Volatility

This paper develops a general convolutional neural network (CNN) framework for detecting heterogeneous event-driven dynamics in univariate time series windows. We show that the induced CNN class exactly represents classifiers based on range, maximum drawup, maximum drawdown and slope change, and uniformly approximates realised volatility and autoregressive explosiveness on compact domains. We further establish error bounds for representative rules in finite samples and an oracle inequality for learning across them. Simulations show that the proposed model can match or outperform classifiers based on individual statistics as the training sample grows. In an application to six daily energy price series, a hierarchical CNN distinguishes event windows and event families. Applied without retraining to observations withheld after 20 February 2026, the fitted model identifies predominantly geopolitical dynamics in several oil and refined product series around the outbreak of the 2026 Iran war, while distinguishing a contemporaneous natural gas spike associated with weather.

Generative models for implied volatility surfaces must produce outputs that satisfy static no-arbitrage constraints. We study these constraints in latent space. For a fixed generator, we assign each latent code a scalar margin determined by the no-arbitrage conditions of the generated surface. The codes with nonnegative margin form the admissible latent set. We establish conditions under which strictly admissible codes remain admissible under small perturbations and the boundary of the admissible set is characterized by zero margin. For regular boundary components, we formulate a level-set equation whose local dynamics are directed toward the zero-margin set. The analysis treats the generator as a map from latent variables to surfaces and is therefore not restricted to a particular architecture. It applies to variational autoencoders, generative adversarial networks, and other generative models with a deterministic realization map. Numerical tests recover known boundaries in analytic examples. Experiments with a variational autoencoder trained on Heston surfaces show that similar reconstruction errors can correspond to different admissible regions and that the latent prior may be concentrated inside such a region. The computed boundary can also be used to modify latent codes that generate violating surfaces.

Financial forecasting models are typically developed in full precision, yet production deployment often requires low-precision inference to reduce memory and computational cost. Post-training quantization (PTQ) enables such deployment without retraining. However, reliable activation quantization requires calibration: activation ranges are estimated from historical data before deployment and then remain fixed during future inference. The importance of this deployment choice for financial forecasting remains poorly understood. We present a systematic study of activation calibration for PTQ in cross-sectional volatility forecasting on the S&P 500. Our evaluation covers seven representative neural architectures, eight walk-forward test years (2018-2025), and 560 trained models. We find that activation calibration has little effect at 8 bits but becomes the primary determinant of predictive performance at 4 bits. Under default absolute-maximum (abs-max) calibration, static 4-bit quantization of both weights and activations removes 11-62% of the full-precision mean information coefficient in affected architectures. Replacing abs-max with percentile calibration recovers 53-94% of this degradation in the four most affected architectures. The preferred activation range also varies across market periods. Narrow ranges improve resolution under typical market conditions but lose part of their advantage when test-period market dispersion exceeds the calibration history. These findings show that activation calibration is a first-class deployment decision for reliable 4-bit PTQ in financial forecasting. When substantial degradation remains, 8-bit activations or weight-only 4-bit quantization provide more robust deployment choices.

Financial volatility is regime dependent, yet incorporating regime information into neural networks can also destabilize training. This paper asks where such information should enter a neural cross-sectional volatility forecasting model. We study five-day realized-volatility forecasts for 1,027 U.S. equities using a rolling walk-forward evaluation framework in which information, model capacity, hyperparameter tuning, and random seeds are matched across architectures. We propose RG-ResMoE, a regime-gated residual mixture-of-experts architecture in which regime information is used only for expert routing rather than for direct forecasting. The base predictor models volatility from stock features, while a gating network uses regime state variables to route residual corrections. RG-ResMoE consistently outperforms a capacity-matched MLP in both forecasting accuracy and training stability in the main U.S. study. Similar gains are observed on an independent Japanese panel. The integration pathway is decisive: appending the same regime variables directly to the forecasting input degrades both predictive performance and training stability, whereas restricting them to the routing gate improves accuracy and Value-at-Risk calibration. Hard routing consistently underperforms soft routing. The results suggest that, in compact neural volatility forecasting models, the primary value of mixture-of-experts models lies less in increasing model capacity than in controlling how nonstationary regime information influences prediction.

Volatility control converts risk estimates into portfolio exposure, yet existing approaches often rely on a fixed volatility estimator or a pre-defined control rule that may not adapt to changing market conditions. We propose VolRouter, a modular framework that formulates volatility control as state-conditioned routing over estimator-controller pairs. VolRouter first summarizes market conditions into a control-relevant state profile and then performs routing through three stages: state inference, switch review, and pair selection. The Router can be implemented using rule-based, learnable, or LLM-based decision modules, while portfolio actions remain generated by predefined control policies. We evaluate VolRouter across S&P 500, Multi-Asset, Bitcoin, and USDT volatility-control settings. VolRouter achieves the highest Sharpe ratio in three of four settings. On S&P 500, it improves Sharpe from 0.952 for RV + Naive Scaling to 1.222 while reducing maximum drawdown from 15.10% to 12.58% and daily CVaR from 1.76% to 1.32%. On Multi-Asset, it improves Sharpe from 1.498 to 1.540 and reduces CVaR from 1.56% to 1.18%. Bitcoin shows similar improvements in risk-adjusted performance, while USDT provides a boundary case where simpler state-aware selectors remain competitive. Ablation and sensitivity analyses show that the improvement comes from relative policy evaluation and selective persistent switching rather than simply expanding the policy library. These results suggest that volatility control can be viewed as a policy-selection problem when risk management requirements vary across market states.

Forecasting non-stationary time series remains difficult due to long-range dependencies, local volatility bursts, structural shifts, and nonlinear oscillatory behaviors. Although Transformer-based forecasters are effective for modeling long-term temporal dependencies, their feed-forward blocks typically rely on smooth static activations that are insufficiently sensitive to abrupt regime changes. Motivated by quantitative Transformer designs and oscillator-based nonlinear activations, we propose QFCQT, short for Quantum-Fractal-inspired Chaotically Gated Quantformer, for robust forecasting under complex volatile dynamics. Here, "quantum-fractal-inspired" denotes a computational analogy based on soft oscillator superposition and multi-scale nonlinear responses, rather than a formal quantum-mechanical or fractal-theoretic derivation. QFCQT consists of three main components: (1) a Quantformer-style numerical encoder that directly processes multivariate inputs via linear embedding; (2) a learnable Lee-oscillator activation module that maps scalar pre-activations to dynamic oscillatory responses and summarizes them through Max-over-Time pooling; and (3) a smooth-chaotic gated fusion mechanism that adaptively balances conventional smooth activations and chaos-sensitive responses. Furthermore, instead of using a single fixed oscillator, QFCQT employs a soft superposition of eight parameterized Lee oscillator families to adaptively capture different nonlinear response patterns across regimes. Experiments on ETTh1, ETTh2, and A-share Stock Index benchmarks show that QFCQT consistently outperforms strong baselines, including Informer, LogTrans, LSTMa, HAT, and COTN.

Control policies optimized in simulation can perform poorly in the real system when the parameters $x$ of the simulator are estimated from limited data but the resulting parameter uncertainty is not represented inside the simulation. A common way to incorporate such ambiguity is to simulate each trajectory of the system under a randomly drawn value for $x$. Since the policy cannot observe the drawn value, it must initially choose controls that perform well across many possible parameter values. However, if the policy progressively observes the system, it can often gradually infer the value of $x$, so that ambiguity vanishes. Over time, the policy then specializes to its estimate of $x$ and loses its robustness. This is undesirable in many real systems, where latent factors are expected to shift. In financial markets, for example, a policy hedging a derivative payoff should remain robust to changes in the volatility regime. To induce such continual robustness, we propose training policies in simulators where ambiguity varies with the system's state but does not systematically decay over time. We formalize this requirement as stationary ambiguity: the simulator should induce a stationary filter process over the latent state. We show how to construct such simulators and demonstrate, on hedging problems, that policies trained under stationary ambiguity preserve robustness to latent factors over time, leading to strong performance on real market data. As a modeling principle, stationary ambiguity informs many simulator design decisions: which models make realistic simulators, how their parameters should be randomized, and how simulator and policy should be initialized. While our experiments focus on hedging, stationary ambiguity may also be useful for other sequential control problems driven by exogenous stochastic processes with shifting latent structure.

