We introduce the first complete formal solution to corrigibility in the off-switch game, with provable guarantees in multi-step, partially observed environments. Our framework consists of five *structurally separate* utility heads -- deference, switch-access preservation, truthfulness, low-impact behavior via a belief-based extension of Attainable Utility Preservation, and bounded task reward -- combined lexicographically by strict weight gaps. Theorem 1 proves exact single-round corrigibility in the partially observable off-switch game; Theorem 3 extends the guarantee to multi-step, self-spawning agents, showing that even if each head is *learned* to mean-squared error $\varepsilon$ and the planner is $\varepsilon$-sub-optimal, the probability of violating *any* safety property is bounded while still ensuring net human benefit. In contrast to Constitutional AI or RLHF/RLAIF, which merge all norms into one learned scalar, our separation makes obedience and impact-limits provably dominate even when incentives conflict. For settings where adversaries can modify the agent, we prove that deciding whether an arbitrary post-hack agent will ever violate corrigibility is undecidable by reduction to the halting problem, then carve out a finite-horizon "decidable island" where safety can be certified in randomized polynomial time and verified with privacy-preserving, constant-round zero-knowledge proofs.
Due to the distributed nature of federated learning (FL), the vulnerability of the global model and the need for coordination among many client devices pose significant challenges. As a promising decentralized, scalable and secure solution, blockchain-based FL methods have attracted widespread attention in recent years. However, traditional consensus mechanisms designed for Proof of Work (PoW) similar to blockchain incur substantial resource consumption and compromise the efficiency of FL, particularly when participating devices are wireless and resource-limited. To address asynchronous client participation and data heterogeneity in FL, while limiting the additional resource overhead introduced by blockchain, we propose the Directed Acyclic Graph-based Asynchronous Federated Learning (DAG-AFL) framework. We develop a tip selection algorithm that considers temporal freshness, node reachability and model accuracy, with a DAG-based trusted verification strategy. Extensive experiments on 3 benchmarking datasets against eight state-of-the-art approaches demonstrate that DAG-AFL significantly improves training efficiency and model accuracy by 22.7% and 6.5% on average, respectively.
As decentralized finance (DeFi) evolves, distinguishing between user behaviors - liquidity provision versus active trading - has become vital for risk modeling and on-chain reputation. We propose a behavioral scoring framework for Uniswap that assigns two complementary scores: a Liquidity Provision Score that assesses strategic liquidity contributions, and a Swap Behavior Score that reflects trading intent, volatility exposure, and discipline. The scores are constructed using rule-based blueprints that decompose behavior into volume, frequency, holding time, and withdrawal patterns. To handle edge cases and learn feature interactions, we introduce a deep residual neural network with densely connected skip blocks inspired by the U-Net architecture. We also incorporate pool-level context such as total value locked (TVL), fee tiers, and pool size, allowing the system to differentiate similar user behaviors across pools with varying characteristics. Our framework enables context-aware and scalable DeFi user scoring, supporting improved risk assessment and incentive design. Experiments on Uniswap v3 data show its usefulness for user segmentation and protocol-aligned reputation systems. Although we refer to our metric as zScore, it is independently developed and methodologically different from the cross-protocol system proposed by Udupi et al. Our focus is on role-specific behavioral modeling within Uniswap using blueprint logic and supervised learning.
