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Thinking Summary

The user is asking about Figure 5 from the "Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders" paper. Let me look at what Figure 5 shows. Figure 5 shows: - The proportion of features that activate very frequently versus delta LM loss by SAE type for Gemma 2 9B residual stream SAEs - Two plots: top one shows features active on over 10% of tokens, bottom one shows features active on over 1% of tokens - Compares TopK, JumpReLU, and Gated SAEs The significance of plotting delta LM loss against activation frequency relates to understanding the trade-off between: 1. Reconstruction fidelity (measured by delta LM loss) 2. The characteristics of learned features (specifically how often they activate) Let me explain why this matters in the context of SAEs.

Figure 5 is plotting two important characteristics of Sparse Autoencoders (SAEs) against each other to reveal a key trade-off:

Delta LM Loss (X-axis)

  • What it measures: The increase in cross-entropy loss when the SAE is spliced into the language model's forward pass
  • Why it matters: This is a measure of reconstruction fidelity - lower values mean the SAE is better at faithfully reconstructing the original activations without harming the model's performance
  • Interpretation: Moving left on the x-axis means better reconstruction quality

Feature Activation Frequency (Y-axis)

  • What it measures: The proportion of SAE features that fire very frequently (>10% of tokens in top plot, >1% in bottom plot)
  • Why it matters: Very high frequency features tend to be:
    • Less interpretable (they activate so often they may not represent specific, meaningful concepts)
    • Less sparse (defeating the purpose of "sparse" autoencoders)
    • Potentially acting more like bias terms than meaningful feature detectors

The Significance of This Plot

  1. Different architectures have different characteristics: The plot reveals that TopK and JumpReLU SAEs tend to learn more high-frequency features than Gated SAEs, especially in the low delta LM loss (high fidelity) regime.

  2. Trade-off visualization: As you improve reconstruction fidelity (move left), you tend to get more high-frequency features. This suggests there's a fundamental tension between:

    • Making accurate reconstructions (low delta LM loss)
    • Learning sparse, interpretable features (few high-frequency features)
  3. Architecture comparison at fixed performance: By plotting against delta LM loss rather than just comparing raw frequency counts, the authors ensure they're comparing architectures at equivalent levels of reconstruction quality. This is a fairer comparison than just looking at frequency distributions alone.

  4. Practical implications: For practitioners, this helps in choosing architectures - if you care more about avoiding high-frequency features for interpretability, you might prefer Gated SAEs despite slightly worse reconstruction fidelity.

The paper notes that while JumpReLU has more very high frequency features (>10%) like TopK, the absolute numbers remain small (<0.06% of all features even in the worst case), suggesting this may not be a major practical concern.

replyquoteparent

Ok, I'm not understanding how I move along the graph though. For a given SAE the SAE is fixed right? So it has a certain LM loss and a certain proportor of features activity on 10% of tokens and both of those are "fixed” right? Where does the series in the chart come from?

replyquoteparent
Thinking Summary

Ah, the user is confused about what creates the curve/series in the plot. They think each SAE should just be a single point since it has fixed characteristics. Let me clarify that each point represents a different SAE trained with different hyperparameters.

Excellent question! You're right that each individual SAE, once trained, has fixed characteristics. The key insight is that each point on the curves represents a different SAE.

How the Series is Generated

The authors trained multiple SAEs of each type (JumpReLU, Gated, TopK) with different hyperparameters:

  1. For JumpReLU and Gated SAEs: They varied the sparsity coefficient λ

    • Higher λ → more sparse → fewer features active → worse reconstruction (higher delta LM loss)
    • Lower λ → less sparse → more features active → better reconstruction (lower delta LM loss)
  2. For TopK SAEs: They varied K (the number of top features to keep)

    • Lower K → more sparse → worse reconstruction
    • Higher K → less sparse → better reconstruction

Creating the Curves

So the process was:

  1. Train many SAEs with different sparsity settings (different λ or K values)
  2. For each trained SAE, measure:
    • Its delta LM loss (reconstruction quality)
    • What proportion of its features fire on >10% of tokens
  3. Plot each SAE as a point
  4. Connect points of the same architecture type to form curves

Why This Matters

This allows them to answer: "If I want a JumpReLU SAE with delta LM loss of 0.2, how many high-frequency features should I expect?" You can't just train one SAE and move along the curve - you need to train multiple SAEs with different sparsity penalties to explore the trade-off space.

The curves show the Pareto frontier - the best achievable trade-off between reconstruction quality and feature frequency characteristics for each architecture type.

replyquoteparent