Timescale Dependent Label Inconsistency

• TsDLI is a form of supervision mismatch where labels reliable at one temporal scale become unreliable at finer scales due to semantic shifts.
• It manifests across domains such as EEG emotion recognition, defect prediction, and vulnerability detection with time-varying noise and misalignment.
• Mitigation strategies include probabilistic marginalization, time-indexed noise correction, and transformed supervision frameworks to improve model robustness.

Searching arXiv for the cited papers and TsDLI-related work to ground the article with up-to-date references. arXiv search query: "Timescale Dependent Label Inconsistency" Timescale Dependent Label Inconsistency (TsDLI) denotes a class of supervision mismatches in which a label is reliable at one temporal scale but unreliable, incomplete, or semantically altered at another. The phenomenon is explicit in EEG emotion recognition, where a single trial-level rating is propagated to many short EEG segments although the latent emotional state varies over time, but closely related formulations also appear as temporally imprecise event timestamps, time-varying label noise, cross-version inconsistent labels, and calendar-time label changes in security datasets. Across these literatures, TsDLI is not a single noise model but a family of temporal label pathologies induced by resolution mismatch, annotation delay, evolving knowledge, or time-indexed corruption mechanisms (Zeng et al., 15 Jul 2025, Adams et al., 2016, Nagaraj et al., 2024, Liu et al., 2021, Paramitha et al., 13 Jun 2025).

1. Conceptual scope and defining characteristics

In its most direct formulation, TsDLI arises when labels are collected at a coarse timescale and then reused as if they were exact at a finer timescale. In EEG emotion recognition, a subject provides one global label $y^G$ for an entire trial, while the true latent state $y(t)$ fluctuates during the trial. Training on short windows by assigning every segment the same global label therefore creates a structural inconsistency: the label is meaningful as a whole-trial summary but not necessarily as an instantaneous target. The associated “Full Expectation Assumption” states that

$Y_G = \int_t p(t)\,Y(t)\,dt = E_t[Y(t)],$

so the global rating is interpreted as an expectation over time rather than a constant local state (Zeng et al., 15 Jul 2025).

A second formulation treats TsDLI as explicitly time-varying corruption. In sequential classification, temporal label noise is formalized by a time-indexed confusion matrix $\bm{Q}(t)$, with $[\bm{Q}_t]_{ij} = q_t(\tilde y_t=j \mid y_t=i)$, so the noisy posterior satisfies

$$p(\tilde y_t\mid x_{1:t}) = \bm{Q}_t^\top\, p(y_t\mid x_{1:t}).$$

Here the inconsistency is not only that labels are noisy, but that the noise profile itself changes with time through periodicity, decay, growth, or mixed class-conditional dynamics (Nagaraj et al., 2024).

A third formulation appears in event detection from temporally imprecise supervision. There, observed timestamps are not identical to true event times; they are jittered observations around latent instance times, and missed or spurious observations are permitted. Fine-scale instance labels are therefore unreliable under naive alignment, whereas coarser temporal neighborhoods remain informative (Adams et al., 2016).

A fourth formulation is version- or calendar-time dependent. In multi-version defect prediction, the same source code can receive different labels in different versions, producing inconsistent labels across releases. In vulnerability detection, the label of a code fragment depends on when the vulnerability becomes known: a fragment treated as negative at time $t$ may become positive at time $t' > t$ once a CVE is published. This shifts TsDLI from annotation imprecision to knowledge-dependent label evolution (Liu et al., 2021, Paramitha et al., 13 Jun 2025).

Taken together, these formulations suggest that TsDLI is best understood as structured temporal label inconsistency rather than ordinary i.i.d. mislabeling. The governing issue is that the semantic validity of a label depends on temporal resolution, observation time, or both.

2. Formal representations

One canonical probabilistic representation models latent instance labels $y_i$, latent observation counts $o_i$, and observed noisy timestamps $y(t)$0 given instance features $y(t)$1 and instance times $y(t)$2. The joint model is

$y(t)$3

with a base classifier $y(t)$4, an observation-count model $y(t)$5, and a timestamp noise model $y(t)$6. In the main instantiation, $y(t)$7, while real-data experiments also use a Gaussian mixture. The observed-data likelihood marginalizes latent labels and counts, which makes temporal alignment itself a latent-variable problem rather than a preprocessing step (Adams et al., 2016).

Time-varying label corruption uses a different abstraction. For sequence labels $y(t)$8 and noisy observations $y(t)$9, the temporal label noise function is a matrix-valued map

$Y_G = \int_t p(t)\,Y(t)\,dt = E_t[Y(t)],$0

with row-stochastic, diagonally dominant $Y_G = \int_t p(t)\,Y(t)\,dt = E_t[Y(t)],$1. Under the paper’s assumptions,

$Y_G = \int_t p(t)\,Y(t)\,dt = E_t[Y(t)],$2

so time dependence enters entirely through the confusion matrix at each $Y_G = \int_t p(t)\,Y(t)\,dt = E_t[Y(t)],$3. This formalism captures per-time-step corruption but also supports smooth or periodic global dynamics in the noise process (Nagaraj et al., 2024).