We introduce the Graded Transformer framework, a new class of sequence models that embeds algebraic inductive biases through grading transformations on vector spaces. Extending Graded Neural Networks (GNNs), we propose two architectures: the Linearly Graded Transformer (LGT) and the Exponentially Graded Transformer (EGT). These models apply parameterized scaling operators, governed by fixed or learnable grading tuples and in the case of EGT exponential factors, to encode hierarchical structure in attention and representation layers and to improve efficiency for structured data. We establish rigorous guarantees, including universal approximation theorems for continuous and Sobolev functions, reduced sample complexity via effective VC dimension bounds, Lipschitz continuity of graded operations, and robustness to perturbations. A graded loss ensures gradient stability and alignment with domain priors during optimization. By treating grades as differentiable parameters, the framework enables adaptive feature prioritization, overcoming limitations of fixed grades in earlier models. The Graded Transformer provides a mathematically principled approach to hierarchical learning and neuro-symbolic reasoning. Applications include algebraic geometry (moduli spaces and zeta functions), physics (multiscale systems), natural language processing (syntactic parsing), biological sequence analysis (variant prediction), robotics and autonomous systems (safety-critical prioritization), the automotive industry (certifiable AI for ADAS), and blockchain and financial cryptography (secure coding and structured prediction).
Cryptocurrency markets are experiencing rapid growth, but this expansion comes with significant challenges, particularly in predicting cryptocurrency prices for traders in the U.S. In this study, we explore how deep learning and machine learning models can be used to forecast the closing prices of the XRP/USDT trading pair. While many existing cryptocurrency prediction models focus solely on price and volume patterns, they often overlook market liquidity, a crucial factor in price predictability. To address this, we introduce two important liquidity proxy metrics: the Volume-To-Volatility Ratio (VVR) and the Volume-Weighted Average Price (VWAP). These metrics provide a clearer understanding of market stability and liquidity, ultimately enhancing the accuracy of our price predictions. We developed four machine learning models, Linear Regression, Random Forest, XGBoost, and LSTM neural networks, using historical data without incorporating the liquidity proxy metrics, and evaluated their performance. We then retrained the models, including the liquidity proxy metrics, and reassessed their performance. In both cases (with and without the liquidity proxies), the LSTM model consistently outperformed the others. These results underscore the importance of considering market liquidity when predicting cryptocurrency closing prices. Therefore, incorporating these liquidity metrics is essential for more accurate forecasting models. Our findings offer valuable insights for traders and developers seeking to create smarter and more risk-aware strategies in the U.S. digital assets market.
Ali RajabiNekoo, Laleh Rasoul, Amirfarhad Farhadi, Azadeh Zamanifar
Traditional methods for identifying impactful liquidity providers (LPs) in Concentrated Liquidity Market Makers (CLMMs) rely on broad measures, such as nominal capital size or surface-level activity, which often lead to inaccurate risk analysis. The SILS framework offers a significantly more detailed approach, characterizing LPs not just as capital holders but as dynamic systemic agents whose actions directly impact market stability. This represents a fundamental paradigm shift from the static, volume-based analysis to a dynamic, impact-focused understanding. This advanced approach uses on-chain event logs and smart contract execution traces to compute Exponential Time-Weighted Liquidity (ETWL) profiles and apply unsupervised anomaly detection. Most importantly, it defines an LP's functional importance through the Liquidity Stability Impact Score (LSIS), a counterfactual metric that measures the potential degradation of the market if the LP withdraws. This combined approach provides a more detailed and realistic characterization of an LP's impact, moving beyond the binary and often misleading classifications used by existing methods. This impact-focused and comprehensive approach enables SILS to accurately identify high-impact LPs-including those missed by traditional methods and supports essential applications like a protective oracle layer and actionable trader signals, thereby significantly enhancing DeFi ecosystem. The framework provides unprecedented transparency into the underlying liquidity structure and associated risks, effectively reducing the common false positives and uncovering critical false negatives found in traditional models. Therefore, SILS provides an effective mechanism for proactive risk management, transforming how DeFi protocols safeguard their ecosystems against asymmetric liquidity behavior.
