Thirty-two landmarks match the ranking accuracy of full cross-sectional attention on a 300-stock A-share panel. The cost grows linearly with universe size instead of quadratically. Guo correctly treats the claim as an equivalence test.
MASTER forecasts stocks through five stages. Step 3 contains the inter-stock multi-head attention, where each stock's prediction can depend on the day's entire cross-section. Its 329,216 parameters account for 42.5% of the model's 775,041. Removing the stage cuts IC from 0.0646 to 0.0482 on seed 0, a 25.3% decline.
The data comes from the open-source MASTER CSI300 panel, covering roughly 300 A-shares at daily frequency. There are 222 features: 158 Alpha158 technical factors, 63 market features and one label. Guo retains the original split, including 619 test days. The label, close(t+5)/close(t+1) minus one, measures a four-day forward return after a one-day gap. IC and Rank IC are the primary metrics throughout. Long-short Sharpe appears only in the large-universe test.
Nearly uniform attention carries the signal
The learned attention weights are almost flat. Mean per-row entropy reaches 5.63 nats, close to ln(300) = 5.70, while perplexity is 278 out of 300 stocks. A decomposition shows that the uniform 1/N broadcast accounts for 98.7% of the energy. Cross-sectional variance comes entirely from the remaining 1.3%, the deviation from uniformity.
Enforcing exact uniformity leaves IC at 0.0491 and Rank IC at 0.0514 on seed 0. Across four seeds, removing the module gives a floor of IC 0.050 plus/minus 0.001 and Rank IC 0.052 plus/minus 0.002.
The deviation matrix has low rank. Effective rank is about 65 out of 300, and the top ten singular values contain 96.5% of the squared Frobenius norm. Among 208 individual day-by-head matrices, median effective rank is 65 (IQR 45 to 81).
This is the opening for Nyström. It reconstructs the full attention matrix from sampled reference stocks, using m = 32 landmarks resampled on every forward pass. Across five seeds at CSI300, Nyström delivers IC 0.059 plus/minus 0.002 and Rank IC 0.066 plus/minus 0.003. The original records 0.058 plus/minus 0.007 and 0.066 plus/minus 0.003. Two one-sided tests certify Rank IC equivalence within 0.005 (p = 0.003). IC clears only the wider 0.008 margin (p = 0.028; at 0.005 it is p = 0.099).
At CSI800, both metrics pass the 0.005 band over ten seeds (IC p = 0.038, Rank IC p = 0.034). Increasing the landmarks to m = 80, preserving the 10% coverage ratio, adds nothing.
Why correlation graphs lose
Correlation-based neighbours remove the wrong information. Hard masking attention to those neighbours produces IC 0.045 plus/minus 0.004 and Rank IC 0.049 plus/minus 0.002 across four seeds. Those results fall below the floor from deleting the module entirely (paired t against the original, p = 0.040).
The paper's efficient-attention sweep on CSI300 reaches the same place. TopK with K = 16 reports IC 0.052 plus/minus 0.004 and Rank IC 0.064 plus/minus 0.004 over five seeds. Guo gives the mechanism directly. The top 16 weights have perplexity 15.9 out of 16, so subtracting a constant from nearly equal values creates no useful differentiation. Sharpening requires support across a range around 1/N.
Sparsification has nothing to retain.
The relationship between attention and similarity carries the opposite sign assumed by the related-stock-graph literature. Pairwise attention versus pairwise return correlation has Spearman rho of -0.614 across 73,910 pairs. Among the 71,165 industry-labelled pairs, it is -0.645, then -0.627 partial after controlling for same-industry membership, beta difference and volatility difference. Same-industry pairs receive lower weight (b = -0.011, p = 3e-4). Per-day rho stays negative on every test day. Stocks that co-move attract less attention.
Low rank arrives before training
This is where I stop treating the result as a market discovery. Guo measures the deviation spectrum in 10 randomly initialized, untrained MASTER models. Effective rank is 59 plus/minus 7, and top-ten energy is 95.6 plus/minus 0.9%. The trained model reaches a rank of about 65 with 96.5%. Guo's conclusion is direct: softmax attention over N items inherently produces low-rank structure.
Low rank alone has no value. A rank-32 attention pattern learned end-to-end falls to IC 0.0478 and Rank IC 0.0500 on seed 0. Each stock receives a 32-dimensional embedding, with scores generated from inner products and fixed across days. The floor is 0.0482 and 0.0514.
Freezing attention at the average matrix does little better. The average is an oracle computed on the test set, which the paper says gives the static pattern its best chance. Even so, it recovers about 47% of Rank IC value relative to the floor and only about 9% of IC value. Nyström preserves the day-by-day QK routing instead. The attention pattern fully decorrelates in about 20 trading days: lagged centred cosine similarity is 0.967 at lag 1, 0.665 at lag 5 and 0.048 at lag 20. The SVD-to-risk-factor mapping remains suggestive rather than load-bearing. PC1 contains 79.5% of energy and correlates 0.48 with volatility.
