Beyond Linear Superposition: Discovering Climate Features in AI Weather Models with KAN-SAE

Minjong Cheon

arxiv: 2605.17493 · v1 · pith:ZOAW47DUnew · submitted 2026-05-17 · 💻 cs.LG · cs.AI· cs.CV· physics.ao-ph

Beyond Linear Superposition: Discovering Climate Features in AI Weather Models with KAN-SAE

Minjong Cheon This is my paper

Pith reviewed 2026-05-20 14:43 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.CVphysics.ao-ph

keywords KAN-SAEsparse autoencodersmechanistic interpretabilityAI weather predictionclimate featuresnonlinear activationsB-splinesfeature discovery

0 comments

The pith

Nonlinear B-spline activations in sparse autoencoders recover climate features in AI weather models that linear methods miss.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces KAN-SAE, a sparse autoencoder that replaces standard linear or ReLU encoders with learnable per-feature B-spline activations drawn from Kolmogorov-Arnold Networks. This change enables each latent dimension to develop its own nonlinear gating profile, leading to substantially more alive features and the unsupervised discovery of specific climate phenomena such as a European heatwave pattern and a western Pacific typhoon tracker. These findings are validated through lower inter-feature redundancy and causal steering experiments on the Sonny weather prediction model. A sympathetic reader would care because the work shows that the linear superposition assumption common in mechanistic interpretability tools fails to capture the nonlinear dynamics encoded in modern AI weather models.

Core claim

KAN-SAE replaces the encoder of a standard sparse autoencoder with per-feature learnable B-spline activations, allowing nonlinear gating for each latent dimension. When applied to representations from the Sonny deep learning weather model, it recovers 975 alive features versus 566 for a linear baseline, achieves 20 percent lower redundancy at comparable reconstruction fidelity, and identifies an interpretable European heatwave feature concentrated over western Europe plus a western Pacific typhoon tracker, both confirmed by causal steering interventions.

What carries the argument

KAN-SAE encoder, which substitutes standard ReLU with learnable per-feature B-spline activations from Kolmogorov-Arnold Networks to produce nonlinear gating profiles for each latent dimension.

If this is right

Mechanistic understanding of how AI weather models internally encode specific physical climate events becomes feasible without supervision.
Feature steering can be used to test and potentially correct model behavior on targeted phenomena such as heatwaves or typhoons.
Lower inter-feature redundancy simplifies the extraction of distinct, interpretable latents compared with linear baselines.
Nonlinear activations prove necessary for recovering climate features that remain invisible under the linear superposition assumption.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Similar nonlinear SAE variants could be tested on other transformer-based scientific models to check whether linear baselines systematically miss domain-specific structures.
The method opens the possibility of designing weather models with built-in nonlinear interpretability rather than relying solely on post-hoc analysis.
One could measure whether the additional features improve downstream tasks such as bias detection or extreme-event forecasting accuracy.
If the B-spline approach generalizes, it suggests revisiting linear assumptions in interpretability work across other nonlinear physical simulation domains.

Load-bearing premise

The increase in alive features and the identified climate patterns reflect genuine physical phenomena encoded in the model rather than artifacts from the B-spline parameterization or post-hoc selection.

What would settle it

A causal steering experiment in which activating the typhoon feature produces no measurable change in predicted typhoon paths or intensities in the Sonny model output.

Figures

Figures reproduced from arXiv: 2605.17493 by Minjong Cheon.

**Figure 1.** Figure 1: KAN-SAE architecture. Top: Overview of the probe pipeline. Layer-5 residual-stream activations from SONNY (x ∈ R 384) are encoded into a high-dimensional sparse latent space and decoded to reconstruct the original activations xˆ. Bottom: Detailed encoder–decoder structure. The encoder projects x through Wenc, then applies a per-feature B-spline activation ϕj (·) (shown with diverse learned profiles, contra… view at source ↗

**Figure 2.** Figure 2: KAN-SAE feature population analysis. (a–c) B-spline shape diversity: representative curves, nonlinearity score histogram (902 convex, 73 concave; median 0.43), and mean response by shape class. (d–f) Dead-feature comparison: alive/dead grids, ranked activation curves, and days-active distributions. KAN-SAE sustains activation across its full dictionary (median 51/53 days) while LIN-SAE collapses to a media… view at source ↗

**Figure 3.** Figure 3: Inter-feature redundancy comparison. (a) KDE of pairwise [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: B-spline activation analysis. (a) Learned response curve for F590 (EU heatwave feature, red) vs. linear [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗

**Figure 5.** Figure 5: Climate feature case studies for the 2019 European heatwave (top, a–c) and Typhoon Mangkhut 2018 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

**Figure 6.** Figure 6: Causal steering of feature F590 over EU heatwave days (25–29 June 2019). (a) [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗

**Figure 7.** Figure 7: Push–pull circuit driving the Layer-5 heatwave feature F590. (a,d) Activation maps of the inhibitory feature [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗

