arxiv: 2605.08153 · v1 · submitted 2026-05-04 · 💻 cs.LG · cs.GT

Recognition: 2 theorem links

· Lean Theorem

Temporal-Decay Shapley: A Time-Aware Data Valuation Framework for Time-Series Data

Chuwen Pang , Bing Mi , Kongyang Chen

Authors on Pith no claims yet

Pith reviewed 2026-05-12 03:13 UTC · model grok-4.3

classification 💻 cs.LG cs.GT

keywords temporal decayShapley valuetime-series datadata valuationnoise detectionmulti-scale fusionmachine learning

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The pith

Temporal decay in Shapley values yields more accurate valuations for time-series training samples.

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

This paper argues that standard data valuation techniques overlook how the usefulness of time-series samples shifts with time, leading to suboptimal results when selecting data or spotting noise. The authors address this by embedding decay mechanisms that down-weight older samples and a fusion strategy that blends insights from multiple time scales into the Shapley computation. If the approach holds, machine learning pipelines for sequential data can select training examples more reliably, improving model performance while reducing the drag from outdated or corrupted observations. Sympathetic readers would see this as closing a practical gap for applications that rely on evolving streams such as forecasting or sensor monitoring.

Core claim

The authors establish that modifying the Shapley value formula with exponential or power-exponential decay weights, plus an adaptive multi-scale fusion step that balances short-term and long-term contributions, produces sample valuations that better reflect the time-varying importance of data points in sequential datasets.

What carries the argument

Temporal decay weights inserted into the Shapley value summation, using exponential or power-exponential functions, together with parallel multi-scale valuation and sample-level adaptive fusion.

If this is right

The methods outperform traditional Shapley approaches on noise detection and high-value data identification tasks.
Performance gains become more pronounced in settings with strong temporal dependencies.
Multi-scale fusion allows effective balancing of recent hotspot samples against longer-term foundational ones.
Overall robustness of data valuation increases for time-series machine learning workflows.

Where Pith is reading between the lines

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

Similar decay adjustments could be tested on other non-stationary data such as video frames or event streams to check if the gains generalize.
The framework suggests data retention policies for time-series archives should prioritize recent samples according to measured decay rates.
Practitioners might integrate these valuations into active learning loops to decide which new observations to keep versus discard over long deployments.

Load-bearing premise

Sample value in time-series data follows an exponential or power-exponential decay whose parameters can be set without introducing new bias, and a multi-scale rule can correctly combine short-term and long-term effects.

What would settle it

On a synthetic time-series dataset engineered with known ground-truth decay rates and labeled noise, the proposed methods would fail to rank high-value and noisy samples more accurately than non-temporal Shapley baselines.

Figures

Figures reproduced from arXiv: 2605.08153 by Bing Mi, Chuwen Pang, Kongyang Chen.

**Figure 1.** Figure 1: Overview of the temporal Shapley valuation framework. The upper temporal pathway maps sample freshness or staleness to temporal weights, while the lower utility pathway provides marginal utilities. The two pathways are combined in the Shapley approximation process based on permutation sampling, producing sample valuations for downstream tasks such as noise detection and data removal. IV. METHODOLOGY To add… view at source ↗

**Figure 2.** Figure 2: High-value data removal under the LR model, where the performance of different valuation methods changes as the removal ratio increases [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Figure 3: High-value data removal under the NB model, where the performance of different valuation methods changes as the removal ratio increases. B. Data Valuation Methods In the field of data valuation, Jia et al. proposed the Fast Approximate Shapley method in 2019 [2], which reduces the computational complexity from O(2 N) to O(M · N) through Monte Carlo sampling, providing a feasible path for largescale data v… view at source ↗

read the original abstract

With the rapid development of machine learning applications on time-series data, accurately assessing the value of training samples has become essential for data selection, noise detection, and model optimization. However, traditional data valuation methods usually assume that samples are independent and identically distributed, and thus ignore the time-varying nature of sample value in time-series data. This paper proposes an improved temporal Shapley data valuation method that enables accurate sample valuation for time-series data through a temporal decay mechanism and a multi-scale fusion strategy. Specifically, we propose three progressively enhanced temporal Shapley methods. Temporal-Decay Shapley (TDS) incorporates temporal information into Shapley value computation through exponential decay weights; the improved TDS adopts power exponential decay to better adapt to nonlinear temporal drift; and Multi-Scale Temporal-Decay Shapley (MS-TDS) constructs a multi-scale fusion mechanism that balances the value of short-term hotspot samples and long-term foundational samples through parallel multi-scale valuation and sample-level adaptive fusion. Experimental results show that the proposed methods generally outperform traditional methods in noise detection and high-value data identification tasks, with more evident advantages under most strongly temporal settings, thereby effectively improving the accuracy and robustness of data valuation.