Calendar-time TsDLI can be written as a time-indexed label function. A formalization used for vulnerability detection defines

$Y_G = \int_t p(t)\,Y(t)\,dt = E_t[Y(t)],$4

with an additional undefined state before code availability in the fuller version of the construction. This makes explicit that the same input $Y_G = \int_t p(t)\,Y(t)\,dt = E_t[Y(t)],$5 may change label across time solely because the underlying vulnerability becomes known later (Paramitha et al., 13 Jun 2025).

A related but distinct representation appears in EEG regularization. The predicted local outputs $Y_G = \int_t p(t)\,Y(t)\,dt = E_t[Y(t)],$6 live on a discrete emotion graph with Laplacian $Y_G = \int_t p(t)\,Y(t)\,dt = E_t[Y(t)],$7 and pseudoinverse $Y_G = \int_t p(t)\,Y(t)\,dt = E_t[Y(t)],$8. The graph metric encodes that transitions between nearby emotion levels are cheaper than large jumps, introducing a geometry over labels rather than a confusion process (Zeng et al., 15 Jul 2025).

3. Methodological responses

Probabilistic marginalization is the central response to temporally imprecise event labels. Instead of snapping each noisy timestamp to the nearest instance, the detection model sums over all consistent alignments. Posterior marginals such as $Y_G = \int_t p(t)\,Y(t)\,dt = E_t[Y(t)],$9, $\bm{Q}(t)$0, and $\bm{Q}(t)$1 are computed by a forward–backward style dynamic program with forward terms $\bm{Q}(t)$2 and backward terms $\bm{Q}(t)$3. The overall likelihood is $\bm{Q}(t)$4. Computational complexity is $\bm{Q}(t)$5 in general and $\bm{Q}(t)$6 when each instance generates at most one observation. Training uses gradient-based maximization of the marginal log-likelihood rather than EM (Adams et al., 2016).

When label corruption is modeled by $\bm{Q}(t)$7, the principal correction mechanism is the forward sequence loss

$\bm{Q}(t)$8

which is noise-robust when $\bm{Q}(t)$9 is known. Three estimation strategies are proposed when it is unknown: TENOR, which jointly learns $[\bm{Q}_t]_{ij} = q_t(\tilde y_t=j \mid y_t=i)$0 and a continuous neural parameterization $[\bm{Q}_t]_{ij} = q_t(\tilde y_t=j \mid y_t=i)$1 under an augmented Lagrangian and minimum-volume regularization; VolMinTime, which learns an independent $[\bm{Q}_t]_{ij} = q_t(\tilde y_t=j \mid y_t=i)$2 at each time step; and AnchorTime, which estimates $[\bm{Q}_t]_{ij} = q_t(\tilde y_t=j \mid y_t=i)$3 from per-time anchor points and then retrains with forward correction. Backward correction is also derived but reported as numerically unstable in practice (Nagaraj et al., 2024).

In forecasting, the remedy is not a noise process but a transformed supervision space. TransDF computes an SVD of the normalized label matrix $[\bm{Q}_t]_{ij} = q_t(\tilde y_t=j \mid y_t=i)$4, yielding $[\bm{Q}_t]_{ij} = q_t(\tilde y_t=j \mid y_t=i)$5, and projects labels and predictions into decorrelated components $[\bm{Q}_t]_{ij} = q_t(\tilde y_t=j \mid y_t=i)$6, $[\bm{Q}_t]_{ij} = q_t(\tilde y_t=j \mid y_t=i)$7. The transformed loss aligns only the top $[\bm{Q}_t]_{ij} = q_t(\tilde y_t=j \mid y_t=i)$8 components,

$[\bm{Q}_t]_{ij} = q_t(\tilde y_t=j \mid y_t=i)$9

and is combined with temporal MSE through

$$p(\tilde y_t\mid x_{1:t}) = \bm{Q}_t^\top\, p(y_t\mid x_{1:t}).$$0

This is presented as a response to label autocorrelation and excessive task count across forecast horizons; a plausible implication is that it addresses a TsDLI-adjacent inconsistency between per-step supervision and the actual sequence-level covariance structure (Wang et al., 23 May 2025).

