{"id":"b26ac79a-697d-4fa6-8bd8-42602d81af4b","arxiv_id":"2505.08199","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"MDMixer improves long-term time series forecasting by generating parallel multi-granularity predictions, mixing them from coarse to fine, and adaptively weighting each channel's scales, reaching a 4.64% average MAE reduction over TimeMixer on eight benchmarks.","lead":"Researchers propose MDMixer, a neural network that predicts long-term time series by analyzing the data at multiple time scales, handling trend and seasonal parts separately, and weighing the scales per data channel. It reports average error reductions of a few percent over prior MLP-based forecasters on standard benchmarks, while using less training time and memory.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"MAE comparison is confounded by training-loss mismatch: MDMixer is trained with L1 loss while baseline numbers come from MSE-optimized models, inflating the reported 4.64% MAE improvement.","rationale":"The reader's weakest assumption identified baseline comparability as the key risk, and I agree that the baselines are not re-run and lack error bars. My stress test sharpens this into a specific, overlooked aspect of comparability: MDMixer is trained with an L1/MAE loss, while the cited baseline numbers were produced by models trained with MSE. Because the headline claim is specifically about MAE, this mismatch directly inflates the reported advantage. The internal evidence is strong: MDMixer tends to win on MAE while losing on MSE in several cells, and the aggregate MAE gain (4.64%) is much larger than the MSE gain (2.50%), a signature of optimizing the evaluation metric. This concern is testable by retraining baselines with the same loss. If the gap shrinks, the paper's central claim would need to be revised to a more modest claim of MAE improvement under a different training objective. If the gap persists, the architecture itself is validated. I do not think this warrants rejection, because the method is clearly described and the MSE improvement (2.50%) suggests some genuine benefit; rather, the paper should be accepted only conditionally on providing fair baseline comparisons, including matched training losses and rerun baselines. Hence the verdict remains CONDITIONAL, matching the reader, though for a more specific reason. My concern is new relative to the reader's rationale, which focused on stale numbers and lack of error bars, so my agreement is partial.","tokens_in":17896,"tokens_out":9482,"duration_ms":95176,"concrete_test":"Retrain TimeMixer (and optionally iTransformer and PatchTST) on the same eight datasets using the same look-back length (96), same train/validation/test splits, same data normalization, and, crucially, the same L1/MAE loss and the same three seeds as MDMixer, keeping the original models' default hyperparameters. Recompute the average MAE improvement of MDMixer over TimeMixer. If the gap falls below about 2% or reverses, the 4.64% headline is inflated by the training-loss mismatch; if the gap persists at the reported level, the concern is refuted.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 4.1.3 states that MDMixer is trained with MAE ('We use MAE as the loss function'), and Section 3.5 defines the main loss as the L1 norm. The baselines in Table 2, including TimeMixer, iTransformer, and PatchTST, are taken from their original publications, which optimize MSE. The central claim of a 4.64% average MAE improvement over TimeMixer is therefore not an architecture comparison under matched training objectives. The pattern in Table 2 supports this concern: MDMixer frequently has worse MSE but better MAE than TimeMixer (e.g., ETTh1 96/192, Traffic 96/192/336/720), which is exactly what one expects from directly optimizing L1. Moreover, the aggregate MAE gain (4.64%) is nearly twice the aggregate MSE gain (2.50%), suggesting that part of the headline margin reflects the loss function rather than the multi-scale representation learning. The paper never discloses the baselines' training losses or retrains them with the same objective, so the comparability assumption underlying the central claim is not met.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes MDMixer, an MLP-based framework for long-term time series forecasting. The architecture combines multi-granularity parallel prediction heads (MPP), iterative coarse-to-fine mixing (MIM), a channel-dependent adaptive weighting gate (AMWG), and a dual-branch trend/seasonal decomposition with linear and MLP predictors. An auxiliary alignment loss supervises intermediate predictions against downsampled ground truth. Experiments on eight standard benchmarks report an average MAE improvement of 4.64% over TimeMixer, along with improved training efficiency and an interpretability visualization. The paper also shows that adding its dual-branch decomposition to linear baselines improves their accuracy.","tokens_in":18134,"tokens_out":6025,"duration_ms":58803,"significance":"If the reported comparison were clean, MDMixer would be a useful contribution: the architecture is clearly described, the ablation study isolates the role of each module, the