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

The temporal decay extension to Shapley valuation is a reasonable step for time-series data but the experiments leave it unclear whether gains come from the mechanism or from extra tunable parameters.

read the letter

The core contribution is extending Shapley data valuation beyond the i.i.d. assumption by adding temporal decay to sample weights. They define three variants: Temporal-Decay Shapley using exponential decay, an improved version with power-exponential decay for nonlinear drift, and Multi-Scale Temporal-Decay Shapley that runs parallel valuations at different scales then fuses them adaptively at the sample level. This directly targets the time-varying value of samples in drifting series, which standard Shapley methods ignore. The multi-scale fusion is the most distinctive piece, as it tries to balance recent high-impact points against longer-term structure without discarding either. That framing is useful for anyone doing data selection or noise filtering on time-series training sets. The reported experiments claim consistent outperformance on noise detection and high-value sample identification, with larger edges in strongly temporal regimes. If the full results include proper baselines and controls, the idea could help practitioners prune or weight data more sensibly. The main soft spot is the handling of free parameters. Decay rates and fusion weights are chosen per dataset to match its temporal characteristics, yet the abstract and stress-test note give no detail on whether selection used the same evaluation metrics, cross-validation that avoids leakage, or fixed defaults that transfer. When parameters are tuned this way, performance gains can be explained by added flexibility rather than by correctly capturing time decay. Without evidence of parameter-robust versions or external validation, the central experimental claim rests on thin ground. The math itself looks like a straightforward reweighting of the usual Shapley sum, so the soundness hinges on the experiments rather than any deep theoretical novelty. This paper is aimed at researchers working on data valuation or data-centric ML for time series. A reader already using Shapley for sample importance would find the temporal adaptation worth trying, though they would need to implement their own parameter controls. It deserves peer review because the problem is real, the proposal is concrete, and the gap it fills is clear, even if revisions must tighten the experimental protocol around parameter choice.

Referee Report

3 major / 3 minor

Summary. The paper introduces three variants of Shapley-based data valuation for time-series: Temporal-Decay Shapley (TDS) using exponential decay weights, an improved TDS with power-exponential decay, and Multi-Scale Temporal-Decay Shapley (MS-TDS) that adds parallel multi-scale valuation with adaptive sample-level fusion. It claims these methods outperform standard Shapley and other baselines on noise detection and high-value sample identification tasks, with larger gains in strongly temporal regimes.

Significance. If the performance advantages can be shown to arise from the temporal modeling rather than from dataset-specific tuning of the decay rates and fusion weights, the framework would address a genuine gap in applying data valuation to non-i.i.d. time-series data and could support improved sample selection and noise filtering in forecasting, anomaly detection, and other temporal ML pipelines.

major comments (3)

[§4] §4 (Experimental Setup): The manuscript provides no information on how the decay-rate parameters (λ for TDS, α for power-exponential TDS) and the multi-scale fusion weights are selected. It is therefore impossible to determine whether these quantities were fixed in advance, chosen by cross-validation on the same noise-detection or value-ranking metrics used for evaluation, or tuned per dataset. This omission directly affects the central claim of superiority, because any reported gains could be explained by the additional degrees of freedom rather than by the temporal-decay mechanism itself.
[§4.3] §4.3 and Tables 2–4: No statistical significance tests (e.g., paired t-tests or Wilcoxon tests across multiple random seeds or data splits) are reported for the claimed outperformance. Given that the methods introduce at least one free parameter per variant, the absence of significance assessment leaves the headline result only weakly supported.
[§3.2] §3.2–3.3 (Definition of MS-TDS): The multi-scale fusion rule is presented as balancing short-term and long-term contributions, yet the fusion weights are described as “sample-level adaptive” without an explicit, parameter-free formula or a demonstration that the adaptation rule itself does not require additional fitting on the downstream task. This creates a circularity risk for the performance claims.

minor comments (3)

[§3] The notation for the decay functions (exponential vs. power-exponential) and the multi-scale fusion operator should be made fully explicit in §3, including the precise functional forms and any normalization constants.
The paper should cite and briefly contrast with prior work on time-aware or non-stationary Shapley values (e.g., recent extensions of Data Shapley to streaming or temporal settings) to clarify the incremental contribution.
Figure captions and axis labels in the experimental figures are occasionally terse; adding explicit statements of what each curve represents (e.g., “TDS with λ tuned on validation set”) would improve readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. These points highlight important aspects of experimental rigor and clarity that we will address in the revision. Below we respond point-by-point to the major comments.

read point-by-point responses

Referee: [§4] §4 (Experimental Setup): The manuscript provides no information on how the decay-rate parameters (λ for TDS, α for power-exponential TDS) and the multi-scale fusion weights are selected. It is therefore impossible to determine whether these quantities were fixed in advance, chosen by cross-validation on the same noise-detection or value-ranking metrics used for evaluation, or tuned per dataset. This omission directly affects the central claim of superiority, because any reported gains could be explained by the additional degrees of freedom rather than by the temporal-decay mechanism itself.

