SynthSAEBench: Evaluating Sparse Autoencoders on Scalable Realistic Synthetic Data

Abstract: Improving Sparse Autoencoders (SAEs) requires benchmarks that can precisely validate architectural innovations. However, current SAE benchmarks on LLMs are often too noisy to differentiate architectural improvements, and current synthetic data experiments are too small-scale and unrealistic to provide meaningful comparisons. We introduce SynthSAEBench, a toolkit for generating large-scale synthetic data with realistic feature characteristics including correlation, hierarchy, and superposition, and a standardized benchmark model, SynthSAEBench-16k, enabling direct comparison of SAE architectures. Our benchmark reproduces several previously observed LLM SAE phenomena, including the disconnect between reconstruction and latent quality metrics, poor SAE probing results, and a precision-recall trade-off mediated by L0. We further use our benchmark to identify a new failure mode: Matching Pursuit SAEs exploit superposition noise to improve reconstruction without learning ground-truth features, suggesting that more expressive encoders can easily overfit. SynthSAEBench complements LLM benchmarks by providing ground-truth features and controlled ablations, enabling researchers to precisely diagnose SAE failure modes and validate architectural improvements before scaling to LLMs.

• The paper demonstrates that even when the linear representation hypothesis holds, current SAE designs fail to recover all ground-truth features.
• The paper reveals a precision-recall trade-off where architectures like MP-SAEs overfit superposition noise, compromising latent feature alignment.
• The paper shows that tailored auxiliary losses and hierarchical synthetic data can mitigate dead latent issues, guiding improvements in SAE design.

SynthSAEBench: A Comprehensive Benchmark for Sparse Autoencoder Evaluation on Realistic Synthetic Data

Motivation and Synthetic Data Model

Sparse Autoencoders (SAEs) have become central tools for feature interpretability in large neural models by attempting to recover a sparse, disentangled dictionary from layer activations. However, advances in SAE architectures have been constrained by inadequate benchmarks: LLM activations provide complex, noisy, and ground-truth-lacking scenarios, while prior synthetic data models are limited in scale or realism. "SynthSAEBench: Evaluating Sparse Autoencoders on Scalable Realistic Synthetic Data" (2602.14687) proposes a remedy by introducing a controlled, large-scale, yet realistic, synthetic data generator and a standardized benchmark configuration, SynthSAEBench-16k.

The synthetic data generator extends the classic Bernoulli-Gaussian model with a suite of configurable, realistic properties: feature superposition, configurable feature correlations, explicit hierarchical structure, heterogeneous firing probabilities (defaulting to Zipfian), and variable firing magnitudes. Efficient, memory-scalable algorithms support the generation of tens of thousands of features on a single GPU, even with nontrivial low-rank correlation structure among firing events.

Figure 2: Overview of the process for generating a single training activation (a), which includes correlation, firing probabilities, hierarchical constraints, and application of the feature dictionary.

Benchmark Model: SynthSAEBench-16k

The core benchmark, SynthSAEBench-16k, models activations as linear combinations of $16,\!384$ ground-truth features projected via a 768-dimensional hidden space, resulting in moderate superposition ($\rho_{\text{mm}} \approx 0.15$). Firing probabilities are Zipfian, spanning from $p_{\max} = 0.4$ to $p_{\min} = 5\times10^{-4}$, with distribution shown below.

Figure 1: Firing probabilities for SynthSAEBench-16k features, exhibiting the desired power law behavior.

Hierarchical dependencies include mutually exclusive subtrees rooted in a forest, instantiated to reflect concept hierarchies such as those in language or vision; this is visualized as follows:

Figure 3: Distribution of hierarchical subtrees and their depths for SynthSAEBench-16k, highlighting the prevalence and structure of the hierarchy.

Random low-rank correlations ($r=25$, $s=0.1$) inject global dependencies beyond the imposed hierarchy, and feature firing magnitudes are linearly interpolated and varied with a folded normal scheme. The benchmark is designed for efficiency: 200M training samples of 16k-feature activations can be generated in minutes on a modern GPU.

