{"id":"681e412d-dd5b-4f6e-bfee-3791047d37d9","arxiv_id":"2506.03267","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A time-frequency uncertainty bound can tell when a model's time-domain and frequency-domain attributions point to different features, making multi-domain explanations necessary.","lead":"This paper shows that explaining a time series model in only one domain, time or frequency, can hide features, and proposes an uncertainty principle test to detect when both domains are needed. It applies a known signal-processing bound to pairs of AI attributions and reports frequent violations across models and datasets.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Sufficiency claim depends on unproven Fourier-pair relation between domain attributions; wrapper methods violate it even for linear models, so UP violations may be XAI artifacts.","rationale":"The reader's weakest assumption is exactly the load-bearing point. Theorem 2 (Donoho–Stark) constrains a vector and its DFT; the paper applies it to two independently generated attribution vectors. For the contrapositive to imply 'different features,' the authors must assume that a feature's time and frequency attributions are Fourier counterparts. Section III.A asserts this only verbally and then explicitly says the two attributions are not Fourier counterparts. With the wrapper method W(f)=M(FFT^{-1}f), the frequency attribution is computed with respect to f, while the time attribution is computed with respect to x; for nonlinear models with baselines (DeepLIFT, IG, KernelSHAP), these are not related by the DFT. Even for a linear model, InputXGradient gives A_t = x ⊙ w and A_f = f ⊙ F^*w, while DFT(A_t) = F(x ⊙ w), a convolution. Therefore, UP violations can be pure artifacts of the attribution method's non-equivariance. The paper's synthetic validation does not control for this: the model may genuinely respond to non-feature frequencies (Section IV.C), but that is a statement about the model, not about whether the two attributions represent the same feature. The central sufficiency claim requires that the attribution algorithm itself would produce Fourier counterparts for a single feature. A controlled linear-model test (or an analytic proof for a class of methods) would settle it. If the test shows violations for a single-feature model, the paper must be reframed as 'UP violation is a heuristic indicator' rather than a sufficient condition, and the empirical claims need null-model baselines. The reader's conditional verdict is appropriate; no stronger action is needed pending this test, so the verdict remains UNCHANGED.","tokens_in":16861,"tokens_out":11068,"duration_ms":141037,"concrete_test":"Construct a controlled linear model M(x)=w·x, where w is a single time-localized kernel (e.g., nonzero on indices 10–14) and inputs x contain only that shapelet feature; no training is needed because weights are known. For each XAI method (DeepLIFT, IG, GradientSHAP, InputXGradient, Occlusion, and Saliency as a control), generate time attribution A_t and wrapper frequency attribution A_f exactly as in Algorithm 1, over 1000 samples. Compute the UP violation rate. If any non-LIME method yields >0% violations, the sufficient condition is false: the model uses only one feature, yet the attributions violate the bound. Additionally, compute the normalized Fourier-pair error ||A_f − |FFT(A_t)|||_2 / ||A_f||_2; if this error is large for methods that produce violations, the assumed Fourier relationship is empirically absent.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—'UP violation is a sufficient condition that the time and frequency attributions do not highlight the same feature'—requires that when a single model feature is faithfully reported in both domains, the frequency attribution is the DFT of the time attribution (or its magnitude), so the Donoho–Stark bound applies. Section III.A asserts this informally ('if the attributions in the time and frequency domains are both localized, then the features they represent cannot be the same') but never proves it, and it explicitly states the opposite: 'time and frequency attributions are generated independently... not Fourier counterparts of each other.' For the wrapper model W(f)=M(FFT^{-1}f), the raw gradient does transform as a Fourier pair, but practical attribution methods do not. For example, InputXGradient gives A_t = x ⊙ ∇M in time and A_f = f ⊙ F^*∇M in frequency, while DFT(A_t) = F(x ⊙ ∇M), a convolution, not a product. Thus UP violations can reflect baseline/path or input-scaling artifacts (as the paper itself notes for LIME sparsity) rather than two genuinely distinct model features. The synthetic ground-truth experiments cannot resolve this because the model is not restricted to a known single feature; Table I even shows UP violations on single-feature samples, which the authors attribute to model frequency response rather than XAI infidelity. Without a proof or controlled test