of excitation to inhibition. However, the strength of inhibitory synapses from PV interneurons to excitatory neurons was enhanced, which may rebalance this ratio. Indeed, Arid1b haploinsufficiency in projection neurons was insufficient to cause social deficits and seizure phenotypes observed in a preclinical germline haploinsufficient mouse model. Our data suggest that while excitatory projection neurons likely contribute to autistic phenotypes, pathology in these cells is not the primary cause.

Brd4::Nutm1 fusion gene initiates NUT carcinoma in vivo.

NUT carcinoma (NC) is an aggressive cancer with no effective treatment. About 70% of NUT carcinoma is associated with chromosome translocation events that lead to the formation of a BRD4::NUTM1 fusion gene. Because the BRD4::NUTM1 gene is unequivocally cytotoxic when ectopically expressed in cell lines, questions remain on whether the fusion gene can initiate NC. Here, we report the first genetically engineered mouse model for NUT carcinoma that recapitulates the human t(15;19) chromosome translocation in mice. We demonstrated that the mouse t(2;17) syntenic chromosome translocation, forming the Brd4::Nutm1 fusion gene, could induce aggressive carcinomas in mice. The tumors present histopathological and molecular features similar to human NC, with enrichment of undifferentiated cells. Similar to the reports of human NC incidence, Brd4::Nutm1 can induce NC from a broad range of tissues with a strong phenotypical variability. The consistent induction of poorly differentiated carcinoma demonstrated a strong reprogramming activity of BRD4::NUTM1. The new mouse model provided a critical preclinical model for NC that will lead to better understanding and therapy development for NC.

Yes Associated Transcriptional Regulator 1 (YAP1) and WW Domain Containing Transcription Regulator (WWTR1) are required for murine pregnancy initiation.

Endometrial stromal cell decidualization is required for pregnancy success. Although this process is integral to fertility, many of the intricate molecular mechanisms contributing to decidualization remain undefined. One pathway that has been implicated in endometrial stromal cell decidualization in humans in vitro is the Hippo signaling pathway. Two previously conducted studies showed that the effectors of the Hippo signaling pathway, YAP1 and WWTR1, were required for decidualization of primary stromal cells in culture. To investigate the in vivo role of YAP1 and WWTR1 in decidualization and pregnancy initiation, we generated a Progesterone Cre mediated partial double knockout (pdKO) of Yap1 and Wwtr1. Female pdKOs exhibited subfertility, a compromised decidualization response, partial interruption in embryo transport, blunted endometrial receptivity, delayed implantation and subsequent embryonic development, and a unique transcriptional profile. Bulk mRNA sequencing revealed aberrant maternal remodeling evidenced by significant alterations in extracellular matrix proteins at 7.5 days post-coitus in pdKO dams and enrichment for terms associated with fertility-compromising diseases like pre-eclampsia and endometriosis. Our results indicate a required role for YAP1 and WWTR1 for successful mammalian uterine function and pregnancy success.

Stagewise Training With Exponentially Growing Training Sets.

In the world of big data, training large-scale machine learning problems has gained considerable attention. Numerous innovative optimization strategies have been presented in recent years to accelerate the large-scale training process. However, the possibility of further accelerating the training process of various optimization algorithms remains an unresolved subject. To begin addressing this difficult problem, we exploit the researched findings that when training data are independent and identically distributed, the learning problem on a smaller dataset is not significantly different from the original one. Upon that, we propose a stagewise training technique that grows the size of the training set exponentially while solving nonsmooth subproblem. We demonstrate that our stagewise training via exponentially growing the size of the training sets (STEGSs) are compatible with a large number of proximal gradient descent and gradient hard thresholding (GHT) techniques. Interestingly, we demonstrate that STEGS can greatly reduce overall complexity while maintaining statistical accuracy or even surpassing the intrinsic error introduced by GHT approaches. In addition, we analyze the effect of the training data growth rate on the overall complexity. The practical results of applying l2,1 -and l0 -norms to a variety of large-scale real-world datasets not only corroborate our theories but also demonstrate the benefits of our STEGS framework.

Rapid discrimination of four Salmonella enterica serovars: A performance comparison between benchtop and handheld Raman spectrometers.

