Related papers: Exactly solvable models of adaptive networks
Many NP-complete constraint satisfaction problems appear to undergo a "phase transition'' from solubility to insolubility when the constraint density passes through a critical threshold. In all such cases it is easy to derive upper bounds…
Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few.…
We consider the random 2-satisfiability problem, in which each instance is a formula that is the conjunction of m clauses of the form (x or y), chosen uniformly at random from among all 2-clauses on n Boolean variables and their negations.…
Quantization is a technique for reducing deep neural networks (DNNs) training and inference times, which is crucial for training in resource constrained environments or applications where inference is time critical. State-of-the-art (SOTA)…
Large language models (LLMs) have shown remarkable reasoning capabilities, yet aligning such abilities to small language models (SLMs) remains a challenge due to distributional mismatches and limited model capacity. Existing reasoning…
The dynamic cavity method provides the most efficient way to evaluate probabilities of dynamic trajectories in systems of stochastic units with unidirectional sparse interactions. It is closely related to sum-product algorithms widely used…
We analyze, by means of statistical mechanics, a sparse network with random competitive interactions among dichotomic variables pasted on the nodes, namely a Viana-Bray model. The model is described by an infinite series of order parameters…
Neural NLP models are often miscalibrated and overconfident, assigning high confidence to incorrect predictions and failing to express uncertainty during internal evidence aggregation. This undermines selective prediction and high-stakes…
We study a mean field model of a complex network, focusing on edge and triangle densities. Our first result is the derivation of a variational characterization of the entropy density, compatible with the infinite node limit. We then…
We developed a scheme for evaluating the size of the largest connected subnetwork (giant component) in random networks and the percolation threshold when sites (nodes) and/or bonds (edges) are removed from the networks based on the cavity…
We consider a general model in which there is a coupled dynamics of node states and links states in a network. This coupled dynamics coevolves with dynamical changes of the topology of the network caused by a link rewiring mechanism. Such…
Decentralized optimization methods have been in the focus of optimization community due to their scalability, increasing popularity of parallel algorithms and many applications. In this work, we study saddle point problems of sum type,…
Phase transitions in many complex combinational problems have been widely studied in the past decade. In this paper, we investigate phase transitions in the knowledge compilation empirically, where DFA, OBDD and d-DNNF are chosen as the…
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…
Time series forecasting is crucial for various applications, such as weather, traffic, electricity, and energy predictions. Currently, common time series forecasting methods are based on Transformers. However, existing approaches primarily…
Models of the consensus of the individual state in social systems have been the subject of recent researches in the physics literature. We investigate how network structures coevolve with the individual state under the framework of social…
Predictable adaptation of network depths can be an effective way to control inference latency and meet the resource condition of various devices. However, previous adaptive depth networks do not provide general principles and a formal…
One of the most studied models of SAT is random SAT. In this model, instances are composed from clauses chosen uniformly randomly and independently of each other. This model may be unsatisfactory in that it fails to describe various…
Neural networks are fragile when confronted with data that significantly deviates from their training distribution. This is true in particular for simulation-based inference methods, such as neural amortized Bayesian inference (ABI), where…
The goal of this chapter is to review the main ideas that underlie the cavity method for disordered models defined on random graphs, as well as present some of its outcomes, focusing on the random constraint satisfaction problems for which…