WeatherMixer: Unified Weather Mixing Model

• WeatherMixer is a design pattern that decomposes weather phenomena into specialized branches such as geometry, frequency, and channel for tailored modeling.
• It supports applications from LiDAR denoising to image restoration and ensemble forecasting, achieving improved accuracy metrics across tasks.
• This architectural motif integrates complementary weather representations to address heterogeneous, adverse meteorological conditions in a unified framework.

Searching arXiv for papers related to “WeatherMixer” and adjacent “mixer”/MoE weather modeling concepts. WeatherMixer is not a single canonical architecture in the provided literature, but a recurring design pattern for weather-related learning systems that explicitly mix complementary representations, modalities, or expert predictions in order to model adverse weather, atmospheric dynamics, or severe-weather reasoning. In this sense, the term spans several technical regimes: mixer-style neural architectures for LiDAR denoising in rain, fog, and snow; task-conditioned image restoration under mixed weather; mixture-of-experts forecasters and postprocessors for atmospheric prediction; multimodal systems that combine weather “ingredients” for severe-weather analysis; and large-scale MLP-based global weather models whose computation scales linearly with input size (Zhao et al., 2024). A plausible implication is that “WeatherMixer” functions less as a single named method than as an organizing concept for architectures that separate and recombine weather-relevant structure across geometry, frequency, channels, tasks, modalities, or expert submodels (Kieckhefen et al., 8 Jul 2025).

1. Conceptual scope and definitions

In the most general sense supported by the literature, a WeatherMixer is a model that treats weather effects or weather forecasts as arising from multiple partially complementary factors and then learns how to combine them. The provided sources instantiate this idea in several ways. In adverse-weather LiDAR denoising, TripleMixer is described as conceptually a “WeatherMixer” because it mixes geometry, frequency, and channel dimensions to separate weather-induced noise from valid scene structure (Zhao et al., 2024). In mixed-weather image restoration, the “task transformer and adaptive mixup strategy” paper is explicitly framed as the kind of capability a conceptual WeatherMixer needs: to understand, disentangle, and remove multiple overlapping degradations such as rain, snow, haze, and adherent raindrops (Wen et al., 2024). In global forecasting, EWMoE is described as a ViT-style encoder–decoder “WeatherMixer” that mixes atmospheric variables locally and experts globally via a sparsely gated MoE layer (Gan et al., 2024). In precipitation prediction, the knowledge-guided adaptive MoE formulation is presented as a WeatherMixer that adaptively combines heterogeneous weather data streams such as radar, satellite, and surface fields (Jiang et al., 14 Sep 2025). In ensemble postprocessing, MIXMOS and MIXSAMOS-GB offer a mixture-based WeatherMixer for calibrated probabilistic forecasts (Jobst, 2024).

These instantiations differ in task and modality, but they share a common structural idea: the weather problem is decomposed into subspaces, branches, or experts, and the final prediction emerges from learned recombination. Depending on the application, what is being mixed can be 3D point neighborhoods and wavelet sub-bands, task tokens and decoder features, atmospheric variables and expert FFNs, model forecasts and bias maps, or multimodal observational streams. This suggests that WeatherMixer is best understood as a family of architectures rather than a single model definition.

A second recurring property is that the “mixture” may be literal or architectural. Some papers use explicit mixture formulations with weights summing to one, as in MoWE’s synthesized deterministic forecast

$$\hat{Y}(t, \mathbf{r}, v) = \sum_{i=1}^N W_i(t, \mathbf{r}, v)\, E_i(t, \mathbf{r}, v) + b(t, \mathbf{r}, v),$$

with softmax-normalized weights over experts (Chakraborty et al., 10 Sep 2025). Others use implicit mixing through architectural blocks, such as TripleMixer’s Geometry Mixer, Frequency Mixer, and Channel Mixer, or WPMixer’s patch and embedding mixers over wavelet-decomposed time series (Zhao et al., 2024).

2. Representation mixing in adverse-weather perception

A central WeatherMixer-style instantiation appears in LiDAR denoising for adverse weather. TripleMixer addresses point-wise denoising of 3D LiDAR point clouds under rain, fog, and snow, with datasets represented as

$\{(P_i, L_i)\mid i=1,\dots,N\},$

where each point is $p=(x,y,z,i,r)$, with Cartesian coordinates, intensity, and 3D range, and labels include both object classes and weather noise classes (Zhao et al., 2024). The paper introduces two large-scale datasets, Weather-KITTI and Weather-NuScenes, and a three-branch model comprising the Geometry Mixer Layer, Frequency Mixer Layer, and Channel Mixer Layer (Zhao et al., 2024).