Foodborne illnesses, particularly those caused by Salmonella enterica with its extensive array of over 2600 serovars, present a significant public health challenge. Therefore, prompt and precise identification of S. enterica serovars is essential for clinical relevance, which facilitates the understanding of S. enterica transmission routes and the determination of outbreak sources. Classical serotyping methods via molecular subtyping and genomic markers currently suffer from various limitations, such as labour intensiveness, time consumption, etc. Therefore, there is a pressing need to develop new diagnostic techniques. Surface-enhanced Raman spectroscopy (SERS) is a non-invasive diagnostic technique that can generate Raman spectra, based on which rapid and accurate discrimination of bacterial pathogens could be achieved. To generate SERS spectra, a Raman spectrometer is needed to detect and collect signals, which are divided into two types: the expensive benchtop spectrometer and the inexpensive handheld spectrometer. In this study, we compared the performance of two Raman spectrometers to discriminate four closely associated S. enterica serovars, that is, S. enterica subsp. enterica serovar dublin, enteritidis, typhi and typhimurium. Six machine learning algorithms were applied to analyse these SERS spectra. The support vector machine (SVM) model showed the highest accuracy for both handheld (99.97%) and benchtop (99.38%) Raman spectrometers. This study demonstrated that handheld Raman spectrometers achieved similar prediction accuracy as benchtop spectrometers when combined with machine learning models, providing an effective solution for rapid, accurate and cost-effective identification of closely associated S. enterica serovars.

Early hippocampal high-amplitude rhythmic spikes predict post-traumatic epilepsy in mice.

Oscillations, a highly conserved brain function across mammalian species, are pivotal in brain physiology and pathology. Traumatic brain injury (TBI) often leads to subacute and chronic brain oscillatory alterations associated with complications like post-traumatic epilepsy (PTE) in patients and animal models. Our recent work longitudinally recorded local field potential from the contralateral hippocampus of 12 strains of recombinant inbred Collaborative Cross (CC) mice alongside classical laboratory inbred C57BL/6J mice after lateral fluid percussion injury. In this study, we profiled the acute (<12 hr post-injury) and subacute (12-48 hr post-injury) hippocampal oscillatory responses to TBI and evaluated their predictive value for PTE. We found dynamic high-amplitude rhythmic spikes with elevated power density and reduced entropy that prevailed during the acute phase in CC031 mice who later developed PTE. This characteristic early brain oscillatory alteration is absent in CC031 sham controls or other CC and reference C57BL/6J strains that did not develop PTE after TBI. Our work provides quantitative measures linking early brain oscillation to PTE at a population level in mice under controlled experimental conditions. These findings will offer insights into circuit mechanisms and potential targets for neuromodulatory intervention.

Deep learning assists detection of esophageal cancer and precursor lesions in a prospective, randomized controlled study.

Endoscopy is the primary modality for detecting asymptomatic esophageal squamous cell carcinoma (ESCC) and precancerous lesions. Improving detection rate remains challenging. We developed a system based on deep convolutional neural networks (CNNs) for detecting esophageal cancer and precancerous lesions [high-risk esophageal lesions (HrELs)] and validated its efficacy in improving HrEL detection rate in clinical practice (trial registration ChiCTR2100044126 at www.chictr.org.cn). Between April 2021 and March 2022, 3117 patients ≥50 years old were consecutively recruited from Taizhou Hospital, Zhejiang Province, and randomly assigned 1:1 to an experimental group (CNN-assisted endoscopy) or a control group (unassisted endoscopy) based on block randomization. The primary endpoint was the HrEL detection rate. In the intention-to-treat population, the HrEL detection rate [28 of 1556 (1.8%)] was significantly higher in the experimental group than in the control group [14 of 1561 (0.9%), P = 0.029], and the experimental group detection rate was twice that of the control group. Similar findings were observed between the experimental and control groups [28 of 1524 (1.9%) versus 13 of 1534 (0.9%), respectively; P = 0.021]. The system's sensitivity, specificity, and accuracy for detecting HrELs were 89.7, 98.5, and 98.2%, respectively. No adverse events occurred. The proposed system thus improved HrEL detection rate during endoscopy and was safe. Deep learning assistance may enhance early diagnosis and treatment of esophageal cancer and may become a useful tool for esophageal cancer screening.

