julius schmidt// bachelor thesis | leuphana 2026
Liquid neural networks vs. classical models
Do liquid neural networks forecast daily financial returns better than classical models? I tested 11 liquid variants against 8 established baselines on ten years of AAPL, JPM and SPY data. The answer is no: none of the 120 corrected comparisons was significant.
The best variant, a sparsely wired CfC, topped the point metrics on all three assets. Its lead was not significant, and its directional edge matched simply always predicting “up”: market drift, not skill. A clean no, measured properly, is worth more than a flattering chart.
Python | walk-forward over 5 seeds | Diebold–Mariano + Holm | 300 tests | graded 1.0
How I tested it
- The questionLiquid neural networks (LTC, CfC) change their dynamics with the input. On paper that suits noisy financial time series. Does it beat the classical bar in practice?
- The data (ƒ)Ten years of daily prices for AAPL, JPM and SPY, plus macro series from FRED. Every feature is built from information available on that day.
- The protocolWalk-forward evaluation: train on the past, forecast the next window, move on. Every neural model runs over 5 seeds, so a lucky run cannot win.
- The testDiebold–Mariano tests with small-sample correction for each liquid model against each baseline, Holm-adjusted across all 120 comparisons.
- The result0 of 120 significant. The best CfC sits level with the ARMA baselines. The limit is the data, not the model: daily returns carry too little signal for extra capacity to pay off.
Code, figures and the thesis are public, with an agent quick start to reproduce or extend the benchmark. Code on GitHub | Thesis (PDF)