The Geometry Mixer Layer performs voxelization, KNN-based local point mixing, attentive pooling, and residual fusion. Its local feature computation is given by

$$l_i^k = \text{MLP}\left(p_i \oplus p_i^k \oplus (p_i - p_i^k)\right),$$

followed by attention weights

$$c_i^k = \text{Softmax}\bigl(FC(l_i^k)\bigr), \qquad f_i = \sum_{k=1}^{K} c_i^k \odot l_i^k,$$

and residual fusion

$$F_i = \text{Max}\bigl(\text{MLP}(f_i)\bigr) \oplus p_i.$$

This branch mixes local 3D geometry and intensity/range context, with the stated goal of preserving interpretability and stability (Zhao et al., 2024).

The Frequency Mixer Layer is explicitly identified as the core “WeatherMixer” component in the provided exposition. It projects features onto YZ, XZ, and XY planes, applies multi-scale lifting wavelet decomposition, and fuses low- and high-frequency content. The projected feature grids are decomposed into $LL$, $LH$, $HL$, and $HH$ sub-bands, concatenated as

$\{(P_i, L_i)\mid i=1,\dots,N\},$0

then mixed back through

$\{(P_i, L_i)\mid i=1,\dots,N\},$1

The stated interpretation is that structural scene components tend to reside in low-frequency bands, whereas weather noise often behaves as high-frequency clutter (Zhao et al., 2024).

The Channel Mixer Layer then refines these multi-resolution 2D features with

$\{(P_i, L_i)\mid i=1,\dots,N\},$2

before reprojecting features back to 3D for point-wise classification (Zhao et al., 2024). In ablations on WADS, removing FMX causes a larger mIoU drop than removing GMX or CMX, and the full TripleMixer achieves Precision 96.38, Recall 93.93, F1 95.13, and mIoU 90.73 on WADS (Zhao et al., 2024). On Weather-KITTI and Weather-NuScenes, it achieves average mIoU values of 96.31 and 97.21, respectively (Zhao et al., 2024).

This branch-structured formulation is one of the clearest concrete realizations of a WeatherMixer: weather corruption is not modeled as a monolithic nuisance, but as a separable interaction among geometric inconsistency, spectral irregularity, and channel-level context. The same paper also reports downstream semantic segmentation gains when denoised point clouds are fed into SalsaNext, Cylinder3D, and PolarNet, with mIoU improvements of $\{(P_i, L_i)\mid i=1,\dots,N\},$3, $\{(P_i, L_i)\mid i=1,\dots,N\},$4, and $\{(P_i, L_i)\mid i=1,\dots,N\},$5, respectively (Zhao et al., 2024).

3. Mixed-weather restoration and probabilistic weather composition

A second WeatherMixer regime appears in image restoration under compound weather. The model in “Multiple weather images restoration using the task transformer and adaptive mixup strategy” targets a degraded RGB image

$\{(P_i, L_i)\mid i=1,\dots,N\},$6

affected by unknown, possibly mixed adverse weather, and aims to recover a clean image $\{(P_i, L_i)\mid i=1,\dots,N\},$7 without explicit weather labels at test time (Wen et al., 2024). Its architecture combines a Task Transformer with external learnable queries, a Task Sequence Generator, Fast Fourier Convolution, and Adaptive Mixup (Wen et al., 2024).

The Task Intra-patch Block modifies self-attention by replacing image-derived queries with learnable task queries:

$\{(P_i, L_i)\mid i=1,\dots,N\},$8

The interpretation given in the source is that these queries act as weather-task prototypes, while image features serve as keys and values (Wen et al., 2024). The Task Sequence Generator then fuses multi-scale outputs into a task feature query vector map $\{(P_i, L_i)\mid i=1,\dots,N\},$9, used in

$p=(x,y,z,i,r)$0

This is the mechanism by which the model estimates the weather configuration and conditions attention on it (Wen et al., 2024).