Asynchronous Parallel Large-Scale Gaussian Process Regression.

Gaussian process regression (GPR) is an important nonparametric learning method in machine learning research with many real-world applications. It is well known that training large-scale GPR is a challenging task due to the required heavy computational cost and large volume memory. To address this challenging problem, in this article, we propose an asynchronous doubly stochastic gradient algorithm to handle the large-scale training of GPR. We formulate the GPR to a convex optimization problem, i.e., kernel ridge regression. After that, in order to efficiently solve this convex kernel problem, we first use the random feature mapping method to approximate the kernel model and then utilize two unbiased stochastic approximations, i.e., stochastic variance reduced gradient and stochastic coordinate descent, to update the solution asynchronously and in parallel. In this way, our algorithm scales well in both sample size and dimensionality, and speeds up the training computation. More importantly, we prove that our algorithm has a global linear convergence rate. Our experimental results on eight large-scale benchmark datasets with both regression and classification tasks show that the proposed algorithm outperforms the existing state-of-the-art GPR methods.

The Updated Mouse Universal Genotyping Array Bioinformatic Pipeline Improves Genetic QC in Laboratory Mice.

The MiniMUGA genotyping array is a popular tool for genetic QC of laboratory mice and genotyping of samples from most types of experimental crosses involving laboratory strains, particularly for reduced complexity crosses. The content of the production version of the MiniMUGA array is fixed; however, there is the opportunity to improve array's performance and the associated report's usefulness by leveraging thousands of samples genotyped since the initial description of MiniMUGA in 2020. Here we report our efforts to update and improve marker annotation, increase the number and the reliability of the consensus genotypes for inbred strains and increase the number of constructs that can reliably be detected with MiniMUGA. In addition, we have implemented key changes in the informatics pipeline to identify and quantify the contribution of specific genetic backgrounds to the makeup of a given sample, remove arbitrary thresholds, include the Y Chromosome and mitochondrial genome in the ideogram, and improve robust detection of the presence of commercially available substrains based on diagnostic alleles. Finally, we have made changes to the layout of the report, to simplify the interpretation and completeness of the analysis and added a table summarizing the ideogram. We believe that these changes will be of general interest to the mouse research community and will be instrumental in our goal of improving the rigor and reproducibility of mouse-based biomedical research.

When local governments' stay-at-home orders meet the white house's "opening up america again".

In the current polarized political climate, citizens frequently face conflicting directives from their local and federal government officials. For instance, on April 16th, 2020, The White House launched the "Opening up America Again" (OuAA) campaign while many U.S. counties had stay-at-home orders. We created a panel data set of U.S. counties to study the impact of U.S. counties' stay-at-home orders on community mobility before and after The White House's campaign to reopen the country. Our results suggest that before the OuAA campaign, stay-at-home orders substantially decreased the time spent in retail and recreation businesses. However, after the launch of the OuAA campaign, the time spent at retail and recreational businesses in a typical conservative county increased significantly more than in liberal counties (23% increase in a typical conservative county vs. 9% increase in a typical liberal county). We also found that in conservative counties with stay-at-home orders, time spent at retail and recreational businesses increased less than in those without stay-at-home orders. These findings illuminate that when federal and local government policies are at odds, residents decide which policies to adhere to based on the alignment between their political ideology and the government body. Our findings highlight the substantial importance of each government body in forming citizens' behaviors, offering practical implications for policy makers during natural disasters.

Obtaining Lower Query Complexities Through Lightweight Zeroth-Order Proximal Gradient Algorithms.