**Figure 8.** Figure 8: Reconstruction fidelity comparison between [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗

read the original abstract

Deep learning weather prediction models achieve remarkable predictive skill yet remain largely opaque: we know little about how they represent physical climate phenomena internally. Mechanistic interpretability through Sparse Autoencoders (SAEs) offers a principled route to decomposing these representations, but existing SAEs assume strictly linear feature superposition - a constraint ill-suited for the highly nonlinear atmospheric dynamics encoded in modern transformers. We introduce KAN-SAE, a sparse autoencoder whose encoder replaces the standard ReLU with learnable per-feature B-spline activations drawn from Kolmogorov-Arnold Networks (KANs), allowing each latent dimension to develop its own nonlinear gating profile. Applied to Sonny, KAN-SAE discovers 975 alive features (vs. 566 for a linear baseline, a 72% improvement) with 20% lower inter-feature redundancy and comparable reconstruction fidelity. Without any climate supervision, KAN-SAE identifies an interpretable European heatwave feature spatially concentrated over western Europe, and a western Pacific typhoon tracker confirmed by causal steering experiments. Our results demonstrate that nonlinear activations are essential for mechanistic interpretability of deep learning weather prediction models, recovering climate features that remain invisible to linear baselines.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

KAN-SAE gets more alive features and surfaces some climate patterns in a weather model, but the gains could easily trace to extra parameters in the B-splines rather than nonlinearity itself.

read the letter

The main thing here is that the authors replace the usual ReLU in a sparse autoencoder with per-feature B-splines from Kolmogorov-Arnold networks and apply it to the internal activations of a weather prediction transformer called Sonny. They report 975 alive features against 566 for the linear baseline, about 20% less redundancy, and two unsupervised features that look like a European heatwave and a western Pacific typhoon tracker, with some steering checks to back them up. That combination is new enough to notice, and the qualitative examples are the part that actually lands: finding spatially coherent climate signals without supervision is useful for people who want to debug these models. The reconstruction fidelity stays comparable, which is a small positive point. The paper does a decent job showing that linear SAEs miss some of these patterns in this particular model. The soft spot is exactly the one the stress-test flags. Each B-spline carries its own grid and knot parameters, so the per-latent capacity is higher than a standard SAE. Without an ablation that matches parameter count or fixes the spline grid size, the jump in alive features and the emergence of the heatwave and typhoon directions could just be extra expressivity or post-selection effects rather than proof that nonlinearity is required for disentangling atmospheric representations. The abstract gives no error bars, no dataset split details, and no controls for how “alive” is defined or how redundancy is measured, so those numbers are hard to interpret yet. The full text apparently adds some methods, but the core comparison still needs tighter controls to hold up. This is the kind of work that belongs in a reading group for people working on mechanistic interpretability for scientific ML, especially climate applications. It is not ready to cite as settled evidence that nonlinear activations are essential, but it is worth following if the authors tighten the ablations. I would send it to peer review; the topic matters and the empirical direction is worth referee time even if the current version needs substantial revision on the controls.

Referee Report

3 major / 3 minor

Summary. The paper introduces KAN-SAE, a sparse autoencoder variant that replaces the standard ReLU encoder with per-feature learnable B-spline activations drawn from Kolmogorov-Arnold Networks. Applied to the Sonny deep learning weather prediction model, KAN-SAE recovers 975 alive features (versus 566 for a linear SAE baseline), reports 20% lower inter-feature redundancy at comparable reconstruction fidelity, and identifies unsupervised climate features including a European heatwave pattern and a western Pacific typhoon tracker. These features are validated through causal steering experiments. The central claim is that nonlinear activations are required to recover physically meaningful representations that remain invisible under linear superposition assumptions.

Significance. If the core empirical findings hold after addressing capacity controls, the work would provide concrete evidence that standard linear SAEs are insufficient for mechanistic interpretability of nonlinear atmospheric dynamics in transformer-based weather models. The unsupervised discovery of spatially coherent, steerable climate features (heatwave and typhoon) without explicit supervision is a notable strength, as is the focus on a real deployed model (Sonny). This could influence future SAE designs in scientific ML domains where dynamics are inherently nonlinear.

major comments (3)

Methods section (KAN-SAE architecture description): The comparison between KAN-SAE and the linear baseline does not isolate nonlinearity from increased per-latent capacity. Each B-spline activation introduces its own grid size, knot locations, and coefficient parameters, raising the effective degrees of freedom per feature relative to a standard ReLU or linear encoder. The reported 72% increase in alive features and the emergence of the European heatwave / typhoon features could therefore arise from this extra expressivity or from post-hoc selection rather than a fundamental requirement for nonlinearity. A parameter-matched linear control (e.g., wider linear encoder or explicit parameter count ablation) is needed to support the claim that nonlinear activations are essential.
Experiments section (steering validation): The causal steering experiments confirming the typhoon tracker and heatwave features lack quantitative metrics. While qualitative spatial concentration is described, the manuscript should report specific effects on downstream variables (e.g., change in 2 m temperature anomaly over western Europe or track error for typhoon events) together with statistical significance across multiple seeds or runs.
Results section (redundancy and alive-feature counts): The 20% lower inter-feature redundancy claim is presented without the precise definition of the redundancy metric (e.g., pairwise cosine similarity, mutual information, or activation correlation threshold) or error bars across independent training runs. This makes it difficult to judge whether the improvement is robust or sensitive to hyperparameter choices such as sparsity coefficient or spline grid resolution.

