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

Weijia Han; Lisha Qu

cs.LGOct 29, 2026

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

Authors: Weijia Han, Lisha Qu

Organizations: University of Washington, Seattle, Washington, USA · University of Washington, Bothell, Washington, USA

Abstract

Factor models are central to asset pricing and portfolio construction, but neural factors are often difficult to interpret, and their effect on portfolio risk is unclear. A sparse autoencoder (SAE) may address both concerns by describing daily returns across many assets with only a few active features. We ask whether this sparse representation produces stable financial factors and better-diversified portfolios. We study cryptocurrency returns, use equities as a secondary test, and compare the SAE with common benchmarks in a time-ordered evaluation. We find consistently lower volatility in SAE portfolios and link this result to lower correlations among the selected assets. However, the SAE does not outperform a simple contrarian strategy on risk-adjusted return, and its factor identities are not stable across training runs. Our contribution is to show that sparse coding can support portfolio diversification, while clearly separating this risk effect from claims about alpha or stable factor identities.

Figures & tables

Figure 1. Pipeline from the daily crypto return cross-section $\mathbf{x}_{t}$ through a sparse code and reconstructed-return ranking to a contrarian quintile basket. Under strictly pre-fold selection, the chosen $K{=}128$ SAE reduces rank-scale long-short volatility by $23\%$ on average relative to matched- $K$ PCA ( $20$ – $26\%$ in all five folds). Pipeline from a daily cross-section of 433 cryptocurrency returns through a sparse code and a contrarian long-short basket. The final bars show lower confirmed rank-scale volatility for SAE than PCA.

Model	Return	Volatility	Sharpe
Naive	$+47.9$	$7.7$	$+6.20$
SAE- $K{=}64$	$+13.9$	$\mathbf{4.2}$	$\mathbf{+3.28}$
PCA- $K{=}64$	$+18.1$	$6.8$	$+2.67$
DenseAE- $K{=}64$	$+16.3$	$6.4$	$+2.53$
NMF- $K{=}64$	$+14.1$	$7.0$	$+2.02$

Table 1. Exploratory contrarian portfolios at matched

K{=}64

on the crypto static test split. Rank-scale values support cross-method comparison only; all values are pre-cost. Bold marks the best factor model; PCA uses exact SVD.

Fold	SAE Vol.	PCA Vol.	DenseAE Vol.	$\Delta\rho_{\mathrm{lf}}$
0	$6.6$	$9.7$	$10.2$	$-0.048$
1	$5.5$	$8.5$	$8.4$	$-0.032$
2	$5.2$	$7.3$	$7.3$	$-0.025$
3	$5.9$	$9.7$	$9.7$	$-0.039$
4	$4.5$	$7.4$	$7.1$	$-0.030$
5	$4.2$	$7.1$	$7.2$	$-0.030$

Table 2. Exploratory

K{=}64

ten-fold robustness analysis (

994

-day initial training window,

99

-day test folds, rotating seeds). Volatility is annualised on the rank scale;

\Delta\rho_{\mathrm{lf}}

is the leak-free trailing

60

-day long-basket correlation gap (SAE

-

PCA).

Figure 2. Exploratory day-

t

-eligible raw-return results at matched

K{=}64

. (a) SAE volatility reduction relative to PCA is positive in all five folds. (b) Pre-cost annualised Sharpe; the naive contrarian leads both reconstruction models. Panel a is a five-bar chart showing a positive SAE volatility reduction relative to PCA in every walk-forward fold. Panel b compares pre-cost raw-return Sharpe ratios for the naive, SAE, and PCA portfolios.

Figure 3. Exploratory

K{=}64

diagnostics. (a) Mean within-basket pairwise correlations. (b) SAE–PCA volatility reduction across five universe definitions and ten folds; cells share underlying days. Panel a compares long- and short-basket correlations for SAE, DenseAE, and PCA, with SAE lowest on both sides. Panel b shows positive SAE volatility reduction in every fold under five universe definitions.

