Here we consider the problem of all the possible orders of a linguistic structure formed by $n$ elements, for instance, subject, direct object and verb ($n=3$) or subject, direct object, indirect object and verb ($n=4$). We investigate if the frequency of the $n!$ possible orders is constrained by two principles. First, entropy minimization, a principle that has been suggested to shape natural communication systems at distinct levels of organization. Second, swap distance minimization, namely a preference for word orders that require fewer swaps of adjacent elements to be produced from a source order. Here we present average swap distance, a novel score for research on swap distance minimization, and investigate the theoretical distribution of that score for any $n$: its minimum and maximum values and its expected value in die rolling experiments or when the word order frequencies are shuffled. We investigate whether entropy and average swap distance are significantly small in distinct linguistic structures with $n=3$ or $n=4$ in agreement with the corresponding minimization principles. We find strong evidence of entropy minimization and swap distance minimization with respect to a die rolling experiment. The evidence of these two forces with respect to a Polya urn process is strong for $n=4$ but weaker for $n=3$. We still find evidence of swap distance minimization when word order frequencies are shuffled, indicating that swap distance minimization effects are beyond pressure to minimize word order entropy.

Distance minimization is a general principle of language. A special case of this principle in the domain of word order is swap distance minimization. This principle predicts that variations from a canonical order that are reached by fewer swaps of adjacent constituents are lest costly and thus more likely. Here we investigate the principle in the context of the triple formed by subject (S), object (O) and verb (V). We introduce the concept of word order rotation as a cognitive underpinning of that prediction. When the canonical order of a language is SOV, the principle predicts SOV < SVO, OSV < VSO, OVS < VOS, in order of increasing cognitive cost. We test the prediction in three flexible order SOV languages: Korean (Koreanic), Malayalam (Dravidian), and Sinhalese (Indo-European). Evidence of swap distance minimization is found in all three languages, but it is weaker in Sinhalese. Swap distance minimization is stronger than a preference for the canonical order in Korean and especially Malayalam.

We present a general framework for symmetrizing an arbitrary neural-network architecture and making it equivariant with respect to a given group. We build upon the proposals of Kim et al. (2023); Kaba et al. (2023) for symmetrization, and improve them by replacing their conversion of neural features into group representations, with an optimization whose loss intuitively measures the distance between group orbits. This change makes our approach applicable to a broader range of matrix groups, such as the Lorentz group O(1, 3), than these two proposals. We experimentally show our method's competitiveness on the SO(2) image classification task, and also its increased generality on the task with O(1, 3). Our implementation will be made accessible at https://github.com/

Graph clustering is the process of grouping vertices into densely connected sets called clusters. We tailor two mathematical programming formulations from the literature, to this problem. In doing so, we obtain a heuristic approximation to the intra-cluster density maximization problem. We use two variations of a Boltzmann machine heuristic to obtain numerical solutions. For benchmarking purposes, we compare solution quality and computational performances to those obtained using a commercial solver, Gurobi. We also compare clustering quality to the clusters obtained using the popular Louvain modularity maximization method. Our initial results clearly demonstrate the superiority of our problem formulations. They also establish the superiority of the Boltzmann machine over the traditional exact solver. In the case of smaller less complex graphs, Boltzmann machines provide the same solutions as Gurobi, but with solution times that are orders of magnitude lower. In the case of larger and more complex graphs, Gurobi fails to return meaningful results within a reasonable time frame. Finally, we also note that both our clustering formulations, the distance minimization and $K$-medoids, yield clusters of superior quality to those obtained with the Louvain algorithm.

Many planning methods rely on the use of an immediate reward function as a portable and succinct representation of desired behavior. Rewards are often inferred from demonstrated behavior that is assumed to be near-optimal. We examine a framework, Distance Minimization IRL (DM-IRL), for learning reward functions from scores an expert assigns to possibly suboptimal demonstrations. By changing the expert’s role from a demonstrator to a judge, DM-IRL relaxes some of the assumptions present in IRL, enabling learning from the scoring of arbitrary demonstration trajectories with unknown transition functions. DM-IRL complements existing IRL approaches by addressing different assumptions about the expert. We show that DM-IRL is robust to expert scoring error and prove that finding a policy that produces maximally informative trajectories for an expert to score is strongly NP-hard. Experimentally, we demonstrate that the reward function DM-IRL learns from an MDP with an unknown transition model can transfer to an agent with known characteristics in a novel environment, and we achieve successful learning with limited available training data.