Motion prediction –forecasting the future trajectories of surrounding vehicles, pedestrians and cyclists is a safety-critical component of the autonomous-driving pipeline that must run in real time on embedded hardware. State-of-the-art predictors, however, are trained on compute clusters and are too large to run on a single consumer GPU, placing both ends of the contemporary pipeline out of reach for an individual researcher. This thesis asks how small a competitive trajectory predictor can be made before its accuracy degrades, and whether the lost accuracy can be recovered through knowledge distillation without enlarging the model or worsening the calibration a downstream planner depends on. The study uses HiVT, a transformer-based Laplace-mixture predictor that is small enough to be both trained and run on a single GPU, evaluated on the Argoverse 1 benchmark. The accuracy–capacity trade-off is first characterised by sweeping the embedding width (128, 64, 32, 16) and locating the point at which a from-scratch student falls measurably below the teacher. The mode-permutation problem is then identified: because HiVT trains its mixture modes with a winner-takes-all loss, the mode slots of two independently trained models do not correspond, so any distillation term that aligns modes by index supervises the student with self-contradictory targets. To resolve this, a permutation-invariant mixture negative-log-likelihood objective is derived that treats the teacher’s modes as an order-free set of soft targets and supports unequal mode counts, with a proof of invariance. Experiments show that a mean-target variant of this objective recovers roughly 84% of the HiVT 32→ HiVT-64 capacity gap (−9.2% minFDE over a matched non-distilled baseline) at zero added inference cost, but degrades full-distribution calibration (mixture NLL +41%, calibration error 5×) by discarding the teacher’s predictive variance. A distribution-matching objective that also distils the teacher’s per-mode scales removes this penalty entirely, leaving the student better calibrated than both the non distilled baseline and the teacher while retaining the full geometric gain. The benefit grows as the student shrinks: at width 16 (55× smaller than the teacher) distribution-matching distillation improves minFDE by −22.7%—roughly 2.5× the width-32 gain—recovering ∼81% of the width-16→width-32 gap, with calibration improving rather than degrading. Distillation thus buys close to a full size-class of accuracy for free, and most where capacity is scarcest. A final efficiency analysis quantifies the deployment frontier: parameter and memory savings are fixed and unconditional (15× at width 32, 55× at width 16), whereas the single-scene latency speed-up is far sublinear and batch-dependent (on CPU ∼3× online, rising to ∼5.5× under modest batching), locating the compression benefit primarily in memory footprint. Overall, the answer to how small a competitive HiVT can be made is encouraging: with a permutation-invariant, calibration-preserving distillation loss, a 55×-smaller student reaches roughly the accuracy of an un-distilled model nearly four times its size at no calibration cost.
Executive Summary This paper introduces a deterministic mathematical framework for nested learning designed to eliminate catastrophic forgetting in continuous learning systems. Standing as the first Proof of Concept (POC) of its type ever made, it completely flips the traditional AI safety paradigm. Instead of letting all data into a model and relying on post-hoc, probabilistic safeguards or heuristic mitigations to fix corruption after it occurs, this architecture implements an immutable mathematical gatekeeper called the H2E Sheriff. By filtering incoming data at the doorstep, it ensures that incoherent or corrupting inputs are rejected before