Joint-Embedding Predictive Architectures (JEPAs) learn compact latent world models by predicting future embeddings, but no single coordinate of the latent is designated to encode task progression. We carve the JEPA latent into two orthogonal subspaces with disjoint roles: a low-dimensional progression subspace shaped by a cosine-margin triplet loss, and a high-dimensional content subspace regularised by the existing SIGReg objective of LeWM. We prove that the two anti-collapse forces act on disjoint coordinates, so they compose additively rather than competing on the same dimensions. Our method, SD-JEPA improves over the LeWM baseline on the majority of its control benchmarks at matched compute, and outperforms the strongest non-LeWM JEPA baseline on Push-T; a subspace-ablation falsifier confirms the split is the load-bearing ingredient. Beyond planning, the resulting 1-D angular progression coordinate functions as a scene-aware compass on the latent. It advances with task progress, regresses when the agent backtracks, and under controlled perturbations both spikes and relocalises to a semantically appropriate new task-phase sector, separating the moment of surprise from its meaning in a way that prediction-error scalars cannot. Three quantitative tests back this up: |Δθ_t| outperforms the standard latent-prediction-error surprise at localising semantic events on 40 held-out cube episodes by up to +0.18 pooled AUROC (97.5
This work presents numerical experiments aimed at verifying solutions of Poisson’s equation using two existing methodologies. First, block-diagonalization is employed to block-encode the matrix derived from Poisson’s equation through the finite difference method (FDM), significantly improving computational complexity from N to log (N) , where N is the matrix size. Second, the Quantum Singular Value Transformation (QSVT) algorithm is applied to invert the matrix. However, while block-diagonalization improves the complexity in N, QSVT introduces a bottleneck due to its linear dependency on the condition number κ , which grows exponentially with N, posing challenges for large-scale problems. As far as we know, this is the first numerical experiments solving problems with matrix size N=1024 and condition number κ =500000 ; the largest matrix size and condition number from existing works are 16 and <100 , respectively.
Estimating the health state of turbofan engines is a challenging ill-posed inverse problem, hindered by sparse sensing and complex nonlinear thermodynamics. Research in this area remains fragmented, with comparisons limited by the use of unrealistic datasets and insufficient exploration of the exploitation of temporal information. This work investigates how to recover component-level health indicators from operational sensor data under realistic degradation and maintenance patterns. To support this study, we introduce a new dataset that incorporates industry-oriented complexities such as maintenance events and usage changes. Using this dataset, we establish an initial benchmark that compares steady-state and nonstationary data-driven models, and Bayesian filters, classic families of methods used to solve this problem. In addition to this benchmark, we introduce self-supervised learning (SSL) approaches that learn latent representations without access to true health labels, a scenario reflective of real-world operational constraints. By comparing the downstream estimation performance of these unsupervised representations against the direct prediction baselines, we establish a practical lower bound on the difficulty of solving this inverse problem. Our results reveal that traditional filters remain strong baselines, while SSL methods reveal the intrinsic complexity of health estimation and highlight the need for more advanced and interpretable inference strategies. For reproducibility, both the generated dataset and the implementation used in this work are made accessible.
Post-quantum migration increases WebPKI authentication cost, but authenticating a compressed certificate object does not by itself preserve the mutable authorization context under which a relying party accepts it. We formalize context closure: the authenticated projection accepted by a verifier must determine the selected authorization semantics it claims, relative to declared source contracts and event-coverage witnesses. We instantiate this idea with , a two-plane post-quantum construction that authenticates mutable CA-context state in an update plane while the warm path carries only state-local dependency references selected by explicit profile negotiation. In a pinned CCADB reconstruction, we obtain 44,912 path/view contexts and 16,858 physical CA lineages across Apple, Chrome, Microsoft, and Mozilla views. The core compiler yields m_50=6, m_95=16, and m_max=18 typed dependencies. A warm LR+ selector therefore costs 296, 776, and 872 bytes at median, p95, and maximum, compared with 3,842, 5,932, and 6,350 bytes for a one-signature stateless bundle carrying the same dependency vector. The retained all-view closure state is 16.15 MB, and per-view lifecycle crossovers range from 19.60 to 50.41 median-path warm authentications/day under the stated checkpoint and update model. The implementation and evaluation artifact are available at https://github.com/nserser/LR-WebPKI
