SAE-Xplainers: Rule-Based Feature Interpretation for Extreme Earth Events

Hugo Porta; Emanuele Dalsasso; Chang Xu; Theo Gnassounou; Devis Tuia

cs.LGAug 20, 2026

SAE-Xplainers: Rule-Based Feature Interpretation for Extreme Earth Events

Authors: Hugo Porta, Emanuele Dalsasso, Chang Xu, Theo Gnassounou, Devis Tuia

Organizations: EPFL, Switzerland · Université Grenoble Alpes, France · Inria, France

Abstract

The emergence of large-scale Weather and Climate (W&C) datasets offers new opportunities for modeling extreme Earth events (ExEE) and their impacts using deep learning. However, their adoption in operational settings remains limited by the lack of models' interpretability. While for conventional text and image modalities, tools such as Sparse Autoencoders (SAEs) have proven effective for extracting human-understandable concepts, their use for the analysis of ExEE remains challenging due to the nature of W&C data. To address this, we introduce (i) a geographic location-based modulation of the inputs of SAE to capture the local semantic meaning of environmental patterns, and (ii) an ensemble of rule-based SAE-Xplainers to interpret the resulting high-dimensional features derived from complex, multi-modal environmental predictors. We evaluate our method on three ExEE types: the prediction of fires, and the detection of tropical cyclones and atmospheric rivers. We show that SAE input modulation improves both reconstruction performance and feature utilization, and that our SAE-Xplainers enable faithful interpretation of complex climatic patterns by unfolding them into human-understandable rules that are consistent with the scientific literature, while also supporting the identification of feature absorption.

Figures & tables

Figure 1: (Top): In computer vision, human users or Vision-Language Models (VLMs) can easily infer the semantic meaning of the SAE features via their activations. (Bottom): In ExEE tasks, the semantic meaning of SAE features cannot be inferred from their activation maps. We propose to learn rule-based models to interpret the features from the input variables (T2M, Rel-Hum, …, see Table 3 in supplementary material for definition), replacing human or VLM analysis.

Figure 2: Overview of our framework. (Top): GeoTopK is trained on the modulated patch activations jointly with the location encoder. (Bottom): For a given SAE feature, a SAE-Xplainer is trained via Skope-Rules to predict the binarized activations of selected input patches, where the negatives are sampled adversarially in the neighborhood of positives.

Figure 3: Similar environmental conditions (ENV) can lead to different ExEE probabilities due to local effects, requiring models to learn location-dependent features.

Table 1: Quantitative Comparison of TopK and GeoTopK on ClimaX and ViT last residual stream, fine-tuned on SeasFire and ClimateNet, respectively. Bold means best score, underline means similar score (difference is

\leq 0.005

Figure 4: SAE-Xplainers quantitative analysis. (a): Faithfulness of our SAE-Xplainers interpretations across Skope-Rules parametrization of ClimaX Neurons, Prototypes, and GeoTopK feature activations. (b): Evolution of the scores related to absorption across SAE-Xplainers parametrizations.

Figure 5: Sample-level feature interpretability for a ClimaX feature fine-tuned on SeasFire. (Left $\rightarrow$ Right): Feature activations, model prediction masks ( no fires regions are masked), SAE-Xplainer rule visualizations with binary masks (unsatisfied rule regions are masked), and input variables highlighting the rule support. The complete rule set for this feature is displayed in supplementary material Figure 11.

Figure 6: Semantic structure of the rules in the SAE-Xplainers of the 50 most fire-specific GeoTopK features. The levels represent the tree-like structure of each rule, while the nodes describe the categories of the conditions; N indicates the number of rules.

Metric	Neurons	Prototypes	GeoTopK
$\text{Tr}_{\text{cond}}\uparrow$	0.33	0.50	0.46
$\text{Inv}_{\text{cond}}\downarrow$	0.16	0.20	0.02

Table 2: Ratio of rule sets containing true (Tr) and inverse (Inv) conditions for fire-specific dimensions.

Dataset	Acronym	Name	Units	Type	Source
SeasFire	lst_day	Land Surface Temperature (Day)	K	Land Surface (Weather)	MODIS
	ndvi	Normalized Difference Vegetation Index	unitless	Vegetation	MODIS
	mslp	Mean Sea Level Pressure	Pa	Weather	ERA5
	rel_hum	Relative Humidity	$\%$	Weather	ERA5
	ssrd	Surface Solar Radiation Downwards	$\text{MJ}\cdot\text{m}^{-2}$	Weather	ERA5
	sst	Sea Surface Temperature	K	Climate	ERA5

Table 3: Summary of predictors used from SeasFire and ClimateNet datasets in our paper.

