MoFE: A Novel Mixture-of-Experts Framework with Fourier Neural Operators for Cryptocurrency Forecasting

Forecasting cryptocurrency prices remains a formidable challenge due to inherent non-stationarity, abrupt regime shifts, and multi-scale stochastic dependencies. Conventional deep learning models often struggle to capture complex underlying dynamics, frequently resulting in persistent phase-lagged predictions. To address these limitations, we propose MoFE, a novel deep learning framework that integrates Fourier Neural Operators (FNOs) within a Mixture-of-Experts (MoE) architecture. Rooted in the theoretical framework of stochastic differential equations, MoFE conceptualizes cryptocurrency volatility as a superposition of multi-frequency components, which includes user network based fundamental growth, mining costs and halving mechanism caused seasonal volatility, and market sentiment-induced chaos. Specifically, specialized adaptive FNO (AFNO) and Convolution dual-domain experts learn continuous function-to-function mappings to encapsulate global spectral trends, cyclical adjustments and microstructures, while a dynamic gating based MoE mechanism enables adaptive strategy switching across diverse market regimes. Extensive experiments on Bitcoin datasets spanning January 2020 to December 2025 demonstrate that MoFE achieves state-of-the-art (SOTA) performance in both T+1 and T+5 forecasting horizons. Notably, the model effectively mitigates the phase-lag effect, delivering superior Directional Accuracy (DA) and Information Coefficient (IC). In high-fidelity simulated trading environments, these predictive gains transfer into significant excess returns and robust risk-adjusted performance, characterized by a high Sharpe ratio.

Financial Numerical Prediction and Allocation as Token Generation

Financial prediction typically relies on task-specific regression, ranking, or policy heads, separating the language model from the numerical object ultimately evaluated. We investigate whether a causal language model can instead represent forecasts and decisions directly through constrained token generation. FinATOM introduces a unified, head-free interface for three-step stock-return forecasting and dynamic five-ETF allocation. The forecasting model autoregressively emits volatility-standardized return tokens and is trained with ordinal and ranking supervision followed by a one-epoch token-level policy stage. The allocation model generates normalized long-only weights; supervised fine-tuning imitates a causal mean--variance anchor, and DAPO-augmented GRPO optimizes realized 21-day Sharpe subject to anchor consistency. In 2023--2025 ETF tests, the allocation policy improves pooled gross Sharpe from 1.428 to 1.529 and net Sharpe under a 5-bp transaction-cost model from 1.394 to 1.494. The multimodal allocation input attains the highest three-period mean Sharpe of 1.540, with its clearest advantage in 2025. On FinTexTS, the SFT and policy strategies achieve 73.52\%/2.68 and 73.72\%/2.69 cumulative-return/Sharpe, respectively. These results support the feasibility of direct language-model token generation for financial numerical prediction and decision-making, while motivating broader tests across assets, regimes, and random seeds.

Hybrid Neural-Classical Correction for Frozen Time Series Foundation Models: A Comprehensive Ablation Study on High-Frequency Stock Prediction

Foundation models for time series forecasting demonstrate impressive zero-shot generalization but often underperform on specialized domains such as high-frequency finance. We present a comprehensive study of hybrid neural-classical correction for adapting frozen TimesFM (200M parameters) to stock return prediction during the volatile opening trading hour. We compare two neural correction architectures - AttnCorrect (multi-head self-attention, approximately 471K parameters) and GatedLinear (low-rank bilinear projection with gating, approximately 49K parameters) - each augmented with Random Forest residual learning. Through systematic ablation across 10 major technology stocks (NVDA, MSFT, AAPL, GOOG, GOOGL, AMZN, META, AVGO, TSLA, NFLX) spanning 2 million data points, we reveal critical insights: (1) The hybrid neural-classical approach achieves 0.597 pooled correlation and 6.4x mean per-day correlation improvement over frozen TimesFM; (2) Classical residual learning (Random Forest) provides the largest single-component contribution, matching or exceeding the neural correction component; (3) Simpler neural architectures surprisingly outperform complex ones when classical residual learning is removed; (4) Self-attention provides the largest neural-only contribution. GatedLinear+RF achieves best overall performance with 9x fewer neural parameters than AttnCorrect+RF. We report three complementary correlation metrics - mean per-day, cross-day cumulative, and pooled - to provide a complete picture of predictive quality. Our results provide practical guidance: effective foundation model adaptation requires careful integration of neural and classical components, with classical methods playing a crucial complementary role.