In EEG emotion recognition, two graph-theoretic regularizers are proposed. Local Variation Loss penalizes adjacent prediction differences in commute-time distance,

$$p(\tilde y_t\mid x_{1:t}) = \bm{Q}_t^\top\, p(y_t\mid x_{1:t}).$$1

while Local-Global Consistency Loss penalizes dispersion around the mean prediction,

$$p(\tilde y_t\mid x_{1:t}) = \bm{Q}_t^\top\, p(y_t\mid x_{1:t}).$$2

Both are architecture-agnostic and are theoretically equivalent up to scaling constants when $$p(\tilde y_t\mid x_{1:t}) = \bm{Q}_t^\top\, p(y_t\mid x_{1:t}).$$3 is positive semidefinite (Zeng et al., 15 Jul 2025).

Data-centric responses also appear. TSILI detects inconsistent labels in multi-version defect datasets by grouping modules across versions, normalizing code after removing comments and collapsing whitespace, and marking identical code fragments with different labels as inconsistent. In vulnerability detection, a complementary strategy restructures a retrospective dataset into time-indexed train, retrospective-test, and perspective-test splits so that both training and evaluation respect what labels are available at time $$p(\tilde y_t\mid x_{1:t}) = \bm{Q}_t^\top\, p(y_t\mid x_{1:t}).$$4 (Liu et al., 2021, Paramitha et al., 13 Jun 2025).

4. Empirical manifestations across domains

On real mobile-health data, learning from temporally imprecise labels outperforms several alternatives, including assuming timestamps are noise-free, transforming the problem into multiple instance learning, and training on manually realigned labels. The experiments use two smoking-puff datasets: mPuff with 4 subjects, 13 sessions, 179 positive and 3180 negative instances, and puffMarker with 6 subjects, 30 sessions, 305 positive and 7623 negative instances. Under synthetic noise, increasing timestamp jitter $$p(\tilde y_t\mid x_{1:t}) = \bm{Q}_t^\top\, p(y_t\mid x_{1:t}).$$5 or decreasing observation probability $$p(\tilde y_t\mid x_{1:t}) = \bm{Q}_t^\top\, p(y_t\mid x_{1:t}).$$6 degrades naive snapping and MI strongly, while the probabilistic model degrades much more slowly; even at $$p(\tilde y_t\mid x_{1:t}) = \bm{Q}_t^\top\, p(y_t\mid x_{1:t}).$$7, only about 65% of true positives retain positive labels under naive snapping (Adams et al., 2016).

For per-time-step temporal label noise, experiments span HAR, HAR70, EEG Eye State, EEG Sleep staging, and HMM-based synthetic sequences with static, exponential, linear, sigmoidal, sinusoidal, and mixed class-conditional noise. Temporal methods outperform static ones across these settings, and TENOR consistently attains the lowest reconstruction error $$p(\tilde y_t\mid x_{1:t}) = \bm{Q}_t^\top\, p(y_t\mid x_{1:t}).$$8 together with the highest clean-test accuracy. The reported pattern is that explicitly modeling the time dependence of the confusion process becomes increasingly beneficial as noise severity grows (Nagaraj et al., 2024).

In long-horizon forecasting, the empirical issue is not mislabeled samples but inconsistent horizon-wise supervision under strong autocorrelation. TransDF is evaluated on ETT, ECL, Traffic, Weather, and PEMS benchmarks and improves multiple baseline architectures. One reported example is ETTh1 with Fredformer, where average MSE decreases from 0.447 under DF to 0.431 under TransDF. Ablations show that both decorrelation and target-count reduction matter: keeping all decorrelated components improves over DF, random reduction alone also improves over DF, and the full combination performs best (Wang et al., 23 May 2025).

In software defect prediction, inconsistent labels are pervasive. Across five multi-version datasets, 94% of versions have $$p(\tilde y_t\mid x_{1:t}) = \bm{Q}_t^\top\, p(y_t\mid x_{1:t}).$$9, average $t$0 is about 9%, and some versions reach 70%; 86% of versions have $t$1, average $t$2 is about 16%, the maximum is about 74%, and average $t$3 is about 8%. These inconsistencies significantly affect both model performance and interpretation: in cross-version defect prediction, average mean $t$4 includes approximately 6.25% for F1, 11.57% for RI, 42.49% for RR, and 14.12% for ACC, while feature-importance rankings shift substantially between models trained with and without inconsistent instances (Liu et al., 2021).

In vulnerability detection, time-aware evaluation reveals a different manifestation of TsDLI. Datasets constructed from BigVul and VulDeepecker are restructured into yearly slices with retrospective training and both retrospective and perspective testing. The trend analysis reports that performance changes inconsistently across years rather than improving monotonically, and the Mann–Kendall test finds no significant monotonic trend for precision on perspective testing in any dataset-model combination and only one significant increasing recall trend, for VulDeepecker on its NVD dataset. The recall gap between retrospective and perspective testing is typically negative, indicating that retrospective evaluation is systematically optimistic (Paramitha et al., 13 Jun 2025).

