arxiv: 2605.09195 · v1 · submitted 2026-05-09 · 💻 cs.AI

Recognition: no theorem link

The Geometry of Forgetting: Temporal Knowledge Drift as an Independent Axis in LLM Representations

Ahmed Heakl, Dani Bouch, Fan Zhang, Preslav Nakov, Rania Elbadry, Yuxia Wang, Zhuohan Xie

Pith reviewed 2026-05-12 01:50 UTC · model grok-4.3

classification 💻 cs.AI

keywords temporal knowledge driftLLM representationsresidual streamgeometric orthogonalityknowledge update detectionlinear probesMLP retrieval circuit

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The pith

Temporal knowledge drift is encoded as a direction in LLM residual streams that is geometrically orthogonal to correctness and uncertainty.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that whether a fact stored in an LLM has become outdated since training appears as an independent direction in the model's internal activations. This direction lies orthogonal to the signals that indicate whether an answer is correct or how uncertain the model is about it. Consequently, techniques that monitor correctness or uncertainty cannot identify drift by design. The claim is supported by a linear probe that detects drift with high accuracy while entropy-based and other standard methods perform near random, plus multiple geometric tests that confirm the separation. The same internal circuit handles both outdated facts and invented ones, which further prevents confidence measures from distinguishing them.

Core claim

Temporal drift, defined as whether a stored fact has changed since training, is encoded as a direction in the residual stream geometrically orthogonal to both correctness and uncertainty. A linear probe trained on drift labels reaches AUROC 0.83-0.95 across six models, while methods using token entropy, semantic entropy, CCS, and SAPLMA stay near chance at 0.49-0.57. Five tests verify orthogonality through low weight cosines, low score correlations, bidirectional null-space projection, iterative null-space projection, and difference-of-means dissociation. The MLP retrieval circuit produces nearly identical dynamics for stale recall and confabulation, and cross-cutoff experiments show the pro

What carries the argument

The drift direction in the residual stream, isolated by linear probes on temporal labels and verified as orthogonal via cosine similarity, correlation, and null-space projection tests.

If this is right

Any method that operates only on correctness or uncertainty signals is blind to temporal drift by construction.
The MLP retrieval circuit produces identical internal dynamics for both outdated facts and confabulations, so output confidence cannot separate them.
A probe trained on drift labels can distinguish models whose training predates a fact's change from those trained after it, even when given identical inputs.
Five independent geometric tests, including null-space projections, all confirm that the drift direction shares almost no variance with correctness or uncertainty directions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Targeting this specific direction during model updates could allow selective refresh of outdated knowledge without affecting other representations.
The same geometric separation might apply to other forms of knowledge inconsistency, such as contradictions within a single training corpus.
Internal monitoring of this axis could support systems that flag and request updates for stale information without full retraining.

Load-bearing premise

The observed geometric orthogonality between drift, correctness, and uncertainty reflects a general structural property of LLMs rather than an artifact of the six tested models or chosen facts.

What would settle it

Finding a strong correlation (r > 0.5) between a drift probe and an uncertainty or correctness measure on a new set of facts or an additional model would contradict the orthogonality claim.

Figures

Figures reproduced from arXiv: 2605.09195 by Ahmed Heakl, Dani Bouch, Fan Zhang, Preslav Nakov, Rania Elbadry, Yuxia Wang, Zhuohan Xie.

**Figure 1.** Figure 1: Drift probe score vs. fact transition year. Scores remain strongly negative for precutoff transitions and cross zero only near each model’s training cutoff (shaded), confirming the probe tracks temporal validity. Large language models produce outdated answers with the same fluency and confidence as correct ones. Asked who heads a government, runs a firm, or coaches a team in 2025, a model trained in 2022… view at source ↗

**Figure 2.** Figure 2: Drift is decoded along an axis near-orthogonal to both correctness and uncertainty (Mistral-7B, L6). Decoding is_drifted from each score gives AUROC 0.99 for drift, 0.71 for correctness, 0.54 for uncertainty; only drift carries the signal. The correctness–uncertainty correlation (r=−0.24) is the expected dependence between non-drift axes (§5); drift remains independent. output-level statistics (entropy, to… view at source ↗

