Sparse Autoencoders as Implicit Diversification Regularisers for Cross-Sectional Cryptocurrency Returns

What it claims

Weijia Han and Lisha Qu (University of Washington) train an ℓ1 sparse autoencoder on daily cross-sections of 433 Binance crypto returns. They rank assets by the reconstruction to build contrarian long-short baskets. The paper is accepted at ICAIF '26 (Milan, November 2026) and released under CC BY 4.0. Under strictly pre-fold hyperparameter selection, the K=128 SAE has 20 to 26% lower long-short volatility than matched-K PCA in all five confirmation folds, with a mean of 23%. The authors attribute this to lower correlation within baskets, not to picking low-volatility assets. They make no alpha, forecasting or asset-pricing claim and frame the SAE as a "bottleneck-induced diversification regulariser."

How it works

• Preprocessing. Daily close-to-close log returns are winsorised at the 1st/99th percentile per day. They are then mapped to clipped (0.01, 0.99) inverse-normal rank scores in the van der Waerden style.
• Model. A ReLU encoder produces a nonnegative K-dimensional code. The linear decoder is tied to the encoder and has unit-ℓ2 columns.
• Loss. Reconstruction error counts only observed cells, plus a per-day mean ℓ1 penalty. Missing inputs are zero-filled for the forward pass, but the mask keeps the decoder from learning missingness patterns.
• Data handling. Splits are chronological (70/10/20). Gaps of up to three days are forward-filled. Training uses Adam.
• Portfolio rule. Assets are ranked on the reconstruction. The strategy goes long the lowest quintile and short the highest, equal-weighted, and earns the day t+1 return.
• Baselines. The same quintile rule is applied to PCA (exact SVD), a dense autoencoder (λ=0), NMF, ICA, sparse PCA and dictionary learning. A naive contrarian ranks on the raw same-day return.

Evidence

Data. The crypto panel is Binance USDT pairs, 2019-01-01 to 2024-12-31, covering 1,988 days after filtering. Stablecoins and leveraged tokens are excluded. The equity panel is 200 S&P 500 stocks from Yahoo Finance, 2015 to 2024.

Selection. The model was selected from an 18-configuration grid fitted on the first 748 days. The grid covered K ∈ {32, 64, 128}, λ ∈ {10⁻³, 10⁻², 10⁻¹} and two learning rates, and selection picked K=128, λ=0.1, η=10⁻³. It was then evaluated on five 248-day folds.

Volatility versus PCA. Volatility is 20 to 26% lower in every fold. The Sharpe gap over PCA is +0.33, but it holds in only 4 of 5 folds and is not significant (p=0.14).

K sweep at λ=0.1. The volatility reduction is positive in every fold at every K:

The Sharpe gap is significantly negative for K≥256 (p≤0.039).

Mechanism (exploratory, K=64). Within-basket pairwise correlation is 0.008 for the SAE versus 0.039 for PCA (p<0.001).

Overlay control. A Ledoit–Wolf minimum-variance overlay on the naive contrarian closes about 73% of its volatility gap to the SAE. The overlay uses a trailing 60-day covariance. The SAE is still less volatile in 4 of 5 folds, but the difference is not significant (p=0.057, two-sided).

Return. The naive contrarian beats the SAE on Sharpe by 2.91 on the rank scale (p=0.002) and by 2.48 in money units (p=0.009). A lagged-return MLP in the style of Gu et al. widens that gap.

Survivorship check. The authors added a fold-specific eligibility rule, under which 322 to 367 assets qualify per fold. The SAE–PCA Sharpe gap is +1.15±0.80 (9 of 10 folds, p=0.001), and volatility is lower in 10 of 10 folds, by 34% on average.

Equities. The lowest realised volatility is 6.6%. The SAE factors have a maximum correlation of 0.147 with FF5+MOM. The SAE–PCA Sharpe gap is −0.20 (p=0.160), and the SAE trails the naive contrarian by 0.66 (p=0.072).

Limits

• Not a tradable backtest. Positions are entered at the same close that forms the signal. The authors call this non-executable and treat the results as signal evidence only.
• No costs, no capacity claim. All results are pre-cost, and daily data cannot support execution or capacity claims.
• Rank-scale Sharpes. These are artefacts of the transform and are valid only for comparing methods.
• Unstable factors. Factor identities do not reproduce across seeds, so the "monosemantic factor" motivation is not supported.
• K=64 results are exploratory. Their selection window and checkpoint choice overlap the test folds.
• Not point-in-time. The crypto coverage filter uses full-sample information. The equity list is a static early-2025 constituent set and carries survivorship bias.
• Missing returns. At evaluation, missing returns count as zero, which matters because the contrarian strategy buys recent losers.
• Baselines. There is no characteristic (Barra-type) baseline, because the panel lacks fundamentals.
• Training. Validation loss was still falling at the epoch cap.
• Not covered here. The fetched text ends at Section 4.1 and does not mention released code or data.