arXiv subjects

Haochun Ma

Publications and source records attributed to Haochun Ma.

4 recordsLinked to original sources

arXiv2026

Distinguishing indistinguishable attractors: Unsupervised anomaly detection with reservoir computers

Detecting when a nonlinear dynamical system departs from its normal regime is a recurring problem across the sciences, from cardiology to climate and energy systems. We show that a very simple Kolmogorov--Smirnov test on the output weights of a reservoir computer is highly sensitive to regime changes in nonlinear dynamical systems, including those invisible to both classical nonlinear measures and modern deep-learning detectors. The core idea of our algorithm is to treat the readout layer of a reservoir computer as a representation of the input dynamics. Since the input mapping and the reservoir itself are random and fixed, the trained output weights are the only object encoding the system at hand. We summarize this fingerprint by the empirical cumulative distribution function of the readout weights and compare it to a reference band built from the training data. This unsupervised, online detector distinguishes two visually indistinguishable butterfly-shaped attractors, resolves parameter drifts seven times smaller than the strongest deep-learning baseline, flags noise four orders of magnitude below the signal, and identifies ventricular flutter in a clinical ECG recording. More broadly, we aim to establish a perspective on reservoir computers in which the trained output weights are treated as a representation of the learned system in their own right, rather than merely as a means to forecasting.

cs.LG↗

arXiv2025

A Step Towards a Solution to the Confidence-Driven Liquidity Trap Morass

Depending on the persistence of a one-off shock bringing the economy to the Effective Lower Bound (ELB), the standard New Keynesian model predicts starkly different conclusions. We offer a potential solution to this morass by assuming that the one-off shock is such that the economy necessarily leaves the ELB in finite time. Under these assumptions, we prove that the confidence-driven liquidity trap \`a la \cite{mertens2014fiscal} doesn't arise as an equilibrium outcome and that there is a unique path back for a given steady state. Furthermore, under our shock specification the effect of government spending on consumption is necessarily positive and does not switch signs but may grow unbounded \textemdash a puzzle.

econ.GN↗

arXiv2025

Tailored minimal reservoir computing: on the bidirectional connection between nonlinearities in the reservoir and in data

We study how the degree of nonlinearity in the input data affects the optimal design of reservoir computers, focusing on how closely the model's nonlinearity should align with that of the data. By reducing minimal RCs to a single tunable nonlinearity parameter, we explore how the predictive performance varies with the degree of nonlinearity in the reservoir. To provide controlled testbeds, we generalize to the fractional Halvorsen system, a novel chaotic system with fractional exponents. Our experiments reveal that the prediction performance is maximized when the reservoir's nonlinearity matches the nonlinearity present in the data. In cases where multiple nonlinearities are present in the data, we find that the correlation dimension of the predicted signal is reconstructed correctly when the smallest nonlinearity is matched. We use this observation to propose a method for estimating the minimal nonlinearity in unknown time series by sweeping the reservoir exponent and identifying the transition to a successful reconstruction. Applying this method to both synthetic and real-world datasets, including financial time series, we demonstrate its practical viability. Finally, we transfer these insights to classical RC by augmenting traditional architectures with fractional, generalized reservoir states. This yields performance gains, particularly in resource-constrained scenarios such as physical reservoirs, where increasing reservoir size is impractical or economically unviable. Our work provides a principled route toward tailoring RCs to the intrinsic complexity of the systems they aim to model.

cs.LG↗

arXiv2023

Linear and nonlinear causality in financial markets

Identifying and quantifying co-dependence between financial instruments is a key challenge for researchers and practitioners in the financial industry. Linear measures such as the Pearson correlation are still widely used today, although their limited explanatory power is well known. In this paper we present a much more general framework for assessing co-dependencies by identifying and interpreting linear and nonlinear causalities in the complex system of financial markets. To do so, we use two different causal inference methods, transfer entropy and convergent cross-mapping, and employ Fourier transform surrogates to separate their linear and nonlinear contributions. We find that stock indices in Germany and the U.S. exhibit a significant degree of nonlinear causality and that correlation, while a very good proxy for linear causality, disregards nonlinear effects and hence underestimates causality itself. The presented framework enables the measurement of nonlinear causality, the correlation-causality fallacy, and motivates how causality can be used for inferring market signals, pair trading, and risk management of portfolios. Our results suggest that linear and nonlinear causality can be used as early warning indicators of abnormal market behavior, allowing for better trading strategies and risk management.

q-fin.ST↗