The Geometry of Forgetting: Temporal Knowledge Drift as an Independent Axis in LLM Representations
Authors: Rania Elbadry, Ahmed Heakl, Fan Zhang, Dani Bouch, Yuxia Wang, Preslav Nakov, Zhuohan Xie
Organizations: Mohamed bin Zayed University of Artificial Intelligence (MBZUAI) · INSAIT, Sofia University
Abstract
Large language models confidently produce outdated answers, and no existing method can detect them. We show this is not an engineering failure but a structural one: temporal drift, whether a stored fact has changed since training, is encoded as a direction in the residual stream geometrically orthogonal to both correctness and uncertainty. Any method operating on correctness or uncertainty signals is therefore blind to drift by construction. We verify this across six instruction-tuned models. A linear probe trained directly on drift labels achieves AUROC 0.83--0.95; methods based on token entropy, semantic entropy, CCS, and SAPLMA all remain near chance (0.49--0.57). Five tests confirm the geometric orthogonality: weight cosines (∣cos∣≤0.14), score correlations (∣r∣≤0.20), bidirectional null-space projection (∣Δ∣≤0.008), iterative null-space projection with k=10, and difference-of-means dissociation. Mechanistically, the MLP retrieval circuit produces identical dynamics for stale recall and confabulation (r>0.81, six models), explaining why output confidence cannot separate them. A cross-cutoff experiment holds inputs constant and varies only the model: the probe fires on the model whose training predates the fact's transition and stays silent otherwise (P(A>B)=0.975--0.998, twelve model pairs), confirming it reads model-internal knowledge state rather than input properties. Our code and datasets will be publicly released.
Large language models can store both outdated facts and newer superseding facts in their parameters, but standard prompting may still elicit the outdated answer. We formalize this problem as Parametric Temporal Conflict (PTC) and introduce Temporal Attractor Steering (TAS), a three-stage test-time intervention that detects likely conflicts, identifies a conflict-critical layer, and steers hidden states toward newer-fact representations without retraining or external retrieval. We construct an 8,746-record verified benchmark across five Wikidata relations and evaluate four open-weight language models from three families: Qwen-2.5-1.5B/7B, Mistral-7B-v0.3, and Llama-3.1-8B. Single-layer activation patching achieves answer-flip rates of 0.72-0.85 across all models. End-to-end TAS resolves 29-57% of PTC cases while preserving 85-99% accuracy on non-conflict queries, outperforming a matched ITI baseline on three of four models. These results show that outdated parametric knowledge can be selectively overridden at inference time.
Elias Hossain, Sourav Saha, Umesh Chandra Biswas +1
Large language models (LLMs) generate not only reasoning text, but also token-level confidence trajectories that record how uncertainty evolves during inference. Whether these trajectories are relevant to reasoning correctness remains unclear. Here we show that confidence trajectories encode a content-agnostic confidence geometry associated with trace-level final-answer correctness. Using only token-level confidence values, without access to the input question, reasoning text, hidden states, or external verifiers, we find that low-dimensional representations of confidence trajectories separate correct from incorrect reasoning traces. Across GSM8K, MATH, and MMLU, this geometric separation is quantitatively linked to downstream predictability: stronger clustering of correct and incorrect traces, measured by the Davies--Bouldin index, consistently corresponds to higher correctness-discrimination AUC. We further show that correctness-related information is enriched in the tail of reasoning, suggesting that late-stage confidence dynamics carry key correctness signals. We propose NeuralConf, a lightweight estimator that learns from confidence trajectories for correctness evaluation. Under a fixed trace budget, NeuralConf-derived scores improve confidence-weighted answer aggregation over majority voting, tail confidence, and other static baselines. These results reveal that LLMs expose trace-intrinsic statistical signals of correctness through their own confidence dynamics, offering a route to improve inference using information already present within generation.
Updating a language model's knowledge through fine-tuning is essential for keeping its outputs current, yet can also induce factual forgetting and new hallucinations. Prior work shows that long-tail knowledge is harder to acquire and newly memorized long-tail facts are difficult to retain during later fine-tuning. We study a complementary question: among facts that a model has encoded correctly, which are most vulnerable to collateral corruption during other updates? To investigate this question under a realistic factual distribution, we construct a large-scale graph FACTPROP of verified Wikipedia facts by linking triples that share head or tail entities, thereby preserving connections among factual knowledge. We fine-tune models on factual statements and measure correct-to-incorrect facts after each update. Our results reveal a pattern distinct from prior findings on long-tail vulnerability during acquisition and retention: among facts that models already answer correctly, those associated with highly connected entities are more likely to be corrupted by neighboring updates, and updates to such facts propagate errors more broadly. Structural popularity therefore predicts both vulnerability and downstream damage. Inspired by this finding, we propose Popularity-based Anchoring (PopAnchor), a lightweight rehearsal strategy that preserves a small set of popular facts and reduces forgetting.