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FARE: Factor-Aware Retrieval with Error-Guided Fusion for Retail Forecasting
Chenghao Gu, Zhuokang Shen, Shenghao Wu, Tingxuan Zhu, Weiyi Luo, Haifeng Tang
TL;DR
Retail forecasting faces scarce historical precedents for complete target-week factor combinations, even when individual factors have occurred before. FARE retrieves partial factor matches and fuses them with a shape reference and backbone forecast using error-guided gates. Across four retail datasets, it reduces WAPE for five backbones, with average reductions ranging from 4.06% to 14.63%.
Problem
Complete target-week factor combinations can have few precedents, making it difficult to retrieve useful matches and assess their varying reliability across series.
Source: §1 · p. 2Method
FARE retrieves historical weeks separately for each known target-week factor and uses two gates, guided by shrunk development errors and current disagreements, to combine references with a backbone.
Source: §1 · p. 2Results
Average relative WAPE reductions were 11.46% on Favorita, 4.06% on M5, 14.63% on Rossmann, and 10.16% on Rohlik across all 20 pairings of five backbones and four benchmarks.
Source: §8 · p. 14Takeaways & Limitations
The experiments support conditioning retrieval on known future conditions, shrinking per-series reliability estimates toward a pooled mean, and separating reference composition from correction strength.
Source: §8 · p. 15Evidence covers two known factors and seven-day forecasts on four retail datasets; generalization to combinations absent from all training data remains open.
Source: §7 · p. 14
Abstract
from arXiv · showhide
Retail sales forecasting underpins inventory planning, yet promotions and calendar events reshape short-term demand. Although each factor usually has historical occurrences, the complete factor combination of a target week often has few precedents. The challenge is therefore to retrieve informative partial matches and weight them by their reliability, which varies across series. We propose FARE(Factor-Aware Retrieval with Error-Guided Fusion), which ranks historical weeks separately for each known target-week factor and merges the selected weeks into a factor reference under a fixed budget. Guided by shrunk errors from completed development weeks and the current disagreement among candidates, a first gate mixes this factor reference with a shape reference from similar sales histories, and a second gate controls how strongly the mixture corrects a backbone forecast. Both gates remain fixed during testing. On Favorita, M5, Rossmann, and Rohlik, FARE reduces the weighted absolute percentage error (WAPE) of five backbones by 11.46%, 4.06%, 14.63%, and 10.16% on average. With Chronos-2 frozen, FARE also outperforms conventional and existing enhancement methods, including supervised residual correction and retrieval augmentation. Code is available at https://github.com/HousonGu/FARE .
1 Introduction
Retail demand is reshaped by promotions and calendar events, but complete target-week factor combinations may have few historical precedents. FARE retrieves partial factor matches and uses error-guided gates to combine them with sales-shape references and a backbone forecast.
1 Introduction
- Retail sales forecasts support inventory replenishment and supply-chain planning, while promotions and calendar events alter product-level demand over short horizons.The target-week schedules are known at forecast time, but partial historical matches may be needed when the full factor combination is rare.Source: §1 · p. 1
- When complete factor combinations are scarce, complete-match retrieval discards useful precedents, while partial references can disagree and have reliability that varies across series.Similar past sales alone do not ensure that a trajectory reflects the target week's promotion or calendar conditions.Source: §1 · p. 2
- FARE ranks historical weeks separately for each known target-week factor, merges selected weeks into a factor reference, and fuses references with a backbone forecast through two error-guided gates.The gates set reference composition and the strength of its correction to the backbone, using shrunk errors from completed development weeks and current candidate disagreements.Source: §1 · p. 2
- FARE builds an eight-window factor-conditioned partial reference under a fixed retrieval budget and uses separate gates for reference composition and correction strength.The convex weights return continuously to the backbone; experiments assess reference selection and allocation on four retail datasets with five backbones.Source: §1 · p. 3
2 Related Work
Prior work uses retail factors as forecast inputs, retrieves historical trajectories, and combines forecasts using learned weights. FARE instead constructs factor-conditioned reference forecasts and separates reference mixing from total reference contribution.