Preprocessing tightens the claim
Equivalence is certified solely on IC and Rank IC. Table 3 gives 90% CIs of IC [-0.005, +0.007] against the 0.008 margin, and Rank IC [-0.002, +0.001] against the 0.005 margin. The paper runs no equivalence test at portfolio level or net of costs.
Preprocessing also changes the result. With per-day cross-sectional z-scoring, the original model's IC rises by 0.005 and seed variance falls 5.8 times. Nyström does not change. The Rank IC TOST p moves from 0.003 to 0.120. Guo presents this plainly as a boundary on the claim: once inputs are better conditioned, full attention extracts structure missed by the low-rank approximation.
Then scale enters.
Below N of roughly 1,300, Nyström runs slower than full attention, as the paper acknowledges. At N = 300 on a T4, latency is 5.90 ms versus 1.65 ms, and training takes about 2x longer per epoch. Savings appear above that point. At N = 3,500, latency improves 5.5x and memory use is 298 MB against 1,350 MB. Full attention runs out of memory at N = 12,000, while Nyström uses 974 MB.
Yet at N of about 3,500, no cross-stock module significantly outperforms a per-stock LSTM. The test uses an adapted configuration with 17 OHLCV features, d_model 64 and no market gating. PureLSTM achieves IC 0.043 plus/minus 0.002 and Rank IC 0.056 plus/minus 0.003. MASTER plus Nyström-32 reaches 0.037 plus/minus 0.008 and 0.050 plus/minus 0.016, with paired t p = 0.27 and p = 0.53 on four seeds.
This is the paper's own finding (iii), stated in the abstract and repeated in the conclusion. Guo attributes the result to the adapted large-N configuration rather than the original architecture. The conclusion proposes testing Nyström inside MASTER's full architecture at larger scales. Equivalence is established where compute barely matters; where compute matters, the module ceases to pay. A single-seed run at that scale once showed a clean trade-off, then four seeds erased it.
Reported Sharpes at this scale are 5.6 plus/minus 0.5 for PureLSTM and 5.6 plus/minus 1.1 for MASTER plus Nyström-32. They cover 383 test days in 2019-2020 across four seeds. The paper states that every reported Sharpe ratio is frictionless, without transaction costs, slippage or market impact. Guo also describes a high-turnover market with short-selling restrictions. These figures work as diagnostics of ordering quality.
Our US large-cap adaptation
We could not trade the paper's market. We rebuilt the MASTER-plus-Nyström-32 ranker for 500 cap-ranked US equities, using 17 OHLCV-derived stock features and four benchmark features. The model uses d_model 256, two heads and 32 landmarks resampled during each forward pass. A six-iteration Newton-Schulz pseudo-inverse completes the calculation. We retained the paper's label, close(t+5)/close(t+1) minus one. The portfolio rebalances daily into inverse-volatility long and short baskets containing 25 names each. Because the market differs, this remains an adaptation.
Our backtest covers 2020-01-02 to 2024-07-01. It produced total return -50.8%, Sharpe -0.58, maximum drawdown -63.33%, Calmar -0.23, realised volatility 19.5%, 84,097 trades, win rate 44.45% and profit factor 0.91. Every figure is net of $0.0040 per share commissions with a $1.00 order minimum. Short borrow, financing on permitted leverage and market impact are not charged, leaving the true result worse than -50.8%.
The paper's 5.6 plus/minus 1.1 comes from its large-scale validation at N of about 3,500 across four seeds. It measures the Nyström-32 cross-stock module in the adapted large-N configuration, with d_model 64 and no market gating. Our result is -0.58. The sign reverses, though the books differ: a costless A-share portfolio over 383 days in 2019-2020 versus a net US large-cap portfolio over 1,131 days.
Setup explains much of the gap. All paper results are estimated on Chinese A-shares, and Guo confines the claims to one model in one market. The paper configuration closest to ours is already null, with p = 0.27 on IC against a per-stock LSTM and an IC standard deviation of 0.008 at that scale.
Material details of our architecture remain underdetermined against the paper. The temporal lookback is unresolved, while the deployed Step 3 configuration uses T = 8. Our minimum history is 120 days. We retained market gating and d_model 256; the paper's large-N variant removes gating and uses 64. Our sample includes the COVID crash, the 2021 squeeze and the 2022 drawdown. Selecting only the extreme 25 names on each side of 500 probably gives up the breadth through which a weak IC can average out.
The paper's tercile analysis at CSI300 assigns about 77% of IC covariance to the top tercile by absolute return, the extreme movers. Our persistently negative Sharpe and 0.91 profit factor suggest realised IC at or below zero in this cross-section. Our implementation is the first suspect. This was one automated pass rather than a verdict on the authors' work.
One result would change my view: a portfolio-level equivalence test, net of costs, on a universe above 1,300 names where the cross-stock module already has an established positive IC. Until then, the lasting contribution is diagnostic, and a good one. Near-uniform attention leaves sparse stock graphs with nothing to preserve. Low-rank approximation survives because softmax attention over N names begins low-rank before learning.
Our backtest stops at 2024-07-01, and everything after that date is deliberately left untouched so the same strategy can be checked out of sample later.