{"id":"69cb63ab-d087-4ab8-a9dd-7dcc5782dd15","arxiv_id":"2506.19856","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Firm similarity from accounting ratios can generate momentum spillover signals, and a QCML-learned similarity reports higher backtested Sharpe ratios than Euclidean similarity.","lead":"The paper proposes a new measure of firm similarity based on accounting and valuation ratios, and uses it to build momentum spillover trading signals. It compares a simple Euclidean version of the measure with a quantum-inspired machine learning version, and reports that the learned version achieves higher backtested Sharpe ratios.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central claim of QCML outperformance rests on a single full-sample Sharpe comparison without any significance testing; given the two signals are highly correlated, the 0.37 Sharpe gap at the 252-day horizon may be within sampling noise.","rationale":"The reader's weakest_assumption was the proprietary covariance estimator. While that is a genuine reproducibility concern, it is not the most load-bearing for the specific claim of QCML outperformance, because the same covariance estimator is used for both portfolios; a miscalibrated covariance could inflate or deflate both Sharpe ratios but would not necessarily overturn the relative ranking. The more direct threat is statistical: the paper offers no evidence that the 0.37 Sharpe gap at the 252-day horizon is anything more than sampling variation. The signals are highly correlated by the paper's own admission, and the 252-day signal has a half-life of about 91 days, so the effective sample size over the 2014-2024 test period is on the order of tens of independent observations, not thousands. A formal Sharpe-ratio equality test is the natural, decisive check. I therefore partially agree with the reader: the proprietary covariance is worth flagging, but the significance question is more central. Because the concern is empirical and addressable with a supplementary test, the conditional verdict remains appropriate.","tokens_in":11910,"tokens_out":4135,"duration_ms":47746,"concrete_test":"Compute the Ledoit-Wolf (2008) studentized bootstrap test for the equality of the full-sample Sharpe ratios of the 252-day QCML and Euclidean portfolio return series, using the daily portfolio returns and a HAC estimator for the covariance of the moment conditions. If the 95% confidence interval for the Sharpe difference contains zero (or p>0.05), the central outperformance claim is not statistically supported. Report the same test for the combined signal. This requires only the daily return series of the two portfolios, which should be made available even if the proprietary covariance estimator is not.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The claim that QCML similarity outperforms Euclidean similarity is supported only by point-estimate Sharpe ratios in Tables 2 and 4, with no standard errors, confidence intervals, or tests of equality. This is especially problematic because the two signals are highly correlated, as the paper reports average daily cross-sectional correlations of 0.74-0.78 in Section 6.2. For the headline 252-day comparison, the QCML Sharpe is 1.10 vs 0.73 for Euclidean, a difference of 0.37. But the 252-day signal uses overlapping returns over a 10-year test period, and the QCML signal has a half-life of 90.9 days (Section 6.2), so the effective number of independent observations is far smaller than the 2,500 daily returns; a difference of this size may not be statistically distinguishable from zero. The paper also selectively emphasizes the 252-day horizon: the 21-day QCML signal (1.38) is essentially tied with the Euclidean 21-day signal (1.35), and the combined signal improves only from 1.24 to 1.42. No multiple-testing correction is applied across the four horizons and subperiods examined. Additionally, the conclusion quotes different Sharpe ratios (1.12 vs 0.76 and 1.43 vs 1.26) than the abstract and Section 6.2 (1.10 vs 0.73 and 1.42 vs 1.24), which undermines confidence in the precision of the reported numbers. Without a formal test, the central claim that QCML outperforms is not established.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces Characteristic Vector Linkages (CVLs) as a proxy for firm linkages based on vectors of firm characteristics, and constructs momentum spillover trading signals from two similarity measures: a simple Euclidean similarity and a learned similarity based on Quantum Cognition Machine Learning (QCML). The QCML model is trained on 63-day forward returns using data from October 2007 through August 2013, with parameters held fixed during the evaluation period from January 2014 through June 2024. The authors report Sharpe ratios for portfolios formed from the spillover signals at 21-, 63-, 126-, and 252-day input horizons and a combined signal, and claim that QCML similarity outperforms Euclidean similarity, especially at the 252-day horizon (full-sample