of Fourier-pair equivalence, the sufficient-condition claim is unsupported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper argues that presenting only a single explanation domain (time or frequency) is insufficient for deep time series models. It proposes to use the Donoho-Stark uncertainty principle (Theorem 2, Eq. (4)) as a sufficient condition: if the time-domain and frequency-domain attributions violate the bound Nt*Nf >= N(1-(eps_t+eps_f))^2, then the features they highlight cannot be the same, so both domains should be presented. The frequency attributions are obtained via the authors' explanation-space wrapper. The method is evaluated with seven XAI methods on five architectures and on synthetic and real datasets, reporting frequent UP violations across many settings.","tokens_in":17021,"tokens_out":6797,"duration_ms":80717,"significance":"If the central sufficiency claim were correct, this would be a practically useful and theoretically grounded diagnostic for multi-domain explanation, and the paper provides a broad empirical survey of a relevant phenomenon: time- and frequency-domain attributions can be simultaneously localized. The qualitative examples (e.g., StarLightCurves, MIMIC) are instructive, and the LIME aggregation idea is a useful practical note. However, the paper's main contribution as stated is a sufficient condition, and that condition is unsupported and in fact contradicted by the paper's own mathematical setup; the empirical results cannot compensate for this because they inherit the same ambiguity. No code is released, and the frequency-attribution framework is taken from the authors' prior work [2], which is not independently validated here.","major_comments":[{"comment":"The claim that a UP violation is a sufficient condition for the time- and frequency-domain attributions to represent different features is unproven and, as stated, false. The Donoho-Stark bound applies to a signal and its DFT, not to arbitrary pairs of attributions. The paper explicitly states that the attributions are generated independently and are 'not Fourier counterparts of each other.' For the wrapper model W(f)=M(FFT^{-1} f), attribution pairs computed by gradient-based methods are generally not DFT pairs even when the model uses a single well-defined feature. For a linear model M(x)=w·x, InputXGradient gives A_t = x⊙w in time and A_f = f⊙(F w) in frequency, whereas DFT(A_t) = (F x) * (F w) (a convolution) rather than A_f. These two attributions can be simultaneously sparse for a single-feature model (e.g., a shapelet weight w and a narrowband input x), yielding a UP violation that is an artifact of the attribution method, not evidence of two distinct model features. Thus the paper's sufficiency assertion, and the statement in Section V that the approach 'essentially gives no false positive,' are not justified.","section":"Section III.A, Theorem 2 / Eq. (4)"},{"comment":"The post-hoc exclusion of LIME results weakens the empirical claim. The paper first reports very high violation rates for LIME in Tables I and II and then says 'We ignore the results of LIME here' because its sparsity regularization artificially induces UP violations. This directly illustrates that UP violations can be method artifacts, not indicators of genuinely distinct features, and the exclusion criterion is introduced only after seeing the results. A pre-registered or otherwise justified exclusion rule would be needed to avoid the appearance of cherry-picking. Moreover, the high LIME violation rate is consistent with the concern raised by the unproven Fourier-pair assumption: any method that makes both attributions sparse will violate the bound regardless of the underlying model features.","section":"Section IV-A, Tables I and II, and Section IV-B"},{"comment":"The synthetic ground-truth experiments do not validate the sufficiency condition. Table I shows UP violations on samples that contain only a time feature or only a frequency feature (e.g., DeepLift with InceptionTime: 42% on time-only class 0). The authors argue in Section IV-C that the model's frequency response makes it genuinely responsive to non-features, so these are not false positives. This explanation may be correct, but it means that a UP violation does not tell us whether the attributions highlight features a human would regard as distinct; it can also reflect spurious sensitivity of the specific model/XAI combination. Without a controlled setting in which the model is known to use exactly one feature and the XAI method is verified to be faithful to that feature, the experiment cannot establish that UP violations are a reliable indicator of the need for multi-domain explanation.","section":"Section IV-C and Table I"}],"minor_comments":[{"comment":"The explanation-space wrapper is never formally defined; please specify the wrapper model W(f)=M(FFT^{-1} f) and the exact attribution procedure used on the wrapper, since the paper's technical claims