Large language models increasingly answer questions grounded in structured spatial data such as road networks: in navigation assistants, in conversational interfaces to geographic information, and in tools that maintain digital maps. Their answers are fluent but not verifiable, and in spatial domains a claim about a turn restriction, a lane, or an opening time is either consistent with the map or it is not. This survey reviews the methods by which such claims can be machine-checked. We organize the literature along an argument: models cannot reliably verify their own outputs; external checkers such as program execution and symbolic solvers demonstrably can; constrained decoding guarantees syntactic but not factual validity; execution against the data is the established gold standard of evaluation in the text-to-query literature; and knowledge-graph grounding already supports detect-verify-repair pipelines. We then examine the spatial domain specifically and find a documented gap: existing geospatial benchmarks measure model capability, and none verifies model claims against lane-level, temporal, or version-aware map data. We synthesize a taxonomy of verification mechanisms, compare existing benchmarks by oracle type, and outline a research agenda toward validity contracts and certificates for spatial claims that remain checkable as the underlying map evolves.
Language models are entering systems whose failures matter: vehicles, industrial toolchains, and autonomous agents acting on real infrastructure. At the same time, emerging regulation and safety standards demand not merely safe behavior but evidence of it that a third party can re-check. This survey traces a single architectural idea across three decades of research: an untrusted, powerful component is guarded at runtime by a small, verifiable one, and every intervention leaves evidence. We follow the idea from proof-carrying code, the Simplex architecture, and shielding for learned agents, through runtime monitors for neural components, to its present forms: generate and-verify systems in which a symbolic engine certifies every step of a model’s output, and runtime guardrails that enforce policies over language-model agents. We synthesize a spectrum of verification strength, from statistical judgment to kernel checked proof, analyze which strength each application class and regulatory obligation requires, and identify the open problem of assurance over large, versioned factual world models.
Contemporary sustainability practices in the built environment often focus narrowly on reducing short-term impacts within the boundaries of individual buildings. This Special Issue aims to challenge that paradigm by proposing a broader, resource-centric approach grounded in long-term system balance and post-fossil logic. It argues that sustainability should not merely mitigate harm but actively support resource regeneration. Key issues include the flawed concept of non-renewable resources, the obsolescence of primary energy metrics, insufficient system boundaries, and the undervaluation of residual material impact. Drawing on historical analogies and real-world observations, the paper outlines a framework for a regenerative built environment—where buildings take responsibility for their energy and material footprints and contribute positively over time. It concludes that truly sustainable design must be based on predictable, annual resource budgets and a holistic integration of material, ecological, and human systems. It requires re-inventing the way we evaluate and organize our built environment.
Humans excel at lifelong learning, as the brain has evolved to be robust to distribution shifts and noise in our ever-changing environment. Deep neural networks (DNNs), however, exhibit catastrophic forgetting and the learned representations drift drastically as they encounter a new task. This alludes to a different error-based learning mechanism in the brain. Unlike DNNs, where learning scales linearly with the magnitude of the error, the sensitivity to errors in the brain decreases as a function of their magnitude. To this end, we propose \textit{ESMER} which employs a principled mechanism to modulate error sensitivity in a dual-memory rehearsal-based system. Concretely, it maintains a memory of past errors and uses it to modify the learning dynamics so that the model learns more from small consistent errors compared to large sudden errors. We also propose \textit{Error-Sensitive Reservoir Sampling} to maintain episodic memory, which leverages the error history to pre-select low-loss samples as candidates for the buffer, which are better suited for retaining information. Empirical results show that ESMER effectively reduces forgetting and abrupt drift in representations at the task boundary by gradually adapting to the new task while consolidating knowledge. Remarkably, it also enables the model to learn under high levels of label noise, which is ubiquitous in real-world data streams.