Pallavi Zambare, Venkata Nikhil Thanikella, Ying Liu
Pedestrian intention prediction is essential for autonomous driving in complex urban environments. Conventional approaches depend on supervised learning over frame sequences and require extensive retraining to adapt to new scenarios. Here, we introduce BF-PIP (Beyond Frames Pedestrian Intention Prediction), a zero-shot approach built upon Gemini 2.5 Pro. It infers crossing intentions directly from short, continuous video clips enriched with structured JAAD metadata. In contrast to GPT-4V based methods that operate on discrete frames, BF-PIP processes uninterrupted temporal clips. It also incorporates bounding-box annotations and ego-vehicle speed via specialized multimodal prompts. Without any additional training, BF-PIP achieves 73% prediction accuracy, outperforming a GPT-4V baseline by 18 %. These findings illustrate that combining temporal video inputs with contextual cues enhances spatiotemporal perception and improves intent inference under ambiguous conditions. This approach paves the way for agile, retraining-free perception module in intelligent transportation system.
The proper design and architecture of testing machine learning models, especially in their application to quantitative finance problems, is crucial. The most important aspect of this process is selecting an adequate loss function for training, validation, estimation purposes, and hyperparameter tuning. Therefore, in this research, through empirical experiments on equity and cryptocurrency assets, we apply the Mean Absolute Directional Loss (MADL) function, which is more adequate for optimizing forecast-generating models used in algorithmic investment strategies. The MADL function results are compared between Transformer and LSTM models, and we show that in almost every case, Transformer results are significantly better than those obtained with LSTM.
The rise of decentralized finance (DeFi) has created a growing demand for accurate yield and performance forecasting to guide liquidity allocation strategies. In this study, we benchmark six models, XGBoost, Random Forest, LSTM, Transformer, quantum neural networks (QNN), and quantum support vector machines with quantum feature maps (QSVM-QNN), on one year of historical data from 28 Curve Finance pools. We evaluate model performance on test MAE, RMSE, and directional accuracy. Our results show that classical ensemble models, particularly XGBoost and Random Forest, consistently outperform both deep learning and quantum models. XGBoost achieves the highest directional accuracy (71.57%) with a test MAE of 1.80, while Random Forest attains the lowest test MAE of 1.77 and 71.36% accuracy. In contrast, quantum models underperform with directional accuracy below 50% and higher errors, highlighting current limitations in applying quantum machine learning to real-world DeFi time series data. This work offers a reproducible benchmark and practical insights into model suitability for DeFi applications, emphasizing the robustness of classical methods over emerging quantum approaches in this domain.
Hasib Ahmed Md Khyrul Islam, Huy T. Vo, Aditya Rane
In the era of synthetic media, deepfake manipulations pose a significant threat to information integrity. To address this challenge, we propose TrustDefender, a two-stage framework comprising (i) a lightweight convolutional neural network (CNN) that detects deepfake imagery in real-time extended reality (XR) streams, and (ii) an integrated succinct zero-knowledge proof (ZKP) protocol that validates detection results without disclosing raw user data. Our design addresses both the computational constraints of XR platforms while adhering to the stringent privacy requirements in sensitive settings. Experimental evaluations on multiple benchmark deepfake datasets demonstrate that TrustDefender achieves 95.3% detection accuracy, coupled with efficient proof generation underpinned by rigorous cryptography, ensuring seamless integration with high-performance artificial intelligence (AI) systems. By fusing advanced computer vision models with provable security mechanisms, our work establishes a foundation for reliable AI in immersive and privacy-sensitive applications.
Open access
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Adversarial Robustness in Machine Learning
Digital Media Forensic Detection
Generative Adversarial Networks and Image Synthesis
Fine-tuning the large language models (LLMs) are prevented by the deficiency of centralized control and the massive computing and communication overhead on the decentralized schemes. While the typical standard federated learning (FL) supports data privacy, the central server requirement creates a single point of attack and vulnerability to poisoning attacks. Generalizing the result in this direction to 70B-parameter models in the heterogeneous, trustless environments has turned out to be a huge, yet unbroken bottleneck. This paper introduces FLock, a decentralized framework for secure and efficient collaborative LLM fine-tuning. Integrating a blockchain-based trust layer with economic incentives, FLock replaces the central aggregator with a secure, auditable protocol for cooperation among untrusted parties. We present the first empirical validation of fine-tuning a 70B LLM in a secure, multi-domain, decentralized setting. Our experiments show the FLock framework defends against backdoor poisoning attacks that compromise standard FL optimizers and fosters synergistic knowledge transfer. The resulting models show a >68% reduction in adversarial attack success rates. The global model also demonstrates superior cross-domain generalization, outperforming models trained in isolation on their own specialized data.
