On the Lab. II building site

425 special CDSs in PCN033 (XLSX 29 kb

Gazelle: A Low Latency Framework for Secure Neural Network Inference

The growing popularity of cloud-based machine learning raises a natural question about the privacy guarantees that can be provided in such a setting. Our work tackles this problem in the context where a client wishes to classify private images using a convolutional neural network (CNN) trained by a server. Our goal is to build efficient protocols whereby the client can acquire the classification result without revealing their input to the server, while guaranteeing the privacy of the server's neural network. To this end, we design Gazelle, a scalable and low-latency system for secure neural network inference, using an intricate combination of homomorphic encryption and traditional two-party computation techniques (such as garbled circuits). Gazelle makes three contributions. First, we design the Gazelle homomorphic encryption library which provides fast algorithms for basic homomorphic operations such as SIMD (single instruction multiple data) addition, SIMD multiplication and ciphertext permutation. Second, we implement the Gazelle homomorphic linear algebra kernels which map neural network layers to optimized homomorphic matrix-vector multiplication and convolution routines. Third, we design optimized encryption switching protocols which seamlessly convert between homomorphic and garbled circuit encodings to enable implementation of complete neural network inference. We evaluate our protocols on benchmark neural networks trained on the MNIST and CIFAR-10 datasets and show that Gazelle outperforms the best existing systems such as MiniONN (ACM CCS 2017) by 20 times and Chameleon (Crypto Eprint 2017/1164) by 30 times in online runtime. Similarly when compared with fully homomorphic approaches like CryptoNets (ICML 2016) we demonstrate three orders of magnitude faster online run-time

Relationships of adiponectin to regional adiposity, insulin sensitivity, serum lipids and inflammatory markers in sedentary and endurance-trained Japanese young women

The raw data required to reproduce the findings of “Relationships of adiponectin to regional adiposity, insulin sensitivity, serum lipids and inflammatory markers in sedentary and endurance-trained Japanese young women

The fixation probability for <i>N</i> = 25 with different mutant distances <i>d</i>.

The curve is drawn by the results calculated by our developed algorithm whereas the points are the simulation results. It is noteworthy that the figure is quantitatively similar to Fig 5.</p

Estimating the coefficients <i>σ</i>_<i>k</i>s by simulation.

We establish three sets of individualised aspirations based on the uniform distribution in [0, 1] (see S2 File for details). For three-player games with b0 = b1 = b2 = 0, the estimated coefficients σ0, σ1, σ2 are obtained by linear regression model in the form of σ0a0 + σ1a1 + σ2a2 + Intercept. For rings, the regression coefficients σ0,σ1,σ2 and Intercept are close to 1,2,1 and 0, which agrees perfectly with theoretical calculations Eq (10). In addition, it holds for all the three sets of aspirations, validating the theorem. For well-mixed populations, the d coefficients still hold, consistent with [34]. Thus the coefficients are robust to the heterogeneity in aspiration for both ring and well-mixed population. The confidence interval for the corresponding estimated coefficients (EC) are [EC-ME, EC+ME], where ME in the parentheses is calculated with confidence level 95%. Please refer to the Methods to see the details of the simulation. Population size N = 100, selection intensity β = 5 × 10−2. More details of the simulation are found in S1 File.</p

Average abundance of strategy <i>A</i> as a function of the payoff entry <i>a</i>₀.

Our simulation results clearly show that strategy A is more abundant than strategy B if a0 is approximately greater than 2.0 for regular networks (k = 2) (Panel (a)). This is in perfect agreement with our calculation based on the theorem, i.e., inequality a0 + 2a1 + a2 > b0 + 2b1 + b2 with a1 = 2, a2 = 1, b0 = 4, b1 = 1 and b2 = 1. Note that the criterion a0 > 2 is valid for aspiration across various distributions. It implies that the criterion to favor one strategy over the other is independent of the individualised aspiration, as stated in the theorem. Furthermore, the criterion also holds beyond regular networks (Panel (a)), namely, on random (Panel (b)) and scale-free networks (Panel (c)). It suggests that the criterion can be extrapolated to general population structures. The details of the simulations are as follows: The minimum degree of all the networks is set to be two such that all the individuals have enough neighbours to play the three-player game with. Personal aspirations are randomly assigned in a population with homogeneous aspiration ei = 2 for all i = 1, 2…N (blue ◯), and a population with heterogeneous aspirations generated based on uniform distribution on the interval [0, 5] (red □), bimodal distribution with (orange ◊), and power-law distribution with probability density function f(x) = 2x−3 (purple △). Here, stands for the normal distribution with mean 2.5 and standard deviation 0.5. In addition, the minimum value of aspiration sampled from the power-law distribution is 1.0. In the beginning, we randomly set 45% of the population to be of strategy A and the rest to be of strategy B. At each time step, the focal individual randomly chooses two individuals from its neighborhood and play a single three-player game with them to obtain the payoff. Fermi function is employed as the decision making function for all the individuals. Each data point is the mean of the average abundance of strategy A calculated from three independent runs (5 × 109 samples in each run, 1.5 × 1010 samples in total). In each run, we start sampling after a relaxation time of 5 × 107 time steps. The average abundance of strategy A is obtained by averaging the abundance of strategy A over 5 × 109 time steps. The population size N = 1000. The selection intensity β = 0.005.</p

The conditional fixation time for two mutants in a circle of size <i>N</i> = 6.

The curve is the conditional fixation time obtained through Eq 26 and the points are the simulation results. The iteration time for simulation is 105.</p

Network configuration for two mutants.

If the population size is three, the two mutants have to be connected. If the population size is four or five, the two mutants can be separated by at most one wild-type individual. If the population size is six, the two mutants can be of distance zero, one and two, i.e., three types. In other words, six is the minimum population size of a circle, which gives rise to three distances between two mutants. Thus we adopt the population size six as an illustration model.</p

Average abundance of strategy <i>A</i> for a three-player game with individualised aspirations.

Personal aspirations are randomly assigned based on a uniform distributions on the interval [0, 1] (left panels) or [0, 5] (right panels). Within each class, two sets of aspirations are assigned to represent two populations with different aspirations from the same distribution. In this way, we established two kinds of heterogeneity in aspiration: one resorts to the underlying distribution, and the other is based on the actual values sampled from the same distribution. Intuitively, both of the two heterogeneities would alter the evolutionary outcome. Simulations in line with our theorem, however, show that both kinds of the heterogeneity in aspiration lead to the identical abundance in A for both the well-mixed population (upper panels) and that on rings (lower panels). We illustrate other details of the simulation in the following. In well-mixed populations, the focal individual randomly chooses two individuals from the rest of the population, whereas it plays only with the nearest two neighbours on the ring. In the beginning, we randomly set 5% of the population to be of strategy A and the rest to be of strategy B. For each data point, it is the mean of 20 independent runs. In each run, we iterate the evolutionary process for 1 × 108 generations. The average abundance of strategy A is obtained by averaging abundance of strategy A over the last 5 × 107 generations. The population size N = 100. And the payoff entries are a0 = 3, a1 = 2, a2 = 1, b0 = 4, b1 = 1 and b2 = 1, respectively.</p

State notation of the configuration in a circle.

We assume that there are at most two separated mutant groups. The state is denoted as a triplet (x, a, b). Here x refers to the minimal distance between two mutant groups, a and b represent the group sizes of the smaller group and that of the larger one. The following inequalities holds: a ≤ b and x ≤ N − x − a − b.</p