Jian'an Zhang

Yiyi Wang, Jian'an Zhang, Hongyi Duan et al.

State Space Models (SSMs), particularly recent selective variants like Mamba, have emerged as a leading architecture for sequence modeling, challenging the dominance of Transformers. However, the success of these state-of-the-art models largely relies on heuristically designed selective mechanisms, which lack a rigorous first-principle derivation. This theoretical gap raises questions about their optimality and robustness against spurious correlations. To address this, we introduce the Principle of Predictive Sufficiency, a novel information-theoretic criterion stipulating that an ideal hidden state should be a minimal sufficient statistic of the past for predicting the future. Based on this principle, we propose the Minimal Predictive Sufficiency State Space Model (MPS-SSM), a new framework where the selective mechanism is guided by optimizing an objective function derived from our principle. This approach encourages the model to maximally compress historical information without losing predictive power, thereby learning to ignore non-causal noise and spurious patterns. Extensive experiments on a wide range of benchmark datasets demonstrate that MPS-SSM not only achieves state-of-the-art performance, significantly outperforming existing models in long-term forecasting and noisy scenarios, but also exhibits superior robustness. Furthermore, we show that the MPS principle can be extended as a general regularization framework to enhance other popular architectures, highlighting its broad potential.

Jian'an Zhang

We propose ARBITER, a risk-neutral neural operator for learning joint SPX-VIX term structures under no-arbitrage constraints. ARBITER maps market states to an operator that outputs implied volatility and variance curves while enforcing static arbitrage (calendar, vertical, butterfly), Lipschitz bounds, and monotonicity. The model couples operator learning with constrained decoders and is trained with extragradient-style updates plus projection. We introduce evaluation metrics for derivatives term structures (NAS, CNAS, NI, Dual-Gap, Stability Rate) and show gains over Fourier Neural Operator, DeepONet, and state-space sequence models on historical SPX and VIX data. Ablation studies indicate that tying the SPX and VIX legs reduces Dual-Gap and improves NI, Lipschitz projection stabilizes calibration, and selective state updates improve long-horizon generalization. We provide identifiability and approximation results and describe practical recipes for arbitrage-free interpolation and extrapolation across maturities and strikes.

Hongyi Duan, Haoyang Liu, Jian'an Zhang et al.

We present a JIT PL semantics for ReLU-type networks that compiles models into a guarded CPWL transducer with shared guards. The system adds hyperplanes only when operands are affine on the current cell, maintains global lower/upper envelopes, and uses a budgeted branch-and-bound. We obtain anytime soundness, exactness on fully refined cells, monotone progress, guard-linear complexity (avoiding global $\binom{k}{2}$), dominance pruning, and decidability under finite refinement. The shared carrier supports region extraction, decision complexes, Jacobians, exact/certified Lipschitz, LP/SOCP robustness, and maximal causal influence. A minimal prototype returns certificates or counterexamples with cost proportional to visited subdomains.

Jian'an Zhang

We introduce Tail-Safe, a deployability-oriented framework for derivatives hedging that unifies distributional, risk-sensitive reinforcement learning with a white-box control-barrier-function (CBF) quadratic-program (QP) safety layer tailored to financial constraints. The learning component combines an IQN-based distributional critic with a CVaR objective (IQN--CVaR--PPO) and a Tail-Coverage Controller that regulates quantile sampling through temperature tilting and tail boosting to stabilize small-$α$ estimation. The safety component enforces discrete-time CBF inequalities together with domain-specific constraints -- ellipsoidal no-trade bands, box and rate limits, and a sign-consistency gate -- solved as a convex QP whose telemetry (active sets, tightness, rate utilization, gate scores, slack, and solver status) forms an auditable trail for governance. We provide guarantees of robust forward invariance of the safe set under bounded model mismatch, a minimal-deviation projection interpretation of the QP, a KL-to-DRO upper bound linking per-state KL regularization to worst-case CVaR, concentration and sample-complexity results for the temperature-tilted CVaR estimator, and a CVaR trust-region improvement inequality under KL limits, together with feasibility persistence under expiry-aware tightening. Empirically, in arbitrage-free, microstructure-aware synthetic markets (SSVI $\to$ Dupire $\to$ VIX with ABIDES/MockLOB execution), Tail-Safe improves left-tail risk without degrading central performance and yields zero hard-constraint violations whenever the QP is feasible with zero slack. Telemetry is mapped to governance dashboards and incident workflows to support explainability and auditability. Limitations include reliance on synthetic data and simplified execution to isolate methodological contributions.

Jian'an Zhang

Transaction costs and regime shifts are major reasons why paper portfolios fail in live trading. We introduce FR-LUX (Friction-aware, Regime-conditioned Learning under eXecution costs), a reinforcement learning framework that learns after-cost trading policies and remains robust across volatility-liquidity regimes. FR-LUX integrates three ingredients: (i) a microstructure-consistent execution model combining proportional and impact costs, directly embedded in the reward; (ii) a trade-space trust region that constrains changes in inventory flow rather than logits, yielding stable low-turnover updates; and (iii) explicit regime conditioning so the policy specializes to LL/LH/HL/HH states without fragmenting the data. On a 4 x 5 grid of regimes and cost levels with multiple random seeds, FR-LUX achieves the top average Sharpe ratio with narrow bootstrap confidence intervals, maintains a flatter cost-performance slope than strong baselines, and attains superior risk-return efficiency for a given turnover budget. Pairwise scenario-level improvements are strictly positive and remain statistically significant after multiple-testing corrections. We provide formal guarantees on optimality under convex frictions, monotonic improvement under a KL trust region, long-run turnover bounds and induced inaction bands due to proportional costs, positive value advantage for regime-conditioned policies, and robustness to cost misspecification. The methodology is implementable: costs are calibrated from standard liquidity proxies, scenario-level inference avoids pseudo-replication, and all figures and tables are reproducible from released artifacts.