Foundational modelling of multi-dimensional time-series data in industrial systems presents a central trade-off: channel-dependent (CD) models capture specific cross-variable dynamics but lack robustness and adaptability as model layers are commonly bound to the data dimensionality of the tackled use-case, while channel-independent (CI) models offer generality at the cost of modelling the explicit interactions crucial for system-level predictive regression tasks. To resolve this, we propose the Causally-Guided Pairwise Transformer (CGPT), a novel architecture that integrates a known causal graph as an inductive bias. The core of CGPT is built around a pairwise modeling paradigm, tackling the CD/CI conflict by decomposing the multidimensional data into pairs. The model uses channel-agnostic learnable layers where all parameter dimensions are independent of the number of variables. CGPT enforces a CD information flow at the pair-level and CI-like generalization across pairs. This approach disentangles complex system dynamics and results in a highly flexible architecture that ensures scalability and any-variate adaptability. We validate CGPT on a suite of synthetic and real-world industrial datasets on long-term and one-step forecasting tasks designed to simulate common industrial complexities. Results demonstrate that CGPT significantly outperforms both CI and CD baselines in predictive accuracy and shows competitive performance with end-to-end trained CD models while remaining agnostic to the problem dimensionality.

Transformers have increasingly become the de facto method to model sequential data with state-of-the-art performance. Due to its widespread use, being able to estimate and calibrate its modeling uncertainty is important to understand and design robust transformer models. To achieve this, previous works have used Gaussian processes (GPs) to perform uncertainty calibration for the attention units of transformers and attained notable successes. However, such approaches have to confine the transformers to the space of symmetric attention to ensure the necessary symmetric requirement of their GP's kernel specification, which reduces the representation capacity of the model. To mitigate this restriction, we propose the Correlated Gaussian Process Transformer (CGPT), a new class of transformers whose self-attention units are modeled as cross-covariance between two correlated GPs (CGPs). This allows asymmetries in attention and can enhance the representation capacity of GP-based transformers. We also derive a sparse approximation for CGP to make it scale better. Our empirical studies show that both CGP-based and sparse CGP-based transformers achieve better performance than state-of-the-art GP-based transformers on a variety of benchmark tasks. The code for our experiments is available at https://github.com/MinhLong210/CGP-Transformers.

Semantic dimensions of sound have been playing a central role in understanding the nature of auditory sensory experience as well as the broader relation between perception, language, and meaning. Accordingly, and given the recent proliferation of large language models (LLMs), here we asked whether such models exhibit an organisation of perceptual semantics similar to those observed in humans. Specifically, we prompted ChatGPT, a chatbot based on a state-of-the-art LLM, to rate musical instrument sounds on a set of 20 semantic scales. We elicited multiple responses in separate chats, analogous to having multiple human raters. ChatGPT generated semantic profiles that only partially correlated with human ratings, yet showed robust agreement along well-known psychophysical dimensions of musical sounds such as brightness (bright-dark) and pitch height (deep-high). Exploratory factor analysis suggested the same dimensionality but different spatial configuration of a latent factor space between the chatbot and human ratings. Unexpectedly, the chatbot showed degrees of internal variability that were comparable in magnitude to that of human ratings. Our work highlights the potential of LLMs to capture salient dimensions of human sensory experience.