The Adaptive Mixup stage is especially close to the WeatherMixer label because it explicitly interpolates between shallow and deep features:

$p=(x,y,z,i,r)$1

The provided exposition interprets this as a learned feature-space mixup between “input-domain representation” and “task-domain representation,” allowing the restoration process to adapt to whether the degradation is more local and high-frequency, as with rain streaks, or more global and low-frequency, as with haze (Wen et al., 2024).

The paper’s quantitative excerpt is limited, but on the Raindrop dataset the method achieves SSIM 0.9574, the highest SSIM among listed multi-task models, though not the highest PSNR (Wen et al., 2024). In downstream object detection with YOLOv5 on a 200-object dataset, the degraded input has Errors+Omissions 144 and Avg confidence 0.184, whereas the model’s restored output has 3 errors/omissions and 0.659 average confidence, compared with 0.648 for TransWeather and 0.681 for ground truth (Wen et al., 2024).

A complementary but more explicitly probabilistic view of mixed weather appears in “Modeling Weather Uncertainty for Multi-weather Co-Presence Estimation,” which argues that weather should be modeled as a continuous and transitional status rather than a discrete multi-label classification problem (Bi et al., 2024). MeFormer represents each weather condition $p=(x,y,z,i,r)$2 with a latent Gaussian

$p=(x,y,z,i,r)$3

uses prior–posterior learning with KL regularization,

$p=(x,y,z,i,r)$4

and predicts soft co-presence probabilities $p=(x,y,z,i,r)$5 over 14 fine-grained weather categories (Bi et al., 2024). On the MePe dataset, uncertainty-aware MeFormer improves SSD from $p=(x,y,z,i,r)$6 to $p=(x,y,z,i,r)$7, KL from $p=(x,y,z,i,r)$8 to $p=(x,y,z,i,r)$9, and $$l_i^k = \text{MLP}\left(p_i \oplus p_i^k \oplus (p_i - p_i^k)\right),$$0 from $$l_i^k = \text{MLP}\left(p_i \oplus p_i^k \oplus (p_i - p_i^k)\right),$$1 to $$l_i^k = \text{MLP}\left(p_i \oplus p_i^k \oplus (p_i - p_i^k)\right),$$2 relative to the deterministic baseline (Bi et al., 2024). This suggests a probabilistic WeatherMixer interpretation in which the weather state itself is a mixture vector over latent weather components rather than a single class.

4. Mixture-of-experts and model-combination WeatherMixers for forecasting

In forecasting, WeatherMixer often takes the form of a mixture-of-experts system. EWMoE forecasts global weather on an ERA5 $$l_i^k = \text{MLP}\left(p_i \oplus p_i^k \oplus (p_i - p_i^k)\right),$$3 grid with 20 variables, 6-hourly steps, and a single-step autoregressive formulation

$$l_i^k = \text{MLP}\left(p_i \oplus p_i^k \oplus (p_i - p_i^k)\right),$$4

trained on only 2015–2016, with validation on 2017 and test on 2018 (Gan et al., 2024). Its “meteorology-specific patch embedding” performs cross-attention across variables at each spatial location using a learnable query, yielding a fused token per patch, and then augments tokens with a learned 3D absolute position embedding over altitude, latitude, and longitude (Gan et al., 2024).

Its core MoE layer replaces the dense FFN in each Transformer encoder block. With $$l_i^k = \text{MLP}\left(p_i \oplus p_i^k \oplus (p_i - p_i^k)\right),$$5 experts and top-$$l_i^k = \text{MLP}\left(p_i \oplus p_i^k \oplus (p_i - p_i^k)\right),$$6 routing with $$l_i^k = \text{MLP}\left(p_i \oplus p_i^k \oplus (p_i - p_i^k)\right),$$7, the gating mechanism is

$$l_i^k = \text{MLP}\left(p_i \oplus p_i^k \oplus (p_i - p_i^k)\right),$$8

and the MoE output is

$$l_i^k = \text{MLP}\left(p_i \oplus p_i^k \oplus (p_i - p_i^k)\right),$$9

An auxiliary load-balancing loss

$$c_i^k = \text{Softmax}\bigl(FC(l_i^k)\bigr), \qquad f_i = \sum_{k=1}^{K} c_i^k \odot l_i^k,$$0

encourages more uniform expert use (Gan et al., 2024). The paper reports that EWMoE outperforms FourCastNet and ClimaX at all forecast times and is competitive with Pangu-Weather and GraphCast in ACC and RMSE, despite using only two years of training data and 2× Nvidia RTX 3090 GPUs (Gan et al., 2024). The design lesson given in the source is that a WeatherMixer should mix both variables and experts while strongly encoding Earth geometry and physical variable structure.