Sharpe 1.10 vs. 0.73) and for the combined signal (1.42 vs. 1.24).","tokens_in":12294,"tokens_out":4682,"duration_ms":55474,"significance":"If established, the result would be a useful contribution to the literature on supervised similarity learning for cross-firm return predictability, showing that a learned representation can improve on raw-feature similarity for momentum spillover strategies. The paper has genuine strengths: the temporal split is clean (training ends in 2013, testing starts in 2014), the QCML parameters are static out-of-sample, an ensemble of 50 seeds is used, and the portfolio construction controls for standard characteristics such as size, beta, momentum, and analyst coverage. However, the central claim is not yet supported with adequate statistical evidence, depends on an unreproducible covariance estimator, and contains internal numerical inconsistencies. These issues must be addressed before the outperformance claim can be evaluated.","major_comments":[{"comment":"The central claim that QCML similarity outperforms Euclidean similarity is supported only by point estimates of full-sample Sharpe ratios. No standard errors, confidence intervals, or tests of the equality of Sharpe ratios are reported, despite the paper stating that the two signals have average daily cross-sectional correlations of 0.74-0.78. Because the 252-day signal uses overlapping returns and has a half-life of 90.9 days for QCML and 36.3 days for Euclidean, the effective number of independent observations is far below the roughly 2,500 daily observations in the test period, so the 0.37 Sharpe gap may be within sampling noise. A formal test, such as a bootstrap or HAC-based test of the Sharpe ratio difference, or a Diebold-Mariano test on the daily returns, is required, and the multiple testing across four horizons and three subperiods should be acknowledged.","section":"Section 6.2, Tables 2 and 4"},{"comment":"The portfolio construction uses a daily covariance matrix estimated with a technique proprietary to Duality Group, whose details are not provided. Because the portfolio weights are w = V^{-1} R f, every reported return and Sharpe ratio in Tables 2 and 4 depends on this unobservable matrix. As a result, the central comparison is not independently verifiable or reproducible. The authors should either replace the proprietary estimator with a fully specified standard covariance estimator, provide the code or estimates, or demonstrate that the headline QCML-versus-Euclidean comparison is robust to a range of reasonable covariance estimators.","section":"Section 5.5, footnote 4"},{"comment":"The conclusion reports the 252-day Sharpe comparison as 1.12 versus 0.76 for QCML versus Euclidean, and the combined signal as 1.43 versus 1.26, while Section 6.2 reports the same full-sample comparisons as 1.10 versus 0.73 and 1.42 versus 1.24. This internal inconsistency in the key quantitative claim must be corrected; as written, it is unclear which set of numbers is the authoritative result and undermines confidence in the reported precision.","section":"Conclusion vs. Section 6.2"},{"comment":"The paper does not deduct transaction costs, yet the abstract and conclusion describe the strategies as 'profitable.' Since the portfolios are smoothed over 21 days but the similarity matrices and forecasts are computed daily, turnover is likely substantial. Without reporting average turnover or break-even transaction costs, the economic significance of the Sharpe ratios is not established, particularly for the practical value of the strategy that the abstract promises.","section":"Section 5.5"}],"minor_comments":[{"comment":"The sentence 'from October 2017 through June 2024' appears to be a typo for October 2007, since the QCML training period in Section 5.3 is October 2007 through August 2013 and the test period starts in January 2014.","section":"Section 5.2"},{"comment":"The loss function is written as f(y_t,j, x_t,j, {A_c}, B, w), but the functional form of f is never explicitly defined; please define f or restructure the equation so the argument list matches the expression shown.","section":"Section 3.1, Equation (7)"},{"comment":"The conclusion states that Euclidean Sharpe ratios range from 0.73 to 1.37, but Table 2 includes a full-sample value of 0.71 for the 126-day signal; the range should be corrected.","section":"Conclusion"},{"comment":"Reference [35] is cited merely as 'Risk.net' without a title, volume, or page numbers; a complete citation is needed for a published working paper.","section":"References"},{"comment":"The sentence 'choices of N in [4,32] have been seen to give optimal cross-validated accuracy' should be clarified as reporting prior experimental experience rather than a result of this paper, since this paper only reports results for N=12.","section":"Section 3.1"}],"recommendation":"major_revision","confidential_remarks":"The statistical inference gap and the proprietary covariance estimator are the two main obstacles. The former is fixable by adding formal significance tests; the latter is more serious because it blocks independent verification of every reported Sharpe ratio. The numerical inconsistency between the conclusion and Section 6.2 should be corrected promptly. The paper is within scope for q-fin.ST, but the evidence as it stands is not sufficient to support the abstract's outperformance claim."