depend on this construction.","section":"Section III.A"},{"comment":"The relationship between the sorted thresholds tsteps[i] and fsteps[j] and the resulting Nt, Nf values is described informally; a step-by-step derivation of why this grid search finds the tightest (epsilon_t, epsilon_f) pair for each (Nt, Nf) would improve clarity.","section":"Section III.B, Algorithm 1"},{"comment":"There are several typos: 'UP voilation' should be 'UP violation'; 'stem form' appears to be a misspelling of 'stem from'; in the Figure 1 caption, 'wrapped method' should be 'wrapper method.'","section":"Section IV-A"},{"comment":"The statement 'which essentially gives no false positive' is a claim that depends entirely on the unproven sufficiency property; it should be either proven or removed, given the LIME counterexample and the single-feature violations in Table I.","section":"Section V"},{"comment":"The discussion of MIMICPerformance not being z-normalized is interesting but the connection to UP violations would be clearer if the authors explained how the model exploits the mean value and why that manifests as a frequency-domain feature.","section":"Section IV-A"}],"recommendation":"reject","confidential_remarks":"The paper relies almost exclusively on the authors' own prior work [2] for the core frequency-attribution mechanism, and no independent implementation is provided. The theoretical result is the main selling point, but as written it is not merely missing a proof; the InputXGradient example in the report shows a concrete failure mode in the paper's own framework. The empirical survey could be repurposed as a heuristic study, but the advertised 'sufficient condition' would need to be abandoned, which would amount to a different paper. I would not encourage resubmission without a substantially revised central claim."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper does something new: it brings the Donoho–Stark uncertainty principle into time series XAI as a diagnostic for whether time- and frequency-domain attributions can be trusted as showing the same feature. Algorithm 1 is a clean way to test violations, and the synthetic Figure 1 makes the core intuition vivid. The broad evaluation across five architectures, seven XAI methods, and multiple datasets is more than most interpretability papers bother with, and the discussion of why Saliency never violates the bound is genuinely thoughtful.\n\nThe weak spot is the load-bearing sufficiency claim. The paper is explicit that time and frequency attributions are generated independently and are not Fourier counterparts of each other. That is exactly the problem: Donoho–Stark is a theorem about a signal and its Fourier transform. If the two vectors are not a Fourier pair, a UP violation only tells you that both are localized. Two arbitrary sparse vectors can both be localized for reasons that have nothing to do with distinct features—LIME's sparsity is the paper's own example, and the InputXGradient calculation in the stress test shows that even for a linear model the frequency attribution is not the DFT of the time attribution. So the statement 'UP violation is a sufficient condition that the features are different' is unsupported as written. The paper needs either a proof that same-feature attributions from the same XAI method must satisfy the UP bound, or a controlled experiment with known single-feature models where one can verify that UP violations track genuine feature differences rather than method artifacts.\n\nOther issues are smaller. Reporting LIME results and then excluding them post hoc is awkward; a null baseline (random sparse attributions) would calibrate the violation rates; and there is no code or data release. These are fixable.\n\nI do not think this should be desk-rejected. The diagnostic idea is useful even if the sufficiency claim needs qualification—a UP violation is at minimum a red flag that the two explanations are not telling the same story. With a proof or a carefully controlled validation, this could be a solid contribution. I would send it to peer review, with the expectation of major revision.","headline":"A genuinely new diagnostic idea, but the sufficiency claim needs a proof that attribution pairs obey the uncertainty principle; worth refereeing.","tokens_in":17624,"tokens_out":2217,"would_cite":false,"duration_ms":27050,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that the uncertainty principle gives a sufficient condition that time- and frequency-domain explanations of a deep time series model highlight different features, so presenting only the single most sparse domain can…","keywords":["time series explainability","uncertainty principle","multi-domain explanation","attribution methods","frequency domain","Donoho-Stark bound","explanation space","deep learning interpretability"],"falsifier":"Take a synthetic sample with exactly one known feature, say a single shapelet or a single dominant frequency, and