2.1 Retail Factors and Historical References
- FARE uses separate factor rankings to construct explicit reference trajectories for scarce complete combinations, unlike DD-CZFormer, which learns disentangled drivers for unseen combinations.The cited retrieval approaches use temporal alignment, global and local memories, forecast revision, or retrieved examples and segments in forecasters,,,,,.Source: §2.1 · p. 3
2.2 Adaptive Forecast Combination
- FARE shrinks each candidate's per-series error history toward a global mean before gating, then separately gates reference composition and total reference contribution.Forecast weighting by historical performance can help but carries estimation risks; prior work also shrinks weights or learns them from series features and input meta-features,,,,,.Source: §2.2 · p. 3
3 Problem Definition
The task is to forecast seven daily sales values at each weekly origin from a 56-day series history and known target-week factors. Historical references must be fully observed before the query origin, and forecast output combines a backbone with shape- and factor-based references.
3 Problem Definition
- At each weekly origin, the task predicts seven daily sales values from the preceding 56-day history and target-week factors known at that origin.Examples of known factors include promotions, discounts, SNAP, and calendar indicators.Source: §3 · p. 4
- A historical reference pairs a series' 56-day history with its following seven-day trajectory, which must be fully observed before the query origin.Completed weeks may enter the rolling library, while gate parameters and historical error statistics remain fixed.Source: §3 · p. 4
- FARE combines a backbone prediction, a shape reference from similar sales histories, and a factor reference from separate matches on known target-week factors.The output is a nonnegative daily point forecast, with fusion weights depending on historical errors, current disagreements, and origin features.Source: §3 · p. 4
4 Methodology
FARE constructs shape- and factor-based historical references and combines them with a backbone forecast in two stages. Shrunk historical errors, current disagreements, and forecast-origin features guide the gates, which are fitted on development data.
4 Methodology
- FARE first combines shape and factor references, then uses a second gate to control how much the mixture adjusts the backbone forecast.The references and backbone provide three candidate forecasts, and the two gates combine them into the final forecast.Source: §4 · p. 4, Figure 2 · p. 5
4.1 Three Forecast Candidates
- The shape reference selects eight nearest eligible windows, while factor branches rank partial matches using sales shape and agreement on one known factor.Alternating selection skips duplicates, allocating four windows per branch; the shared library and reference count obey the pre-origin boundary, with fallback to previous-week sales for groups with fewer than eight eligible windows on M5, Rossmann, and Rohlik.Source: §4.1 · pp. 4–6
4.2 Historical Errors Accumulated Forward in Time
- Candidate errors are accumulated from eligible completed forecast days, and series with few observations have their errors shrunk toward the global mean.The gates use the three shrunk errors and log(1 + n); statistics are frozen for evaluation, with development features restricted to origins whose target days precede the current origin.Source: §4.2 · p. 6
4.3 Gating Features
- Gating inputs combine historical errors and current candidate disagreements with series, library, and factor features.Continuous inputs are standardized on gating training rows, and the complete models use 12 to 15 non-intercept inputs depending on dataset.Source: §4.3 · pp. 6–7
4.4 Two Bounded Soft Gates
- The gates use convex weights to separate reference composition from total reference participation, so the forecast returns continuously to the backbone as the second gate approaches zero.The effective weights on the backbone, shape reference, and factor reference are nonnegative and sum to one.Source: §4.4 · p. 7
4.5 Fitting Objective and Optimization
- Gate parameters are fitted on development rows by minimizing a smoothed normalized-error surrogate plus regularization of non-intercept parameters.Evaluation uses unsmoothed WAPE and MAE; optimization uses L-BFGS-B with analytical gradients.Source: §4.5 · p. 7
5 Experimental Setup
The experiments use rolling weekly forecasts across four retail datasets, with chronological fitting, development, and testing periods. They compare FARE and controlled alternatives under shared evaluation rows, then report pooled WAPE and daily-sales MAE.
5.1 Data and Temporal Protocol
- Each origin uses 56 complete calendar days to forecast the next seven nonoverlapping days; four datasets differ in series, factors, and grouping, and incomplete histories are skipped.Favorita origins involving 25 December are skipped because Christmas records are missing; M5 series average zero sales on 62% of development-history days.Source: §5.1 · pp. 7–8
5.2 Comparisons and Controls
- Comparisons use frozen Chronos-2 except in the backbone study, with input, retrieval, error, gate, and output-path controls plus conventional and retrieval-based alternatives.Test labels are not used for fitting, selection, or error calibration; completed test weeks may supply history for later origins.Source: §5.2 · pp. 8–9, §5.1 · p. 8
5.3 Metrics and Implementation
- WAPE pools absolute errors and sales across weeks, while MAE is in daily-sales units and equals WAPE times mean sales on the same targets.The two gates have 32, 26, 30, and 30 trainable parameters on Favorita, M5, Rossmann, and Rohlik, respectively; reference search and sorting scale with library size.Source: §5.3 · p. 10
6 Results and Analysis
FARE improves five backbones across all four datasets, while comparisons and ablations identify dataset-dependent roles for retrieval and allocation.