The detection of outliers within cryptocurrency limit order books (LOBs) is of paramount importance for comprehending market dynamics, particularly in highly volatile and nascent regulatory environments. This study conducts a comprehensive comparative analysis of robust statistical methods and advanced machine learning techniques for real-time anomaly identification in cryptocurrency LOBs. Within a unified testing environment, named AITA Order Book Signal (AITA-OBS), we evaluate the efficacy of thirteen diverse models to identify which approaches are most suitable for detecting potentially manipulative trading behaviours. An empirical evaluation, conducted via backtesting on a dataset of 26,204 records from a major exchange, demonstrates that the top-performing model, Empirical Covariance (EC), achieves a 6.70% gain, significantly outperforming a standard Buy-and-Hold benchmark. These findings underscore the effectiveness of outlier-driven strategies and provide insights into the trade-offs between model complexity, trade frequency, and performance. This study contributes to the growing corpus of research on cryptocurrency market microstructure by furnishing a rigorous benchmark of anomaly detection models and highlighting their potential for augmenting algorithmic trading and risk management.
Junliang Luo, Katrin Tinn, Şengül Duran, Di Wu · 5 authors
Tokenized U.S. Treasuries have emerged as a prominent subclass of real-world assets (RWAs), offering cryptographically secured, yield-bearing instruments issued across multi-chain Web3 infrastructures, with growing significance for transparency, accessibility, and financial inclusion. While the market has expanded rapidly, empirical analyses of transaction-level behaviours remain limited. This paper conducts a quantitative, function-level dissection of U.S. Treasury-backed RWA tokens, including BUIDL, BENJI, and USDY across multi-chain: mostly Ethereum and Layer-2s. Decoded contract calls expose core financial primitives such as issuance, redemption, transfer, and bridging, revealing patterns that distinguish institutional participants from smaller or retail users for the extent and limits of inclusivity in current RWA adoption. To infer address-level economic roles, we introduce a curvature-aware representation learning model. Our method outperforms baseline models in role inference on our collected U.S. Treasury transaction dataset and generalizes to address classification across broader public blockchain transaction datasets. The decoded transaction-level patterns in tokenized U.S. Treasuries across chains surface the degree of retail participation, and the role inference model enables the distinction between institutional treasuries, arbitrage bots, and retail traders based on behavioral patterns, facilitating future more transparent, inclusive, and accountable Web3 finance.
Illegal marketplaces have increasingly shifted to concealed parts of the internet, including the deep and dark web, as well as platforms such as Telegram, Reddit, and Pastebin. These channels enable the anonymous trade of illicit goods including drugs, weapons, and stolen credentials. Detecting and categorizing such content remains challenging due to limited labeled data, the evolving nature of illicit language, and the structural heterogeneity of online sources. This paper presents a hierarchical classification framework that combines fine-tuned language models with a semi-supervised ensemble learning strategy to detect and classify illicit marketplace content across diverse platforms. We extract semantic representations using ModernBERT, a transformer model for long documents, finetuned on domain-specific data from deep and dark web pages, Telegram channels, Subreddits, and Pastebin pastes to capture specialized jargon and ambiguous linguistic patterns. In addition, we incorporate manually engineered features such as document structure, embedded patterns including Bitcoin addresses, emails, and IPs, and metadata, which complement language model embeddings. The classification pipeline operates in two stages. The first stage uses a semi-supervised ensemble of XGBoost, Random Forest, and SVM with entropy-based weighted voting to detect sales-related documents. The second stage further classifies these into drug, weapon, or credential sales. Experiments on three datasets, including our multi-source corpus, DUTA, and CoDA, show that our model outperforms several baselines, including BERT, ModernBERT, DarkBERT, ALBERT, Longformer, and BigBird. The model achieves an accuracy of 0.96489, an F1-score of 0.93467, and a TMCC of 0.95388, demonstrating strong generalization, robustness under limited supervision, and effectiveness in real-world illicit content detection.