compute both attributions. The paper's sufficient-condition logic predicts no UP violation when the model truly uses only that one feature; a confirmed violation on such a sample shows the detector is responding to the explanation method, not to feature mismatch. A more direct test is to take the discrete Fourier transform of the time-domain attribution and compare it with the wrapper-generated frequency attribution: if the two are not approximately a Fourier pair even when the inequality $N_t N_f \\ge N(1-(\\epsilon_t+\\epsilon_f))^2$ holds, the pair does not obey the uncertainty principle's precondition.","tokens_in":16543,"feed_emoji":"⚛️","tokens_out":8334,"duration_ms":85838,"temperature":0.7,"pith_summary":"The paper tries to establish that explaining a deep time series model in a single domain—typically time—is often not enough, because the time-domain attribution and the frequency-domain attribution can highlight genuinely different features. Its tool is the uncertainty principle: a signal cannot be sharply concentrated in both time and frequency, so if two independently generated attributions are both concentrated, the explanations cannot be describing the same feature. The paper uses the Donoho–Stark inequality as a sufficient test for this mismatch and verifies it on a synthetic dataset with known shapelet and frequency features plus several real classification and forecasting datasets. The intended practical consequence is that for many time series applications the end user should be shown both domains, not just the domain in which the attribution is most sparse. The criterion is deliberately one-directional: a violation proves different features, while no violation is inconclusive.","feed_headline":"Uncertainty principle says single-domain AI explanations can mislead","feed_subtitle":"A bound violation means time and frequency attributions point at different features, so users need both.","key_machinery":"The machinery is the Donoho–Stark uncertainty principle for discrete signals, stated with $\\epsilon$-concentration: a sequence is $\\epsilon$-concentrated on an index set if the energy outside that set is at most $\\epsilon$. For a length-$N$ signal, the number $N_t$ of significant time coefficients and $N_f$ of significant frequency coefficients must satisfy $N_t N_f \\ge N(1-(\\epsilon_t+\\epsilon_f))^2$. The paper feeds this inequality a pair of normalized absolute attributions—one computed in the time domain by a standard XAI method, one computed in the frequency domain by the explanation-space wrapper—and performs a grid search over threshold pairs to find the tightest concentrations. If any threshold pair violates the inequality, the algorithm declares a UP violation, meaning the two attribution maps cannot represent the same feature.","core_discovery":"The central claim is that a time-domain attribution and a frequency-domain attribution of the same sample are subject to the same localization trade-off as a function and its Fourier transform, even though the paper generates the two attributions independently rather than by transforming one into the other. If both attributions are simultaneously concentrated, the Donoho–Stark bound $N_t N_f \\ge N(1-(\\epsilon_t+\\epsilon_f))^2$ is violated; the paper takes this violation as a sufficient condition that the two explanations emphasize different features and therefore that both explanations should be presented. The paper supports the claim by showing frequent violations across five model architectures, seven attribution methods, and datasets chosen to contain both time-localized (shapelet-like) and frequency-localized (seasonal, periodic) structure. Its own stated caveat is that the test is conservative: a violation is conclusive, but the absence of a violation leaves open whether the domains agree.","pith_inferences":["Beyond the paper: the whole sufficient-condition reading rests on an unproved premise—that when a time attribution and a frequency attribution describe the same feature, the pair behaves like a Fourier-transform pair. If an XAI method's sparsity or baseline effect creates localization on its own, a violation could be a method artifact rather than evidence of distinct features.","Beyond the paper: the same concentration test could be applied to other conjugate explanation pairs, such as wavelet scales or trend-seasonal decompositions, turning the test into a general 'when is multi-domain explanation needed' detector.","Beyond the paper: the model frequency-response plots suggest a predictive extension—probe a trained model with controlled sinusoids of varying amplitude and frequency, and use the measured response to anticipate which model-XAI combinations will produce UP violations before running any explainer.","Beyond the paper: the paper's own Table I reports violations on single-feature synthetic samples (for example InceptionTime with DeepLIFT on shapelet-only samples). Whether those are genuine model responses