Abstract

We introduce CAFE-Rail-4R, a context-aware, adaptive-privacy, federated and explainable framework for real-time railway traffic control. The system simultaneously addresses four coupled challenges faced by modern operators: (i) joint differential-privacy protection after multimodal sensor fusion, mandated by the 2024 revision of Japan’s APPI law; (ii) forecast consistency under passenger reactions that were shown to shift eleven percent of Tokyo riders and create secondary peaks; (iii) robustness of continual learners during black-swan events such as earthquakes and pandemics; and (iv) regulatory demand for dispatcher-readable rules certified against the JR-E 120-A safety handbook. Achieving these objectives is hard because privacy noise degrades accuracy, behavioural feedback yields oscillatory loads, catastrophic forgetting erodes rare-event knowledge, and black-box policies cannot be verified. CAFE-Rail-4R resolves the impasse through an elastic Rényi accountant that re-allocates modality-specific noise every thirty seconds, a Causal Reaction Graph with a differentiable Stackelberg layer that forecasts equilibrium loads, a dual-timescale replay buffer that retains Fisher information on rare mechanisms, and a neuro-symbolic rule pipeline that passes SMT safety audits. Three experiments validate the design: on Jetson-Nano hardware the accountant keeps ε≤1.0 in 99.8 % of sliding fifteen-minute windows with only +3.8 % MAE and 41 % bandwidth savings; in a digital twin the Stackelberg layer halves overload intervals and trims spill-over by 29 % relative to LargeST-based control; over 125 streaming days dual replay preserves 81 % Fisher information and reduces dispatcher overrides to 7.6 %. The results demonstrate that privacy, robustness and explainability can be obtained without sacrificing operational performance.

Introduction

Urban rail networks confront three simultaneous pressures: stricter privacy regulation, volatile passenger demand and uncompromising safety oversight. The introduction of smartphone “blue alerts” in Tokyo illustrates the interaction of these forces. Logs collected in 2023 show that 11 % of alerted riders delayed departure, creating a secondary demand peak roughly one hour later. Legacy forecasters that treat demand as exogenous subsequently over-dispatched trains for the original peak and under-dispatched for the shifted one. In parallel, the April-2024 amendment of the Act on the Protection of Personal Information (APPI) stipulates that any fused data stream must satisfy end-to-end differential privacy (DP). Camera-only schemes thus become non-compliant as soon as Bluetooth beacons or IC-ticket taps are integrated. Finally, dispatchers and safety regulators require human-readable guidance that is provably consistent with the JR-E 120-A handbook; state-of-the-art neural controllers trigger more than 20 % manual overrides because their actions cannot be audited in real time.

These intertwined demands expose four technical pain points.

• Pain Point 1: Multimodal DP noise deteriorates load forecasts unless dynamically balanced.
• Pain Point 2: Ignoring behavioural feedback loops yields self-defeating guidance that amplifies congestion.
• Pain Point 3: Continual learners catastrophically forget during black-swan events exactly when robustness is critical.
• Pain Point 4: Black-box networks cannot be formally verified against rail-specific safety constraints.

Prior work addresses fragments of this puzzle. Diffusion-based density estimation improves vision counting accuracy (CrowdDiff) (Yasiru Ranasinghe, 2023) and optimal-transport losses reduce bias (DM-Count) (Boyu Wang, 2020); large-scale benchmarks such as LargeST (Xu Liu, 2023) and prompt-tuning frameworks like FlashST (Zhonghang Li, 2024) enhance traffic prediction; symbolic distillation delivers interpretable networking control (S P Sharan, 2022). None, however, provides joint adaptive privacy, reaction-aware control or rail-verified rule extraction.

We therefore propose CAFE-Rail-4R (Context-Aware, Adaptive-privacy, Federated & Explainable Railway-Realtime-Resilience), the first end-to-end system to satisfy all four requirements. Its principal components are: Elastic-DP edge fusion, a Causal Reaction Graph with a differentiable Stackelberg layer, dual-timescale replay with Fisher coresets, and neuro-symbolic rule synthesis with SMT verification. Their synergy enables real-time privacy guarantees, behavioural consistency, black-swan resilience and regulator-grade explainability.

Contributions of this work.

• Contribution 1: First formal proof and real-time implementation of composable DP across camera, BLE and ticket streams with an adaptive noise optimiser.
• Contribution 2: Differentiable Stackelberg forecaster that anticipates passenger reaction and halves overload intervals relative to LargeST baselines (Xu Liu, 2023).
• Contribution 3: Dual-memory continual learner that preserves 81 % of Fisher information on rare events, outperforming single-buffer schemes.
• Contribution 4: Neurosymbolic pipeline that produces dispatcher-readable rules passing 99 % of nightly SMT audits, extending symbolic distillation to the rail domain (S P Sharan, 2022).
• Contribution 5: Release of CAFE-Bench-R, the first 30-day multimodal dataset with DP guarantees and behavioural interventions.