SAE Architectures and Evaluation Metrics

The paper provides rigorous, multi-dimensional evaluation of several leading SAE architectures: standard $L_1$ SAEs, JumpReLU SAEs, BatchTopK SAEs, Matching Pursuit (MP) SAEs, and Matryoshka SAEs. Crucially, both latent sparsity ($L_0$) and dead/unused latents are controlled and measured. Distinguished metrics include:

• Reconstruction quality (Explained Variance $R^2$): Measures how well input activations are reconstructed.
• Feature recovery (mean absolute cosine correlation, MCC): Uses bipartite matching (Hungarian algorithm) to align learned decoder weights with ground-truth feature directions.
• Classification metrics (latent F1, precision, recall): Each latent is treated as a detector of its best-matching ground-truth feature.
• Sparsity dynamics (L0, dead latents): Quantifies activation sparsity and capacity underutilization.

Key Results and Architectural Dynamics

SAE Performance vs. Sparsity

Varying target $L_0$ across architectures reveals fundamental trade-offs:

Figure 4: Explained variance (left), MCC (middle), and F1-score (right) for SAEs across varying $L_0$ values trained on SynthSAEBench-16k.

Matryoshka SAEs demonstrate the highest latent quality (MCC, F1), peaking at $F_1 \approx 0.88$, despite relatively poor reconstruction error. In contrast, MP-SAEs maximize explained variance but exhibit poor latent-feature alignment (MCC, F1). This recapitulates phenomena observed on real LLM activations, demonstrating the fidelity of the synthetic benchmark.

Precision-Recall Trade-off

The well-known trade-off between latent sparsity and the precision/recall of recovered feature detectors is again observed:

Figure 5: Probing precision and recall for SAEs as $L_0$ varies; greater $L_0$ yields higher recall but lower precision.

No architecture achieves near-perfect F1, confirming that even in this idealized, LRH-compliant regime, standard SAEs do not reach the latent disentanglement levels attainable by supervised linear probes (where F1 reaches 0.974). This result starkly demonstrates a concrete ceiling on unsupervised SAE performance, even absent representation mismatch.

Overfitting via Superposition: Matching Pursuit Failure Mode

A novel empirical observation is the ability of more expressive encoders, such as MP-SAEs, to overfit superposition noise—they increase explained variance as feature overlap rises but at the cost of matching true features (MCC and F1 drop):

Figure 6: MP-SAEs show increased variance explained at high superposition, but decreasing MCC and F1, indicating overfitting to spurious feature overlap rather than learning true ground-truth structure.

Dead Latents and Auxiliary Losses

SAE variants differ in their susceptibility to dead (never-firing) latents, affecting capacity and interpretability. JumpReLU is particularly sensitive to initialization and auxiliary loss choice—a TopK auxiliary loss results in fewer dead latents and improved quality. Matryoshka SAEs with a prefix-specific auxiliary loss reduce dead latents notably at low $L_0$.

Implications and Future Directions

The benchmark demonstrates three critical, and at times counter-intuitive, claims with strong empirical support:

1. Even when the Linear Representation Hypothesis holds exactly, current SAE designs are insufficient to recover all ground-truth features. This invalidates the hypothesis that SAE limitations are caused primarily by nonlinearity or representation mismatch in LLMs.
2. Expressive encoders (MP-SAEs) can overfit superposition, degrading feature recovery despite excellent reconstruction, suggesting that increased model expressivity should be paired with constraints or diagnostics that penalize alignment with ground-truth features, not just input fidelity.
3. Observed limitations and architectural distinctions in SAE behavior on real LLM data are recapitulated with synthetic data, confirming that benchmarks with ground-truth structure are invaluable for diagnosing and fixing SAE design flaws.

Practically, these results offer a reproducible, high-throughput testbed for developing and evaluating new SAE architectures, with ablation capabilities for individual phenomena (superposition, hierarchy, correlation). Theoretical implications include a call for more expressive, yet inductively-biased, encoders and for exploring alternatives to the LRH, such as manifold- or Minkowski-based feature hypotheses. The paper also points towards the need for future synthetic benchmarks that encompass a wider range of geometric and statistical feature structures.

Conclusion

SynthSAEBench presents a scalable, configurable, and realistic synthetic data benchmark that exposes both capabilities and fundamental limitations of modern sparse autoencoder architectures (2602.14687). The benchmark captures central empirical phenomena influencing SAE research, delivers strong evidence against classically held explanations for SAE underperformance, and provides a modular foundation for iterative design and evaluation. Coupled with fast evaluation and ground-truth access, SynthSAEBench will likely accelerate the cycle of interpretability-focused architecture innovation and help clarify which representational and architectural assumptions support practical monosemanticity in deep models.