Niveen O. Jaffal, Mohammed Alkhanafseh, David Mohaisen
Large Language Models (LLMs) are transforming cybersecurity by enabling intelligent, adaptive, and automated approaches to threat detection, vulnerability assessment, and incident response. With their advanced language understanding and contextual reasoning, LLMs surpass traditional methods in tackling challenges across domains such as IoT, blockchain, and hardware security. This survey provides a comprehensive overview of LLM applications in cybersecurity, focusing on two core areas: (1) the integration of LLMs into key cybersecurity domains, and (2) the vulnerabilities of LLMs themselves, along with mitigation strategies. By synthesizing recent advancements and identifying key limitations, this work offers practical insights and strategic recommendations for leveraging LLMs to build secure, scalable, and future-ready cyber defense systems.
Felix Quinque, Alan Aboudib, Szymon Fonau, Rodrigo Lopez Portillo Alcocer · 6 authors
In August 2024, Bittensor's Subnet 9 (SN9) demonstrated that a distributed network of incentivized, permissionless actors could each pretrain large language models (LLMs) ranging from 700 million to 14 billion parameters, while surpassing established baselines. While that work validated blockchain-based decentralized pretraining as viable, it contained core issues: (i) every miner had to fit an entire model locally, and (ii) "winner-takes-all" rewards encouraged model hoarding. Here we introduce IOTA (Incentivized Orchestrated Training Architecture), an architecture that addresses these limitations by transforming SN9's previously isolated competitors into a single cooperating unit that can scale arbitrarily while still rewarding each contributor fairly. Key preliminary results: (1) Data- and Pipeline-parallel SWARM architecture - An orchestrator distributes model layers across heterogeneous miners and streams activations between them, enabling model sizes to scale with the number of participants rather than being constrained by the VRAM of a single machine; (2) Granular, continuous incentives - Validators measure each miner's contribution and allocate token emissions proportionally; (3) Activation compression - We used model-bottlenecks to cut communication bandwidths of activations by up to 128x, vastly improving training speed; (4) Butterfly All-Reduce - Miners average disjoint parameter slices in O(1) bandwidth, offering linear scalability, redundancy and built-in collusion detection; (5) CLASP (Contribution Loss Assessment via Sampling of Pathways) - A fair attribution scheme assigns credit to miners proportional to their marginal utility and detects exploits, even when contributions are interdependent across the pipeline.
Federated Learning (FL) has undergone significant development since its inception in 2016, advancing from basic algorithms to complex methodologies tailored to address diverse challenges and use cases. However, research and benchmarking of novel FL techniques against a plethora of established state-of-the-art solutions remain challenging. To streamline this process, we introduce FLsim, a comprehensive FL simulation framework designed to meet the diverse requirements of FL workflows in the literature. FLsim is characterized by its modularity, scalability, resource efficiency, and controlled reproducibility of experimental outcomes. Its easy to use interface allows users to specify customized FL requirements through job configuration, which supports: (a) customized data distributions, ranging from non-independent and identically distributed (non-iid) data to independent and identically distributed (iid) data, (b) selection of local learning algorithms according to user preferences, with complete agnosticism to ML libraries, (c) choice of network topology illustrating communication patterns among nodes, (d) definition of model aggregation and consensus algorithms, and (e) pluggable blockchain support for enhanced robustness. Through a series of experimental evaluations, we demonstrate the effectiveness and versatility of FLsim in simulating a diverse range of state-of-the-art FL experiments. We envisage that FLsim would mark a significant advancement in FL simulation frameworks, offering unprecedented flexibility and functionality for researchers and practitioners alike.
