I would say that most ML methods risk overfitting and it depends very much on the asset class. The only area where more sophisticated ML methods such as deep learning appear to make a major difference is in cash equities, where the feature space is very rich (NLP, news and announcements, corporate earnings, other financials) and the data is relatively good, Corporate bonds are too fractious a market (so many more products than in the equities space) but would be the next area worth considering.
But a lot of the ML guys who start trying to do rates get sorely disappointed. I heard from a guy who had a decent equity fund and wanted to do rates, and set his mind to parsing fed statements (bfd, been there done that, so what), then started asking why they were talking about hiking when PMIs were so low (duh! hadn't been looking at the news). Basically, FI is much harder. Too many products and not enough differentiation--does the announcement affect the 2y or the 5y? I'm not saying it's not feasible at some point but it isn't feasible now.
Simply speaking, DNNs work by dimension reduction. You have the possibility of thousands, perhaps tens of thousands or more parameters. If you have petabytes of image data, then you are doing a good job with dimension reduction. We do not have big data in most trading. Having more data (longer time series) isn't as good as increasing the cross-sectional dimension because we have non-stationary series anyway. Other than equities, analysis of limit order books may be an area where DNN can have applications although the evidence is mixed (domain knowledge is always more important than just throwing data into some model...GIGO).
Non-stationarity alone will reduce the complexity of any good model. The recent paper by AQR on using neural nets (for EQUITY factor extraction) showed that NNs outperformed linear models but that the optimal nets were in fact quite shallow (see Empirical Asset Pricing via Machine Learning).
In general, naive applications of NNs to finance are doomed from the get-go. The paper by Cont and Sirignano applying LSTMs to LOBs on a single-name and pooled basis shows the limits of the approach, where they found pooled data worked far better (pooled data = 1/300 or so the number of parameters as the single name models). They call it 'universal rules' but their interpretation is very generous! it's just that there wasn't enough data (see NN learned universal model. It's pretty clear that a big model applied to tons of data seems to result in just a lack of any understanding. Domain knowledge and lighter touches make for far more robust results.