**Figure 3.** Figure 3: Drift and provenance axes are jointly decodable (Llama-2, controlled layer). A probe separates STALE-RECALL from CONFABULATION at AUROC = 0.96 within the drifted class (Table 3). STABLE-CORRECT and ANACHRONISM (non-drifted cells) cluster at negative drift scores. Layer Plateau and Selection-Bias Bound. Sweeping over 27–43 layers per model introduces winner’s-curse risk. The top-5 layer span in AUROC is … view at source ↗

**Figure 4.** Figure 4: Cross-cutoff drift probe scores on byte-identical inputs. No Existing Method Detects Temporal Drift. We evaluate a comprehensive set of baselines on the controlled (post-cutoff) split ( [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

read the original 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 ($|\cos| \leq 0.14$), score correlations ($|r| \leq 0.20$), bidirectional null-space projection ($|\Delta| \leq 0.008$), 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Temporal drift shows up as its own orthogonal direction in the residual stream, separate from correctness and uncertainty, with several controls that make the claim worth checking.

read the letter

The core point is that outdated facts are not just low-confidence or incorrect outputs; they sit along a distinct direction in the model's activations. A linear probe trained on drift labels reaches AUROC 0.83-0.95 while entropy, CCS, and SAPLMA stay near chance. Five geometric tests line up on orthogonality, the MLP circuit behaves the same for stale recall and confabulation, and the cross-cutoff design keeps the input fixed while swapping models to isolate internal state. That last control is the cleanest part of the work and directly addresses whether the probe is reading model knowledge rather than surface features of the question.

Referee Report

2 major / 2 minor

Summary. The paper claims that temporal knowledge drift (whether a stored fact has changed since an LLM's training) is encoded as a direction in the residual stream that is geometrically orthogonal to directions for correctness and uncertainty. This structural property explains why existing detection methods fail, as shown by linear probes achieving AUROC 0.83-0.95 on drift labels while token entropy, semantic entropy, CCS, and SAPLMA remain near chance (0.49-0.57); five geometric tests (cosines, correlations, null-space projections, difference-of-means) confirm orthogonality; MLP retrieval circuits show identical dynamics for stale recall and confabulation; and cross-cutoff experiments (fixed inputs, varying model training dates) isolate internal state with high consistency (P(A>B)=0.975-0.998).

Significance. If the central claim holds after addressing methodological gaps, the work would be significant for LLM interpretability: it identifies an independent representational axis for temporal drift, provides a mechanistic explanation via circuit analysis, and demonstrates why correctness/uncertainty-based methods are blind to it by construction. Strengths include the convergent multi-test evidence, the cross-cutoff design that holds inputs fixed to isolate model-internal knowledge, and the planned public release of code and datasets, which supports reproducibility.

major comments (2)

[Methods] Methods/Experimental Setup: The manuscript provides no details on dataset construction (fact selection criteria, transition date determination, label verification process), model specifications (exact sizes, training cutoffs for the six instruction-tuned models), or controls for confounds (e.g., input phrasing effects, fact popularity). These omissions are load-bearing because the orthogonality claim and probe performance depend on the independence and quality of the drift labels and the representativeness of the tested models.
[Geometric Tests] Geometric Orthogonality Tests (Abstract and §5): The five tests report low values (e.g., |cos| ≤ 0.14, |r| ≤ 0.20, |Δ| ≤ 0.008), but the paper does not specify whether thresholds were pre-registered, provide p-values or confidence intervals for the dissociation, or test sensitivity to probe training details. This weakens the claim that orthogonality is a robust structural property rather than tied to the specific linear probe or chosen facts.

minor comments (2)