sensitivity analyses cover key hyperparameters, and the efficiency comparison is instructive. The paper's central quantitative claim, however, is the 4.64% average MAE improvement over TimeMixer, and that claim is directly affected by a training-loss mismatch between MDMixer and the baselines. The 'state-of-the-art' wording is also broader than the evidence in Table 2 supports. These issues are fixable, but they require either additional experiments or a substantial restatement of the claims.","major_comments":[{"comment":"The headline comparison is confounded by a training-loss mismatch. Section 4.1.3 states 'We use MAE as the loss function', and Section 3.5 (Eq. 17) defines the main loss as the L1 norm. The baseline numbers in Table 2 are taken from prior publications, which typically optimize MSE, and the paper does not disclose those losses or retrain baselines under the same objective. Since the abstract's central claim is specifically a 4.64% average MAE improvement over TimeMixer, this is not an architecture-matched comparison. The pattern in Table 2 is consistent with the confound: MDMixer frequently shows better MAE but worse or comparable MSE than TimeMixer (e.g., ETTh1 horizon 96: MAE 0.386 vs 0.400 while MSE 0.379 vs 0.375; Traffic horizon 96: MAE 0.275 vs 0.285 while MSE 0.439 vs 0.462). The authors should retrain baselines with L1 loss, or at minimum report an MSE-based comparison and temper the MAE-based claim accordingly.","section":"Section 4.1.3 and Table 2"},{"comment":"The claim of state-of-the-art performance is not supported by the paper's own table. On Traffic, iTransformer achieves better average MSE and MAE (0.428/0.282) than MDMixer (0.465/0.286), and MDMixer is worse than iTransformer on every Traffic horizon. Similarly, on Electricity with horizon 96, iTransformer has MSE 0.148 versus MDMixer's 0.152. The contribution list and conclusion describe MDMixer as 'state-of-the-art' without qualification, but the evidence only supports a comparison against TimeMixer and specific baselines on some datasets. These sweeping claims should be replaced with dataset-specific statements.","section":"Section 4.1.4 and Table 2"},{"comment":"The empirical significance of the claimed improvements is not established because no standard deviations are reported despite the statement that each experiment was repeated three times, and the baseline numbers have no error bars at all. The 'Improvement' row also averages over heterogeneous per-dataset averages without weighting or noting that MDMixer is worse than iTransformer on Traffic in all four horizons. Given that the claimed improvement margins are on the order of 2–5%, the absence of any variability or significance measure makes it impossible to judge whether the differences are meaningful. The authors should report per-cell standard deviations and clearly define the aggregation procedure.","section":"Section 4.1.3 and 'Improvement' row in Table 2"}],"minor_comments":[{"comment":"The sentence 'our method requires fewer parameters (50.2K vs. 34.8K in the Electricity dataset)' appears to state the numbers in the wrong order; as written it says MDMixer requires more parameters when the comparison presumably intends fewer. Please correct to '34.8K vs. 50.2K' or provide the actual values.","section":"Section 4.2"},{"comment":"The caption says 'MSE scores with varying alignment loss weight' but the figure shows both MSE and MAE curves; update the caption to mention both metrics.","section":"Figure 5"},{"comment":"The efficiency comparison says all models use the same batch size and look-back length but does not state the actual batch size, input length, or model-specific hyperparameter settings. Reporting these details would make the efficiency claim reproducible.","section":"Section 4.5"},{"comment":"The 'Improvement' row should explain that the percentage is computed as the average of per-dataset averages, not as a reduction on the pooled dataset. This will help readers interpret the aggregate numbers.","section":"Section 4.1.4, Table 2"},{"comment":"The table caption and text use 'vanilla version', 'modified baselines', and asterisks in a way that is easy to confuse. Clarify that asterisks denote baselines augmented with the decomposition module and that '(Dual-Branch)' denotes the proposed replacement of the trend predictor.","section":"Table 3 caption"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague —\n\nMDMixer is a plausible incremental MLP architecture with one genuinely useful idea: channel-dependent gating across multi-granularity heads, combined with separate linear/MLP branches for seasonal and trend. The paper is clearly written, the ablations give each component a reason to exist, and the dual-branch transplant experiment on DLinear/RLinear/NLinear is a nice way to test the idea outside the full model.