Metric	SeasFire				ClimateNet
Metric	ClimaX	ViT	ProtoSeg	U-Net++*	ClimaX	ViT	ProtoSeg	DeepLabV3+*
PRAUC $\uparrow$	0.6205	0.6150	0.5161	0.6100	-	-	-	-
IoU $\uparrow$	-	-	-	-	0.5385	0.4972	0.4254	0.5247

Table 4: Downstream task performance of ClimaX, ViT, and ProtoSeg fine-tuned on SeasFire and ClimateNet. * denotes results reported from the original papers.

Levels	Parameters
Levels	Max Depth	# Estim.	Min Precision	Min Recall
Low	3	3	0.90	0.20
Mid	4	5	0.80	0.15
High	5	5	0.70	0.10

Table 5: Skope-Rules parametrization across complexity levels. # Estim. denotes the number of estimators.

Metric	Scalar	Shift-Only	Scale-Only	LOAN	LatBias	GeoTopK
${\text{R}^{2}}$ $\uparrow$	0.930	0.936	0.931	0.754	0.928	0.937
$\text{R}^{2}_{\text{worst}}$ $\uparrow$	0.884	0.899	0.889	0.616	0.881	0.901
$\text{R}^{2}_{\text{event}}$ $\uparrow$	0.808	0.802	0.817	0.726	0.806	0.807
MSE $\downarrow$	1.77e-3	1.61e-3	1.73e-3	0.243	1.82e-3	1.59e-3
Dead Features $\downarrow$	0.041	0.004	0.003	0.002	0.107	0.002

Table 6: Ablation study of the geographic modulation in GeoTopK on ClimaX fine-tuned on SeasFire. Bold means best score, underline means similar score (difference is

\leq 0.005

Figure 7: TopK and GeoTopK performance ( Left: Dead Features Rate, Right:

{\text{R}^{2}}

) when scaling the latent dimension size:

N

, at fixed sparsity ratios for ClimaX, fine-tuned on SeasFire.

Panel of Figure 8 — Figure 8: Feature assignment across the Skope-Rules parametrization: low, mid, and high, with or without spatial context.

Figure 9: Exploratory tool for global model interpretations showcasing feature vectors as points in 2 dimensions extracted through a UMAP projection, and color-coded by event class selectivity. When a feature is selected, its rule-based interpretations, geographic activations, and co-occurring features are shown.

Sampling	Metric
Sampling	Stability $\downarrow$	$\text{Weight}_{\text{loc}}$ $\downarrow$	$\text{Tr}_{\text{cond}}\uparrow$
Random	$\textbf{0.688}\pm 0.023$	$0.633\pm 0.059$	$0.490\pm 0.064$
Adversarial	$0.705\pm 0.017$	$\textbf{0.574}\pm 0.071$	$\textbf{0.497}\pm 0.074$

Table 7: Comparison of the sampling strategies for training the SAE-Xplainers on ClimaX fine-tuned on SeasFire. The reported results are average across three runs with their standard deviation.

Category	Usage	Ex. Feature	Description	Reference
NDVI Limits	56%	632	NDVI, a proxy for vegetation productivity, shows a humped relationship with fire risk: both sparse and overly healthy (green) vegetation suppress it.	( Krawchuk et al. 2009 ; Hantson et al. 2016 ; Bowman et al. 2020 )
Population Density Limits	34%	3734	Fire risk peaks at intermediate population density, the wildland–urban interface, since fire ignition rises but fire spread falls with density, producing a humped relationship.	( Calef et al. 2008 ; Hantson et al. 2016 ; Pechony and Shindell 2009 ; Li et al. 2012 )
Low Humidity	30%	49	Low relative humidity dries fuel and soil, favoring ignition and spread, and is thus negatively correlated with fire risk.	( Li et al. 2012 ; Jolly et al. 2015 ; Jain et al. 2022 ; Kudláčková et al. 2025 )
High VPD	26%	3815	Vapor pressure deficit (VPD): air dryness at a given temperature, drives fuel aridity and is positively correlated with ignition and spread.	( Pechony and Shindell 2009 ; Jain et al. 2022 ; Kudláčková et al. 2025 )
Low Precipitation	18%	2728	Precipitation, closely tied to humidity, sustains fuel and soil moisture, and is thus negatively correlated with fire risk.	( Hantson et al. 2016 ; Jolly et al. 2015 ; Kudláčková et al. 2025 )
High Temperature	14%	700	High temperature promotes fuel aridity and is generally positively correlated with fire risk.	( Hantson et al. 2016 ; Bowman et al. 2020 ; Jolly et al. 2015 ; Jain et al. 2022 )

