Time Regularization in Optimal Time Variable Learning

Recently, optimal time variable learning in deep neural networks (DNNs) was introduced in arXiv:2204.08528. In this manuscript we extend the concept by introducing a regularization term that directly relates to the time horizon in discrete dynamical systems. Furthermore, we propose an adaptive pruning approach for Residual Neural Networks (ResNets), which reduces network complexity without compromising expressiveness, while simultaneously decreasing training time. The results are illustrated by applying the proposed concepts to classification tasks on the well known MNIST and Fashion MNIST data sets. Our PyTorch code is available on https://github.com/frederikkoehne/time_variable_learning

Adaptive Step Sizes for Preconditioned Stochastic Gradient Descent

This paper proposes a novel approach to adaptive step sizes in stochastic gradient descent (SGD) by utilizing quantities that we have identified as numerically traceable -- the Lipschitz constant for gradients and a concept of the local variance in search directions. Our findings yield a nearly hyperparameter-free algorithm for stochastic optimization, which has provable convergence properties when applied to quadratic problems and exhibits truly problem adaptive behavior on classical image classification tasks. Our framework enables the potential inclusion of a preconditioner, thereby enabling the implementation of adaptive step sizes for stochastic second-order optimization methods

Sensitivity-Based Layer Insertion for Residual and Feedforward Neural Networks

The training of neural networks requires tedious and often manual tuning of the network architecture. We propose a systematic method to insert new layers during the training process, which eliminates the need to choose a fixed network size before training. Our technique borrows techniques from constrained optimization and is based on first-order sensitivity information of the objective with respect to the virtual parameters that additional layers, if inserted, would offer. We consider fully connected feedforward networks with selected activation functions as well as residual neural networks. In numerical experiments, the proposed sensitivity-based layer insertion technique exhibits improved training decay, compared to not inserting the layer. Furthermore, the computational effort is reduced in comparison to inserting the layer from the beginning. The code is available at \url{https://github.com/LeonieKreis/layer_insertion_sensitivity_based}

Correction to: TGFB-induced factor homeobox 1 (TGIF) expression in breast cancer

Following publication of the original article, the authors noticed an incorrect affiliation for Christine Stürken and Udo Schumacher. The correct affiliations are as follows: Christine Stürken: Institute of Anatomy and Experimental Morphology, University Medical Center Hamburg-Eppendorf, Martinistrasse 52, 20246 Hamburg, Germany. Udo Schumacher: Institute of Anatomy and Experimental Morphology, University Medical Center Hamburg-Eppendorf, Martinistrasse 52, 20246 Hamburg, Germany. The affiliations have been correctly published in this correction and the original article has been updated

TGFB-induced factor homeobox 1 (TGIF) expression in breast cancer

Background: Breast cancer (BC) is the most frequent female cancer and preferentially metastasizes to bone. The transcription factor TGFB-induced factor homeobox 1 (TGIF) is involved in bone metabolism. However, it is not yet known whether TGIF is associated with BC bone metastasis or patient outcome and thus of potential interest. Methods: TGIF expression was analyzed by immunohistochemistry in 1197 formalin-fixed, paraffin-embedded tissue samples from BC patients treated in the GAIN (German Adjuvant Intergroup Node-Positive) study with two adjuvant dose-dense schedules of chemotherapy with or without bisphosphonate ibandronate. TGIF expression was categorized into negative/low and moderate/strong staining. Endpoints were disease-free survival (DFS), overall survival (OS) and time to primary bone metastasis as first site of relapse (TTPBM). Results: We found associations of higher TGIF protein expression with smaller tumor size (p= 0.015), well differentiated phenotype (p< 0.001) and estrogen receptor (ER)-positive BC (p< 0.001). Patients with higher TGIF expression levels showed a significantly longer disease-free (DFS: HR 0.75 [95%CI 0.59–0.95], log-rank p=0.019) and overall survival (OS: HR 0.69 [95%CI 0.50–0.94], log-rank p= 0.019), but no association with TTPBM (HR 0.77 [95%CI 0.51–1.16]; p= 0.213). Univariate analysis in molecular subgroups emphasized that elevated TGIF expression was prognostic for both DFS and OS in ER-positive BC patients (DFS: HR 0.68 [95%CI 0.51–0.91]; log-rank p= 0.009, interaction p= 0.130; OS: HR 0.60 [95%CI 0.41–0.88], log-rank p= 0.008, interaction p= 0.107) and in the HER2-negative subgroup (DFS:HR 0.67 [95%CI 0.50–0.88], log-rank p= 0.004, interaction p= 0.034; OS: HR 0.57 [95%CI 0.40–0.81], log-rank p= 0.002, interaction p= 0.015). Conclusions: Our results suggest that moderate to high TGIF expression is a common feature of breast cancer cells and that this is not associated with bone metastases as first site of relapse. However, a reduced expression is linked to tumor progression, especially in HER2-negative breast cancer

BRCA1-like profile is not significantly associated with survival benefit of non-myeloablative intensified chemotherapy in the GAIN randomized controlled trial

Purpose: The BRCA1-like profile identifies tumors with a defect in homologous recombination due to inactivation of BRCA1. This profile has been shown to predict which stage III breast cancer patients benefit from myeloablative, DNA double-strand-break-inducing chemotherapy. We tested the predictive potential of the BRCA1-like profile for adjuvant non-myeloablative, intensified dose-dense chemotherapy in the GAIN trial. Methods: Lymph node positive breast cancer patients were randomized to 3 × 3 dose-dense cycles of intensified epirubicin, paclitaxel, and cyclophosphamide (ETC) or 4 cycles concurrent epirubicin and cyclophosphamide followed by 10 cycles of weekly paclitaxel combined with 4 cycles capecitabine (EC-TX). Only triple negative breast cancer patients (TNBC) for whom tissue was available were included in these planned analyses. BRCA1-like or non-BRCA1-like copy number profiles were derived from low coverage sequencing data. Results: 119 out of 163 TNBC patients (73%) had a BRCA1-like profile. After median follow-up of 83 months, disease free survival (DFS) was not significantly different between BRCA1-like and non-BRCA1-like patients [adjusted hazard ratio (adj.HR) 1.02; 95% confidence interval (CI) 0.55–1.86], neither was overall survival (OS; adj.HR 1.26; 95% CI 0.58–2.71). When split by BRCA1-like status, DFS and OS were not significantly different between treatments. However, EC-TX seemed to result in a trend to an improvement in DFS in patients with a BRCA1-like tumor, while the reverse accounted for ETC treatment in patients with a non-BRCA1-like tumor (p for interaction = 0.094). Conclusions: The BRCA1-like profile is not associated with survival benefit for a non-myeloablative, intensified regimen in this study population. Considering the limited cohort size, capecitabine might have additional benefit for TNBC patients