New AI Papers Explore Constraint Solving, Gaussian Processes, and Graph Games

Efficient Reformulations of Half-reified Global Constraints using Auxiliary Variables – Bleukx, Verhaeghe, Tsouros, and Guns introduced a method that rewrites half‑reified global constraints with auxiliary variables so that CP solvers can keep their specialized propagators active instead of flattening the model into non‑global constraints. The approach was published on August 15 2026 and is described as a way to avoid the exponential slowdown caused by naive decomposition when solving large problems such as logistics planning ¹. Expert context notes that this builds on early work by Richard Wallace from the 1980s; maintaining global structure through auxiliary variables has long been seen as a crucial optimisation because it keeps search time manageable even when models contain thousands or millions of decision variables.

Information-Based Calibration of Uncertainty Quantification in Product-of-Experts Gaussian Process Models – Ong, Barucca, Pan, and Wang presented GP‑pro‑c, an information‑based calibration technique for product‑of‑experts Gaussian process (GP‑pro) models that reduces overestimated posterior variances without retraining all local experts each iteration. Published on August 15 2026, the paper shows how monotonicity and submodularity properties of information gain are used to define a calibration ratio that scales computationally like O(n²), where n is the number of training samples, rather than requiring full retraining. This follows earlier recognition of the issue since Murphy’s Bayesian Hierarchical Modelling (2003); previous solutions were often too costly. Early results reported improvements up to 5 % in negative log likelihood across several datasets compared with baseline methods ¹.

Variety-Seeking Jump Games on Graphs – Narayanan, Opatrny, Tummala, and Voudouris introduced a class of jump games played on graphs where agents of different types occupy nodes and aim to maximise the variety of types among their neighbours; utility equals the count of distinct neighbour types. The authors proved that while such games can exhibit improving response cycles, they form potential games under four conditions: only two agent types; exactly one empty node; graph degree at most two; or a 3‑regular graph with two empty nodes. They further showed that equilibria always exist on trees, cylinder graphs, and tori, and derived tight bounds on price‑of‑anarchy for social welfare and colourful edges metrics ¹.