\n\nThat said, the headline result is weaker than it looks, and the stress-test note is right: MDMixer is trained with L1 loss (Sec 3.5; Sec 4.1.3) while the baseline numbers come from papers that optimized MSE. Table 2 has the fingerprint—MDMixer frequently has worse MSE but better MAE than TimeMixer (ETTh1 96/192, Traffic all horizons), and the aggregate MAE gain (4.64%) is nearly double the MSE gain (2.50%). That is what direct L1 optimization does. The authors never disclose the baselines' training losses or retrain them under the same objective, so the 4.64% claim should not be read as an architecture comparison. A fixed version would retrain baselines with MAE or train MDMixer with MSE and report both.\n\nMinor but related: no standard deviations despite three seeds, no code release, and the \"Improvement\" row averages percentages over heterogeneous dataset-horizon cells. The SOTA claim in the contributions is also too strong: on Traffic, iTransformer has lower average MAE (0.282 vs 0.286), and on Electricity it wins some MSE cells.\n\nWhat is actually new is the MPP/MIM/AMWG package, and the paper is honest enough in its ablation to show that removing MPP or AMWG hurts. The efficiency comparison is fair within its limits, and the interpretability heatmap is illustrative rather than deep. All soft spots are fixable. The core architecture does not seem to rest on a circular or invented result.\n\nThis is a paper for LTSF practitioners and for anyone who cares about fair benchmarking in time series. It deserves a serious referee, not a desk reject, because the architecture is coherent and the flaw is in the evaluation protocol rather than in the derivation. I would send it back for major revision: disclose or fix the optimization-objective mismatch, release code, report variance, and soften the SOTA wording. If those are addressed, it becomes a solid applied contribution.","headline":"MDMixer is a plausible incremental architecture, but its headline MAE margin over TimeMixer is largely a training-objective artifact and the SOTA claim does not survive close reading.","tokens_in":18636,"tokens_out":4219,"would_cite":false,"duration_ms":40475,"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":"MDMixer claims a 4.64% average MAE improvement over the MLP state of the art (TimeMixer) on eight long-term forecasting benchmarks, with lower training cost.","keywords":["long-term time series forecasting","multi-granularity representation","MLP-based forecasting","seasonal-trend decomposition","adaptive weighting gate","channel-dependent fusion","multi-scale prediction","forecasting efficiency"],"falsifier":"Run TimeMixer, iTransformer, PatchTST, and MDMixer on all eight datasets under one shared codebase, same hardware, same seeds, same normalization, and the same hyperparameter search budget; if TimeMixer's average MAE matches or beats MDMixer, or the gap disappears within seed noise, the central improvement claim fails.","tokens_in":17727,"feed_emoji":"📈","tokens_out":8063,"duration_ms":68593,"temperature":0.7,"pith_summary":"This paper tries to establish that long-term time series forecasting improves when a model explicitly predicts the series at several temporal granularities at once and then lets each data channel decide how much to trust each granularity. The proposed MDMixer architecture runs parallel prediction heads at graduated lengths, mixes them coarse-to-fine, and fuses them with a channel-dependent gating network, on top of a trend/seasonal dual branch. On eight standard benchmarks, the paper reports that this beats the previous best MLP forecaster, TimeMixer, by 2.50% in MSE and 4.64% in MAE on average, while using far less training time and memory than comparable models. The authors also claim the dual-branch design can be transplanted into existing linear models to improve them. A sympathetic reader would care because it suggests simple, efficient MLP architectures can outperform attention-based models without giving up interpretability.","feed_headline":"MDMixer cuts long-term forecast MAE by 4.64% over TimeMixer","feed_subtitle":"Parallel prediction heads and channel-aware gating improve accuracy and cut training time on eight benchmarks.","key_machinery":"The load-bearing mechanism is the Multi-granularity Predictor and Mixer (MPM) block, made of three interacting pieces: MPP, where parallel heads predict at graduated lengths so the model explicitly represents coarse seasonal/trend behavior and fine fluctuations at once; MIM, which iteratively fuses the heads coarse-to-fine by adding each head's output to a linear transformation of the previous cumulative output; and AMWG, a gating network that takes global average-pooled seasonal and trend embeddings, concatenates them, and produces an $H \\times C$ weight tensor, with softmax over heads per channel. A dual-branch decomposition routes the seasonal component through linear predictors and the trend through MLPs, and an auxiliary alignment loss compares each intermediate prediction with a downsampled target. The final prediction is the channel-weighted sum of upsampled head outputs plus their unweighted average, which acts as a stable baseline.","core_discovery":"The central claim is that multi-granularity information should be generated, not just extracted: MDMixer uses a Multi-granularity Parallel Predictor (MPP) whose $H$ heads each output a prediction of length $G_i = g \\cdot i$, so coarse and fine views are produced concurrently from the embedded input; a Multi-granularity Iterative