Authors: We agree that the parameter selection procedure must be documented to substantiate the claims. The decay rates λ and α were selected via a modest grid search on a small validation split that is completely disjoint from the test sets used for noise detection and value ranking; the multi-scale fusion weights were computed adaptively per sample using only quantities internal to the Shapley computation (no downstream labels or metrics). In the revised manuscript we will add an explicit subsection in §4 (and an appendix table) that reports the exact grid ranges, the validation criterion, and the final chosen values for each dataset. This will demonstrate that tuning was performed on held-out data and does not inflate the reported test performance. revision: yes
Referee: [§4.3] §4.3 and Tables 2–4: No statistical significance tests (e.g., paired t-tests or Wilcoxon tests across multiple random seeds or data splits) are reported for the claimed outperformance. Given that the methods introduce at least one free parameter per variant, the absence of significance assessment leaves the headline result only weakly supported.

Authors: We acknowledge that formal significance testing strengthens the evidence. Although the improvements are consistent across five datasets and multiple temporal regimes, we did not report statistical tests in the original submission. In the revision we will repeat all experiments with at least five independent random seeds, add paired t-tests (or Wilcoxon signed-rank tests where normality assumptions fail) to Tables 2–4, and include p-values together with effect-size measures. This will provide quantitative support for the observed advantages. revision: yes
Referee: [§3.2] §3.2–3.3 (Definition of MS-TDS): The multi-scale fusion rule is presented as balancing short-term and long-term contributions, yet the fusion weights are described as “sample-level adaptive” without an explicit, parameter-free formula or a demonstration that the adaptation rule itself does not require additional fitting on the downstream task. This creates a circularity risk for the performance claims.

Authors: The fusion weights in MS-TDS are computed from the empirical variance of per-scale Shapley values for each sample; this rule is deterministic, uses only the valuation outputs themselves, and contains no learnable parameters or reference to downstream task performance. We will revise §3.3 to state the exact formula (a softmax over negated per-sample variances across scales) and add a short argument showing that the adaptation depends solely on the data and the Shapley computation, thereby removing any circularity with the evaluation metrics. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper defines TDS via explicit exponential decay weights on Shapley values, extends it to power-exponential decay for nonlinear drift, and adds MS-TDS via parallel multi-scale valuation plus sample-level adaptive fusion. These are presented as constructive modeling choices rather than reductions of outputs to inputs. No equations or steps are shown to be equivalent by construction to fitted parameters or prior self-citations; experiments compare the resulting valuations against traditional methods on separate noise-detection and identification tasks. The provided text contains no load-bearing self-citations, uniqueness theorems, or renamings of known results, so the derivation remains self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The framework rests on domain assumptions about temporal drift and introduces decay parameters whose values are not derived from first principles.

free parameters (1)

decay rate parameter
Exponential and power-exponential decay weights require a rate or exponent that must be chosen or fitted per dataset or task.

axioms (1)

domain assumption The contribution of a training sample to model performance in time-series data decreases monotonically with its age according to a simple decay function.
This premise is invoked to justify replacing uniform Shapley weights with time-decayed weights.

invented entities (1)

Multi-Scale Temporal-Decay Shapley (MS-TDS) no independent evidence
purpose: To combine valuations computed at multiple temporal resolutions via adaptive sample-level fusion.
Newly constructed mechanism whose correctness is asserted via experiments rather than external validation.

pith-pipeline@v0.9.0 · 5509 in / 1260 out tokens · 64460 ms · 2026-05-12T03:13:04.015883+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel contradicts

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contradicts
CONTRADICTS: the theorem conflicts with this paper passage, or marks a claim that would need revision before publication.

wi = exp(−λ Δt_i) … wi = exp(−λ Δt_i^p) … λ_k = λ / τ_k … a_i = 1/(σ_i² + ε) … φ_MS_i = a_i ∑ φ_i^(k)
IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean reality_from_one_distinction contradicts

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contradicts
CONTRADICTS: the theorem conflicts with this paper passage, or marks a claim that would need revision before publication.

temporal decay mechanism and a multi-scale fusion strategy … parameters (λ, p) … scale set {τ_1, τ_2, τ_3}

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supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
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contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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