Table 8: Details on the categories used for the fire-specific SAE-Xplainers semantic analysis in Figure 6 and their scientific meaning.

Panel of Figure 10 — Figure 10: (a): Top 10 most used conditions (ignoring latitude and longitude) across the fire-specific SAE-Xplainers. The 20% quantiles are denoted: q0, q1, q2, q3, and q4, and so $\text{ndvi}>\text{q2}$ means that NDVI is strictly superior to a threshold in the third 20% quantile. (b): Co-occurrence matrix of the categories assigned to top-50 GeoTopK features. This matrix only records co-occurrence from distinct GeoTopK features, as they can be assigned to multiple categories.

GeoTopK Feature	Eval. Accuracy	Complexity	Rule Set	Conditions
1160	0.92	Mid	mslp <= 101174.00 and lat <= 9.36 and lat > 7.28 and ndvi > 0.31 mslp <= 101140.83 and lat <= 9.36 and lat > 7.28 and lon > 22.72 mslp <= 101157.69 and lat > 3.12 and lon > 26.88 and ndvi > 0.30	mslp <= q1 ndvi > q2
1222	0.99	Low	lat <= 10.00 and lat > 7.28 and lon <= 0.00 lat <= 10.00 and lon <= 0.00 and swvl1 > 0.08 lst_day > 299.44 and lat <= 10.00 and lat > 7.28	swvl1 > q0 lst_day > q2
1547	0.96	Low	lat <= -10.00 and lat > -11.68 and swvl1 > 0.08 lat <= -10.00 and lat > -11.68 and sst <= 116.95 lat <= -10.00 and lat > -11.68 and pop_dens > -0.16	swvl1 > q0 sst <= q0 pop_dens > NaN
944	0.93	Low	lat <= -4.16 and lat > -8.32 and pop_dens > 0.40 lat <= -4.16 and lat > -8.32 and sst <= 74.93 lon <= 15.20 and lon > 13.12	pop_dens > q1 sst <= q0

Table 9: Description of Unknown SAE-Xplainer with in bold the rule condition to further analyze.

Figure 11: Sample-level feature interpretability for a ClimaX feature fine-tuned on SeasFire. (Row 1): Feature activations and model prediction masks ( no fires regions are masked). (Rows 2–3): SAE-Xplainer rule visualizations with binary masks (unsatisfied rule regions are masked) and input variables highlighting the rule support.

Figure 12: Sample-level feature interpretability for a ClimaX feature fine-tuned on SeasFire. (Row 1): Feature activations and model prediction masks ( No Fire regions are masked). (Rows 2–3): SAE-Xplainer rule visualizations with binary masks (unsatisfied rule regions are masked) and input variables highlighting the rule support.

Figure 13: Sample-level feature interpretability for a ClimaX feature fine-tuned on ClimateNet and linked to Atmospheric Rivers . (Row 1): Feature activations, model prediction masks ( No Event regions are masked), and high feature activation window of analysis. (Rows 2–3): SAE-Xplainer rule visualizations with binary masks (unsatisfied rule regions are masked) and input variables highlighting the rule support.

Figure 14: Sample-level feature interpretability for a ClimaX feature fine-tuned on ClimateNet and linked to Atmospheric Rivers . (Row 1): Feature activations, model prediction masks ( No Event regions are masked), and high feature activation window of analysis. (Rows 2–3): SAE-Xplainer rule visualizations with binary masks (unsatisfied rule regions are masked) and input variables highlighting the rule support.

Figure 15: (Left): Example of identified feature group with absorption for ClimateNet. (Right): Co-occurrence matrix for those features computed over the whole dataset.

Figure 16: (Left): Example of identified feature group with absorption for SeasFire. (Right): Co-occurrence matrix for those features computed over the whole dataset.

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