they can ever modify or overwrite stored knowledge, ensuring absolute preservation of prior learning by architectural design. Theoretical Foundation & Key Components The framework anchors AI learning governance to absolute mathematical ground truths rather than learned data distributions or human preferences. Arithmetic Spectral Theory (AST): Synthesizes four classical transforms—Laplace, Euler, Fourier, and Mellin—into a single spectral operator, the L-EFM operator. At the critical line ($\sigma = 0.5$), the normalized magnitude of this operator evaluates to exactly 1 over prime sets, creating a universal coherence invariant. Empirical testing across diverse finite prime-related sets demonstrates that the system achieves a steady-state spectral coherence of exactly 0.5 at this critical line. Safety Thresholds ($\Lambda$): Computed directly from the Euler attenuation product over the first $n$ primes rather than being trained on data. The framework identifies $\Lambda_{12} = 0.9944590549$ as the primary perimeter gate boundary. The H2E Sheriff Manifold: Maps real-valued input embeddings onto the product manifold $\mathbb{H}^2 \times SPD(3)$. Incoming data is geometrically evaluated against a prime-anchored reference center ($x^*$) constructed from normalized prime coordinates. Spectral Risk Overlap Index (SROI): A metric determining an embedding's proximity to the coherent reference center on the manifold. Inputs are processed via a strict decision rule: accepted into the knowledge base if $SROI > \Lambda$, and conservatively rejected if $SROI \le \Lambda$. Experimental Validation The framework was validated using 10-dimensional vectors with controlled noise levels under a deterministic seed and 50-decimal-place precision. Threshold Discrimination: Calibration experiments confirmed that the $\Lambda_{12}$ threshold cleanly separates stable, coherent embeddings (noise $< 1.0$) from erratic, incoherent ones (noise $\ge 2.0$). Knowledge Base Integrity: During nested learning protocols featuring mixed streams of inputs, the H2E Sheriff successfully blocked corrupting data. In a stream of 30 inputs, all 12 incoherent attempts were rejected at the gate. The final knowledge base retained an average SROI of 0.996076, demonstrating zero degradation of stored knowledge and complete preservation of prior learning. Current Limitations & Future Work As the first exploratory POC mapping absolute prime structures to continuous AI safety boundaries, the paper transparently identifies clear vectors for future scaling and development: Dimensionality & Scaling: The initial validation operates on 10-dimensional embeddings and compact knowledge bases. Because the geodesic distance and matrix logarithm calculations on $SPD(3)$ scale cubically ($O(n^3)$), evaluation on large-scale, high-dimensional neural network workloads remains untested. Hyperparameter Selection: The choices for the scaling factor ($\tau = 50$) and the optimal prime set size ($n = 12$) are empirically driven for this distribution and lack a generalized analytical method for automatic selection in new problem domains. Modality Generalization: The threshold was calibrated on Gaussian noise and has not yet been exposed to complex embedding distributions like large language model tokens or image feature vectors. Neural Network Integration: The current implementation acts as a post-hoc filter on static vectors. Integrating this rigid mathematical gatekeeping into backpropagation-based training loops—where internal representations continually shift—remains an open architectural challenge. Theoretical Completeness: The core spectral coherence value of 0.5 at $\sigma = 0.5$ is an empirical invariant observed across finite sets; a formal, universal proof extending this to all infinite prime sets or establishing its absolute equivalence to the Riemann Hypothesis is not yet established.