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the paper is a workmanlike extension of prior QCML similarity work from bonds to equities, with a clean out-of-sample design, but the headline claim—QCML beats Euclidean similarity—rests on Sharpe point estimates from highly correlated signals, with no measure of uncertainty. The gap may well be sampling noise.\n\nWhat's new: this is the first application of the QCML distance-learning machinery to a broad US equity universe, using 15 accounting/valuation characteristics to build firm linkages and then testing momentum spillover strategies. The feature list is thoughtful, the training/test split (train through Aug 2013, test from Jan 2014) is sensible, and the authors are candid about costs—no transaction costs, forecasts not a stand-alone strategy, covariance estimator proprietary. The half-life comparison across horizons is a nice diagnostic.\n\nWhere it falls short: the central claim is not statistically supported. The two signals have daily cross-sectional correlations of 0.74–0.78, and the 252-day QCML Sharpe of 1.10 vs 0.73 for Euclidean is a point estimate with no standard errors, test, or multiple-testing correction. Given overlapping returns and half-lives of 90.9 vs 36.3 days, the effective number of independent observations is small; that 0.37 gap could easily be within noise. Also, the conclusion quotes different numbers (1.12 vs 0.76, 1.43 vs 1.26) than the abstract and Section 6.2 (1.10 vs 0.73, 1.42 vs 1.24)—not reassuring. The data section says 'October 2017' where it must mean 2007. And the proprietary covariance estimator is a black box: if it is miscalibrated, every Sharpe is suspect.\n\nNone of these are fatal, but together they mean the paper does not yet establish its main claim. The methodology is plausible and the extension is non-trivial, so I would send it to a serious referee, but with a clear request for significance tests (bootstrap or HAC), reconciled numbers, and at least as much transparency as possible on the covariance estimator, ideally code. As is, I would not cite it for the claim; I might discuss it as a cautionary example of unreported uncertainty.","headline":"A plausible application of quantum-inspired distance learning to equity momentum spillover, undermined by absent significance tests and a black-box covariance estimator.","tokens_in":12813,"tokens_out":2463,"would_cite":false,"duration_ms":28211,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that firm linkages defined by characteristic-vector similarity can drive momentum spillover, and that a quantum-cognition learned distance beats Euclidean distance, lifting the 252-day Sharpe ratio from 0.73 to 1.10.","keywords":["momentum spillover","firm linkages","characteristic vector linkages","similarity learning","quantum cognition machine learning","distance metric learning","equity return predictability","supervised similarity"],"falsifier":"Reconstruct the same momentum spillover portfolios with a fully published covariance estimator, such as a standard shrinkage estimator, and recompute the 252-day and combined Sharpe ratios; if the QCML advantage over Euclidean disappears or reverses, the claimed outperformance rests on the undisclosed estimator rather than on the learned similarity.","tokens_in":11722,"feed_emoji":"📈","tokens_out":13536,"duration_ms":136136,"temperature":0.7,"pith_summary":"The paper sets out to show that the economic links between firms can be proxied by the similarity of their characteristic vectors—accounting and valuation ratios such as book-to-price, leverage, and profit margin. It names this proxy Characteristic Vector Linkages (CVLs) and tests two ways of turning the proxy into a distance: plain Euclidean distance on the characteristic vectors, and a supervised Quantum Cognition Machine Learning (QCML) distance that maps each firm's characteristics into a quantum state and measures proximity by quantum fidelity. Both distances feed a momentum spillover signal—a firm's expected return is influenced by the lagged returns of firms with similar characteristics—and both produce positive-Sharpe, market-neutral portfolios over January 2014 to June 2024. The central claim is that QCML similarity outperforms Euclidean similarity, especially at long input horizons: the 252-day input return QCML signal reaches a Sharpe ratio of 1.10 versus 0.73 for the Euclidean signal, with more than twice the signal half-life. If this claim holds, supervised similarity learning offers a practical way to extract more persistent cross-firm relationships from public fundamental data.","feed_headline":"Quantum-inspired