Deep Learning Geometry and High-Frequency Trading: Cross-Disciplinary Exploration of Neural Network Architecture Design

The core of the project is to apply deep learning geometry theory to the design of neural network architectures for high-frequency trading. It explores the relationship between the geometric properties of loss landscapes, optimizer dynamics, and financial time series prediction, aiming to design neural network architectures that adapt to the ultra-low latency requirements of high-frequency trading. The high-frequency trading field is technology-intensive, where speed is crucial. Traditional strategies are being transformed by deep learning, and this project is a cross-disciplinary attempt combining mathematical geometry with millisecond-level trading.

High-frequency trading faces four core challenges: 1. Market Microstructure: Analyzing short-term price trends based on order book dynamics; 2. Signal-to-Noise Ratio: Signals are weak at high-frequency scales, with prediction accuracy only slightly above 50%; 3. Latency Sensitivity: The processing chain needs to be completed in microseconds, and complex models are prone to failure due to latency; 4. Market Impact and Capacity Constraints: Large transactions alter market states, limiting the big data advantages of models.

Deep learning geometry reveals the structural characteristics of loss function landscapes: 1. Topological Properties: High-dimensional loss surfaces have structures such as flat minimum regions and low-dimensional canyons; 2. Sharpness and Generalization: Flat minima have better generalization, inspiring the SAM optimization algorithm; 3. NTK Theory: In the early training stage of networks with infinite width, they approximate kernel methods, guiding initialization and learning rates; 4. Implicit Regularization: Optimizers (e.g., gradient descent, Adam) prefer different solution manifolds, which can be regarded as part of architecture design.

Architecture design needs to balance performance and latency: 1. Depth-Width Trade-off: Shallow and wide (3-5 layers) designs ensure inference latency; 2. Activation Function Selection: ReLU is simple but prone to gradient vanishing; smooth functions like Swish optimize landscapes but have slightly higher costs; 3. Skip Connections: Improve gradient flow but increase latency, so they may be simplified or avoided; 4. Attention Mechanisms: Transformer's quadratic complexity is unsuitable; consider linear/local attention variants.

Optimizer selection needs to combine geometric properties: 1. Adaptive Learning Rates (Adam/AdamW): Suitable for sparse gradients but easily converge to sharp minima; 2. Momentum SGD: After parameter tuning, it finds flatter minima, requiring warm-up and annealing strategies; 3. Second-Order Methods: Theoretically fast convergence, but Hessian calculation is impractical; consider approximate methods; 4. SAM Optimization: Explicitly optimizes sharpness to find flat minima, enhancing prediction robustness.

Feature engineering and training strategies address non-stationarity: Feature Engineering: Order book features (spread, imbalance), time aggregation features (moving average, VWAP), technical indicators (RSI, MACD), manifold learning (autoencoders to extract low-dimensional representations); Training Strategies: Rolling training windows (using recent data), online learning (continuous updates to avoid forgetting), ensemble methods (reduce overfitting), adversarial training (enhance robustness).

Backtesting evaluation and hardware deployment are key: Backtesting: Profit and loss analysis (Sharpe ratio, maximum drawdown), transaction cost modeling (slippage, commissions), forward validation (simulate real-time deployment), statistical significance testing (Monte Carlo simulation); Hardware Deployment: FPGA acceleration (microsecond-level latency but complex development), GPU optimization (TensorRT to improve efficiency), CPU optimization (MKL-DNN/OpenVINO), network stack optimization (DPDK/RDMA to reduce latency).

Project limitations: High data acquisition costs, possibly using low-frequency/simulated data; high risk of backtesting overfitting. Ethical controversies: High-frequency trading may increase volatility and flash crash risks, which is unfair to ordinary investors. Project value: Cross-disciplinary innovation promotes the application of deep learning in low-latency scenarios, provides new architectural ideas for financial ML, and future cross-disciplinary attempts will become more common.