The Inference-Compute Frontier and a Latency-Efficient Architecture for Limit Order Book Prediction

We study whether a scaling-law-style inference-compute frontier appears in limit order book prediction. Using FI-2010 and a suite of models ranging from small decision trees to neural LOB architectures, we find that the realized empirical frontier of predictive loss versus structural forward work is well summarized by a power law. In particular, with MLPLOB held out as an architecture family, a power-law fit to the low- and mid-compute non-MLPLOB frontier extrapolates across multiple orders of magnitude and attains $R^2=0.941$ on the excluded high-compute MLPLOB target frontier. A similar exercise in latency space gives substantially weaker results, showing that latency is not merely noisy compute. We use this gap to motivate FastBiNLOB, a dense axis-separable LOB mixer built from hardware-friendly temporal and feature mixing operations. In a five-seed experiment, FastBiNLOB exceeds the published $y_{10}$ and $y_{100}$ macro-F1 targets at notably lower latency than existing published SOTA architectures.

Hierarchical Graph Learning for Calendar Spread Strategies in Commodity Futures Markets

Commodity futures can be represented hierarchically, with underlying assets at the upper level and individual futures contracts at the lower level. Entities at each level can be connected by edges reflecting inherent correlations, with cross-level edges capturing contract-to-underlying asset connections. Building on our observations of these structures, we propose a hierarchical graph learning approach for calendar spread (CS) strategies in commodity futures markets, addressing two significant gaps in the machine-learning literature: (i) the absence of learning-based methods for CS strategies in futures markets, and (ii) the lack of consideration of maturity-dependent interrelationships across commodity futures. We first establish the efficacy of CS strategies by analytically showing that CS strategies can possess higher risk-adjusted returns, measured by the information ratio, and lower risk, measured by variance and delta, than long-only strategies. We then introduce a method to convert learning-based predictions into CS positions. Next, we develop a hierarchical graph learning method that predicts futures price movements by utilizing the maturity-dependent interrelationships, thereby yielding a CS trading algorithm. Empirical results on commodity futures markets traded on the Chicago Mercantile Exchange Group demonstrate that our method outperforms benchmark models in both prediction and trading performance. We find that maturity-dependent interrelationships across commodity futures are instrumental in prediction and that CS trading based on hierarchical graph learning is effective for statistical arbitrage.

Interpretable Factor Decomposition for Decision Intelligence in Large-Scale Financial Markets: Evidence from China's A-Share Market

We present an interpretable machine learning pipeline to decompose Cross-Sectional Equity Return Predictability into auditable factor contribution. We apply an XGBoost model with TreeSHAP attribution and conduct stress testing on 3632 Chinese A-share stocks from 2009 until 2019. Using 60-month, rolling windows over 55 months of out-of-sample data, XGBoost obtains a mean AUC of 0.547 and +2.38%/month (Newey-West t = 5.94; Annualized Sharpe 2.23) long-short spread for the top vs bottom quintiles. This alpha is persistent after adjusting for the Carhart four-factor model (+2.31%/month; t = 7.48). SHAP Decomposition indicates that behavioral signals (turnover and momentum) account for 58.2% of predictive attribution compared to 10.7% for valuation ratios, on average, across 55 industry groups. Ablation analysis serves to cross-validate this ranking and provides evidence that SHAP and ablation diverge in a manner that highlights feature substitutability structure that is largely invisible to either method used in isolation.