Volatility forecasts are commonly evaluated with aggregate accuracy metrics such as RMSE and MAE, but these metrics can hide conditional failures that matter for risk management. This paper proposes a model-agnostic audit framework for evaluating whether volatility forecasts remain reliable across latent market regimes. We learn time-series representations of market-state windows, cluster them into regimes using only training information, assign regimes out of sample, and compare aggregate forecast behavior with regime-conditional bias, tail-underprediction, and underprediction-sensitive economic losses. Applied to daily volatility forecasting across cryptocurrency and ETF assets, the audit shows that models with competitive aggregate accuracy can still exhibit substantial regime-specific bias and severe tail underprediction. The results suggest that volatility forecasting should be evaluated not only by average error, but also by where and how forecasts become unreliable. Our framework shifts forecast evaluation from asking which model is most accurate on average to identifying the market regimes in which apparently accurate forecasts fail conditionally. Reproducibility: https://github.com/arthurchagas1/Latent-Regime-Bias-Auditing-for-Volatility-Forecasting

Local-stochastic volatility (LSV) combines vanilla marginals with richer smile dynamics, but calibration requires a slow, noisy and sequential McKean--Vlasov fixed point. We learn a projection-consistent operator for the calibration triple. Given finite quotes and a stochastic-volatility (SV) backbone, it jointly returns an implied-volatility surface subject to static-arbitrage constraints, its Dupire local volatility, LSV leverage and the conditional moment required by the projection identity. Starting from option-price marginals, we derive a division-free Dupire residual in log-implied-variance coordinates and a quotient Fokker--Planck equation after Gyöngy projection. Deep Operator Network (DeepONet) and Fourier Neural Operator (FNO) implementations enforce quote fit, static-arbitrage, Dupire and projection constraints. For the witness-augmented residual system, we prove conditional identification and empirical consistency under LSV existence and inverse residual stability. In controlled synthetic tests, forward-start and cliquet errors differ from a particle method by 0.1 and 0.2 percentage points, while calibration latency falls from 98.5 to 0.6 ms. Compared with the tested baselines, local-volatility root-mean-square error (RMSE) falls by 36% and leverage RMSE by 7-16%. These results support amortizing the LSV fixed point: the expensive solve moves offline, while online calibration reduces to a single projection-consistent operator evaluation.

Mechanistic interpretability has largely focused on language models and deterministic toy tasks. Much less is known about how sequence models internally represent latent stochastic dynamics under noisy, partially observed observations. We study this question in a controlled multivariate stochastic volatility setting, where models observe only returns while the ground-truth latent volatility state is known to the researcher. This setting provides a useful benchmark for mechanistic interpretability under partial observability: the latent state is hidden from the model but directly available for evaluation. Across architectures, losses, and output heads, we find evidence for a two-stage computation. Hidden representations encode substantial information about the next latent volatility state, and the output head maps this representation to squared return forecasts. Furthermore, in Transformers, latent-state decodability emerges at identifiable architectural stages whose location depends on the volatility period. In long-cycle regimes, this computation simplifies into an explicit latent-state filter consisting of a learned linear projection followed by $\ell^2$ normalization. Output-head replacement further shows that part of the degradation under noisy MSE training arises from readout misalignment rather than representation failure. These results suggest that stochastic volatility models provide a useful benchmark for mechanistic interpretability under noisy latent dynamics and partial observability.

This paper presents an empirical comparison of lexicon-based and Large Language Model (LLM)-based sentiment analysis for extracting market-relevant signals from social media discourse in highly volatile equity markets. Using Reddit data from r/WallStreetBets and focusing on meme stocks (GME, AMC, NOK), we construct time-aligned sentiment indicators and evaluate their relationship with market returns, with particular attention to extreme positive return events in the upper tail of the return distribution. The LLM-based approach generates multidimensional sentiment representations capturing emotional polarity, bullishness, sarcasm likelihood, and topical relevance, whereas the baseline relies on the VADER lexicon-based model. We evaluate both approaches using lead/lag correlation analysis, OLS regression, ROC-AUC-based directional classification, and a quantile-based early-warning framework. The results indicate that LLM-derived indicators provide a richer multidimensional representation and exhibit stronger asset-specific statistical structure than the lexicon-based baseline. However, their relationship with market movements remains heterogeneous across assets, suggesting that increased linguistic expressiveness does not necessarily translate into stable forecasting performance in retail-driven volatility regimes.

Early warning of extreme market volatility is central to financial risk management, but actionable events are rare, nonstationary, and often triggered by exogenous information shocks. In our CSI300 setting, only $\sim$80 positive samples are observed across 791 training days, making heavily supervised multi-source models unstable. We first analyze a 100K-parameter hierarchical text-signal fusion model (HTSF) and find that added parameterization hurts in this low-label regime. Motivated by this failure, we propose \textbf{AAMSF} (Anomaly-Augmented Multi-Signal Fusion), a semisupervised framework that combines Isolation Forest anomaly scores over market indicators, GDELT events, Chinese financial news, and English media with lightweight Ridge score fusion. We further introduce \textbf{T-AAMSF}, a temporal extension for multi-day anomaly accumulation. On CSI300 (2018--2023), AAMSF achieves test AUC-ROC \textbf{0.680}, outperforming the strongest unsupervised baseline (0.630) and neural baseline (0.588), while T-AAMSF improves PR-AUC to 0.291. Ablations reveal strong source asymmetry: GDELT and domestic financial news provide complementary risk signals, whereas English media consistently reduces performance, and learned weighting is unreliable under validation noise. These results suggest an empirical design principle for label-scarce financial risk warning: robust anomaly geometry and source reliability can matter more than supervised representation capacity.

This paper introduces a compact reformulation of a modular end-to-end neural network for global minimum-variance portfolio optimization that decouples model complexity from both look-back window length and universe size. A five-parameter hyperbolic weighted moving average combined with a saturating exponential replaces the original 2,400-parameter lag-transformation layer, and a bidirectional gated-recurrent-unit eigencleaning module together with a streamlined marginal-volatility network reduce total learnable parameters from 39,586 to just 2,175. In out-of-sample tests against state-of-the-art nonlinear-shrinkage and risk-parity benchmarks, the compact network attains the lowest realized portfolio variance without compromising expected return. Under long-only constraints, the variance reduction supports substantially higher leverage while maintaining comparable drawdown control. Validation in a high-fidelity trading simulator that incorporates realistic margin-call dynamics confirms enhanced over-leverage resilience. These findings demonstrate that end-to-end variance-minimization architectures can achieve substantial parameter efficiency and robust capital-efficiency gains without sacrificing risk-adjusted performance.

Volatility forecasting is dominated by persistence and measurement noise, leaving limited residual structure for nonlinear models to exploit. We introduce Susceptible Architectures (SUSA), a reservoir-design principle for volatility forecasting, and its two concrete implementations, based on complex-valued open-chain and periodic reservoirs and regime-conditioned experts to interpret reservoir features across calm, onset, recovery, and persistent-stress states. We also implement open-system $q$-qubit counterparts in Qiskit while retaining a common AR-Ridge anchor and a bounded residual correction trained under QLIKE. We evaluate models on 16 U.S. equity and exchange-traded-fund series using three disjoint chronological training, validation, and test folds, a 12-observation input window, and a five-observation forecast horizon. The proposed models perform competitively with GARCH, achieving statistically significant QLIKE improvements for specific assets (IWM, XLP). Also models' forecasts complement HARQ-style predictions: a stacked ensemble improves mean QLIKE by 0.0116 over its strongest constituent and wins in 75% of test scenarios.

