UAR-LoRA: Uncertainty-Aware Rank-Adaptive Low-Rank Adaptation for Lifelong Knowledge Editing

Lifelong knowledge editing keeps a deployed large language model factually current one edit at a time, so thousands of corrections must accumulate without eroding earlier edits or unrelated knowledge. Existing low-rank adapter editors do not control, for each arriving edit, how much capacity its expert takes, which queries reach it and where it sits: a rank fixed before the stream starves hard corrections, a router without a calibrated threshold serves queries the pool should leave to the frozen base, and randomly initialised experts overlap earlier ones. We propose UAR-LoRA, an uncertainty-aware, rank-adaptive framework that treats capacity, admissibility and geometry as three conditions of one heuristic capacity-coherence criterion and meets them as each expert enters the pool. An Entropy Probe and Adaptive Rank Selector sizes each expert from the frozen base's predictive entropy, a Confidence-Gated Router returns queries below a calibrated threshold to the frozen base, and a Rank-Aware Orthogonal Initialiser places each new expert in directions no earlier expert occupies while free ones remain, with a truncated-SVD fallback once they run out. Averaged over three backbones on CounterFact at $T=1000$, UAR-LoRA reaches mean Reliability $92.9$ against $90.4$ for ELDER, and on LLaMA-2-7B it lowers Expected Calibration Error from $0.19$ to $0.11$ at a $0.44\times$ trainable-parameter ratio relative to fixed rank-$32$ LoRA. No single-module variant exceeds $91.0$ Reliability against $93.0$ with all three, and the probe matches a fixed rank of $32$ at $0.44\times$ rather than $1.09\times$. Forgetting also accumulates more slowly: over $5000$ ZsRE edits UAR-LoRA retains $94.1$ Reliability where ELDER falls to $86.2$, losing $2.4$ points from the first edit against ELDER's $7.8$.