Claim	Evidence	Status
Volatility reduction	Strict $K{=}128$ : $20$ – $26\%$ , $5/5$ folds; exploratory $K{=}64$ : $32$ – $37\%$ , $5/5$	supported
Within-basket decorrelation	Exploratory $K{=}64$ : leak-free $\Delta{=}{-}0.033$ , $10/10$ folds	supported
Low-volatility selection	$K{=}64$ SAE–PCA idiosyncratic volatility $+2.7$ pp, $p{<}0.001$	not supported
Sharpe against structured baselines	Exploratory $K{=}64$ suggestive; strict $K{=}128$ : $+0.33$ , $p{=}0.14$	suggestive
Incremental Sharpe against naive	Rank-scale gap $-2.91$ ; day- $t$ -eligible raw-return gap $-2.48$	not supported
Seed-reproducible identities	Matched cosine $0.13$ compared with random $0.12$ ; best match $0.23$	not supported

Table 3. Summary of empirical findings. Strict confirmation applies only to the

K{=}128

volatility result; the

K{=}64

evidence is exploratory.

Figure 4. Factor stability and correlations. (a) Mean Hungarian-matched decoder cosine by fold; the shaded band is the random-dictionary $95\%$ reference interval. (b) Descriptive equity-sample correlations with FF5+MOM ( $\max|\rho|{=}0.147$ ), short of a joint spanning test. Panel a compares the mean matched decoder cosine in each fold with a narrow random-dictionary reference band; the observed values are only slightly above random. Panel b is a heat map of small positive and negative correlations between 64 equity-sample SAE factors and six FF5 plus momentum series.

Finance

Finance studies markets, institutions, and financial decisions using data and models to understand risk, value, and resource allocation.

See all 283 papers

Unstable Features, Reproducible Subspaces: Understanding Seed Dependence in Sparse Autoencoders
Jun 10, 2026Gleb Gerasimov, Timofei Rusalev, Nikita Balagansky +3Representation Identifiability Sparse Autoencoders
T-Tech
Kronecker Factorization Improves Efficiency and Interpretability of Sparse Autoencoders
May 28, 2025Vadim Kurochkin, Yaroslav Aksenov, Daniil Laptev +2Representation Learning Activation Sparsity
T-Tech
Diminishing Returns of Data in Sparse Autoencoders: Functional Behavior does not Guarantee Feature Reproducibility
Oct 14, 2026Sambit Ghosh, Madelyn Mathai, R. Venkatesh Babu +1Sparse Autoencoders Data-Efficient Learning
IBM · Indian Institute of Science · University of Virginia

Jun 10, 2026J/K move · Enter open · S save

Unstable Features, Reproducible Subspaces: Understanding Seed Dependence in Sparse Autoencoders

Gleb Gerasimov, Timofei Rusalev, Nikita Balagansky, Daniil Laptev+2

T-Tech

Representation Identifiability Sparse Autoencoders Mechanistic Interpretability

Open paper AskPDF arXiv

Sparse autoencoders (SAEs) are widely used to interpret neural network representations, but their utility depends on whether the learned features are reproducible across training runs. We study this question through feature stability: for each SAE feature, we estimate the probability that a similar feature reappears in an independently trained SAE. This yields a scalable per-feature signal that separates stable from unstable features. In a large-scale study across seeds, models, layers, dictionary sizes, and SAE variants, we find a pronounced functional asymmetry: stable features carry most of the reconstruction- and prediction-relevant signal, while unstable features have weak marginal impact and are dominated by low-frequency surface-form triggers in both activation statistics and automatic explanations. Geometrically, unstable features are individually non-reproducible but concentrate in reproducible lower-rank subspaces, suggesting that seed dependence often reflects basis ambiguity within a shared region of activation space rather than pure noise. A controlled synthetic model makes this mechanism explicit, showing that low-rank ground-truth features can be recovered at the subspace level while remaining non-identifiable as individual SAE latents across seeds. Finally, by pooling unique cross-seed features, we construct more stable SAEs while preserving explained variance in this setting. Together, these results show that unstable features are not merely failed or noisy latents: they have weak individual functional impact, but reflect reproducible low-dimensional structure that standard SAEs resolve differently across seeds.

Abstract

Finance

Explore similar work

Unstable Features, Reproducible Subspaces: Understanding Seed Dependence in Sparse Autoencoders

Kronecker Factorization Improves Efficiency and Interpretability of Sparse Autoencoders

Diminishing Returns of Data in Sparse Autoencoders: Functional Behavior does not Guarantee Feature Reproducibility