Predicting extreme price movements in high-frequency financial markets is a challenging task due to non-stationarity, heavy-tailed return distributions, and severe class imbalance. In particular, rare but impactful events are often difficult to detect using conventional modeling approaches, which typically treat extreme movements as isolated observations. This study proposes a volatility-aware approach for extreme event detection using high-frequency Bitcoin limit order book (LOB) data. Motivated by empirical evidence of volatility clustering, the target formulation is extended to incorporate both large future returns and high-volatility regimes. This redefinition increases the proportion of informative samples and aligns the learning objective with the underlying market dynamics. Using a tree-based model (XGBoost) with time-series cross-validation and imbalance-aware evaluation, the proposed method achieves a Precision-Recall AUC of approximately 0.40, significantly outperforming the baseline formulation with a PR-AUC of around 0.06. This represents more than a sixfold improvement in detecting rare events. The results highlight that target design plays a critical role in financial machine learning, often exceeding the impact of model complexity. By incorporating volatility structure into the labeling process, the proposed approach provides a more effective and realistic framework for extreme event detection in high-frequency cryptocurrency markets.

Financial observations are continuous, heterogeneous, and noisy, whereas decoder-only next-token models are usually built around discrete symbolic inputs. We introduce Vector-Input Autoregressive Inference for Ordinal-Return Modeling (VAIOM), a decoder-only Transformer for probabilistic next-return modeling on one-hour foreign-exchange bars. VAIOM separates input representation from output likelihood: continuous multivariate financial-event vectors preserve numerical structure at the input, while a categorical distribution over the next volatility-normalized return bucket supports cross-entropy training and likelihood evaluation. The selected 0.9M Hybrid Continuous Input model combines continuous event features with categorical asset metadata, a Mixture-of-Market-States return head, Gap, volatility-regime, and Ordinal auxiliary objectives, and full-sequence supervision. Models and preprocessing are fit using pre-2024 Train data; models are selected on 2024H2 Validation and evaluated without refitting on two 2025 Test periods. Across three independent training seeds, every model outperforms fixed single-bar LightGBM baseline in both Test halves. For the canonical checkpoint, paired gains over LightGBM are 0.029 and 0.043 bits per event. Validation experiments show that continuous input improves over discrete-token input under the same categorical return objective, full-sequence supervision improves over last-position training, and auxiliary representation shaping together with a mixture-structured return head improves return likelihood in controlled comparisons. A supporting capacity study finds that the smallest evaluated complete architecture rung achieves the strongest Validation likelihood on the present corpus.

Financial sentiment extraction has largely relied on news text and supervised extraction against return labels alone, leaving 10-K filings -- and volatility, the target risk disclosure is arguably best suited to informing -- comparatively unexplored. We extend a supervised lexicon-learning approach to 10-K filings and their Item 1A risk-factor sections, training sentiment scores against both return and volatility labels at three levels of aggregation: sector, portfolio, and individual firm. Across 1,383 filings from 94 Nasdaq-100 technology constituents (2006--2023), we evaluate the resulting twelve sentiment metrics on classification accuracy, correlation with realised market outcomes, and qualitative lexical content. Full-filing text produces more accurate sentiment at the sector and portfolio level for both targets, but this reverses at the individual-firm level, where the narrower Item 1A section performs better -- an effect we attribute to the interaction between document volume and the amount of independent training signal available at each level of aggregation. A Loughran-McDonald dictionary baseline is consistently, strongly negatively correlated with price at every level tested, underscoring the value of a supervised approach for regulatory disclosure text. These findings, and the design choices they motivate, establish the sentiment-generation methodology underlying a subsequent, larger-scale, multi-source system.

The adoption of non-parametric machine learning models for regulatory capital estimation introduces a fundamental governance challenge: the inability to explain model outputs in a manner auditable by supervisory bodies. This 'black box' problem remains a major barrier to the adoption of Gaussian Process Regression (GPR) and related ML architectures in ICAAP and CCAR workflows despite their predictive advantages over traditional parametric approaches. This paper addresses this barrier through SHARC (SHAP for Regulatory Capital), an explainability framework for the Hybrid GPR-HS architecture and its stress-testing extension. SHapley Additive exPlanations (SHAP), derived from cooperative game theory and satisfying the properties of Local Accuracy, Missingness, Consistency, and Efficiency, are applied to Stressed Value-at-Risk (SVaR) outputs under three macro scenarios: West Asia War, Climate Risk, and AI Bubble/Regulatory Burden. SHARC decomposes SVaR into baseline, mean-driven, and volatility-driven components, enabling transparent linkage between scenario design and capital outcomes. Two findings emerge. First, SHARC consistently links non-linear SVaR outputs to underlying scenario inputs, confirming framework fidelity and providing auditable traceability of capital drivers. Second, under stress conditions, the mean return component (directional loss magnitude) dominates the variance component (volatility baseline) in determining capital levels, with implications for capital limit-setting, position management, and hedging strategy. The results establish SHARC as a regulator-aligned explainability layer that makes the Hybrid GPR-HS framework fully auditable and consistent with FRTB, ICAAP Pillar 2, and CCAR transparency requirements.

Reinforcement Learning (RL) has emerged as a powerful approach in financial trading, enabling agents to learn optimal strategies through direct market interaction. However, financial markets are highly uncertain, with price fluctuations driven by stochastic volatility, model limitations, and regime shifts. Traditional RL models struggle in dynamic environments, often failing to adapt to sudden market disruptions, leading to suboptimal trading decisions. To address this challenge, we propose an uncertainty-aware RL framework that integrates distributional, epistemic, and aleatoric uncertainty estimations. Our approach enhances uncertainty estimation using SHAP-weighted reconstruction uncertainty, MC Dropout, and an LSTM-based technical indicator consensus mechanism. Experimental results on five major U.S. stock indices demonstrate that RL agents equipped with uncertainty estimation significantly outperform traditional models in return and risk management. This study advances uncertainty estimation in RL-based financial trading, with future research extending its application to other asset classes and alternative RL architectures for greater adaptability.

Predicting thermal volatility in high-performance EV powertrains is difficult as internal temperatures are rarely observable outside the lab, and models calibrated on lab drive cycles fail when deployed against real-world loads. We study this lab-to-track transfer problem using conformal prediction, offering distribution-free uncertainty bounds. We implement Ensemble Batch Prediction Intervals (EnbPI; Xu & Xie, 2021), a leave-one-out bootstrap-ensemble conformal method for autocorrelated time series, and calibrate it on real CALCE lithium-ion cycler data (A123 SP20 cells, FUDS profile). We evaluate it under a genuine, measured covariate shift: a second real CALCE test condition (US06 Highway Driving Schedule at 45°C). The unweighted EnbPI bound, achieving its nominal 95% coverage in-distribution (measured: 95.00%), degrades to 70.13% empirical coverage under this real shift. We introduce a weighted EnbPI procedure combining EnbPI's ensemble residuals with density-ratio weighting (Tibshirani et al., 2019), estimating the density ratio via a probabilistic domain classifier. This recovers coverage to 72.42%, a modest, honestly-reported improvement, not a complete fix. We additionally apply the calibrated model to real 2023 Formula 1 telemetry (Monza and Silverstone, driver VER) as an unsupervised out-of-distribution diagnostic. Because no internal thermal channel exists in public trackside telemetry, we report only unsupervised flag rates (65.6% at Monza, 58.0% at Silverstone, well above the 5% in-distribution base rate) and note inconsistent associations between flags and braking/DRS zones. We conclude that conformal domain adaptation is a promising but only partially solved tool for this problem, detailing exactly where it falls short.

In financial forecasting, predictive performance depends not only on which model is trained, but also on how the trained model is deployed. We study this issue in multi-horizon volatility forecasting. Our starting point is that a trained multi-output (MIMO) forecaster does not define a single deployable predictor: by changing the inference-time rollout rule, the same trained model induces a family of forecasts with different accuracy and cost profiles. Across 20 stock-volatility series, three forecast horizons, and architectures ranging from linear models to PatchTST, we find that non-default rollout rules often improve over standard MIMO deployment. However, the best fixed rule varies substantially across architectures and horizons, making any single static replacement unreliable. We therefore evaluate validation-based deployment policies over the induced rule family. Under the primary MSE objective, validation-selected singletons provide a low-cost improvement over default MIMO, while small rule subsets recover much of the benefit of larger ensembles at substantially lower inference cost. We also find that policy rankings are metric-sensitive: MSE-selected policies do not transfer uniformly to QLIKE, a finance-standard volatility loss. These results show that inference-time deployment is a meaningful source of adaptiveness in financial forecasting, and that trained volatility forecasters should be evaluated not only by their architecture, but also by their deployment policy.

