The Inference Report

Over the past ten years Tensor Network Kernel Machines have enabled efficient nonlinear system identification through the use of low-rank tensor networks. The goal of this article is to provide the reader with a basic understanding of this model class in terms of its two defining properties. Furthermore, both the optimization and regularization of such models are discussed, together with recent developments and starting points for further exploration.

The ENTSO-E Transparency Platform publishes generation, load, and cross-border power flows for European bidding zones. The values carry undocumented errors and violate energy conservation, and data reconciliation consists in correcting them to satisfy that balance. In this work, we formulate data reconciliation as Bayesian inference. Classical methods implicitly take a uniform prior, which we replace with a diffusion model estimated from the observations alone by empirical-Bayes expectation-maximization. The resulting posterior is sampled with a guided process whose projection step makes every sample satisfy the balance exactly. On synthetic systems of six to thirty-five bidding zones, built from ENTSO-E resource-adequacy data, the diffusion prior gives the most accurate reconciliation, increasingly so as the system grows. Its credible intervals are calibrated or conservative, and it remains the most accurate under a misspecified noise covariance. Finally, when the generation of entire zones goes unreported, the classical methods fail while the learned prior recovers it from cross-zone structure.

Truncated backpropagation through time reduces the computational burden of training recurrent models by restricting gradient computations to shorter temporal contexts. This induces two distinct boundary effects: missing past information perturbs the forward state evolution, while truncating the backward recursion omits future information. This motivates decoupling the interval over which gradient contributions are averaged for the parameter update from the surrounding temporal context over which they are computed. Under exponential decay of the state-transition Jacobians and mild regularity conditions, this leads to a two-sided gradient turnpike property: the error between truncated- and full-context gradient contributions decays exponentially with the distance from both context boundaries. We derive bounds for the averaged update gradient, yielding guarantees on gradient alignment and approximate full-context stationarity; under unbiased interval sampling and a Polyak-Lojasiewicz condition, these further imply a bound on the resulting optimality gap. Numerical experiments on the Wiener-Hammerstein benchmark illustrate the role of past and future context and the trade-off between predictive performance and computational cost.

The Musical Metaverse (MM) enables geographically distributed musicians, audiences, sound engineers, and AI agents to interact through synchronized audio, visual, kinematic, and haptic streams, imposing latency, synchronization, bandwidth, and scalability requirements that are difficult to satisfy with conventional bit-level communication. This paper argues that semantic communication, understood here as the transmission of musically meaningful information rather than raw audio-visual-haptic samples, provides a principled communication paradigm for the MM. We define the MM from a communication perspective and derive modality-specific require ments; propose a three-pillar framework for musical semantic communication comprising semantics extraction, semantic-aware orchestration, and cross-modal semantic synchronization; survey representative work across semantic communication, music AI and edge orchestration, identifying the gaps that prevent their integration; and propose a semantic-first reference architecture based on device-side semantic encoders, edge semantic routers, and cross-modal semantic synchronization. The resulting framework positions the MM as a concrete and demanding use case for 6G semantic communication.

Can market notices read by a large language model (LLM) improve short-horizon electricity price spike forecasts? We study five regions of Australia's National Electricity Market. A local LLM extracted features once per notice, only notices visible at the forecast origin were used, and a gradient-boosting model produced onset probabilities. In an out-of-sample development back-test (July 2022 to July 2024), notice features did not lower the 60-minute Brier score of a numeric model including the market operator's next-hour forecasts. At 24 hours they did, but rule-based features did so almost equally and attribution to notice content was not established. A locally frozen protocol, not publicly deposited, governed a retrospective single-use holdout from 15 August to 17 October 2026. At 60 minutes, the hypothesis that LLM features lower the numeric model's Brier score was not established (H1; relative Brier skill -0.09%), so the planned comparison with rule-based features was not tested (H2). At 24 hours, the hypothesis that LLM features lower the score against a text-free control was not established (H3; +0.37%, 95% CI [-9.74, 1.39], inconclusive). By the frozen wording rule the non-significant 24-hour improvement comes mainly from recalibration and cannot be attributed to notice content, although post hoc the decomposition could not separate recalibration from resolution. The 24-hour base rate was 1.56% on the holdout against 14.0% in development. With 5 onsets on 3 days and 24-hour positives in 2 of 22 three-day blocks, the holdout neither established nor excluded a 24-hour effect.

Port-Hamiltonian models describe physical systems by separating stored energy, dissipation and external inputs. Learning such models from data requires a choice of representation and fitting method. We compare using neural networks, analytic expressions and combinations of the two for representing the different components of the port-Hamiltonian system, and compare fitting the models with gradient-based optimisation or sparse regression. Testing on simulations of mechanical and electrical systems, with and without added noise, we present prediction accuracy and computational cost of the different approaches.