Advancements in cloud computing have boosted Machine Learning as a Service (MLaaS), highlighting the challenge of scheduling tasks under latency and deadline constraints. Neural network compression offers the latency and energy consumption reduction in data centers, aligning with efforts to minimize cloud computing’s carbon footprint, despite some accuracy loss.

Considerable research efforts have recently been made to show that a random neural network $N$ contains subnetworks capable of accurately approximating any given neural network that is sufficiently smaller than $N$, without any training. This line of research, known as the Strong Lottery Ticket Hypothesis (SLTH), was originally motivated by the weaker Lottery Ticket Hypothesis, which states that a sufficiently large random neural network $N$ contains sparse subnetworks that can be trained efficiently to achieve performance comparable to that of training the entire network $N$. Despite its original motivation, results on the SLTH have so far not provided any guarantee on the size of subnetworks. Such limitation is due to the nature of the main technical tool leveraged by these results, the Random Subset Sum (RSS) Problem. Informally, the RSS Problem asks how large a random i.i.d. sample $\Omega$ should be so that we are able to approximate any number in $[-1,1]$, up to an error of $ \epsilon$, as the sum of a suitable subset of $\Omega$. We provide the first proof of the SLTH in classical settings, such as dense and equivariant networks, with guarantees on the sparsity of the subnetworks. Central to our results, is the proof of an essentially tight bound on the Random Fixed-Size Subset Sum Problem (RFSS), a variant of the RSS Problem in which we only ask for subsets of a given size, which is of independent interest.

There is a wide variety of message-passing communication models, ranging from synchronous "rendez-vous" communications to fully asynchronous/out-of-order communications. For large-scale distributed systems, the communication model is determined by the transport layer of the network, and a few classes of orders of message delivery (FIFO, causally ordered) have been identified in the early days of distributed computing. For local-scale message-passing applications, e.g., running on a single machine, the communication model may be determined by the actual implementation of message buffers and by how FIFO queues are used. While large-scale communication models, such as causal ordering, are defined by logical axioms, local-scale models are often defined by an operational semantics. In this work, we connect these two approaches, and we present a unified hierarchy of communication models encompassing both large-scale and local-scale models, based on their concurrent behaviors. We also show that all the communication models we consider can be axiomatized in the monadic second order logic, and may therefore benefit from several bounded verification techniques based on bounded special treewidth.