[Abstract] Abstract: The range of AUROC values (0.83--0.95) and model count (six) are reported without naming the models or providing a table of per-model results, which would aid immediate assessment of consistency.
[Abstract] Notation: The cross-cutoff probability P(A>B) is introduced without a brief definition or reference to the exact statistical test used across the twelve model pairs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their insightful comments and the opportunity to clarify and strengthen our work. Below, we provide point-by-point responses to the major comments, indicating the revisions we will implement.

read point-by-point responses

Referee: Methods/Experimental Setup: The manuscript provides no details on dataset construction (fact selection criteria, transition date determination, label verification process), model specifications (exact sizes, training cutoffs for the six instruction-tuned models), or controls for confounds (e.g., input phrasing effects, fact popularity). These omissions are load-bearing because the orthogonality claim and probe performance depend on the independence and quality of the drift labels and the representativeness of the tested models.

Authors: We concur that more comprehensive details in the Methods section are necessary for reproducibility and to substantiate the claims. In the revised manuscript, we will include: detailed fact selection criteria, emphasizing facts with clear, documented transition dates from sources like official records and edit histories; the methodology for determining transition dates through multi-source verification; and the label verification process, including manual review and agreement metrics on sampled facts. Model specifications will be expanded to list all six models with their exact parameter sizes and training data cutoffs. For confounds, we will describe our controls, including the use of varied input phrasings for each fact and stratification by estimated fact popularity. These details, along with the promised public release of code and datasets, will allow readers to fully assess the quality of the drift labels and the generalizability across models. We believe this will resolve the concerns regarding the load-bearing aspects of the experimental setup. revision: yes
Referee: Geometric Orthogonality Tests (Abstract and §5): The five tests report low values (e.g., |cos| ≤ 0.14, |r| ≤ 0.20, |Δ| ≤ 0.008), but the paper does not specify whether thresholds were pre-registered, provide p-values or confidence intervals for the dissociation, or test sensitivity to probe training details. This weakens the claim that orthogonality is a robust structural property rather than tied to the specific linear probe or chosen facts.

Authors: The geometric tests were designed to provide convergent evidence of orthogonality using multiple independent methods. The thresholds reflect standard practices in representation geometry where correlations below 0.2 indicate substantial independence. We did not pre-register specific thresholds, as the work involved iterative exploration of the representational structure. To address this, the revised paper will incorporate p-values derived from permutation tests for each metric, along with bootstrap-derived confidence intervals to quantify the precision of the dissociation. Additionally, we will report sensitivity analyses that vary probe training parameters, such as the number of training examples and regularization, as well as different random subsets of facts, to confirm that the orthogonality holds robustly. The cross-cutoff experiments, which isolate model-internal states without relying on probes, provide complementary evidence that is less sensitive to these choices. These enhancements will bolster the claim of a robust structural property. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation is empirically self-contained

full rationale

The paper's claims rest on direct empirical measurements across six models: linear-probe AUROCs on drift labels (0.83-0.95), near-chance performance of entropy/CCS/SAPLMA baselines (0.49-0.57), five independent geometric tests (cosines ≤0.14, correlations ≤0.20, bidirectional/iterative null-space projections ≤0.008, difference-of-means), MLP circuit correlations (r>0.81), and the cross-cutoff design that holds inputs fixed while varying only model training dates (P(A>B)=0.975-0.998). None of these steps reduce by construction to fitted parameters, self-citations, or definitional renaming; orthogonality is measured rather than assumed, and the cross-cutoff supplies an external falsification check on internal state. The central claim therefore remains independent of its own inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The claim rests on empirical linear separability of drift in activation space and standard vector-space assumptions; no new physical entities or ad-hoc constants are introduced.

free parameters (1)

linear probe weights
Weights are fitted to drift labels on the six models.

axioms (1)

standard math Residual stream activations form a vector space in which directions can be meaningfully orthogonal.
Invoked when reporting cosine similarities and null-space projections.

pith-pipeline@v0.9.0 · 5608 in / 1261 out tokens · 58095 ms · 2026-05-12T01:50:46.767723+00:00 · methodology

discussion (0)

Reference graph

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Institutional review board (IRB) approvals or equivalent for research with human subjects Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or ...

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