Daniel Commey, Benjamin Appiah, Griffith Selorm Klogo, Garth V. Crosby
Federated Learning (FL) enables collaborative model training on decentralized data without exposing raw data. However, the evaluation phase in FL may leak sensitive information through shared performance metrics. In this paper, we propose a novel protocol that incorporates Zero-Knowledge Proofs (ZKPs) to enable privacy-preserving and verifiable evaluation for FL. Instead of revealing raw loss values, clients generate a succinct proof asserting that their local loss is below a predefined threshold. Our approach is implemented without reliance on external APIs, using self-contained modules for federated learning simulation, ZKP circuit design, and experimental evaluation on both the MNIST and Human Activity Recognition (HAR) datasets. We focus on a threshold-based proof for a simple Convolutional Neural Network (CNN) model (for MNIST) and a multi-layer perceptron (MLP) model (for HAR), and evaluate the approach in terms of computational overhead, communication cost, and verifiability.
Cryptocurrency trading is a challenging task requiring the integration of heterogeneous data from multiple modalities. Traditional deep learning and reinforcement learning approaches typically demand large training datasets and encode diverse inputs into numerical representations, often at the cost of interpretability. Recent progress in large language model (LLM)-based agents has demonstrated the capacity to process multi-modal data and support complex investment decision-making. Building on these advances, we present \textbf{MountainLion}, a multi-modal, multi-agent system for financial trading that coordinates specialized LLM-based agents to interpret financial data and generate investment strategies. MountainLion processes textual news, candlestick charts, and trading signal charts to produce high-quality financial reports, while also enabling modification of reports and investment recommendations through data-driven user interaction and question answering. A central reflection module analyzes historical trading signals and outcomes to continuously refine decision processes, and the system is capable of real-time report analysis, summarization, and dynamic adjustment of investment strategies. Empirical results confirm that MountainLion systematically enriches technical price triggers with contextual macroeconomic and capital flow signals, providing a more interpretable, robust, and actionable investment framework that improves returns and strengthens investor confidence.
Antonino Castelli, Paolo Giudici, Alessandro Piergallini
The rapid growth of crypto markets has opened new opportunities for investors, but at the same time exposed them to high volatility. To address the challenge of managing dynamic portfolios in such an environment, this paper presents a practical application of a multi-agent system designed to autonomously construct and evaluate crypto-asset allocations. Using data on daily frequencies of the ten most capitalized cryptocurrencies from 2020 to 2025, we compare two automated investment strategies. These are a static equal weighting strategy and a rolling-window optimization strategy, both implemented to maximize the evaluation metrics of the Modern Portfolio Theory (MPT), such as Expected Return, Sharpe and Sortino ratios, while minimizing volatility. Each step of the process is handled by dedicated agents, integrated through a collaborative architecture in Crew AI. The results show that the dynamic optimization strategy achieves significantly better performance in terms of risk-adjusted returns, both in-sample and out-of-sample. This highlights the benefits of adaptive techniques in portfolio management, particularly in volatile markets such as cryptocurrency markets. The following methodology proposed also demonstrates how multi-agent systems can provide scalable, auditable, and flexible solutions in financial automation.