minor comments (3)

Abstract and §1: The phrase 'comparable reconstruction fidelity' should be accompanied by explicit numbers (e.g., MSE or L2 reconstruction error on held-out data) to allow readers to assess any fidelity-interpretability trade-off.
Notation: Define the exact form of the B-spline activation (order, number of knots, grid range) in the main text rather than relegating all details to the appendix; this would improve reproducibility.
Figure captions: Ensure that all panels in the feature visualization figures explicitly label the linear baseline versus KAN-SAE for direct visual comparison.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive feedback on our manuscript. We have carefully considered each major comment and provide point-by-point responses below. Where revisions are needed, we have updated the manuscript accordingly to address the concerns.

read point-by-point responses

Referee: Methods section (KAN-SAE architecture description): The comparison between KAN-SAE and the linear baseline does not isolate nonlinearity from increased per-latent capacity. Each B-spline activation introduces its own grid size, knot locations, and coefficient parameters, raising the effective degrees of freedom per feature relative to a standard ReLU or linear encoder. The reported 72% increase in alive features and the emergence of the European heatwave / typhoon features could therefore arise from this extra expressivity or from post-hoc selection rather than a fundamental requirement for nonlinearity. A parameter-matched linear control (e.g., wider linear encoder or explicit parameter count ablation) is needed to support the claim that nonlinear activations are essential.

Authors: We agree that a fair comparison requires controlling for model capacity. In the revised manuscript, we have added an ablation study with a parameter-matched linear SAE baseline. Specifically, we increased the hidden dimension of the linear encoder to match the total number of parameters in the KAN-SAE (accounting for the spline coefficients and grid parameters). This control confirms that the higher number of alive features and the discovery of interpretable climate patterns are attributable to the nonlinear activations rather than increased capacity alone. We report the results in a new subsection of the Experiments section. revision: yes
Referee: Experiments section (steering validation): The causal steering experiments confirming the typhoon tracker and heatwave features lack quantitative metrics. While qualitative spatial concentration is described, the manuscript should report specific effects on downstream variables (e.g., change in 2 m temperature anomaly over western Europe or track error for typhoon events) together with statistical significance across multiple seeds or runs.

Authors: We appreciate this suggestion for strengthening the validation. In the revised manuscript, we have added quantitative metrics for the steering experiments. For the European heatwave feature, we report the average change in 2m temperature anomaly over western Europe when steering the feature, along with p-values from t-tests across 10 independent runs. For the typhoon tracker, we include the reduction in track error for typhoon events in the western Pacific, with statistical significance. These results are presented in Table 3 and Figure 5 of the revised version. revision: yes
Referee: Results section (redundancy and alive-feature counts): The 20% lower inter-feature redundancy claim is presented without the precise definition of the redundancy metric (e.g., pairwise cosine similarity, mutual information, or activation correlation threshold) or error bars across independent training runs. This makes it difficult to judge whether the improvement is robust or sensitive to hyperparameter choices such as sparsity coefficient or spline grid resolution.

Authors: We have clarified the redundancy metric in the revised manuscript: it is defined as the mean pairwise cosine similarity between the decoder weights of alive features, thresholded at an activation correlation of 0.1. Additionally, we now report error bars representing the standard deviation across five independent training runs with different random seeds. The 20% reduction in redundancy for KAN-SAE remains statistically significant (p < 0.05) and is robust to variations in the sparsity coefficient and spline grid resolution, as shown in the updated Results section and Appendix B. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical results from KAN-SAE application stand independently

full rationale

The paper reports empirical outcomes from applying a KAN-based sparse autoencoder (with per-feature B-spline activations) to an AI weather model, including higher counts of alive features, reduced redundancy, and unsupervised discovery of specific climate patterns such as a European heatwave feature and typhoon tracker. No equations, derivations, or self-referential definitions appear that reduce these outcomes to fitted parameters by construction or to load-bearing self-citations. The comparison to a linear SAE baseline is presented as an external empirical contrast rather than a mathematical identity or renamed input. The central claim of nonlinearity's necessity rests on observed differences in feature recovery, which remain falsifiable against the reported metrics and do not collapse into the architecture's parameterization itself.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities. The method implicitly assumes that per-feature B-splines can be learned without destabilizing the sparsity objective or introducing spurious nonlinearities.

pith-pipeline@v0.9.0 · 5739 in / 1141 out tokens · 47932 ms · 2026-05-20T14:43:55.829985+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We replace ReLU with a bank of M learnable univariate B-spline functions {ϕ_j} one per latent dimension: z_j = ϕ_j([W_enc(x−b_pre)+b_enc]_j)
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean J_uniquely_calibrated_via_higher_derivative unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

KAN-SAE discovers 975 alive features (vs. 566 for a linear baseline, a 72% improvement) with 20% lower inter-feature redundancy

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supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
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contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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work page arXiv 2024