We call these cooperative graphical models .

Here we introduce methods to extend the approach to models with higher-order potentials and develop theoretical insights. In particular, we show that the triplet-consistent polytope TRI is unique in being'universally rooted'.

From now on, we can therefore focus on proving (24).

Modeling the evolution of high-dimensional systems from limited snapshot observations at irregular time points poses a significant challenge in quantitative biology and related fields. Traditional approaches often rely on dimensionality reduction techniques, which can oversimplify the dynamics and fail to capture critical transient behaviors in non-equilibrium systems. We present Multi-Marginal Stochastic Flow Matching (MMSFM), a novel extension of simulation-free score and flow matching methods to the multi-marginal setting, enabling the alignment of high-dimensional data measured at non-equidistant time points without reducing dimensionality. The use of measure-valued splines enhances robustness to irregular snapshot timing, and score matching prevents overfitting in high-dimensional spaces. We validate our framework on several synthetic and benchmark datasets, including gene expression data collected at uneven time points and an image progression task, demonstrating the method's versatility.

I think the proposed graphical model is interesting and novel. The authors provide a lower bound and a fully convex upper bound for partition function. In particular, variational upper/lower bound are formulated by using pairwise graphical models, e.g. The author also provides algorithms, Frank-Wolfe, PGD and BP, for finding upper/lower bound. The experimental results shows that cooperative graphical models and its variational methods performs better than pairwise graphical models for image segmentation.

The idea of uprooting and rerooting graphical models was introduced specifically for binary pairwise models by Weller [19] as a way to transform a model to any of a whole equivalence class of related models, such that inference on any one model yields inference results for all others. This is very helpful since inference, or relevant bounds, may be much easier to obtain or more accurate for some model in the class. Here we introduce methods to extend the approach to models with higher-order potentials and develop theoretical insights. In particular, we show that the triplet-consistent polytope TRI is unique in being'universally rooted'. We demonstrate empirically that rerooting can significantly improve accuracy of methods of inference for higher-order models at negligible computational cost.

Conceptual spaces represent entities in terms of their primitive semantic features. Such representations are highly valuable but they are notoriously difficult to learn, especially when it comes to modelling perceptual and subjective features. Distilling conceptual spaces from Large Language Models (LLMs) has recently emerged as a promising strategy, but existing work has been limited to probing pre-trained LLMs using relatively simple zero-shot strategies. We focus in particular on the task of ranking entities according to a given conceptual space dimension. Unfortunately, we cannot directly fine-tune LLMs on this task, because ground truth rankings for conceptual space dimensions are rare. We therefore use more readily available features as training data and analyse whether the ranking capabilities of the resulting models transfer to perceptual and subjective features. We find that this is indeed the case, to some extent, but having at least some perceptual and subjective features in the training data seems essential for achieving the best results.

We study a rich family of distributions that capture variable interactions significantly more expressive than those representable with low-treewidth or pairwise graphical models, or log-supermodular models. We call these cooperative graphical models. Yet, this family retains structure, which we carefully exploit for efficient inference techniques. Our algorithms combine the polyhedral structure of submodular functions in new ways with variational inference methods to obtain both lower and upper bounds on the partition function. While our fully convex upper bound is minimized as an SDP or via tree-reweighted belief propagation, our lower bound is tightened via belief propagation or mean-field algorithms. The resulting algorithms are easy to implement and, as our experiments show, effectively obtain good bounds and marginals for synthetic and real-world examples.

Natural Language Processing tasks such as resolving the coreference of events require understanding the relations between two text snippets. These tasks are typically formulated as (binary) classification problems over independently induced representations of the text snippets. In this work, we develop a Pairwise Representation Learning (PairwiseRL) scheme for the event mention pairs, in which we jointly encode a pair of text snippets so that the representation of each mention in the pair is induced in the context of the other one. Furthermore, our representation supports a finer, structured representation of the text snippet to facilitate encoding events and their arguments. We show that PairwiseRL, despite its simplicity, outperforms the prior state-of-the-art event coreference systems on both cross-document and within-document event coreference benchmarks. We also conduct in-depth analysis in terms of the improvement and the limitation of pairwise representation so as to provide insights for future work.

Sentence Ordering refers to the task of rearranging a set of sentences into the appropriate coherent order. For this task, most previous approaches have explored global context-based end-to-end methods using Sequence Generation techniques. In this paper, we put forward a set of robust local and global context-based pairwise ordering strategies, leveraging which our prediction strategies outperform all previous works in this domain. Our proposed encoding method utilizes the paragraph's rich global contextual information to predict the pairwise order using novel transformer architectures. Analysis of the two proposed decoding strategies helps better explain error propagation in pairwise models. This approach is the most accurate pure pairwise model and our encoding strategy also significantly improves the performance of other recent approaches that use pairwise models, including the previous state-of-the-art, demonstrating the research novelty and generalizability of this work. Additionally, we show how the pre-training task for ALBERT helps it to significantly outperform BERT, despite having considerably lesser parameters. The extensive experimental results, architectural analysis and ablation studies demonstrate the effectiveness and superiority of the proposed models compared to the previous state-of-the-art, besides providing a much better understanding of the functioning of pairwise models.