A different forecasting-style WeatherMixer is MoWE, which does not learn a new weather model from scratch but learns how to mix existing expert forecasts from Pangu-Weather, Aurora, and FCN3 (Chakraborty et al., 10 Sep 2025). Its ViT-based gating network takes stacked expert forecasts and lead time as input and predicts weight maps plus a bias map:

$$c_i^k = \text{Softmax}\bigl(FC(l_i^k)\bigr), \qquad f_i = \sum_{k=1}^{K} c_i^k \odot l_i^k,$$1

with final forecast

$$c_i^k = \text{Softmax}\bigl(FC(l_i^k)\bigr), \qquad f_i = \sum_{k=1}^{K} c_i^k \odot l_i^k,$$2

The weights are softmax-normalized across experts at each grid point and variable (Chakraborty et al., 10 Sep 2025). The model achieves up to a 10% lower RMSE than the best-performing AI weather model on a 2-day forecast horizon, and the Small version with ~9M parameters is reported to be already close to the Base version with ~25M parameters (Chakraborty et al., 10 Sep 2025). Qualitative analysis shows that the learned weights favor Aurora at 6 hours but become more balanced among FCN3, Aurora, and Pangu by 24–48 hours, with spatial patterns influenced by coastlines and continents (Chakraborty et al., 10 Sep 2025).

Knowledge-guided Adaptive MoE for precipitation prediction extends the WeatherMixer idea to multimodal climate data integration. Here, 16 MLP experts are pretrained with a diversity objective

$$c_i^k = \text{Softmax}\bigl(FC(l_i^k)\bigr), \qquad f_i = \sum_{k=1}^{K} c_i^k \odot l_i^k,$$3

then frozen while a router learns mixture weights $$c_i^k = \text{Softmax}\bigl(FC(l_i^k)\bigr), \qquad f_i = \sum_{k=1}^{K} c_i^k \odot l_i^k,$$4 and forms predictions

$$c_i^k = \text{Softmax}\bigl(FC(l_i^k)\bigr), \qquad f_i = \sum_{k=1}^{K} c_i^k \odot l_i^k,$$5

On the Hurricane Ian dataset, Adaptive MoE achieves MAE 0.212 (±0.005), MSE 0.057 (±0.002), and RMSE 0.238 (±0.003), outperforming MLP, LSTM, Transformer, and naive MoE baselines (Jiang et al., 14 Sep 2025). The source emphasizes knowledge-guided grouping into momentum, temperature, moisture, mass, cloud, and radiation categories, which gives meteorological meaning to the emerging expert specializations (Jiang et al., 14 Sep 2025).

Together these papers define a forecasting WeatherMixer as a model that mixes variable-wise structure, modality-specific or regime-specific experts, and even fully trained external forecast systems.

5. Statistical and probabilistic postprocessing WeatherMixers

A classical but still highly relevant WeatherMixer formulation appears in statistical postprocessing. “Seamless multi-model postprocessing for air temperature forecasts in complex topography” combines a convection-permitting regional ensemble (COSMO-E) and a global ensemble (IFS-ENS) using a mixed EMOS regression (Keller et al., 2020). For single-model EMOS, temperature is modeled as

$$c_i^k = \text{Softmax}\bigl(FC(l_i^k)\bigr), \qquad f_i = \sum_{k=1}^{K} c_i^k \odot l_i^k,$$6

with

$$c_i^k = \text{Softmax}\bigl(FC(l_i^k)\bigr), \qquad f_i = \sum_{k=1}^{K} c_i^k \odot l_i^k,$$7

The mixed multi-model extension becomes

$$c_i^k = \text{Softmax}\bigl(FC(l_i^k)\bigr), \qquad f_i = \sum_{k=1}^{K} c_i^k \odot l_i^k,$$8

This “Mixed EMOS” improves annual mean CRPS from 1.54 for raw COSMO to 1.05, corresponding to about a 30% improvement relative to raw COSMO, and outperforms either single-model EMOS by 8–12% (Keller et al., 2020). The paper notes that valleys profit particularly from the combination, which indicates that WeatherMixer-style combination can be especially useful where model errors differ systematically across terrain regimes (Keller et al., 2020).