6.2 Ablation Study
- Random references are the most damaging variant on every dataset; beyond retrieval, bottlenecks differ: factor matching on Rossmann, candidate weighting on Favorita, and error estimation and retrieval on M5 and Rohlik.The complete model outperforms every variant on all four datasets.Source: §6.2 · pp. 10–11
6.1 Comparison with Existing Methods
- 6.81% and 6.69% further WAPE reductions over TimeFuse on Favorita and Rohlik, while FARE beats LightGBM residual correction and XGBoost by 3.64% and 1.32% on M5 and Rossmann.The comparisons use frozen Chronos-2; FARE fits only 26 to 30 gate parameters.Source: §6.1 · p. 10, Table 2 · p. 11
6.3 Mechanism Analysis of Reference Provision versus Allocation
- Fixing either α or β raises WAPE across all four datasets; on M5, one-level softmax and fixed, global-weight, and hard-selection blends degrade the backbone while FARE improves it.The mechanism analysis attributes the two-level design to separating what to mix from how far to move the forecast.Source: §6.3 · pp. 11–12, Figure 3 · p. 13
6.4 Complementarity Across Forecasting Backbones
- 11.46%, 4.06%, 14.63%, and 10.16% average WAPE reductions across Favorita, M5, Rossmann, and Rohlik, respectively, as FARE improves all five backbones on every dataset.On Rossmann, FARE narrows the cross-backbone WAPE range from 8.19 to 3.83 points; fused SparseTSF still trails unfused Chronos-2 on M5.Source: §6.4 · pp. 12–14, Table 4 · p. 13
6.5 Temporal Consistency and Remaining Regressions
- With Chronos-2, FARE improves 22 of 25 Favorita origins, every M5 and Rohlik origin, and 24 of 26 Rossmann origins, but trails the backbone at three Favorita and two Rossmann origins.It beats the same-form one-level softmax at every Rossmann and Rohlik origin.Source: §6.5 · p. 14
7 Discussion and Limitations
The discussion recommends factor-aware retrieval and shrunk, per-series reliability estimates, while noting the evaluation’s scope and limits on recovering demand changes missed by all candidates.
7 Discussion and Limitations
- Known target-week factors belong in the retrieval key, and per-series error estimates should be shrunk toward a pooled mean.Retrieval and allocation ablations can indicate which level to improve first on a new dataset; FARE adds 26 to 32 parameters to a frozen backbone, but its gates are refit for each backbone.Source: §7 · p. 14
- The evidence covers two known factors, seven-day forecasts, and four retail datasets; generalization to combinations absent from all training data remains open.The discussion also proposes evaluating across levels of combination support to identify when partial retrieval helps most.Source: §7 · p. 14
- Error statistics and gate parameters stay fixed during testing, with similar average gains across the first and second test-period halves on M5, Rossmann, and Rohlik.Reported half-period gains are 4.19 and 4.13 points on M5, 4.97 and 6.59 on Rossmann, and 2.38 and 1.90 on Rohlik.Source: §7 · p. 14
- When all candidates miss the same demand change, convex fusion cannot recover it; richer candidate forecasts are one proposed remedy.Source: §7 · p. 14
8 Conclusion
FARE improves forecasting across the evaluated backbone–benchmark pairings. The conclusion favors per-series reliability estimates shrunk toward a pooled mean and separate gates for reference composition and correction strength.
8 Conclusion
- Across all 20 pairings of five backbones and four benchmarks, FARE lowers WAPE and MAE, with average relative WAPE reductions of 11.46% on Favorita, 4.06% on M5, 14.63% on Rossmann, and 10.16% on Rohlik.Source: §8 · p. 14
- FARE adds only a few dozen parameters to a frozen backbone.Source: §8 · p. 14
- Under scarce evidence, candidate reliability should be estimated per series and shrunk toward a pooled mean; separating reference composition from correction strength outperforms one-level and fixed allocation.Source: §8 · p. 15