Zeroth-order (ZO) optimization is one key technique for machine learning problems where gradient calculation is expensive or impossible. Several variance, reduced ZO proximal algorithms have been proposed to speed up ZO optimization for nonsmooth problems, and all of them opted for the coordinated ZO estimator against the random ZO estimator when approximating the true gradient, since the former is more accurate. While the random ZO estimator introduces a larger error and makes convergence analysis more challenging compared to coordinated ZO estimator, it requires only O(1) computation, which is significantly less than O(d) computation of the coordinated ZO estimator, with d being dimension of the problem space. To take advantage of the computationally efficient nature of the random ZO estimator, we first propose a ZO objective decrease (ZOOD) property that can incorporate two different types of errors in the upper bound of convergence rate. Next, we propose two generic reduction frameworks for ZO optimization, which can automatically derive the convergence results for convex and nonconvex problems, respectively, as long as the convergence rate for the inner solver satisfies the ZOOD property. With the application of two reduction frameworks on our proposed ZOR-ProxSVRG and ZOR-ProxSAGA, two variance-reduced ZO proximal algorithms with fully random ZO estimators, we improve the state-of-the-art function query complexities from Omindn1/2ε2,dε3 to O˜n+dε2 under d>n12 for nonconvex problems, and from Odε2 to O˜nlog1ε+dε for convex problems. Finally, we conduct experiments to verify the superiority of our proposed methods.

Differential Analysis of Blood Routine Examination Parameters in Patients with Upper Gastrointestinal Bleeding and Lower Gastrointestinal Bleeding.

Background: This study addresses the critical need for differentiating between upper and lower gastrointestinal bleeding by focusing on blood routine parameters to enhance diagnostic precision. Objective: This study aims to identify and compare specific blood routine parameters to determine their efficacy in distinguishing between upper and lower gastrointestinal bleeding for improved clinical decision-making. Methods: This retrospective study analyzed 119 patients with gastrointestinal bleeding (GIB) admitted to our hospital between January 2017 and June 2020. Among them, 86 were diagnosed with upper GIB (UGIB) and 33 with lower GIB (LGIB). After admission, peripheral blood samples were collected for a comprehensive blood routine examination, including white blood cell count (WBC), red blood cell count (RBC), hemoglobin (Hb), platelet count (PLT), blood urea nitrogen (BUN), creatinine (Cr), and BUN to Cr ratio (BUN/Cr ratio). Differences in blood routine parameters were compared between the UGIB and LGIB groups. Receiver Operating Characteristic (ROC) curve analysis was conducted to assess the efficacy of blood routine examinations in differentiating between UGIB and LGIB. Results: The study revealed no significant differences in WBC and Cr levels between LGIB and UGIB patients (P > .05). However, UGIB patients exhibited statistically lower levels of RBC, Hb, and PLT, along with higher BUN and BUN/Cr ratio levels compared to LGIB patients (P < .05). Pearson correlation coefficient analysis indicated an inverse correlation of BUN/Cr with RBC, Hb, and PLT in GIB patients and a positive association between BUN/Cr and BUN (P < .05). ROC analysis demonstrated that RBC, Hb, PLT, BUN, and BUN/Cr ratios were effective in distinguishing UGIB from LGIB (P < .05). Conclusions: Blood routine parameters, including RBC, Hb, PLT, BUN, and BUN/Cr ratio, are valuable in differentiating between UGIB and LGIB. These parameters can serve as early evaluation indexes for GIB, facilitating timely intervention and treatment to enhance therapeutic outcomes.

Direct visualization and 3D reconstruction of conductive filaments in aSiO2 material-based memristive device.

Observation of conductive filaments has greatly aided the development of theoretical models of memristive devices. In this work, we visualized and reconstructed the conductive filaments in a Cu/Cu-doped SiO2/W device employing a focused ion beam (FIB) as a milling technique. The SEM images taken from the device after 150 DC sweep cycles showed that Joule heat played a vital role in determining the morphology of a conductive filament, where the vaporization of the conductive filament resulted in the creation of defects, including particles, voids, and cavities. The competition between the formation and vaporization of conductive filaments generally induces a remarkable current fluctuation. Since Cu-doped SiO2 was utilized as the electrolyte, the vapors exfoliated adjacent single layers. FIB milling proceeded in top-down and front-back modes; thus, a 3D model of conductive filaments and defects was constructed according to a series of FIB-SEM images. This methodology is promising for a future failure analysis of memristive devices.

GENERATION OF TOLEROGENIC DENDRITIC CELLS UNDER THE PERSISTENT INFLAMMATION STIMULATION.