Modern finance relies heavily on complex machine learning models to find patterns in the stock market. However, as these AI models get more complicated, they often memorize short-term market noise instead of finding companies with real, lasting value. We designed this research to test if Benjamin Graham's classic value investing rules could act as a mathematical "low-pass filter" to keep these modern models in check. We built three different sets of features - pure Graham rules, modern market factors, and a mix of both - and tested them against highly complex models (XGBoost and AutoGluon) using 20 years of S&P 500 data. By applying a strict buy-and-hold strategy over a four-year test period (March 2022 to March 2026), the results showed that more complex algorithms do not always win. While the AutoGluon model captured high returns (222.68%), it suffered a substantial 39.78% drop because it bought volatile tech stocks right before the market crashed. On the other hand, the pure Graham Random Forest achieved the highest overall return (232.13%) with much less risk (1.38 Calmar Ratio). Furthermore, the Combined Random Forest successfully mixed momentum with Graham's rules, making a 202.91% return while keeping the lowest maximum drop (34.53%) of any model tested. Ultimately, this research proves that Graham's "margin of safety" isn't outdated; it is actually a highly effective way to prevent modern AI from taking on too much risk.

Financial time series forecasting presents structural challenges absent from standard benchmarks. Log-returns are non-stationary, exhibit exceptionally low signal-to-noise (SNR) ratios, and are governed by regime-dependent temporal dependencies. We identify a key limitation of state-of-the-art (SOTA) time series models in financial settings. A fixed context window is mismatched to the time-varying optimal look-back of non-stationary price processes. We propose the Regime-Aware Variable-context Expert Network (RAVEN), a Mixture-of-Experts framework designed to adaptively determine the temporal context for each input sample. Instead of relying on a fixed look-back horizon, RAVEN constructs a hierarchy of nested contiguous windows whose lengths are determined by the data itself. Specifically, RAVEN scores patches by learned importance in reverse chronological order and applies the Cumulative Importance Thresholding (CIT) mechanism to derive nested prefix windows, each routed to a scale-specialized expert. A Global Compressed Representation (GCR) branch runs in parallel over the full context, preserving global temporal coherence that local experts cannot guarantee. Because the nested routing induces structured overlap among expert inputs, we introduce a Correlation-Aware Weighting (CAW) to align variable-length expert outputs and penalize pairwise cosine similarity prior to aggregation. Experiments on cumulative log-return prediction (HS300, S&P500) and fund sales forecasting demonstrate that RAVEN achieves SOTA performances, improves Pearson correlation by 9.2% on HS300 and 20.2% on S&P500, and reduces MSE by 18.2% on fund sales forecasting, while achieving the best results in 14 of 16 metrics on four PEMS traffic benchmarks.

We present a convolutional variational autoencoder for cryptocurrency implied-volatility surfaces, together with a deployable predictor that combines it with a quadratic smile re-fit through a deterministic per-tenor routing rule. Trained on 6,034 fully-filled hourly Binance Options surfaces of BTC and ETH spanning May-October 2023 and parameterised on a common $6 \times 7$ tenor-delta grid, the model attains a hidden-cell surface-completion RMSE in the 0.94-1.56 vol-point range across both markets and mask rates 10-50%. The hybrid predictor attains 0.83 vol points at 50% masking against 7.00 for the smile re-fit alone, an eightfold reduction obtained at no additional inference cost. Under structurally-correlated hole patterns that emulate the withdrawal of an entire tenor of strikes, the smile re-fit incurs 9.6-13.1 vol points of error while the learned model remains at 1.5-1.9, isolating a regime in which the generative model is the only viable predictor. Joint training on BTC and ETH improves the in-distribution model on both markets by 9-27% relative to the better-performing single-symbol counterpart, indicating a substantially shared vol-surface manifold across the two largest cryptocurrencies over the observation window. The hybrid is calendar- and butterfly-arbitrage-free at the listed strikes, a property that the parametric smile re-fit alone fails at high mask rates. The per-snapshot reconstruction error of the trained model flags the late-October ETF-anticipation rally and the August $17$, $2023$ flash crash as elevated-error periods without supervision. All training and evaluation infrastructure is released to support reproducible follow-on work.

Can financial news reliably predict short-term stock movements? Despite advances in large language models, this question remains unresolved. We revisit this problem using a zero-shot natural language processing framework, investigating whether models can extract actionable signals from financial news without domain-specific training. We design a structured pipeline that combines zero-shot natural language inference with temporal aggregation, explicitly modelling recency and event-dependent impact horizons when integrating information across articles. To address the need for transparency in high-stakes settings, we introduce a multi-layered explainability framework that links predictions to token-level, article-level, and aggregate evidence, and produces grounded natural language rationales. Across multiple models and prediction horizons, we find that zero-shot approaches consistently fail to outperform simple baselines, with particularly weak performance on negative movements, suggesting deeper structural limitations in mapping news sentiment to short-term price dynamics. However, explainability signals reliably distinguish between trustworthy and unreliable predictions, offering practical value even when accuracy is limited. These findings highlight the limits of zero-shot financial NLP and motivate a shift toward decision-support systems that prioritise transparency and uncertainty awareness. Code: https://github.com/alimert05/zero-shot-stock-xai

Modern option-learning systems operate in two coordinates: price space, where markets quote and no-arbitrage constraints are most naturally enforced, and implied volatility (IV) space, where volatility surfaces are smoothed, regularized, and evaluated. The bottleneck is interface, not approximation: Jäckel's seminal "Let's Be Rational" (LBR) solver already inverts the Black-Scholes price to machine precision efficiently. What is missing is a differentiable layer that preserves LBR in the forward pass and avoids backpropagating through its branch logic. Such a layer must also confront the unavoidable singularity of the inverse map in the low-vega regime, where the sensitivity 1/vega diverges as vega -> 0. We close this gap with PIVOT, the Price-Implied-Volatility Objective Translator. PIVOT keeps the LBR forward pass intact and supplies the backward pass by implicit differentiation through the smooth Black-Scholes/Black-76 price map, with an explicit gating contract: invalid domains return NaN, well-conditioned rows receive the exact 1/vega gradient, and low-vega rows are attenuated rather than silently regularized. On a single H100, a fused Triton kernel reaches 1.79e9 IV/s at machine precision (9.3e-14 max relative error vs. the reference C solver); end-to-end label generation sustains 48.9M/s on synthetic chains and 16.6M/s on SPX OptionMetrics. In a HyperIV-style one-day reproduction on SPX, PIVOT-augmented objectives Pareto-dominate the baselines, reducing held-out price MAE by up to 43.4% and the strongest three-seed gated objective improving price MAE by 38.8% and IV MAE by 21.3% jointly; cross-asset results on RUT, VIX, and NDX show directional price-MAE gains of 40.1%, 24.2%, and 16.7%, while an ungated IV-roundtrip control collapses to a degenerate near-zero surface, confirming the gate as a correctness contract rather than a tuning knob.

Financial forecasting is difficult due to low signal-to-noise ratios, latent factors, heavy tails, regime shifts, and jumps. Real-world benchmarks offer limited failure attribution: researchers can observe underperformance, but often cannot isolate why because mechanisms are unobservable and entangled. Real financial data reveal only one realized path, making it difficult to assess tail-risk calibration or data efficiency. We introduce FinStressTS, a mechanism-aware synthetic benchmark that links model behavior to controlled structural causes. FinStressTS comprises 30 diagnostic environments around six mechanism families: volatility clustering, multi-scale persistence, heavy-tailed shocks, regime switching, self-exciting jumps, and zero-inflated processes. We evaluate two tasks: point forecasting, using NMAE across five settings, and probabilistic forecasting, using CRPS under known data-generating mechanisms. We benchmark 15 models, from classical methods (HAR, VAR) to Transformer forecasters (PatchTST, iTransformer) and deep probabilistic architectures (DeepAR, TSFlow), and use learning curves to measure sample efficiency. Our evaluation reveals three insights. First, performance is mechanism-dependent: autoregressive and linear models are highly competitive, and often outperform Transformer-based models, in several volatility-, tail-, and jump-driven environments. Second, distributional alignment matters: parametric probabilistic models such as DeepAR calibrate well in stationary settings, while flexible models can help when distributions become multimodal or sparse. Third, neural models often require more data to match simple baselines, with larger gains mainly when learning latent regimes or complex distributions. FinStressTS provides an open framework for diagnosing failure modes and advancing risk-aware forecasting.

