Lewis signaling games are a class of simple communication games for simulating the emergence of language. In these games, two agents must agree on a communication protocol in order to solve a cooperative task. Previous work has shown that agents trained to play this game with reinforcement learning tend to develop languages that display undesirable properties from a linguistic point of view (lack of generalization, lack of compositionality, etc). In this paper, we aim to provide better understanding of this phenomenon by analytically studying the learning problem in Lewis games. As a core contribution, we demonstrate that the standard objective in Lewis games can be decomposed in two components: a co-adaptation loss and an information loss. This decomposition enables us to surface two potential sources of overfitting, which we show may undermine the emergence of a structured communication protocol. In particular, when we control for overfitting on the co-adaptation loss, we recover desired properties in the emergent languages: they are more compositional and generalize better.

In theory, the choice of ReLU0(0) in [0,1] for a neural network has a negligible influence both on backpropagation and training. Yet, in the real world, 32 bits default precision combined with the size of deep learning problems makes it a hyperparameter of training methods. We investigate the importance of the value of ReLU0(0) for several precision levels (16, 32, 64 bits), on various networks (fully connected, VGG, ResNet) and datasets (MNIST, CIFAR10, SVHN, ImageNet). We observe considerable variations of backpropagation outputs which occur around half of the time in 32 bits precision. The effect disappears with double precision, while it is systematic at 16 bits. For vanilla SGD training, the choice ReLU0(0) = 0 seems to be the most efficient. For our experiments on ImageNet the gain in test accuracy over ReLU0(0) = 1 was more than 10 points (two runs). We also evidence that reconditioning approaches as batch-norm or ADAM tend to buffer the influence of ReLU0(0)'s value. Overall, the message we convey is that algorithmic differentiation of nonsmooth problems potentially hides parameters that could be tuned advantageously.

Algorithm 2 details the pseudocode for the partition function used in LaMCTS, which we use in LaP3 as well. Algorithm 2 Partition Function 1: Input: Input Space Ω, Samples St, Node partition threshold Nthres, Partitioning Latent Model s(x) 2: Set V0 = {Ω} 3: Set Vqueue = {Ω} 4: while Vqueue 6= do 5: Ωp Vqueue.pop(0) It is clear that Fk(y) is a monotonically decreasing function with Fk(0) = 1 and limy + Fk(y) = 0. Here we assume it is strictly decreasing so that Fk(y) has a well-defined inverse function F 1k . In the following, we will omit the subscript k for brevity. P[f(xi) g y|xi Ωk] (4) = 1 Fntk (y) (5) Note that 1 is due to the fact that all samples x1,...,xnt are independently drawn within the region Ωk.

We consider the problem where nclients transmit d-dimensional real-valued vectors using dp1 `op1qqbits each, in a manner that allows the receiver to approximately reconstruct their mean. Such compression problems naturally arise in distributed and federated learning. We provide novel mathematical results and derive computationally efficient algorithms that are more accurate than previous compression techniques. We evaluate our methods on a collection of distributed and federated learning tasks, using a variety of datasets, and show a consistent improvement over the state of the art.