firm similarity out-trades Euclidean distance","feed_subtitle":"Supervised quantum-cognition distance lifts the 252-day spillover signal's Sharpe ratio from 0.73 to 1.10.","key_machinery":"The central object is the Characteristic Vector Linkage (CVL), defined as the pairwise similarity of firms computed from a vector of characteristics, and the key machinery is the QCML distance. QCML maps each firm's characteristic vector $x_{t,j}$ to the ground state $\\psi_{t,j}$ of an error Hamiltonian $H(x_{t,j},\\{A_c\\}) = \\sum_c (A_c - x^c_{t,j} I)^2$, where the $A_c$ are learned Hermitian observables; with a learned target observable $B$, the model is trained to forecast 63-day forward returns. Despite the name, this is a classical algorithm built on quantum-state mathematics. Proximity between states is measured by quantum fidelity $f(\\psi_i,\\psi_j)=|\\langle \\psi_i | \\psi_j \\rangle|^2$, converted to the Bures distance $D_{\\mathrm{QCML}}=\\sqrt{2-2|\\langle \\psi_i | \\psi_j \\rangle|}$, and then to similarity $S=e^{-\\gamma D^2}$. The momentum spillover signal for firm $j$ is $f_{l,t,j} = \\sum_i w_{t,j,i} r_{t-l:t-1,i}$ with weights $w_{t,j,i}=S_{j,i}/\\sum_i S_{j,i}$, evaluated in daily mean-variance optimal portfolios with zero exposure to standard controls. The Euclidean variant runs the same pipeline with $D$ equal to the Euclidean distance of the raw characteristic vectors; apart from rescaling $\\gamma$ so the two distances have comparable medians, the central difference is the learned versus unlearned distance.","core_discovery":"On the paper's own terms, the discovery is that Characteristic Vector Linkages are a working basis for momentum spillover, and that learning the distance function with QCML makes the linkages more robust. Firms are represented by a vector of $C$ characteristics; QCML learns $C$ Hermitian observables $A_c$ and a target observable $B$ so that each firm's ground state $\\psi_{t,j}$ of the error Hamiltonian $H(x_{t,j},\\{A_c\\}) = \\sum_c (A_c - x^c_{t,j} I)^2$ predicts 63-day forward returns. The distance between two firms is the Bures distance built from quantum fidelity, $D_{\\mathrm{QCML}} = \\sqrt{2 - 2|\\langle \\psi_i | \\psi_j \\rangle|}$, and similarity is $e^{-\\gamma D^2}$. Portfolios formed from the resulting spillover signal—lagged returns weighted by similarity—are market neutral and neutralized against analyst coverage, momentum, size, and industry controls. The paper reports that QCML similarity beats Euclidean similarity for every input return horizon, with the largest edge at 252 days (Sharpe 1.10 vs 0.73) and in the combined signal (1.42 vs 1.24), while also yielding materially longer signal half-lives, which it reads as evidence that the learned relationships are more persistent and less noisy.","pith_inferences":["A direct robustness test would replace the proprietary covariance estimator with a fully published estimator and re-run the strategies; the reported gap between QCML and Euclidean could shrink or vanish, because the covariance matrix enters every Sharpe ratio.","Because QCML is trained on 63-day forward returns, the learned similarity encodes a return-horizon-specific notion of relatedness; training on earnings surprises or revenue growth would likely produce different linkages, a variation the paper itself leaves open.","The longer half-lives of the QCML signals suggest the learned linkages are more persistent; one could test this by checking whether top QCML-linked pairs coincide with observable supply-chain or shared-analyst links, or by measuring their co-movement after June 2024.","The distance-learning recipe is asset-class agnostic; porting it to corporate bonds, currencies, or risk clustering would test whether the improvement over Euclidean distance generalizes beyond US equities."],"forward_implications":["Characteristic Vector Linkages formed from Euclidean distance on accounting and valuation ratios are alone enough to construct positive-Sharpe momentum spillover portfolios, with full-sample Sharpe ratios between 0.71 and 1.35 depending on the input return horizon.","Supervised QCML similarity improves on Euclidean similarity for every input horizon tested, and the improvement grows with the horizon: the 252-day input return Sharpe rises from 0.73 to 1.10 while the signal half-life rises from 36.3 to 90.9 days.","The combined 21/63/126/252-day QCML signal reaches a Sharpe of 1.42 versus 1.24 for Euclidean, with roughly 1.6 times the half-life.","Because the QCML parameters are trained once on data from October 2007 through August 2013 and then held static, periodic retraining or online updating is an available path to further gains.","Both approaches weaken in the January 2021 through June 2024 sub-period, but the QCML signals retain a modest edge and draw less of their performance from the strongest sub-period."],"supporting_citations":[{"why":"Defines the QCML training algorithm, the ground-state energy decomposition, and the noise-resistance