A more explicitly mixture-distribution WeatherMixer is given by “Gradient-Boosted Mixture Regression Models for Postprocessing Ensemble Weather Forecasts” (Jobst, 2024). Its general mixture regression is

$$c_i^k = \text{Softmax}\bigl(FC(l_i^k)\bigr), \qquad f_i = \sum_{k=1}^{K} c_i^k \odot l_i^k,$$9

with softmax-normalized weights and Gaussian components in the temperature case (Jobst, 2024). The paper introduces MIXMOS, MIXSAMOS, and MIXSAMOS-GB. MIXSAMOS uses standardized anomalies

$$F_i = \text{Max}\bigl(\text{MLP}(f_i)\bigr) \oplus p_i.$$0

and similarly standardized forecast covariates, so that static multi-year training becomes possible without explicit rolling windows (Jobst, 2024). MIXSAMOS-GB then applies non-cyclic gradient boosting to select covariates jointly across mixture weights, component means, and component scales.

In the Germany 2m temperature case study, the raw ensemble has CRPS 1.03, while SAMOS, MIXSAMOS, SAMOS-GB, and MIXSAMOS-GB achieve 0.74, 0.72, 0.71, and 0.69, respectively; corresponding RMSE values are 1.39, 1.38, 1.33, and 1.33, versus 1.76 for the raw ensemble (Jobst, 2024). MIXSAMOS-GB is reported as best overall, with the flattest PIT histograms and the strongest station-wise skill improvements (Jobst, 2024). This provides a WeatherMixer interpretation at the distributional level: the predictive density itself is a learned mixture, with components linked to exchangeable forecast groups such as perturbed members and the control forecast.

Another probabilistic variant appears in crowd-sourced weather data interpolation, where a Gaussian–uniform mixture density network models an observation as

$$F_i = \text{Max}\bigl(\text{MLP}(f_i)\bigr) \oplus p_i.$$1

with a Gaussian signal component and a uniform outlier component centered on the learned mean (Kirkwood et al., 2022). On WOW temperature data from about 1900 unofficial stations across the British Isles, the model achieves $$F_i = \text{Max}\bigl(\text{MLP}(f_i)\bigr) \oplus p_i.$$2 and RMSE = 1.15 °C, while simultaneously learning outlier probabilities $$F_i = \text{Max}\bigl(\text{MLP}(f_i)\bigr) \oplus p_i.$$3 (Kirkwood et al., 2022). Although this is not a forecast combination method, it is a WeatherMixer in the sense that trustworthy signal and contaminating sensor noise are separated through a learned probabilistic mixture.

6. Multiscale MLP mixing and large-scale weather modeling systems

The WeatherMixer label also applies to MLP-based architectures whose main operation is mixing over time or spatial tokens. WPMixer, while a general long-term time-series forecaster rather than a dedicated meteorological model, is explicitly positioned for weather forecasting among other applications (Murad et al., 2024). Given

$$F_i = \text{Max}\bigl(\text{MLP}(f_i)\bigr) \oplus p_i.$$4

it applies multi-level discrete wavelet decomposition,

$$F_i = \text{Max}\bigl(\text{MLP}(f_i)\bigr) \oplus p_i.$$5

then processes each resolution branch via patching, linear embedding, Patch Mixer, and Embedding Mixer, before reconstructing the forecast with inverse wavelet transform (Murad et al., 2024). On the Weather benchmark, WPMixer reports average MSE 0.217 and MAE 0.252, compared with 0.222/0.262 for TimeMixer and 0.226/0.264 for PatchTST (Murad et al., 2024). The paper’s design rationale is that wavelet decomposition preserves multi-resolution temporal structure more effectively than moving-average seasonal/trend decomposition, which is relevant to weather time series with daily, synoptic, and event-scale variability (Murad et al., 2024).