ABSTRACT: Immunosuppression, commonly accompanied by persistent inflammation, is a key feature in the later phase of sepsis. However, the pathophysiological mechanisms underlying this phenomenon remain unclear. Dendritic cells (DCs), specifically tolerogenic DCs (tolDCs), play a crucial role in this process by regulating immune responses through inducing T cell anergy and releasing anti-inflammatory cytokines. Nevertheless, the existing cell models are inadequate for investigating tolDCs during the immunosuppressive phase of sepsis. Therefore, this study aimed to develop a novel in vitro model to generate tolDCs under chronic inflammatory conditions. We have successfully generated tolDCs by exposing them to sublethal lipopolysaccharide (LPS) for 72 h while preserving cell viability. Considering that IL-10-induced tolDCs (IL-10-tolDCs) are well-established models, we compared the immunological tolerance between LPS-tolDCs and IL-10-tolDCs. Our findings indicated that both LPS-tolDCs and IL-10-tolDCs exhibited reduced expression of maturation markers, whereas their levels of inhibitory markers were elevated. Furthermore, the immunoregulatory activities of LPS-tolDCs and IL-10-tolDCs were found to be comparable. These dysfunctions include impaired antigen presenting capacity and suppression of T cell activation, proliferation, and differentiation. Notably, compared with IL-10-tolDCs, LPS-tolDCs showed a reduced response in maturation and cytokine production upon stimulation, indicating their potential as a better model for research. Overall, in comparison with IL-10-tolDCs, our data suggest that the immunological dysfunctions shown in LPS-tolDCs could more effectively elucidate the increased susceptibility to secondary infections during sepsis. Consequently, LPS-tolDCs have emerged as promising therapeutic targets for ameliorating the immunosuppressed state in septic patients.

Global Model Selection for Semi-Supervised Support Vector Machine via Solution Paths.

Semi-supervised support vector machine (S 3 VM) is important because it can use plentiful unlabeled data to improve the generalization accuracy of traditional SVMs. In order to achieve good performance, it is necessary for S 3 VM to take some effective measures to select hyperparameters. However, model selection for semi-supervised models is still a key open problem. Existing methods for semi-supervised models to search for the optimal parameter values are usually computationally demanding, especially those ones with grid search. To address this challenging problem, in this article, we first propose solution paths of S 3 VM (SPS 3 VM), which can track the solutions of the nonconvex S 3 VM with respect to the hyperparameters. Specifically, we apply incremental and decremental learning methods to update the solution and let it satisfy the Karush-Kuhn-Tucker (KKT) conditions. Based on the SPS 3 VM and the piecewise linearity of model function, we can find the model with the minimum cross-validation (CV) error for the entire range of candidate hyperparameters by computing the error path of S 3 VM. Our SPS 3 VM is the first solution path algorithm for nonconvex optimization problem of semi-supervised learning models. We also provide the finite convergence analysis and computational complexity of SPS 3 VM. Experimental results on a variety of benchmark datasets not only verify that our SPS 3 VM can globally search the hyperparameters (regularization and ramp loss parameters) but also show a huge reduction of computational time while retaining similar or slightly better generalization performance compared with the grid search approach.

On the Number of Linear Regions of Convolutional Neural Networks With Piecewise Linear Activations.

One fundamental problem in deep learning is understanding the excellent performance of deep Neural Networks (NNs) in practice. An explanation for the superiority of NNs is that they can realize a large family of complicated functions, i.e., they have powerful expressivity. The expressivity of a Neural Network with Piecewise Linear activations (PLNN) can be quantified by the maximal number of linear regions it can separate its input space into. In this paper, we provide several mathematical results needed for studying the linear regions of Convolutional Neural Networks with Piecewise Linear activations (PLCNNs), and use them to derive the maximal and average numbers of linear regions for one-layer PLCNNs. Furthermore, we obtain upper and lower bounds for the number of linear regions of multi-layer PLCNNs. Our results suggest that deeper PLCNNs have more powerful expressivity than shallow PLCNNs, while PLCNNs have more expressivity than fully-connected PLNNs per parameter, in terms of the number of linear regions.