This paper introduces a physics-informed generative framework that resolves the fundamental conflict between the statistical flexibility of deep learning and the rigorous theoretical constraints of fixed-income modeling. We demonstrate that standard generative models and unconstrained statistical extrapolations suffer from "manifold collapse" and severe arbitrage violations when forecasting term structures across diverse macroeconomic regimes. To overcome this, we propose a two-stage architecture. First, a Student-t Conditional Variational Autoencoder with Dynamic Level Injection (CVAEsT+LS) extracts a robust, heavy-tailed term structure manifold, effectively decoupling macroeconomic shape dynamics from absolute base rates. Second, the latent dynamic evolution is governed by a continuous-time Neural Stochastic Differential Equation (SDE) strictly penalized by a No-Arbitrage Partial Differential Equation (PDE). Empirical results across multiple sovereign currencies (USD, GBP, JPY) confirm that our synergistic approach drastically reduces out-of-sample forecasting errors -- achieving an exceptional 6.58 bps Mean Tenor RMSE -- and successfully overcomes the massive parallel drift and zero-lower-bound violations exhibited by the classical HJM model in extreme environments. Furthermore, through phase space vector field analysis, we demonstrate the model's superior capability in unsupervised macroeconomic regime detection and high-quality continuous-time scenario generation. Ultimately, this research provides a highly scalable, mathematically sound evolutionary engine for term structure modeling.

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 .

Parallel tempering (PT), also known as replica exchange, is the go-to workhorse for simulations of multi-modal distributions. The key to the success of PT is to adopt efficient swap schemes. The popular deterministic even-odd (DEO) scheme exploits the non-reversibility property and has successfully reduced the communication cost from $O(P^2)$ to $O(P)$ given sufficiently many $P$ chains. However, such an innovation largely disappears in big data due to the limited chains and few bias-corrected swaps. To handle this issue, we generalize the DEO scheme to promote non-reversibility and propose a few solutions to tackle the underlying bias caused by the geometric stopping time. Notably, in big data scenarios, we obtain an appealing communication cost $O(P\log P)$ based on the optimal window size. In addition, we also adopt stochastic gradient descent (SGD) with large and constant learning rates as exploration kernels. Such a user-friendly nature enables us to conduct approximation tasks for complex posteriors without much tuning costs.