Bayesian latent space models offer a principled approach to network representation, but rely on correct specification of both geometry and link function. Real-world networks often violate these assumptions, exhibiting geometric mismatch and structural anomalies that break standard metric properties. We show that such misspecification pushes the data-generating distribution outside the model class, causing Bayesian inference to become overconfident and poorly calibrated. To address this, we propose a generalized posterior framework for random geometric graphs. We introduce Link-Sequential R-SafeBayes, a method that exploits dyadic conditional independence to estimate prequential risk and adaptively tune posterior regularization. Experiments on synthetic and real-world networks demonstrate improved calibration, better link prediction performance, and a reliable criterion for selecting latent geometries across Euclidean, spherical, and hyperbolic spaces.

This paper presents a novel value-aware approach to product recommendation that simultaneously addresses the high dimensionality and sparsity of user-item data while explicitly incorporating the contribution of each product and user to overall sales revenue. The proposed framework encodes revenue contributions in the user-item matrix and computes customer similarity directly on this basis using suitable distance measures. This enables the segmentation of users according to the revenue-based similarity of their purchase baskets and supports recommendations aligned with profitability objectives. We compare conventional similarity metrics with a novel alternative tailored to high-dimensional contexts and propose three recommendation strategies based on revenue share, product popularity, and expected profit generation. The effectiveness of the proposed method is validated through simulation experiments and a real-world application using the UCI Online Retail dataset.

Bounding and predicting the generalization gap of overparameterized neural networks remains a central open problem in theoretical machine learning. There is a recent and growing body of literature that proposes the framework of fractals to model optimization trajectories of neural networks, motivating generalization bounds and measures based on the fractal dimension of the trajectory. Notably, the persistent homology dimension has been proposed to correlate with the generalization gap.

Experimental results showthattheproposed metriclearning algorithm improves both certified robust errors and empirical robust errors (errors under adversarial attacks).

We define the heat-geodesic dissimilarity based on V aradhan's formula and the two-sided heat

Robust Metric Learning (ARML) method can obtain a more "robust" metric on this example.

Many metric learning tasks, such as triplet learning, nearest neighbor retrieval, and visualization, are treated primarily as embedding tasks where the ultimate metric is some variant of the Euclidean distance (e.g., cosine or Mahalanobis), and the algorithm must learn to embed points into the pre-chosen space. The study of non-Euclidean geometries is often not explored, which we believe is due to a lack of tools for learning non-Euclidean measures of distance. Recent work has shown that Bregman divergences can be learned from data, opening a promising approach to learning asymmetric distances. We propose a new approach to learning arbitrary Bergman divergences in a differentiable manner via input convex neural networks and show that it overcomes significant limitations of previous works. We also demonstrate that our method more faithfully learns divergences over a set of both new and previously studied tasks, including asymmetric regression, ranking, and clustering. Our tests further extend to known asymmetric, but non-Bregman tasks, where our method still performs competitively despite misspecification, showing the general utility of our approach for asymmetric learning. Learning a task-relevant metric among samples is a common application of machine learning, with use in retrieval, clustering, and ranking. A classic example of retrieval is in visual recognition where, given an object image, the system tries to identify the class based on an existing labeled dataset. To do this, the model can learn a measure of similarity between pairs of images, assigning small distances between images of the same object type. Given the broad successes of deep learning, there has been a recent surge of interest in deep metric learning--using neural networks to automatically learn these similarities (Hoffer & Ailon, 2015; Huang et al., 2016; Zhang et al., 2020). The traditional approach to deep metric learning learns an embedding function over the input space so that a simple distance measure between pairs of embeddings corresponds to task-relevant spatial relations between the inputs. The embedding function f is computed by a neural network, which is learned to encode those spatial relations. First, it is used to define the loss functions, such as triplet or contrastive loss, to dictate how this distance should be used to capture task-relevant properties of the input space. Second, since f is trained to optimize the loss function, the distance influences the learned embedding f.

Meanings of words change over time and across domains. Detecting the semantic changes of words is an important task for various NLP applications that must make time-sensitive predictions. We consider the problem of predicting whether a given target word, $w$, changes its meaning between two different text corpora, $\mathcal{C}_1$ and $\mathcal{C}_2$. For this purpose, we propose $\textit{Swapping-based Semantic Change Detection}$ (SSCD), an unsupervised method that randomly swaps contexts between $\mathcal{C}_1$ and $\mathcal{C}_2$ where $w$ occurs. We then look at the distribution of contextualised word embeddings of $w$, obtained from a pretrained masked language model (MLM), representing the meaning of $w$ in its occurrence contexts in $\mathcal{C}_1$ and $\mathcal{C}_2$. Intuitively, if the meaning of $w$ does not change between $\mathcal{C}_1$ and $\mathcal{C}_2$, we would expect the distributions of contextualised word embeddings of $w$ to remain the same before and after this random swapping process. Despite its simplicity, we demonstrate that even by using pretrained MLMs without any fine-tuning, our proposed context swapping method accurately predicts the semantic changes of words in four languages (English, German, Swedish, and Latin) and across different time spans (over 50 years and about five years). Moreover, our method achieves significant performance improvements compared to strong baselines for the English semantic change prediction task. Source code is available at https://github.com/a1da4/svp-swap .