Probabilistic time series forecasting has attracted increasing attention in financial applications due to the need to quantify risk and uncertainty in future observations. We propose ProbRes, a post-hoc probabilistic calibration method that explicitly learns and incorporates volatility dynamics into probabilistic forecasting, enabling effective handling of heteroskedastic data. During training, ProbRes employs two architecture-agnostic modules to separately model the conditional mean and conditional volatility. At the inference stage, it generates predictive distributions by resampling normalized residuals. ProbRes is applicable to both univariate and multivariate time series and remains robust under a wide range of error distributions, including non-Gaussian innovations with conditional heteroskedasticity. Theoretical results demonstrate ProbRes's validity and experiments on both synthetic and real-world datasets show that ProbRes accurately captures predictive distributions and produces well-calibrated prediction intervals.

Latent state-space models are widely used to study partially observed dynamical systems, yet most formulations assume that process variability is independent of latent-state position. In many biological, behavioral, and physiological systems, however, variability may depend systematically on the underlying dynamical state, producing structured stochasticity that is not captured by constant-variance models. We introduce a state-coupled stochastic volatility framework in which latent process variance depends on displacement from a latent equilibrium. To estimate this relationship under partial observation, we develop a particle expectation-maximization procedure combining bootstrap particle filtering and backward trajectory smoothing. The model includes a coupling parameter, $γ$, that quantifies the strength of association between latent-state position and process variability. A large-scale simulation benchmark evaluated recovery and detection performance across varying coupling strengths, observation noise levels, trajectory lengths, and persistence regimes. The proposed framework consistently reduced recovery bias relative to an observed-state heteroskedastic proxy, with the largest improvements occurring under strong coupling. Recovery performance improved with increasing latent persistence, while detection performance remained competitive across a broad range of conditions and became increasingly advantageous as observation noise increased. Taken together, the results demonstrate that state-coupled volatility can be identified and estimated under partial observation when latent-state structure is explicitly modeled. The framework provides a practical methodological foundation for studying state-dependent variability and evaluating whether structured stochasticity contributes information about system dynamics beyond that contained in mean-state trajectories alone.

Forecasting agricultural commodity prices in emerging economies is difficult due to high volatility, frequent supply disruptions, and strong cultural influences on demand. This study introduces the Kalimati Vegetable Price Index (KVPI), a new inverse-volatility weighted composite index that aggregates 135 daily wholesale commodities from Kathmandu over ten years (2013-2023). By creating a stable macro-level signal, the KVPI reduces the noise inherent in modelling individual crops. A rich set of 64 causally valid features was developed, including festival lead-lag effects, rolling statistics, and calendar variables. Fourteen forecasting models spanning statistical, tree-based, deep learning, hybrid, and transformer architectures were rigorously evaluated across short (7-day), medium (14- and 30-day), and long-term (90-day) horizons. Tree-based ensembles proved notably robust, while classical statistical models and complex transformers struggled with the noisy dataset. The proposed Momentum-Corrected Online Stacking Ensemble achieved the strongest performance, yielding a Root Mean Square Error (RMSE) of 1.771, an exceptionally low Mean Absolute Percentage Error (MAPE) of 0.68%, and explaining 84.5% of the variance (R-squared = 0.845) at the 90-day horizon. This open-source pipeline provides policymakers and supply chain actors in Nepal and similar markets with a practical, reliable tool for anticipating price movements and strengthening food security.

Schrödinger bridges for time series (SBTS) generate synthetic paths by projecting, in relative entropy, a Brownian reference onto the path laws that match the joint distribution of the data on the observation grid. The Brownian reference, however, fixes the quadratic variation of the generated paths, which is restrictive when stochastic volatility, correlated noise, or rank-deficient covariance structures must be reproduced. We introduce "Triangular-Reference Schrödinger Bridges for Time Series" (TR-SBTS), which keeps the entropy-projection backbone of SBTS but replaces the Brownian reference by a triangular, volatility-informed, intervalwise frozen reference on a state augmented with latent covariance descriptors. The construction remains a single entropy projection on the augmented state: the minimiser is the $h$-transform of the reference, and on each frozen interval the optimal drift has the logarithmic-gradient form $b^\star(t,x)=A\,\nabla\log H(t,x)$, intrinsic to the active covariance directions when the frozen covariance $A$ is degenerate. We prove stability of the frozen approximation and consistency of the associated regularised kernel estimators, describe a reference-aware Nadaraya--Watson implementation of the conditional next-increment law, and evaluate the construction on numerical experiments.

Predicting stock price movements during Earnings Announcements (EAs) is a significant challenge due to market noise and high-impact price discontinuities. In this study, we evaluate whether pre-announcement news sentiment, firm fundamentals, and recent market dynamics jointly predict the directional price movement of equities on EA days. We construct a multi-modal feature space combining 15 fundamental metrics, 3 price-based technical indicators and sentiment scores derived from financial news articles processed using FinBERT. We compare a Long Short-Term Memory (LSTM) network and a Transformer-based architecture against a logistic regression baseline, and further assess all models with and without sentiment features to quantify their incremental value. Our results indicate that while the LSTM demonstrates higher precision through a conservative safe-bet strategy, the Transformer model exhibits superior sensitivity in identifying volatile movements, achieving a higher macro F1-score, with ablation experiments showing a consistent benefit from incorporating news sentiment.

Time series driven by unobserved latent states frequently exhibit abrupt jump discontinuities whose timing and magnitude cannot be predicted from observed history alone. Classical jump-diffusion models offer a principled mathematical framework but assume rigid parametric forms, while recent neural jump models operate on fully observed trajectories without inferring the hidden states that govern the dynamics. We propose \textit{Deep ZakaiJ}, a latent-state model for partially observed jump-diffusion systems that embeds the Zakai nonlinear filtering equation into a neural encoder--decoder architecture. The encoder recursively updates a belief over the latent state via Strang splitting into three interpretable substeps: prior propagation, diffusion innovation, and jump innovation, yielding a differentiable, first-order-accurate approximation of the exact filtering evolution. The decoder is a structured jump-diffusion model explicitly conditioned on the filtered belief, preserving the separation between continuous dynamics and discontinuous shocks. On synthetic, financial, and oceanographic datasets, \textit{Deep ZakaiJ} improves distributional forecasts while remaining competitive in point accuracy, achieving calibrated predictive intervals and recovering interpretable latent structure in synthetic and qualitative case studies.

We study the reconstruction of implied volatility surfaces from sparse and noisy option quotes using deep learning models under no-arbitrage constraints. We compare multiple neural architectures, including multilayer perceptrons, convolutional networks, U-Nets, variational autoencoders, and Transformer-based models against classical SVI parameterizations on option market data. Results show that Transformer and U-Net architectures achieve strong reconstruction accuracy, particularly under sparse observation regimes, while soft arbitrage penalties significantly reduce arbitrage violations with moderate impact on reconstruction error. We further analyze the trade-off between accuracy and arbitrage consistency across architectures and regularization strengths.

Conventional wisdom holds that large-batch training is fundamentally incompatible with Reinforcement Learning (RL) - beyond a modest threshold, increasing batch sizes typically yields diminishing returns or performance degradation due to the inherent non-stationarity of the data distribution. We challenge this view by observing that non-stationarity is not a fixed property of RL, but evolves throughout training: early stages exhibit rapid behavioral shifts that demand small batches for plasticity, whereas late stages approach a quasi-stationary regime where large batches enable precise convergence. Motivated by this observation, we propose Adaptive Batch Scaling (ABS), that dynamically adjusts the effective batch size according to the stability of the learning policy. Central to ABS is Behavioral Divergence, a novel metric that quantifies policy non-stationarity by measuring action-level shifts between consecutive updates, which we use to scale batch size inversely to policy volatility. Integrated with the Parallelised Q-Network (PQN) algorithm and evaluated on the ALE benchmark, ABS seamlessly reconciles early-stage plasticity with late-stage stable convergence. Strikingly, contrary to conventional wisdom, our results reveal that the combination of larger networks and larger batch sizes achieves the best performance - a scaling behavior previously thought to be unattainable in RL, now unlocked through adaptive batch control.

