Changing a system’s known input gains may make it possible to detect hidden feedback links using outputs alone, according to a new methods preprint. The key condition is variation: when gains stay constant, different combinations of feedback and hidden confounding can produce the same observations, leaving the network indistinguishable.
The work is a working-paper arXiv preprint, version 2 dated 3 September 2026. It combines identification theory, synthetic experiments and illustrative applications to leveraged-fund rebalancing data from Korea and the United States.
Why the changing gain matters
The proposed setup treats changes in known gains as extra information about how a system responds. By comparing behavior across gain regimes, the method seeks to distinguish feedback coupling from confounding that does not change with the gain.
For the exact fixed-point model, local identification depends on the rank of a stacked Jacobian, a sensitivity map that records how observations change across gain regimes. At least two distinct regimes are necessary, although local identification alone does not guarantee that the same answer is unique everywhere.
The method also has a built-in interpretive limit. Beyond a first-order, or small-change, approximation, its interaction estimate measures sensitivity of the network’s overall response, not necessarily a single direct edge. Directed paths and indirect transmission can contribute to the estimate.
Promising tests, with important caveats
In the main synthetic validation, the researchers simulated five output channels over 750 periods and ran 200 Monte Carlo paths. The design used sparse nonnegative coupling, four true off-diagonal couplings and a known reversal share of 0.85.
Constant gains produced non-identification on every simulated path. With independent gain regimes, the detector’s false-alarm rate was 0.12, compared with 0.22 when the gains followed correlated staircase patterns. Under confounding designed to mimic a reversal, the proposed detector had a false-alarm rate of 0.12, while a level or Granger benchmark reached 0.53. Under confounding with the continuation sign, the benchmark’s rate was 0.04.
The simulations also show why a detected interaction should not automatically be read as proof of a direct connection. The detector flagged 39% of entries with no direct edge but a reachable path elsewhere in the network. For zero entries with no reachable path, its estimated size was 5.3% at a 5% screening rule.
Recovering the broader network is harder
The paper’s pipeline combines first-order regression, a non-iterative singular-value decomposition estimate, bootstrap inference and a constrained refinement method called hard SCA. The theoretical result gives consistency and asymptotic normality around a pseudo-true parameter, meaning the estimate can settle around the best-fitting target of the chosen approximation rather than the exact structural quantity. The projection gap from that structural first-order target is described as modeling error that does not disappear simply by adding more observations.
In a constrained-refinement experiment covering 25 paths, hard SCA was feasible and monotone on every reported path. Compared with box-TRF, it reduced spectral bias from +0.100 to +0.043 and lowered coupling RMSE from 0.078 to 0.055. The result is specific to that design and does not establish a global optimization guarantee.
Uncertainty results were mixed. An outward-score experiment reported a 6.7% size at the 5% boundary, with local power of 25% and 85% in two alternatives. A two-stage basic bootstrap sensitivity interval covered 90% at a nominal 95% level in its own experiment. But a separate full-pipeline diagnostic covered the structural spectral radius in only 50% of basic intervals and 40% of percentile intervals.
A trade-off between alarms and missed changes
The rolling transmission monitor made the usual trade-off visible. Under the most stringent listed rule, the false-alarm rate was 0.10, but 18 of 40 treated paths were missed. The loosest rule missed none of the 40 treated paths. That experiment covered only the transmission branch and used overlapping windows, so it does not settle how a general monitoring system would perform.
The market examples are illustrations, not proof
The Korean application reported a cross-reversal slope with z scores of −2.82 under the reported calculation and −2.72 with Newey-West errors. In a placebo comparison across 183 ordered pairs, the result ranked first, with a rank ratio of 0.0055. The application used a contaminated full-period regressor rather than the clean pre-window moment required by the theory, so it does not provide clean structural identification.
The U.S. staggered panel produced no interaction that survived multiplicity adjustment. Gain-path correlations ranged from 0.81 to 0.91, and the median rolling Gram condition number was 45, pointing to the reported conditioning limitations. The panel’s null pattern therefore does not resolve whether the method can detect weaker interactions in that setting.
Taken together, the evidence supports a narrower conclusion than a general-purpose network detector. The method depends on exogenous gain variation, conditional orthogonality, persistent excitation and stability conditions. Constant or weakly varying gains can leave parameters unidentified, while the spectral boundary is treated as a heuristic under additional assumptions. The case studies are observational and do not establish causal market effects.
The preprint’s strongest contribution is a way to turn changes in a known input gain into structural information when only outputs are available. Its simulations showed a lower false-alarm rate than a benchmark under reversal-mimicking confounding, while also showing that indirect paths can trigger flags. Reliable exact spectral recovery, uniform inference and scalable estimation for larger networks remain open problems.
The front matter reports an Amazon Web Services affiliation and says the views do not represent Amazon Web Services or its affiliates. No funding statement is reported in the supplied text.
Paper data and sources
Original title: Output-Only Identification and Spectral Monitoring of Coupled Feedback Networks with Known Time-Varying Actuation
Authors: Jihwan Woo
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text