to non-features or artifacts of the attribution method is the empirical question that would separate the tool from the conclusion."],"forward_implications":["For any sample where the test fires, a single-domain explanation is insufficient: the time and frequency attribution maps carry distinct information and both should be shown to the user.","On periodic forecasting datasets such as traffic, pedestrian counts, and electricity demand, the frequent violations imply that seasonality is visible in the frequency attribution while last-step effects are visible in the time attribution, so time-only explanations hide a class of learned features.","The conventional rule of presenting the most sparse domain is unsafe, because a non-localized but real feature is diluted across that domain and will not appear as a highlight.","Because the criterion is sufficient but not necessary, the reported violation rates understate how often multi-domain explanation is needed.","The behavior of the XAI method matters: methods with baseline or sparsity mechanisms (such as LIME) can create violations on their own, while a baseline-free method such as Saliency never violated the bound in these experiments."],"supporting_citations":[{"why":"Supplies the Donoho-Stark uncertainty bound and the epsilon-concentration theorem that the paper uses as the violation test.","marker":"[18]"},{"why":"Provides the explanation-space wrapper that produces frequency-domain attributions from a time-trained model independently of the time-domain attribution.","marker":"[2]"},{"why":"Supplies the off-the-shelf implementations of the seven XAI methods whose time and frequency attributions are compared.","marker":"[29]"},{"why":"Surveys the uncertainty-principle theory that motivates transferring the localization trade-off to explainability.","marker":"[5]"}],"fun_headline_variants":["Time or frequency explanations alone can mislead, new bound shows","Uncertainty principle: why time series AI needs both time and frequency explanations","When attributions violate a bound, show both domains to users","New test reveals when single-domain explanations fail for time series","Time and frequency attributions can disagree, so show both"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that an attribution pair describing the same feature in time and frequency behaves like a Fourier-transform pair, so the uncertainty inequality applies to it; the paper asserts this informally but never proves the relationship, and if it fails, a UP violation can reflect the XAI method rather than genuinely different features.","fun_headline_variants_meta":{"raw":{"variants":["Time or frequency explanations alone can mislead, new bound shows","Uncertainty principle: why time series AI needs both time and frequency explanations","When attributions violate a bound, show both domains to users","New test reveals when single-domain explanations fail for time series","Time and frequency attributions can disagree, so show both"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000834,"raw_usage":{"total_tokens":3687,"prompt_tokens":1038,"completion_tokens":2649,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":654,"completion_tokens_details":{"reasoning_tokens":2562}},"tokens_in":654,"tokens_out":2649,"duration_ms":19014,"temperature":1.0,"reasoning_tokens":2562,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T11:07:44.967191+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a synthetic sample with exactly one known feature, say a single shapelet or a single dominant frequency, and compute both attributions. The paper's sufficient-condition logic predicts no UP violation when the model truly uses only that one feature; a confirmed violation on such a sample shows the detector is responding to the explanation method, not to feature mismatch. A more direct test is to take the discrete Fourier transform of the time-domain attribution and compare it with the wrapper-generated frequency attribution: if the two are not approximately a Fourier pair even when the inequality $N_t N_f \\ge N(1-(\\epsilon_t+\\epsilon_f))^2$ holds, the pair does not obey the uncertainty principle's precondition.","supporting_citations":[{"cited_title":"Uncertainty principles and signal recovery,","cited_arxiv_id":null,"evidence_quote":"Supplies the Donoho-Stark uncertainty bound and the epsilon-concentration theorem that the paper uses as the violation test."},{"cited_title":"Explanation Space: A New Perspective into Time Series Interpretability","cited_arxiv_id":"2409.01354","evidence_quote":"Provides the explanation-space wrapper that produces frequency-domain attributions from a time-trained model independently of the time-domain attribution."},{"cited_title":"The uncertainty principle: a mathematical survey,","cited_arxiv_id":null,"evidence_quote":"Surveys the uncertainty-principle theory that motivates transferring the localization trade-off to explainability."}],"review_version":1}