This paper tests whether graph neural networks improve realized volatility forecasts and whether those forecasts improve portfolio performance. Using weekly realized volatility for 465 S&P 500 equities from 2015-2025, Heterogeneous Autoregressive and Long Short-Term Memory baselines are compared against GraphSAGE models built on rolling correlation, sector, and Granger-causal graphs, with and without macro regime features. The empirical finding is that the model with the lowest forecast MSE, the model with the highest cross-sectional ranking accuracy, and the model with the highest portfolio Sharpe ratio are three different models. Forecast accuracy, ranking quality, and portfolio performance are related but not interchangeable objectives. Graph volatility models add value only when the portfolio rule can exploit the cross-sectional structure they encode.

Adaptive decision-making in biological and artificial intelligence requires balancing the exploitation of known outcomes with the exploration of uncertain alternatives. Although prior work suggests that uncertainty generally promotes exploration, it has typically treated distinct sources of environmental uncertainty as equivalent. We consider environments with latent reward states that drift over time (volatility) and are observed through noisy outcomes (stochasticity). Both increase posterior uncertainty, yet we show they drive optimal exploration in opposite directions: volatility enhances it, stochasticity suppresses it. We establish this asymmetry formally by extending the Gittins index framework to Gaussian state-space bandits with latent dynamics. We further derive Cause-Aware Uncertainty-Sensitive Exploration (CAUSE), a closed-form exploration bonus obtained via control-as-inference that inherits the same monotonicities. CAUSE outperforms standard exploration strategies in environments with heterogeneous noise structure, and also improves on a Gittins-per-arm policy whose rested-bandit optimality does not transfer to restless settings. Learning and exploration are governed by the same noise-inference asymmetry, and the framework predicts that pathological noise inference produces \emph{reversed} rather than merely impaired exploration, with implications for computational accounts of psychiatric conditions.

Accurate forecasting of the Volatility-Covariance Matrix (VCV) is central to regulatory capital adequacy processes such as the Internal Capital Adequacy Assessment Process (ICAAP) and the Comprehensive Capital Analysis and Review (CCAR). Traditional econometric models, including GARCH-family and Exponentially Weighted Moving Average (EWMA) approaches, suffer from parametric rigidity, distributional assumptions, and numerical instability under stress, leading to systematic underestimation of tail risk. This paper proposes and validates a novel Hybrid Gaussian Process Regression-Historical Simulation (GPR-HS) framework for estimating Value-at-Risk (VaR) and Expected Shortfall (ES) across a diversified portfolio of seven major global equity indices. The framework decouples the VCV estimation problem: individual asset volatilities are modelled dynamically using Univariate GPR with a Matern 5/2 kernel, while inter-asset correlations are estimated via stable historical covariance. A key methodological contribution is the Aggressive Noise Initialization (ANI) strategy, which sets the initial White Noise kernel variance equal to the empirical variance of the training returns, ensuring Gram matrix positive-definiteness, regularization, and conservative, regulatory-compliant forecasts. Evaluated using an expanding window forward-chaining cross-validation scheme over June 2020 -June 2025, the GPR-HS framework achieves regulatory compliance in the majority of test splits; including a 100% ES pass rate at the portfolio level, while outperforming the static Historical VaR benchmark in 71.4% of univariate cases by Quadratic Loss and 100% of cases by violation count.

As machine learning models grow in complexity, they increasingly struggle with three conflicting demands: the need for high accuracy, the requirement for hardware efficiency, and the necessity of functional stability. Traditional architectures often achieve performance at the expense of spiky or unpredictable behavior, where small changes in input lead to massive swings in output -- a critical flaw for real-world deployment in sensitive environments. This paper introduces ChainzRule (CR), a novel neural architecture designed to harmonize these competing goals. ChainzRule replaces standard piecewise-linear activations with a Polynomial Engine governed by Differential Regularization (DREG). Unlike traditional methods that impose global, coarse-grained constraints on a model's Lipschitz constant, DREG acts as a targeted regularization on intermediate derivatives. This approach suppresses extreme sensitivity without attenuating the representational power inherent in the Polynomial Engine. In head-to-head "Fair Fight" benchmarks, ChainzRule outperformed standard models while using 15.5x fewer parameters. On the MNIST dataset, it reduced peak gradient volatility by an average of 23.1%, ensuring a smoother and more predictable manifold. On Yelp Full ordinal regression under explicit DREG regularization, ChainzRule achieves 70.17% accuracy, validating that derivative-aware regularization is compatible with competitive performance on realistic tasks. By embedding gradient awareness into the architecture via DREG, ChainzRule demonstrates that stability and accuracy need not be competing objectives.

Generating realistic synthetic option prices requires implied volatility as an input, yet implied volatility is itself derived from observed option prices, creating a circular dependency that limits synthetic data for machine-learning and risk-analysis applications. We break this circularity with a pipeline in which implied volatility emerges as an output of a structural model of equity returns. A Jump Hidden Markov Model produces multi-asset price paths with realistic stylized facts and cross-asset tail dependence; a modified Heston variance process, whose mean-reversion target depends on regime state, days to expiration, moneyness, and a market-mood indicator, converts those paths into implied-volatility paths; and a recombining binomial lattice prices American options from the resulting surface. Initializing variance at its mean-reversion target for each strike-expiration pair lets smile, skew, and term structure emerge without external calibration. We calibrate the shape function through a hierarchy spanning a parametric baseline, a globally shared neural surrogate, and a sector-specific neural surrogate fit to a multi-ticker, multi-sector option ladder. A temporal holdout on a multi-day capture isolated scheduled corporate events as the dominant source of test-time generalization error, and calendar-derived earnings-distance and same-sector peer-coupling features recovered the anticipatory portion of that signal. We then apply the framework as a synthetic-data generator on real near-the-money put and call contracts, forward-simulating price paths, and recovering path-conditional implied volatility, finite-difference American Greeks, and terminal short-premium profit and loss from one coherent simulation, and confirm cross-ticker robustness by re-running on a second underlying from a different sector and volatility regime. The framework is released as an open-source Julia package.

This paper introduces a physics-informed generative framework that resolves the fundamental conflict between the statistical flexibility of deep learning and the rigorous theoretical constraints of fixed-income modeling. We demonstrate that standard generative models and unconstrained statistical extrapolations suffer from "manifold collapse" and severe arbitrage violations when forecasting term structures across diverse macroeconomic regimes. To overcome this, we propose a two-stage architecture. First, a Student-t Conditional Variational Autoencoder with Dynamic Level Injection (CVAEsT+LS) extracts a robust, heavy-tailed term structure manifold, effectively decoupling macroeconomic shape dynamics from absolute base rates. Second, the latent dynamic evolution is governed by a continuous-time Neural Stochastic Differential Equation (SDE) strictly penalized by a No-Arbitrage Partial Differential Equation (PDE). Empirical results across multiple sovereign currencies (USD, GBP, JPY) confirm that our synergistic approach drastically reduces out-of-sample forecasting errors -- achieving an exceptional 6.58 bps Mean Tenor RMSE -- and successfully overcomes the massive parallel drift and zero-lower-bound violations exhibited by the classical HJM model in extreme environments. Furthermore, through phase space vector field analysis, we demonstrate the model's superior capability in unsupervised macroeconomic regime detection and high-quality continuous-time scenario generation. Ultimately, this research provides a highly scalable, mathematically sound evolutionary engine for term structure modeling.

Modeling uncertainty in heavy-tailed time series remains a critical challenge for deep probabilistic forecasting models, which often struggle to capture abrupt, extreme events. While Lévy stable distributions offer a natural framework for modeling such non-Gaussian behaviors, the intractability of their probability density functions severely limits conventional likelihood-based inference. To address this, we introduce DeepLévy, a neural framework that learns mixtures of Lévy stable distributions by minimizing the discrepancy between empirical and parametric characteristic functions. DeepLévy incorporates a mixture mechanism that adaptively learns context-dependent weights and parameters over multiple Lévy components, enabling flexible multi-horizon uncertainty modeling. Evaluations on both real and synthetic datasets demonstrate that DeepLévy outperforms state-of-the-art deep probabilistic forecasting approaches in tail risk metrics, especially under extreme volatility.