rationale that underpin the learned distance.","marker":"[10]"},{"why":"Introduces the QCML paradigm as a quantum-state representation learning framework used throughout.","marker":"[25]"},{"why":"Establishes the supervised QCML financial forecasting method with target observables that this paper adapts to similarity learning.","marker":"[38]"},{"why":"Demonstrates the same supervised-similarity technique on high-yield bonds, the direct precursor this paper extends to equity firm linkages.","marker":"[35]"},{"why":"Proposes supervised similarity learning for corporate bonds from Random Forest distances, the line of work the paper continues.","marker":"[21]"},{"why":"Documents the shared-analyst-coverage momentum spillover and supplies a control that the test portfolios must have zero exposure to.","marker":"[1]"},{"why":"Supplies the exponential affinity-matrix construction used to convert distances into similarity scores.","marker":"[26]"},{"why":"Defines quantum fidelity, the probability-based proximity measure at the root of the QCML distance.","marker":"[27]"},{"why":"Provides the Bures distance formula used to turn fidelity into a metric distance.","marker":"[42]"}],"fun_headline_variants":["Quantum-cognition distance lifts spillover Sharpe to 1.10","Learned Bures distance outperforms Euclidean for firm links","Supervised quantum similarity out-trades Euclidean in spillover","QCML firm distance: smarter linkages, longer signal half-life","Quantum-inspired firm similarity beats Euclidean for momentum"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The Sharpe ratios are computed with a daily covariance matrix estimated by a proprietary, undisclosed technique, so if that estimator is miscalibrated or non-reproducible, the reported performance advantage of QCML over Euclidean similarity is not independently verifiable.","fun_headline_variants_meta":{"raw":{"variants":["Quantum-cognition distance lifts spillover Sharpe to 1.10","Learned Bures distance outperforms Euclidean for firm links","Supervised quantum similarity out-trades Euclidean in spillover","QCML firm distance: smarter linkages, longer signal half-life","Quantum-inspired firm similarity beats Euclidean for momentum"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000236,"raw_usage":{"total_tokens":1471,"prompt_tokens":881,"completion_tokens":590,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":497,"completion_tokens_details":{"reasoning_tokens":509}},"tokens_in":497,"tokens_out":590,"duration_ms":6911,"temperature":1.0,"reasoning_tokens":509,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T05:22:49.217579+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Reconstruct the same momentum spillover portfolios with a fully published covariance estimator, such as a standard shrinkage estimator, and recompute the 252-day and combined Sharpe ratios; if the QCML advantage over Euclidean disappears or reverses, the claimed outperformance rests on the undisclosed estimator rather than on the learned similarity.","supporting_citations":[{"cited_title":"Abanov, Jeffrey Berger, Cameron J","cited_arxiv_id":null,"evidence_quote":"Defines the QCML training algorithm, the ground-state energy decomposition, and the noise-resistance rationale that underpin the learned distance."},{"cited_title":"Quantum cognition machine learning: AI needs quantum, 2024","cited_arxiv_id":null,"evidence_quote":"Introduces the QCML paradigm as a quantum-state representation learning framework used throughout."},{"cited_title":"Quantum cognition machine learning: financial forecasting, 2024","cited_arxiv_id":null,"evidence_quote":"Establishes the supervised QCML financial forecasting method with target observables that this paper adapts to similarity learning."},{"cited_title":"Supervised similarity for high-yield bonds, 2025","cited_arxiv_id":null,"evidence_quote":"Demonstrates the same supervised-similarity technique on high-yield bonds, the direct precursor this paper extends to equity firm linkages."},{"cited_title":"Supervised similarity learning for corporate bonds using random forest proximities, 2022","cited_arxiv_id":null,"evidence_quote":"Proposes supervised similarity learning for corporate bonds from Random Forest distances, the line of work the paper continues."},{"cited_title":"Shared analyst coverage: Unifying momentum spillover effects.Journal of Financial Economics, 136(3):649–675, 2020","cited_arxiv_id":null,"evidence_quote":"Documents the shared-analyst-coverage momentum spillover and supplies a control that the test portfolios must have zero exposure to."},{"cited_title":"On spectral clustering: Analysis and an algo- rithm","cited_arxiv_id":null,"evidence_quote":"Supplies the exponential affinity-matrix construction used to convert distances into similarity scores."},{"cited_title":"Springer International Publishing, Cham, 2017","cited_arxiv_id":null,"evidence_quote":"Provides the Bures distance formula used to turn fidelity into a metric distance."}],"review_version":1}