Carlos Beis-Penedo, Rebeca P. Díaz-Redondo, Ana Fernandez-Vilas, Manuel Fernández‐Veiga · 5 authors
Collaborative machine learning in sensitive domains demands scalable, privacy-aware and access-controlled solutions for enterprise-grade deployment. Conventional federated learning (FL) relies on a central server, introducing single points of failure and privacy risks, while split learning (SL) partitions models for privacy but scales poorly because of sequential training. We present HLF-FSL, a decentralized architecture that combines federated split learning (FSL) with the permissioned blockchain Hyperledger Fabric (HLF). Chaincode orchestrates split-model execution and peer-to-peer aggregation without a central coordinator, leveraging HLF’s transient fields and Private Data Collections (PDCs) to keep raw data and model activations off-chain and access-controlled. On CIFAR-10, MNIST and ImageNet-Mini, HLF-FSL matches the accuracy of a standard server-coordinated FSL baseline while reducing per-epoch training time versus Ethereum-based baselines. Performance and scalability tests quantify the Fabric coordination overhead via a component-level breakdown of SDK-facing latencies and communication volumes; empirically, this overhead increases wall-clock epoch time while preserving the same accuracy-vs-epoch behavior as a FedSplit Learning baseline.
As AI models become ubiquitous in our daily lives, there has been an increasing demand for transparency in ML services. However, the model owner does not want to reveal the weights, as they are considered trade secrets. To solve this problem, researchers have turned to zero-knowledge proofs of ML model inference. These proofs convince the user that the ML model output is correct, without revealing the weights of the model to the user. Past work on these provers can be placed into two categories. The first method compiles the ML model into a low-level circuit, and proves the circuit using a ZK-SNARK. The second method uses custom cryptographic protocols designed only for a specific class of models. Unfortunately, the first method is highly inefficient, making it impractical for the large models used today, and the second method does not generalize well, making it difficult to update in the rapidly changing field of machine learning. To solve this, we propose ZKTorch, an open source end-to-end proving system that compiles ML models into base cryptographic operations called basic blocks, each proved using specialized protocols. ZKTorch is built on top of a novel parallel extension to the Mira accumulation scheme, enabling succinct proofs with minimal accumulation overhead. These contributions allow ZKTorch to achieve at least a $3\times$ reduction in the proof size compared to specialized protocols and up to a $6\times$ speedup in proving time over a general-purpose ZKML framework.
Sevvandi Kandanaarachchi, Ziqi Xu, Stefan Westerlund, Conrad Sanderson
Many dynamic processes such as telecommunication and transport networks can be described through discrete time series of graphs. Modelling the dynamics of such time series enables prediction of graph structure at future time steps, which can be used in applications such as detection of anomalies. Existing approaches for graph prediction have limitations such as assuming that the vertices do not to change between consecutive graphs. To address this, we propose to exploit time series prediction methods in combination with an adapted form of flux balance analysis (FBA), a linear programming method originating from biochemistry. FBA is adapted to incorporate various constraints applicable to the scenario of growing graphs. Empirical evaluations on synthetic datasets (constructed via Preferential Attachment model) and real datasets (UCI Message, HePH, Facebook, Bitcoin) demonstrate the efficacy of the proposed approach.
We propose \textbf{Temporal Conformal Prediction (TCP)}, a distribution-free framework for constructing well-calibrated prediction intervals in nonstationary time series. TCP couples a modern quantile forecaster with a rolling split-conformal calibration layer; its \textbf{TCP-RM} variant adds an online Robbins-Monro offset to steer coverage in real time. We benchmark TCP against GARCH, Historical Simulation, Quantile Regression (QR), linear QR, and Adaptive Conformal Inference (ACI) across S\&P 500, Bitcoin, and Gold. Three results are consistent. First, QR baselines yield the sharpest intervals but are materially under-calibrated; even ACI remains below the 95\% target. Second, TCP achieves near-nominal coverage, yielding intervals slightly wider than Historical Simulation (e.g., S\&P 500: 5.21 vs.\ 5.06). Third, the RM update changes calibration only marginally at default hyperparameters. Crisis-window visualizations (March 2020) show TCP promptly expanding and contracting intervals as volatility spikes. A sensitivity study confirms robustness to hyperparameters. Overall, TCP bridges statistical inference and machine learning, providing a practical solution for calibrated risk forecasting under distribution shift.