At the global-modeling end of the spectrum, “Jigsaw: Training Multi-Billion-Parameter AI Weather Models with Optimized Model Parallelism” explicitly introduces WeatherMixer as an MLP-Mixer-style global weather model (Kieckhefen et al., 8 Jul 2025). The architecture uses an encoder–processor–decoder structure on ERA5 $$F_i = \text{Max}\bigl(\text{MLP}(f_i)\bigr) \oplus p_i.$$6 global fields, with surface variables, pressure-level variables, and static fields such as topography and land/sea mask (Kieckhefen et al., 8 Jul 2025). Its processor is a stack of MLP-Mixer blocks performing token mixing across global spatial patches and channel mixing across feature dimensions, with cost linear in sequence length rather than quadratic as in standard self-attention (Kieckhefen et al., 8 Jul 2025).

The system paper emphasizes that WeatherMixer’s architectural simplicity makes it suitable for Jigsaw, a custom model-parallelization scheme combining domain and tensor parallelism with no parameter redundancy. Training scales to 256 GPUs, reaching 9 and 11 PFLOPs, 23% and 28% of theoretical peaks, and 68% and 72% scaling efficiency versus 51% without model parallelism (Kieckhefen et al., 8 Jul 2025). In forecast skill, the paper reports that an MLP-based model can maintain competitive medium-range performance up to 120 h rollouts, though Pangu-Weather remains stronger in the shown comparisons (Kieckhefen et al., 8 Jul 2025). This is a systems-level WeatherMixer: the “mixing” lies in the MLP-Mixer processor, while the contribution of the paper is equally about making such models trainable at multi-billion-parameter scale.

A plausible implication across WPMixer and WeatherMixer is that MLP-style mixing remains attractive in weather contexts when computational scaling, long sequence length, and regular matrix-multiplication structure are primary constraints.

7. Multimodal reasoning, limitations, and broader interpretation

WeatherMixer can also denote systems that mix heterogeneous evidence sources for meteorological reasoning rather than direct field prediction. WeatherQA defines a benchmark for severe-weather reasoning with 8,511 SPC Mesoscale Discussion samples from 2014–2020, each containing 20 images—18 ingredients-based mesoanalysis parameters, one regional surface chart, and one composite radar reflectivity mosaic—plus expert text (Ma et al., 2024). The benchmark poses two tasks: multiple-choice QA for “Areas affected” and multi-class classification of “Concerning” watch potential (Ma et al., 2024).

The paper evaluates GPT-4 Turbo, GPT-4o, Gemini 1.5 Flash, Gemini 1.5 Pro, Claude 3 Opus, and a fine-tuned Llama-based VLM. On “Areas Affected,” the best result is 39.33% accuracy by GPT-4o in 3-shot-CoT; on “Concerning,” the fine-tuned Llama3 8B achieves 45.00% accuracy / 0.42 weighted F1, while GPT-4o reaches 28.83% / 0.31 in 3-shot mode (Ma et al., 2024). Expert meteorologists rate generated MCD-style outputs from GPT-4o and the fine-tuned VLM at 2.288 and 2.213 out of 9 on average, both classified as poor (Ma et al., 2024). The source concludes that current VLMs remain far from expert-level ingredient-based reasoning and that richer training and data integration are necessary.

This multimodal reasoning setting exposes a broader limitation shared by many WeatherMixer designs: weather structure is heterogeneous not only in scale but also in modality, semantics, and uncertainty. Some systems handle this with explicit expert routing; others with learned task queries; others by probabilistic latent mixtures. Yet several recurring limitations are identified across the papers on arXiv. Synthetic data remain prevalent in mixed-weather perception and co-presence estimation (Wen et al., 2024). Domain gaps between synthetic and real adverse weather remain open (Bi et al., 2024). Extreme events, rare regimes, and explicit physics constraints are often underexplored in MoE and MLP-mixer forecasters (Gan et al., 2024). Static single-time snapshots, rather than sequences, still dominate multimodal reasoning benchmarks such as WeatherQA (Ma et al., 2024).

Taken together, the literature suggests that WeatherMixer is best viewed as a unifying research motif for models that decompose weather-related problems into specialized branches and then recombine them with learned structure. In some settings, the decomposition is physical, as with low- and high-frequency weather noise in LiDAR or image degradations. In others, it is statistical, as with mixture distributions or ensemble postprocessing. In still others, it is algorithmic, as with expert routing across atmospheric regimes or forecast systems. The common thesis is that weather problems are rarely monolithic, and systems that expose and exploit this internal heterogeneity can outperform single-stream baselines (Jobst, 2024).