The ability of large language models (LLMs) to mimic human-like intelligence hasledtoasurgeinLLM-based autonomous agents. ThoughrecentLLMsseem capable of planning and reasoning given user instructions, their effectiveness in applying these capabilities for autonomous task solving remains underexplored. This is especially true in enterprise settings, where automated agents hold the promise of a high impact.

The proof involves 3 steps: 1. we first justify the definition of p and q in the extended problem formulation, and show that T It is straighforward to see that, by doing so, we ensure that Γ remains an admissible coupling (see Figure 1 for an illustration). Figure 1: Repartition of the mass for matrices Γ and T. Each of them has a total mass of q A 5 (with a constant A > 2ξ) the GW formulation involves pairs of points. This yields the following cases: Case 1: a > 0. In that case, φ(γ) is a convex function, whose minimum on [0, 1] is reached for γ We have φ(0) = c > 0 and φ(1) = a + b + c. The minimum is then obtained for 0 if a + b > 0, and 1 otherwise. This gives the desired result.

Optimal transport (OT) has been gaining in recent years an increasing attention in the machine learning community, mainly due to its capacity to exploit the geometric property of the samples.

In @ (x) @ t =r (x)r( log (x) log (x)) = r (x)rlog (x) +r2 (x), thatadmits (x). The ODE [2] related dx dt = r log (x) log (x) .