We study long-horizon deployment of a frozen predictor under dynamic covariate shift. A time-domain Poincare inequality first reduces temporal risk volatility to derivative energy. A Jacobian-velocity theorem then supplies the corresponding pathwise control. Given explicit regularity and domination assumptions, the theorem identifies directional tangent energy along the deployment path as the governing quantity. Under low-rank drift, that quantity reduces to directional Jacobian energy in the drift subspace, motivating drift-aligned tangent regularization (DTR) and a matched monitoring proxy. Rather than smoothing the network isotropically, DTR penalizes sensitivity only along estimated drift directions. We validate the theorem-to-method pipeline in four experiments: a synthetic benchmark for the time-domain inequality, a controlled synthetic comparison against isotropic Jacobian regularization, and two frozen-deployment studies on the UCI Air Quality and Tetouan power-consumption datasets. DTR reduces risk volatility and directional gain in the controlled low-rank regime and beats isotropic smoothing there. It also gives validation-selected deployment gains on both real datasets, with the Air Quality subspace estimated from target-orthogonal sensor motion. Moderate drift-subspace misspecification is tolerable while orthogonal misspecification largely removes the benefit.

Time Series Foundation Models (TSFMs) have borrowed the long context paradigm from natural language processing under the premise that feeding more history into the model improves forecast quality. But in stochastic domains, distant history is often just high-frequency noise, not signal. Hence, the proposed work tests whether this premise actually holds by running continuous context architectures (PatchTST included) through the ETTh1 benchmark. The obtained results contradict the premise: an inverse scaling law shows up clearly, with forecasting error rising as context gets longer. A 3,000-step window causes performance to drop by over 68%, evidence that attention mechanisms are poor at ignoring irrelevant historical volatility. Retrieval-Augmented Forecasting (RAFT) is evaluated as an alternative. RAFT achieves a mean squared error (MSE) of 0.379 with a fixed 720-step window and selective retrieval, outperforming both long-context configurations and zero-shot foundation models (Chronos, Moirai) despite requiring far less computation. In addition, the retrieval step injects only the most relevant historical segments as dynamic exogenous variables, which gives the model a context-informed inductive bias it cannot build on its own from raw sequences. Therefore, foundation models going forward need to shift architecturally toward selective retrieval.

Modeling the dynamics of non-stationary stochastic systems requires balancing the representational power of deep learning with the mathematical transparency of classical models. While classical Markov transition operators provide explicit, theoretically grounded rules for system evolution, their empirical estimation collapses due to severe data sparsity when applied to high-resolution, high-noise environments. We explore this statistical barrier using financial time series as a canonical, real-world testbed. To overcome the degeneracy of empirical counting, we introduce a framework that utilizes neural networks strictly as parameterization engines to generate explicit, time-varying Markov transition matrices. By constraining the neural network to output its predictions as a formal stochastic operator, we maintain complete structural interpretability. We demonstrate that these learned operators successfully capture complex regime shifts: the state-conditioned model achieves mean row heterogeneity $\barρ = 0.0073$ while the state-free ablation collapses to exactly zero, and operator row entropy correlates with realized variance at $r = -0.62$ ($p \approx 10^{-251}$), revealing that high-volatility regimes homogenize transition dynamics rather than diversify them. Furthermore, rather than enforcing the Chapman-Kolmogorov equations as a rigid structural requirement, we repurpose them as a localized diagnostic tool to pinpoint specific temporal windows where first-order memory assumptions break down. Ultimately, this framework demonstrates how neural networks can be constrained to make rigorous, classical operator analysis viable for complex real-world time series.

Financial market forecasting is inherently uncertain, yet most deep learning approaches rely on point predictions that provide only single-value estimates without quantifying uncertainty. Such predictions are insufficient for risk-aware decision-making, as they fail to capture the range of possible outcomes and the associated confidence of forecasts.The problem can be solved using prediction intervals, which allow obtaining an upper and lower bound for the prediction, thus enabling uncertainty representation in the model. Yet, the current methods tend to disregard relationships between assets or cannot simultaneously ensure good calibration and sharpness of the resulting intervals in dynamically changing market regimes. In our work, we propose a spatio-temporal graph-based approach with a bi-level chaotic fusion technique to solve this problem. Our model uses separate nonlinear transformation functions to estimate the interval center and width. Additionally, a volatility-aware gating mechanism is used to make predictions dependent on the regime in which the market operates. Temporal dependencies are considered by embedding graph structures and sequentially modeling them. Training is conducted according to a Lower-Upper Bound Estimation (LUBE) objective. Our experimental results show significant improvements compared to existing baselines (LSTM, GRU, GCN, HGNN) when applied to data from 2016 to 2026 with 43 leading companies in eight sectors of the NSE. It provides the lowest Winkler score (0.0778), tightest prediction intervals (PIAW = 0.1407), and highest coverage (PICP = 96.6%), with all differences statistically significant (p < 0.001) according to the Diebold-Mariano test.

Climate volatility, regional production concentration, labor constraints, cyber risk, and dependence on long-distance fresh-produce supply chains expose vulnerabilities in U.S. fresh-produce and specialty-crop systems. Controlled environment agriculture (CEA) can reduce some exposure by moving selected production into protected, sensor-rich environments, but recent failures in venture-backed vertical farming show that CEA cannot be treated as a universal food-security solution. This paper proposes the Controlled Environment Agriculture Resilience Infrastructure Framework, Version 2.0 (CEA-RIF 2.0), for evaluating AI-driven CEA as targeted regional fresh-produce continuity infrastructure. The framework assesses seven dimensions: supply continuity, climate isolation, energy and grid integration, water and nutrient circularity, cyber-physical reliability, economic viability, and governance and deployment. Drawing on U.S. government reports, peer-reviewed CEA and energy literature, demand-response research, cybersecurity standards, international smart-agriculture programs, 2025-2026 financing and policy signals, and public autonomous-greenhouse datasets, the paper argues that AI creates resilience value only when it improves measured operational outcomes such as climate stability, energy flexibility, yield consistency, anomaly detection, labor productivity, and safe recovery from faults. The analysis reframes AI-driven CEA as a cyber-physical infrastructure problem: energy-aware, grid-interactive, secure, interoperable, regionally distributed, financially disciplined, and connected to public resilience goals. The paper concludes with a research agenda for interagency testbeds, open datasets, standardized metrics, demand-response pilots, and cyber-physical reference architectures.

Large Language Models (LLMs) excel at long-context understanding but exhibit significant limitations in long-form generation. Existing studies primarily focus on single-generation quality, generally overlooking the volatility of the output. This volatility not only leads to significant computational costs but also severely impacts the models' reliable application. To address this gap, our work unfolds in three stages: benchmarking, probing, and mitigation. We first propose the VOlatility in Long-form Text Benchmark (VOLTBench), a novel heterogeneous-task benchmark designed to systematically quantify the length volatility of long-form generation. Subsequently, by analyzing attention traces, we conduct an in-depth probe to identify several common internal patterns that cause this volatility. Finally, to mitigate long-form output volatility, we propose Stable Generation via Logits Boosting (GLoBo), a lightweight decoding-stage optimization strategy, designed to significantly enhance both the length accuracy and stability of long-form generation without additional training. Extensive experiments on VOLTBench provide the first systematic confirmation of severe long-form output instability in mainstream models and validate that our proposed method successfully improves the mean output length of the base model by 148% and reduces the length volatility by 69%, while maintaining high generation quality.

Hierarchical Gaussian Filtering (HGF) networks allow for efficient updating of posterior distributions (beliefs) about hidden states of an agent's environment. HGF parent nodes can target the mean or variance of their children. New information entering at input nodes leads to a cascade of belief updates across the network according to one-step update equations for each node's mean and precision (inverse variance). However, the original form of the update equations for variance-targeting parents(volatility coupling) can in some regions of parameter space lead to negative posterior precision, a logical impossibility which causes the updating algorithm to terminate with an error. In this report, we introduce a modified quadratic approximation to the variational energy of volatility-coupled nodes that avoids negative posterior precision. The key idea is to interpolate between two quadratic expansions of the variational energy: one at the prior prediction and one at a second mode whose location is obtained in closed form via the Lambert W function. The resulting update equations are robust across the entire parameter space and faithfully track the variational posterior even for large prediction errors.