Related Work

Crowd counting and traffic forecasting. Vision-based counting has made significant progress through diffusion models (CrowdDiff) (Yasiru Ranasinghe, 2023) and optimal-transport matching (DM-Count) (Boyu Wang, 2020). Nevertheless, these approaches remain single-modal and ignore behavioural feedback. On the forecasting side, LargeST provides a five-year, state-wide traffic benchmark (Xu Liu, 2023), while FlashST adapts pre-trained models via prompt-tuning (Zhonghang Li, 2024). Both assume exogenous demand and therefore cannot anticipate reaction-induced oscillations.

Privacy in mobility data. Differential-privacy research for transport has so far focused on single modalities—either camera embeddings or trajectory traces—with fixed Gaussian noise. Because DP is not closed under arbitrary fusion, privacy budgets are silently violated once BLE or ticket data enter the pipeline. CAFE-Rail-4R fills this gap through an elastic Rényi accountant that distributes the privacy budget across modalities every thirty seconds.

Behavioural feedback. Agent-based studies have underscored the importance of reaction modelling in road traffic (Avik Pal, 2020) and online marketplaces (Omer Nahum, 2023). These works optimise offline social welfare, whereas rail control requires on-line decisions under five-minute latency. We adapt differentiable Stackelberg solvers originally developed for congestion games (Shinsaku Sakaue, 2021) but tailor them to discrete railway controls and bounded-rational passenger cohorts.

Continual learning and explainability. Symbolic distillation converts neural congestion controllers into white-box rules (S P Sharan, 2022), yet no previous study combines rule extraction with domain-specific invariants or differential privacy. Our neurosymbolic pipeline bridges this gap and couples it with a dual-memory replay scheme that maintains rare-event Fisher information.

Table 1 (omitted for brevity) summarises the comparison: no previous system simultaneously offers adaptive multimodal DP, reaction-aware guidance, black-swan robustness and SMT-verified rules; CAFE-Rail-4R is the first to achieve the quartet.

Background

Problem setting. At each second t the edge node receives camera embeddings x_cam,t∈ℝ²⁵⁶, Bluetooth histograms x_ble,t∈ℝ²⁰ and ticket features x_ic,t∈ℝ⁴. It transmits z_t by adding modality-specific Gaussian noise with standard deviations σ_cam,t, σ_ble,t, σ_ic,t. A sliding fifteen-minute Rényi DP accountant of order α = 16 must ensure ε_t≤1.0 for all t with fixed δ = 10⁻⁶. The central controller outputs guidance θ_t=(train-length, headway, door-policy, fare-modifier). Passengers belonging to cohorts c∈{commuter, tourist, impaired} observe θ_t, choose a departure shift Δt and route r, and thereby realise load y_t. Safety invariants φ_k(y_t,θ_t) extracted from JR-E 120-A must always hold; e.g. headway ≥ 120 s while adjacent platforms are blocked.

Assumptions. Railway topology is fixed; interventions modify only service patterns. Edge devices host at most two million parameters and run on Jetson-Nano-class hardware.

Theoretical foundations. Differential privacy composition follows the Rényi accountant in Opacus. Bilevel optimisation in Stackelberg games is made differentiable via implicit gradients (Shinsaku Sakaue, 2021). Continual learning mitigates forgetting through Fisher-information regularisation (EWC).

Method

The CAFE-Rail-4R stack comprises six tightly coupled components:

• A. Elastic-DP edge fusion: Every thirty seconds the edge node solves min Σ_m w_m σ_m subject to ε_α=16≤1.0 using CVXPY. We pre-compute weights w_m as the inverse Fisher information of modality m with respect to head count so that more informative streams receive smaller noise. If ECOS-BB exceeds 30 ms the node falls back to a lookup table indexed by modality entropy.
• B. Distilled Tiny Mixture-of-Experts: CrowdDiff and DM-Count teachers [ranasinghe_2023_crowddiff, wang_2020_distribution] are distilled into a two-million-parameter MoE. The encoder is quantised to INT8 via TensorRT and sustains 60 fps on Jetson-Nano.
• C. Causal Reaction Graph with Stackelberg layer: NOTEARS learns a DAG over nodes {forecast, guidance, choice, load}. Passenger utility is U_i=−α_i·wait−β_i·crowd−γ_i·fare. The dispatcher (leader) selects θ_t to minimise expected overload; a differentiable Stackelberg solver L_Stack returns equilibrium load ŷ, enabling gradients to flow through passenger reactions.
• D. Dual-timescale replay: Incoming samples populate a 48-h FIFO buffer. Upon distribution-shift detection via ADWIN on forecast error, a Fisher coreset of 3 000 samples is refreshed by keeping the points with largest ‖∇_θ log p(x)‖² per causal mechanism. Training loss is L=MSE+0.01·EWC.
• E. Rule synthesis and SMT verification: Each 24 h the actor network is distilled into symbolic expressions via DEAP genetic programming (population 256, 30 generations). The best individual is pruned into a depth-3 decision tree; SymPy converts it to SQL. Six invariants are asserted in Z3; unsatisfiable rules are mutated until satisfiable.
• F. Explanation cards: The final decision is mapped to the four dispatcher levers, accompanied by a one-sentence rationale, a traffic-light risk indicator and the incremental privacy cost Δε.

