reviews: 
Comments: This paper (1) introduces Top-k sparse autoencoders (SAEs), which are novel for language models; (2) trains them on language models ranging in size up to GPT-4; (3) measures the SAE's sparsity/reconstruction tradeoff, finding performance that exceeds the state-of-the-art by a small margin; (4) demonstrate scaling laws for reconstruction accuracy in terms of training FLOPS and SAE width; and (5) measures the SAEs on a range of "downstream" metrics.
Strengths: - This paper makes multiple novel contributions to research on the application of SAEs to language models:
	- The Top-k SAE architecture has not previously been used on language models. (Though they were introduced previously by (Makhzani & Frey, 2013).)
	- Scaling SAEs to a model the size of GPT-4 is a challenge due to the increasing concentration of dead features, and the early works in this field (Cunningham et al, 2023; Bricken et al, 2023) focused on relatively small language models. The scaling done in this paper is not entirely novel, as (Templeton et al, 2024) trained SAEs on the similarly-sized Claude 3 Sonnet, but this paper likely represents contemporaneous, parallel work.
	- Similarly, this paper finds scaling laws that are novel except for (Templeton et al, 2024).
	- This paper investigates several methods for evaluating SAEs beyond sparsity and reconstruction accuracy, which are important for establishing outside validity and utility. Especially appreciated is the metric in lines 311-314, contextualizing downstream loss in terms of a fraction of pre-training compute.

- In addition to the quantitative results, Top-k SAEs provide qualitative benefits over previous SAE architectures:
	- The sparsity level of Top-k SAEs is directly set, instead of relying on an indirect hyperparameter.
	- Top-k SAEs do not suffer from "feature shrinkage" caused by L1-regularization. The authors clearly demonstrate this in the excellent Figure 8.
	- Top-k SAEs have far fewer dead features at large scales.
Weaknesses: - While the authors describe many results, they are not all equally justified.
	- Section 4.2 (Recovering Known Features with 1D Probes) is conceptually very exciting, but somewhat confusing in its details.
		- The magnitude of the probe loss improvement seems very low, from ~0.52 in the worst case to ~0.49 in the best case. Figures 32 and 33 indicate that a similar magnitude of improvement across various run sizes and datasets. This section would therefore benefit from more baselining: what is the best such classifier based on a residual stream neuron? On a linear  probe trained on all the residual stream neurons? On similarly-sized noise?
		- The only such baseline in the paper is that in Figure 32 the caption says that the loss on residual stream channels is 0.600. But the figure shows the loss improving from 0.46 to 0.44 over training, so it seems like almost all of the gain of the SAE occurred in the first <1% of training.
		- The probe losses appear to be averaged across the 61 datasets. This should be clearly stated in the body of the text.
	- Figure 7 is hard to understand, and would benefit from more explanations of its significance.

- There are several typos in the body of the text (see below)
Recommendation: 10
Reviewer confidence: 4
Soundness/correctness: 4
Clarity: 3