Mixer (MIM) then accumulates these predictions coarse-to-fine; and an Adaptive Multi-granularity Weighting Gate (AMWG) assigns softmax-normalized weights over heads for each channel, allowing different variables to rely on different scales. The trend and seasonal components are modeled separately, with linear layers for seasonality and MLPs for trend, and a granularity-aligned loss supervises each intermediate prediction against a downsampled ground truth. The paper reports that this architecture improves average MAE by 4.64% over TimeMixer across eight LTSF benchmarks, also outperforming iTransformer and PatchTST, and that the dual-branch decomposition improves DLinear, RLinear, and NLinear when inserted into them.","pith_inferences":["If the gating mechanism is the active ingredient, the same AMWG module could be grafted onto TimeMixer or other multi-scale mixers; the paper does not test this, but the ablation evidence makes it worth trying.","The alignment loss uses average-pooled targets, so a natural untested variant would use frequency-selective downsampling to force each head to specialize on a cleaner temporal scale.","The sparse head weights on Electricity suggest that head specialization may correspond to interpretable periodic bands; a spectral analysis of each head's learned mapping would test whether the granularity labels are meaningful.","Because the reported margin is averaged over eight datasets with very different channel counts, a per-dataset breakdown would show whether channel-aware fusion matters most in high-dimensional settings like Traffic and Electricity."],"forward_implications":["If MDMixer's results hold, MLP-based forecasting can match or beat transformer models on standard LTSF benchmarks while using a fraction of the training time and memory.","The dual-branch decomposition is claimed to be a transferable module: adding it to DLinear, RLinear, and NLinear improves their accuracy, so existing linear baselines can be upgraded without a full architecture change.","The AMWG weight heatmaps show sparse assignments, with most channels concentrating weight on the coarsest and finest heads; this gives users a per-variable diagnostic of which temporal scale drives each channel.","Longer look-back lengths consistently help MDMixer, unlike attention models, so users with long histories can expect better forecasts as history grows."],"supporting_citations":[{"why":"TimeMixer is the MLP baseline whose average MSE and MAE the paper claims to improve by 2.50% and 4.64%.","marker":"[29]"},{"why":"RLinear supplies the observation that linear maps capture periodic patterns and motivates the MLP-based trend branch.","marker":"[16]"},{"why":"DLinear provides the decomposition-based linear baseline and is one of the models modified in the dual-branch transplant experiments.","marker":"[36]"},{"why":"PatchTST is the patch-based transformer baseline whose results support the claim that patching alone is not enough.","marker":"[23]"},{"why":"iTransformer is the strongest transformer baseline in Table 2, used for the reported 2.21% MSE and 4.10% MAE improvements.","marker":"[17]"},{"why":"Autoformer provides several of the benchmark datasets and the decomposition block that motivates the dual-branch design.","marker":"[33]"},{"why":"Informer supplies the ETT datasets and the train/validation/test protocol followed in the experiments.","marker":"[38]"}],"fun_headline_variants":["MDMixer's parallel multi-scale heads shave 4.64% off forecast MAE","Parallel scale-wise prediction: MDMixer cuts MAE 4.64% over TimeMixer","MDMixer: channel-aware parallel scales deliver 4.64% MAE gain","Multi-granularity parallel prediction: MDMixer trims MAE by 4.64%"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The reported 4.64% MAE margin assumes the baseline numbers taken from prior papers are accurate and comparable; baselines were not re-run by the authors, while MDMixer's numbers are three-seed averages from their own runs, so a same-protocol rerun could shrink or reverse the gap.","fun_headline_variants_meta":{"raw":{"variants":["MDMixer's parallel multi-scale heads shave 4.64% off forecast MAE","Parallel scale-wise prediction: MDMixer cuts MAE 4.64% over TimeMixer","MDMixer: channel-aware parallel scales deliver 4.64% MAE gain","Multi-granularity parallel prediction: MDMixer trims MAE by 4.64%"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001597,"raw_usage":{"total_tokens":6374,"prompt_tokens":968,"completion_tokens":5406,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":584,"completion_tokens_details":{"reasoning_tokens":5306}},"tokens_in":584,"tokens_out":5406,"duration_ms":33995,"temperature":1.0,"reasoning_tokens":5306,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T22:00:42.010217+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run TimeMixer, iTransformer, PatchTST, and MDMixer on all eight datasets under one shared codebase, same hardware, same seeds, same normalization, and the same hyperparameter search budget; if TimeMixer's average MAE matches or beats MDMixer, or the gap disappears within seed noise, the central improvement claim fails.","supporting_citations":[],"review_version":1}