CryptoNets and subsequent work have demonstrated the capability of homomorphic encryption (HE) in the applications of private artificial intelligence (AI). In convolutional neural networks (CNNs), many computations are linear functions such as the convolution layer which can be homomorphically evaluated. However, there are layers such as the activation layer which is comprised of non-linear functions that cannot be homomorphically evaluated. One of the most commonly used methods is approximating these non-linear functions using low-degree polynomials. However, using the approximated polynomials as activation functions introduces errors which could have a significant impact on accuracy in classification tasks. In this paper, we present a systematic method to construct HE-friendly activation functions for CNNs. We first determine what properties in a good activation function contribute to performance by analyzing commonly used functions such as Rectified Linear Units (ReLU) and Sigmoid. Then, we compare polynomial approximation methods and search for an optimal range of approximation for the polynomial activation. We also propose a novel weighted polynomial approximation method tailored to the output distribution of a batch normalization layer. Finally, we demonstrate the effectiveness of our method using several datasets such as MNIST, FMNIST, CIFAR-10.

Decision tree and its generalization of random forests are simple yet powerful machine learning model for many classification and regression problems. Recent works propose how to privately evaluate a decision tree in a two-party setting where the feature vector of the client or the decision tree model (such as the threshold values of its nodes) is kept secret from another party. However, these works cannot be extended trivially to support the outsourcing setting where a third-party who should not have access to the model or the query. Furthermore, their use of an interactive comparison protocol does not support branching program, hence requires interactions with the client to determine the comparison result before resuming the evaluation task. We propose the first secure protocol for collaborative evaluation of random forests contributed by multiple owners. They outsource evaluation tasks to a third-party evaluator. Upon receiving the client's encrypted inputs, the cloud evaluates obliviously on individually encrypted random forest models and calculates the aggregated result. The system is based on our new secure comparison protocol, secure counting protocol, and a multi-key somewhat homomorphic encryption on top of symmetric-key encryption. This allows us to reduce communication overheads while achieving round complexity lower than existing work.

Background/Objectives: Patients with suspicious prostate mpMRI but negative baseline biopsy remain challenging to manage, as some are later diagnosed with clinically significant prostate cancer (csPCa). This study evaluated whether baseline whole-gland radiomic features from T2-weighted imaging and apparent diffusion coefficient (ADC) maps could predict subsequent csPCa detection. Methods: This retrospective radiomics sub-analysis of the MULTIPROS trial included men with suspicious baseline mpMRI findings (PI-RADS v2.0 categories 3–5) and no csPCa detected at baseline biopsy. The primary outcome was subsequent csPCa detection during follow-up, defined as ISUP Grade Group ≥2. Whole-gland prostate segmentation was performed on baseline T2-weighted images using a semi-automated approach with manual refinement, and the resulting T2-derived masks were applied to the spatially corresponding ADC maps. Radiomic features were extracted using PyRadiomics version 3.1.0a2 after standardised preprocessing. Feature robustness was assessed in a 20-patient reproducibility subset using intra- and inter-reader intraclass correlation coefficients, followed by correlation filtering and LASSO-based feature prioritisation. Radiomics-only, clinicoradiological-only, and clinicoradiological–radiomic logistic regression models were evaluated using stratified five-fold cross-validation. Results: T2-based modelling included 151 patients, of whom 36/151 (23.8%) had subsequent csPCa detected; the median time to csPCa detection or last follow-up was 64 months. ADC analyses included 144 patients, of whom 34/144 (23.6%) had subsequent csPCa detected. The T2 clinicoradiological–radiomic model achieved a mean AUC of 0.696 ± 0.060, compared with 0.713 ± 0.072 for the T2 clinicoradiological-only model and 0.456 ± 0.091 for the T2 radiomics-only model. In the ADC-available cohort, ADC radiomics-only, ADC clinicoradiological–radiomic, and combined T2 + ADC clinicoradiological–radiomic models achieved mean AUCs of 0.684 ± 0.052, 0.635 ± 0.157, and 0.663 ± 0.106, respectively. Calibration was imperfect, with deviations at higher predicted probabilities and overprediction in the highest predicted-risk bin. Conclusions: Baseline whole-gland MRI radiomics showed limited and inconsistent predictive value for subsequent csPCa detection after negative biopsy and did not demonstrate consistent incremental improvement over clinicoradiological predictors. These findings are exploratory and hypothesis-generating, and external validation is required before clinical use.