The statistical essence of the Transformer architecture has long remained elusive: Is it a universal approximator, or a neural network version of known computational algorithms? Through rigorous algebraic proof, we show that the latter better describes Transformer's basic nature: Ordinary Least Squares (OLS) is a special case of the single-layer Linear Transformer. Using the spectral decomposition of the empirical covariance matrix, we construct a specific parameter setting where the attention mechanism's forward pass becomes mathematically equivalent to the OLS closed-form projection. This means attention can solve the problem in one forward pass, not by iterating. Building upon this prototypical case, we further uncover a decoupled slow and fast memory mechanism within Transformers. Finally, the evolution from our established linear prototype to standard Transformers is discussed. This progression facilitates the transition of the Hopfield energy function from linear to exponential memory capacity, thereby establishing a clear continuity between modern deep architectures and classical statistical inference.

Large language models (LLMs) are rapidly evolving into autonomous agents that cooperate across organizational boundaries, enabling joint disaster response, supply-chain optimization, and other tasks that demand decentralized expertise without surrendering data ownership. Yet, cross-domain collaboration shatters the unified trust assumptions behind current alignment and containment techniques. An agent benign in isolation may, when receiving messages from an untrusted peer, leak secrets or violate policy, producing risks driven by emergent multi-agent dynamics rather than classical software bugs. This position paper maps the security agenda for cross-domain multi-agent LLM systems. We introduce seven categories of novel security challenges, for each of which we also present plausible attacks, security evaluation metrics, and future research guidelines.

Many real-world problems, such as Markov Logic Networks (MLNs) with evidence, can be represented as a highly symmetric graphical model perturbed by additional potentials. In these models, variational inference approaches that exploit exact model symmetries are often forced to ground the entire problem, while methods that exploit approximate symmetries (such as by constructing an over-symmetric approximate model) offer no guarantees on solution quality. In this paper, we present a method based on a lifted variant of the generalized dual decomposition (GenDD) for marginal MAP inference which provides a principled way to exploit symmetric sub-structures in a graphical model. We develop a coarse-to-fine inference procedure that provides any-time upper bounds on the objective. The upper bound property of GenDD provides a principled way to guide the refinement process, providing good any-time performance and eventually arriving at the ground optimal solution.

Solving constrained combinatorial optimisation problems via MAP inference is often achieved by introducing extra potential functions for each constraint. This can result in very high order potentials, e.g. a 2nd-order objective with pairwise potentials and a quadratic constraint over all N variables would correspond to an unconstrained objective with an order-N potential. This limits the practicality of such an approach, since inference with high order potentials is tractable only for a few special classes of functions. We propose an approach which is able to solve constrained combinatorial problems using belief propagation without increasing the order. For example, in our scheme the 2nd-order problem above remains order 2 instead of order N. Experiments on applications ranging from foreground detection, image reconstruction, quadratic knapsack, and the M-best solutions problem demonstrate the effectiveness and efficiency of our method. Moreover, we show several situations in which our approach outperforms commercial solvers like CPLEX and others designed for specific constrained MAP inference problems.

We present a dual decomposition approach to the tree-reweighted belief propagation objective. Each tree in the tree-reweighted bound yields one subproblem, which can be solved with the sum-product algorithm. The master problem is a simple differentiable optimization, to which a standard optimization method can be applied. Experimental results on 10x10 Ising models show the dual decomposition approach using L-BFGS is similar in settings where message-passing converges quickly, and one to two orders of magnitude faster in settings where message-passing requires many iterations, specifically high accuracy convergence, and strong interactions.