In EEG emotion recognition, experiments on DREAMER and DEAP under 20% and 40% symmetric label noise show that LVL achieves the best aggregate rank across backbones and metrics, while LGCL frequently ranks second. The qualitative gains are consistent with the intended TsDLI mitigation: fewer and smaller jumps in predicted trajectories, lower local fluctuation, and improved local-global coherence (Zeng et al., 15 Jul 2025).

5. Evaluation and interpretation

TsDLI complicates evaluation because a high score against noisy or temporally mismatched labels does not imply that the model respects local dynamics, future label evolution, or cross-timescale consistency. Different subfields have therefore adopted different diagnostic protocols.

In EEG, standard F1 and Top-2 accuracy are supplemented by temporal-coherence metrics. The local fluctuation statistic is

$t$5

and connected-components analysis over thresholds $t$6 yields $t$7, the critical threshold

$t$8

and the area $t$9 under the $t' > t$0 curve. A weighted Borda Count gives equal total weight to quantitative and qualitative metrics, so accuracy and temporal interpretability are jointly assessed rather than traded off implicitly (Zeng et al., 15 Jul 2025).

In defect prediction, the evaluation protocol explicitly compares noisy-training and cleaned-training models on the same cleaned test set using precision, recall, F1, AUC, ER, RI, AP, RR, Popt, and ACC. The paper defines both an absolute relative change

$t' > t$1

and a performance gain ratio $t' > t$2 relative to a random model, then uses 1000 bootstrap samples and 95% confidence intervals to test whether inconsistent labels materially change results (Liu et al., 2021).

In vulnerability detection, evaluation is intrinsically temporal. For each timeline date $t' > t$3, the methodology constructs a retrospective test set using labels known by $t' > t$4 and a perspective test set using labels that become known in $t' > t$5. Temporal stability is then assessed with the Mann–Kendall statistic

$t' > t$6

with the corresponding standardized $t' > t$7 statistic and Bonferroni-adjusted significance. This protocol evaluates whether a model actually improves as more data and more stable labels become available, rather than only whether it fits a final retrospective labeling function (Paramitha et al., 13 Jun 2025).

A broader interpretive point follows from these studies. TsDLI is often mistaken for generic noisy labeling, but the evidence indicates that the central failure mode is mismatch between the semantics of the label and the temporal granularity or temporal vantage point at which it is used. This helps explain why simple relabeling, coarse bagging, or static robust-loss methods are often insufficient.

6. Limitations, misconceptions, and open directions

A common misconception is that TsDLI is reducible to annotation error. The defect-prediction literature shows that inconsistent labels can arise from genuine temporal mechanisms, such as extrinsic bugs, as well as from mislabeling due to SZZ-based, time-window, or affected-version collection procedures. Similarly, in vulnerability detection, a past negative label may later become positive not because the sample changed, but because the knowledge state changed (Liu et al., 2021, Paramitha et al., 13 Jun 2025).

Another misconception is that temporal modeling at a single scale fully resolves the problem. Existing formulations usually fix one temporal abstraction: instance timestamps in event detection, per-time-step confusion matrices in sequential classification, a static label covariance transform in forecasting, or a fixed emotion graph in EEG. The papers themselves identify missing structure, including multiple annotators, non-stationary noise, event durations, richer sequential base models, explicit multi-timescale decompositions, context-dependent corruption $t' > t$8, sequence-specific or annotator-specific noise functions, and finer-grained time-aware evaluation protocols (Adams et al., 2016, Nagaraj et al., 2024).

Methodological limitations are also domain-specific. Temporal-noise estimation assumes feature–noise independence given clean labels and often a single global $t' > t$9 shared across sequences. TransDF uses a static linear transform and may be suboptimal under regime shifts or when low-variance components are semantically critical. LVL and LGCL regularize predictions rather than recovering true local labels, and their emotion graph is hand-designed. Time-aware vulnerability evaluation still relies on approximations to code availability dates and yearly slicing because finer intervals would produce too few events in current datasets (Wang et al., 23 May 2025, Zeng et al., 15 Jul 2025, Paramitha et al., 13 Jun 2025).

The cumulative literature suggests several durable research directions. One is explicit multi-timescale modeling, in which slow drift, periodic variation, local jitter, and calendar-time label changes are represented jointly rather than separately. Another is integrating temporal label uncertainty directly into training objectives rather than treating it as a preprocessing nuisance. A third is re-examining empirical conclusions obtained from datasets with strong temporal inconsistency, since the reported performance, identified positives, and inferred feature importance can all shift materially when TsDLI is acknowledged (Nagaraj et al., 2024, Liu et al., 2021).

TsDLI therefore occupies a broad position within modern machine learning for time-dependent data: it links weak supervision, noisy-label learning, temporal alignment, nonstationary evaluation, and structured regularization. The unifying principle is that the validity of supervision is itself time-indexed, so any method that ignores temporal scale in label construction, corruption, or evaluation risks optimizing against the wrong target.