Online conformal prediction must balance fast adaptation to distribution shift against stable coverage: feedback-driven methods react quickly but become volatile, while strongly discounted Bayesian methods lag and inflate intervals at tight coverage. We introduce \textbf{State-Adaptive Bayesian Conformal Prediction (SA-BCP)}, which forms the predictive quantile as a gated convex combination of long-term temporal inertia and local spatial evidence from a kernel density estimate, controlled by a single interpretable evidence threshold $K$. We establish three results: (i) asymptotic marginal validity of the resulting intervals up to a gate-controlled bias that vanishes as spatial evidence accumulates (exact under recurrent states); (ii) a closed-form expression for the MSE-optimal threshold, $K^*_{\mathrm{MSE}}=α(1-α)/M^{\mathcal{T}}$, trading the coverage-indicator (Bernoulli) variance against the temporal structural bias $M^{\mathcal{T}}$; and (iii) a rolling-origin procedure for selecting $K$ online -- consistent under stationarity, with $O(\sqrt{T\log N})$ regret against the best fixed $K$ and, for a segmented variant, a sublinear dynamic-regret bound under sublinearly many ($B_T=o(T)$) threshold shifts. Across four financial-volatility and weather datasets, three target coverage levels, and eight baselines, SA-BCP attains at-or-above-nominal coverage in most settings while producing substantially sharper intervals -- up to roughly $3\times$ lower Winkler score than discounted Bayesian CP at the tightest coverage -- and a coverage-matched audit confirms these efficiency gains are not an artifact of under-coverage. We disclose our principal limitation: a volatility-specialized CF-GARCH competitor remains more efficient on its home volatility-base series, though it does not transfer across domains.

Limit order books can transition rapidly from stable to stressed conditions, yet standard early-warning signals such as order flow imbalance and short-term volatility are inherently reactive. We formalise this limitation via a three-regime causal data-generating process (stable $\to$ latent build-up $\to$ stress) in which a latent deterioration phase creates a prediction window prior to observable stress. Under mild assumptions on temporal drift and regime persistence, we establish identifiability of the latent build-up regime and derive guarantees for strictly positive expected lead-time and non-trivial probability of early detection. We propose a trigger-based detector combining MAX aggregation of complementary signal channels, a rising-edge condition, and adaptive thresholding. Across 200 simulations, the method achieves mean lead-time $+18.6 \pm 3.2$ timesteps with perfect precision and moderate coverage, outperforming classical change-point and microstructure baselines. A preliminary application to one week of BTC/USDT order book data shows consistent positive lead-times while baselines remain reactive. Results degrade in low signal-to-noise and short build-up regimes, consistent with theory.

In a global derivatives market with notional values in the hundreds of trillions of dollars, the accuracy and efficiency of pricing models are of fundamental importance, with direct implications for risk management, capital allocation, and regulatory compliance. In this work, we employ the Black-Scholes-Merton (BSM) framework not as an end in itself, but as a controlled benchmark environment in which to rigorously assess the capabilities of quantum machine learning methods. We propose a fully quantum approach to option pricing based on Quantum Neural Networks (QNNs), and, to the best of our knowledge, present one of the first implementations of such a methodology on currently available quantum hardware. Specifically, we investigate whether QNNs, by exploiting the geometric structure of Hilbert space, can effectively approximate option pricing functions. Our implementation utilizes a compact 2-qubit QNN architecture evaluated across multiple state-of-the-art quantum processors, including IBM Fez, IQM Garnet, IonQ Forte, and Rigetti Ankaa-3. This cross-platform study reveals distinct hardware-dependent performance characteristics while demonstrating that accurate pricing approximations can be achieved consistently across different devices despite the constraints of Noisy Intermediate-Scale Quantum (NISQ) hardware. The results provide empirical evidence that QNN-based approaches constitute a viable framework for derivative pricing. While the analysis is conducted within the BSM setting, the broader significance lies in the potential extension of these methods to more realistic and computationally demanding models, including local volatility, stochastic volatility, and interest rate frameworks commonly used in practice.

Non-stationary sequences arise naturally in control, forecasting, and decision-making. The data-generating process shifts at unknown times, and models must detect the change, discard or downweight obsolete evidence, and adapt to new dynamics on the fly. Transformer-based foundation models increasingly rely on in-context learning for time series forecasting, tabular prediction, and continuous control. As these models are deployed in non-stationary environments, understanding their ability to detect and adapt to regime shifts is important. We formalize this as an in-context change-point detection problem and formally establish the existence of transformer models that solve this problem. Our construction demonstrates that model complexity, in layers and parameters, depends on the level of information available about the change-point location, from no knowledge to knowing exact timing. We validate our results with experiments on synthetic linear regression and linear dynamical systems, where trained transformers match the performance of optimal baselines across information levels. We also show that encoding and incorporating changepoint knowledge indeed improves the real-world performance of a pretrained foundation models on infectious disease forecasting and on financial volatility forecasting around Federal Open Market Committee (FOMC) announcements without retraining, demonstrating practical applicability to real-world regime changes.

Cryptocurrency trading increasingly depends on timely integration of heterogeneous web information and market microstructure signals to support short-horizon decision making under extreme volatility. However, existing trading systems struggle to jointly reason over noisy multi-source web evidence while maintaining robustness to rapid price shocks at sub-second timescales. The first challenge lies in synthesizing unstructured web content, social sentiment, and structured OHLCV signals into coherent and interpretable trading decisions without amplifying spurious correlations, while the second challenge concerns risk control, as slow deliberative reasoning pipelines are ill-suited for handling abrupt market shocks that require immediate defensive responses. To address these challenges, we propose WebCryptoAgent, an agentic trading framework that decomposes web-informed decision making into modality-specific agents and consolidates their outputs into a unified evidence document for confidence-calibrated reasoning. We further introduce a decoupled control architecture that separates strategic hourly reasoning from a real-time second-level risk model, enabling fast shock detection and protective intervention independent of the trading loop. Extensive experiments on real-world cryptocurrency markets demonstrate that WebCryptoAgent improves trading stability, reduces spurious activity, and enhances tail-risk handling compared to existing baselines. Code will be available at https://github.com/AIGeeksGroup/WebCryptoAgent.

Can AI Agents simulate real-world trading environments to investigate the impact of external factors on stock trading activities (e.g., macroeconomics, policy changes, company fundamentals, and global events)? These factors, which frequently influence trading behaviors, are critical elements in the quest for maximizing investors' profits. Our work attempts to solve this problem through large language model based agents. We have developed a multi-agent AI system called StockAgent, driven by LLMs, designed to simulate investors' trading behaviors in response to the real stock market. The StockAgent allows users to evaluate the impact of different external factors on investor trading and to analyze trading behavior and profitability effects. Additionally, StockAgent avoids the test set leakage issue present in existing trading simulation systems based on AI Agents. Specifically, it prevents the model from leveraging prior knowledge it may have acquired related to the test data. We evaluate different LLMs under the framework of StockAgent in a stock trading environment that closely resembles real-world conditions. The experimental results demonstrate the impact of key external factors on stock market trading, including trading behavior and stock price fluctuation rules. This research explores the study of agents' free trading gaps in the context of no prior knowledge related to market data. The patterns identified through StockAgent simulations provide valuable insights for LLM-based investment advice and stock recommendation. The code is available at https://github.com/MingyuJ666/Stockagent.

We examine whether financial news can improve realised volatility forecasting using a parsimonious NLP-based framework that incorporates specialised financial word embeddings alongside general-purpose alternatives. News-only forecasts contain useful predictive information but generally do not outperform strong volatility-history benchmarks. Crucially, combining stock-related news forecasts with a strong volatility-history benchmark lowers forecast losses for several specifications and increases realised utility, providing evidence consistent with forecast complementarity. Performance varies across news types, embedding representations, and volatility regimes. SHAP attributions associate forecast variation with economically interpretable firm-specific and macroeconomic news themes.