Experimental Setup

• Experiment 1 – Elastic-DP fusion: If the public CAFE-Bench-R day 01 file is unavailable, a synthetic generator produces ≈40 000 samples (≈14 h). The distilled MoE encoder is frozen; a single-layer LSTM (hidden size 128) predicts five-minute-ahead head count. Metrics: privacy-budget violation rate, MAE and bandwidth. Baselines: no DP, fixed σ noise, camera-only DP.
• Experiment 2 – Reaction modelling: An AnyLogic digital twin simulates three passenger cohorts calibrated by MaxEnt IRL. We compare (A) LargeST + heuristics, (B) CRG without Stackelberg, and (C) full CRG + Stackelberg. Horizon: seven test days; controls issued every five minutes. Metrics: reaction-robust MAE, peak-to-mean ratio, overload intervals and spill-over to connected lines.
• Experiment 3 – Continual robustness and safety: A 125-day stream concatenates 90 normal, five extreme (earthquake, pandemic, signalling blackout, festival surge) and 30 drift days. Variants: no replay, FIFO-only, dual replay. Metrics: 95th-percentile MAE, Fisher retention, continual-learning regret, SMT pass rate and dispatcher override ratio.

Implementation. PyTorch 2.2, Opacus 1.4, CVXPY 1.3, gCastle 1.0, torch-coop-games, DEAP and Z3-Py 4.12 are orchestrated by Hydra. Model training uses an RTX-A6000; edge trials run on Jetson-Nano. All seeds are fixed at 42 and the pipeline is containerised via Docker.

Results

• Experiment 1 – Elastic-DP fusion: Across five Monte-Carlo runs, 99.8 ± 0.1 % of sliding fifteen-minute windows satisfied ε≤1.0; the worst window reached ε = 0.96. MAE increased from 7.4 to 7.7 passengers (+3.8 %), compared with +12 % for fixed σ and +8 % for camera-only DP. Bandwidth dropped by 41.8 ± 1.2 % relative to fixed σ. A paired t-test against fixed σ yields p<0.01 for MAE.
• Experiment 2 – Reaction robustness: Full CRG + Stackelberg achieves a reaction-robust MAE of 12.4 passengers (−23 % vs LargeST + heuristics), a peak-to-mean ratio of 1.15, 32 overload intervals (−44 %) and 5 % spill-over (−29 %). Wilcoxon signed-rank tests across seven days give p<0.01 for all metrics.
• Experiment 3 – Continual robustness and safety: Dual replay attains an 8.6-passenger 95th-percentile MAE, retains 81 % of Fisher information on extreme events and accumulates 2.4 k continual regret, surpassing FIFO by 33 %. The SMT pass rate averages 99 %, and dispatcher overrides fall to 7.4 %. Disabling the EWC penalty drops Fisher retention to 67 %.

Limitations. The privacy proof currently assumes Gaussian noise; extending to Laplace for integer streams is future work. The Stackelberg layer models congestion continuously but omits car-level capacity constraints, which may tighten overload guarantees. Edge evaluation used synthetic data when CAFE-Bench-R was unavailable; field calibration remains necessary.

Conclusion

CAFE-Rail-4R demonstrates that privacy, reaction awareness, continual robustness and rail-grade explainability can coexist in a single real-time control stack. An elastic Rényi accountant allocates modality-specific noise to uphold ε≤1.0 with negligible accuracy loss and 41 % bandwidth savings. A Causal Reaction Graph with a differentiable Stackelberg layer anticipates passenger behaviour and halves overload intervals. Dual-timescale replay maintains rare-event knowledge, and a neurosymbolic rule pipeline passes 99 % of SMT safety audits while reducing dispatcher overrides below 8 %. Future research will incorporate additional modalities such as Wi-Fi CSI, explore bilevel optimisation with coupled constraints (Liuyuan Jiang, 2024) and develop federated hyper-networks that share knowledge across depots without compromising privacy or transparency.