A Case Study Application of the Xenopoulos Genetic‑Historical Logic System (X‑GHLS) https://github.com/kxenopoulou/epameinondas_xenopoulos_epistemology-of-logic_genetic-historical-logic Author: Katerina XenopoulouORCID: 0009‑0004‑9057‑7432Version: 4.0 (Complete)Publication Date: February 25, 2026 Data and Experimental Setup Dataset: Our World in Data — COVID‑19 GreeceTime Span: January 5, 2020 – August 4, 2024Total Observations: 1,674 daily recordsOut‑of‑Sample Predictions: 1,667Overall Forecast Accuracy: 98.31%Evaluation Metrics: MAPE 1.69% | R² 0.999 | RMSE 120 cases ABSTRACT We present the first complete empirical validation of the Xenopoulos Genetic‑Historical Logic System (X‑GHLS) on real‑world epidemiological data. While the theoretical framework of X‑GHLS establishes 33 philosophical principles and the XEPTQLRI metric for quantifying dialectical tension, this study demonstrates its practical application in forecasting COVID‑19 dynamics in Greece over a 4.5‑year period (January 2020 – August 2024, N = 1,674 days). The system achieves exceptional predictive performance: MAPE: 1.69% (Mean Absolute Percentage Error) R²: 0.999 (Coefficient of Determination) RMSE: 120 cases (Root Mean Square Error) Overall Accuracy: 98.31% Total Predictions: 1,667 Phase analysis reveals that the pandemic was in crisis mode (τ₅ and above) for 1,212 days (72.7% of the total), explaining why conventional statistical models struggle with such highly nonlinear dynamics. The system successfully detects all major COVID‑19 waves in Greece and provides early warning signals through the XEPTQLRI index. Comparative analysis with state‑of‑the‑art models (2026) demonstrates that X‑GHLS outperforms: TimesFM (Google): 3.2% MAPE Chronos‑2: 3.5% MAPE TiRex: 3.8% MAPE Transformer architectures: 4.2% MAPE LSTM networks: 5.8% MAPE ARIMA: 8.5% MAPE The 33rd Principle (Advanced Dialectical Negation) proves crucial for qualitative jump detection, enabling the system to adapt to regime changes that cause other models to fail. The complete mathematical formalization of all 33 principles is provided, with full reproducibility through the open‑source implementation. Environmental and economic advantages are equally striking: zero training cost, 0.001 kWh per prediction (vs 200 kWh for foundation models), zero carbon footprint (vs 100+ tons CO₂), and full interpretability through the 10 dialectical phases (τ₀–τ₉). This work constitutes the first large‑scale empirical validation of a dialectical logic system on real‑world time series data, demonstrating that philosophical principles can be mathematically formalized into predictive models that outperform state‑of‑the‑art machine learning architectures. Keywords: X‑GHLS; dialectical logic; COVID‑19 forecasting; time series analysis; XEPTQLRI index; 33 principles; phase transition detection; qualitative jump; Our World in Data Data Source: Our World in Data — COVID‑19 Greece DatasetCode Availability: Upon request for academic collaborationCorresponding Author: Katerina Xenopoulou (katerinaxenopoulou@gmail.com) 📊 Summary Table (for Abstract) Metric Value Comparison MAPE 1.69% 3.2% (TimesFM) R² 0.999 0.99 (Chronos‑2) Accuracy 98.31% 96.8% (TimesFM) Days Analyzed 1,674 — Predictions 1,667 — Crisis Phases (τ₅+) 1,212 days 72.7% of total 📊 KEY RESULTS Metric Value MAPE 1.69% R² 0.999 RMSE 120 cases Accuracy 98.31% Predictions 1,667 Time span 2020–2024 (1,674 days) 📈 GRAPHICAL RESULTS 1: COVID-19 Cases in Greece (2020–2024)] 2: Dialectical Phases (τ₀–τ₉) with XEPTQLRI Coloring] 3: XEPTQLRI Index with Phase Thresholds] 4: Actual vs Predicted Cases] 🏆 COMPARISON WITH STATE-OF-THE-ART MODELS (2026) Model MAPE Training Cost Energy / Prediction CO₂ Emissions Interpretability XENOPOULOS 1.69% €0 0.001 kWh 0 kg Full (33 principles) TimesFM (Google) ~3.2% €200,000+ 200 kWh 100+ tons Black box Chronos-2 ~3.5% €50,000+ 50 kWh 25 tons Black box TiRex ~3.8% €15,000+ 15 kWh 7.5 tons Limited Transformer ~4.2% €100,000+ 100 kWh 50 tons Black box LSTM ~5.8% €5,000+ 5 kWh 2.5 tons Limited ARIMA ~8.5% €0 0.001 kWh 0 kg Statistical 🔬 DETAILED ANALYSIS BY PHASE Phase Days Mean XEPTQLRI Mean Tension Confidence Description τ₀ 64 0.40 0.064 0.85 Stability τ₁ 35 1.23 0.153 0.85 Stability τ₂ 28 1.71 0.213 0.75 Pattern repetition τ₃ 14 2.88 0.360 0.65 Growing instability τ₄ 14 4.00 0.499 0.55 System saturation τ₅ 147 5.15 0.644 0.40 QUALITATIVE JUMP τ₆ 154 6.02 0.752 0.30 Paradoxical state τ₇ 462 7.06 0.883 0.20 Transcendence τ₈ 749 7.83 0.978 0.20 Transcendence Key observation: The pandemic was in crisis mode (τ₅ and above) for 1,212 days (72.7% of the total), explaining why conventional models struggled to adapt. 🌍 ENVIRONMENTAL & ECONOMIC IMPACT Model Training Cost CO₂ Emissions Equivalent XENOPOULOS €0 0 kg 0 flights TimesFM €200,000+ 100+ tons 200 flights Athens–London Chronos-2 €50,000+ 25 tons 50 flights LSTM €5,000+ 2.5 tons 5 flights 🎯 WHY THIS IS REVOLUTIONARY # Advantage XENOPOULOS Other Models 1 Accuracy 98.31% 91.5% – 96.8% 2 Training Cost €0 €5,000 – €200,000+ 3 Energy per Prediction 0.001 kWh 5 – 200 kWh 4 CO₂ Footprint 0 kg 2.5 – 100+ tons 5 Interpretability Full (33 principles) Black box / Limited 6 Phase Detection Yes (τ₀–τ₉) No 📖 THE 33 PRINCIPLES A. Dialectical Principles (1–4, 12, 16, 18, 26) # Principle 1 Synthesis of Formal and Dialectical Logic 2 Dialectical Contradiction as Creative Force 3 Dialectic of Stasis and Motion 4 Integration of Otherness 12 Dialectical Perception of Infinity 16 Logic of Process 18 Law of State Succession 26 The Concept of Aufhebung B. Theory of Knowledge (5–7, 13, 17, 19, 27, 28) # Principle 5 Historical-Genetic Approach 6 Dialectic of Theory and Practice 7 Transitional Nature of Truth 13 Genetic Logic 17 Restructuring of Dialectical Thought 19 Repetition and Historical Dialectic 27 Triple Coincidence (Sπ, Sα, f(x)) 28 Suszko Triad (L, B, Θ) C. Mathematical Formalization (21–25, 32) # Principle 21 The N[Fi(Gj)] Operator 22 INRC Group (Piaget) 23 XEPTQLRI Index 24 Ten Dialectical Stages (τ₀–τ₉) 25 Dubarle Operators (△, ▼, ▽, ▲) 32 Rogowski Np Operator D. Innovative Applications (8–11, 14–15, 20, 29–31) # Principle 8 Interdisciplinary Application of Dialectics 9 Synthesis of Unity and Differentiation 10 Transcendence of Static Logic 11 Dynamic Perception of Reality 14 Negation as Creative Force 15 Quantitative and Qualitative Change 20 Dual Nature of the "Now-Present" 29 Illusion of Stability 30 Application to Artificial Intelligence 31 Critical Transition Prediction E. The 33rd Principle – Advanced Dialectical Negation f(A) = -A · P · H · (1 + M) + ε Parameter Description A Dialectical tension (from thesis–antithesis conflict) P Predictive capacity of current phase H Historical memory (weight of previous predictions) M Transitional factor (proportional to XEPTQLRI) ε Stochastic noise (uncertainty modeling) 📊 THE XEPTQLRI INDEX AND PHASES τ₀–τ₉ Phase XEPTQLRI Range Description τ₀ < 0.8 Stability τ₁ 0.8 – 1.5 First deviation τ₂ 1.5 – 2.5 Pattern repetition τ₃ 2.5 – 3.5 Incompatibility τ₄ 3.5 – 4.5 System saturation τ₅ 4.5 – 5.5 Qualitative jump τ₆ 5.5 – 6.5 Paradox τ₇ 6.5 – 7.5 Transcendence τ₈ 7.5 – 8.5 Permanent dialectics τ₉ > 8.5 Absolute synthesis 🧠 INTERPRETATION OF RESULTS Feature Description Early phase change detection The system "knows" when it enters crisis mode (τ₅ and above) and adapts predictions accordingly Paradox management In phases τ₆–τ₈, where behavior becomes nonlinear, confidence decreases and stochastic factors increase Historical memory Parameter H in the 33rd Principle incorporates knowledge from previous predictions, creating dialectical learning 🔮 FUTURE DIRECTIONS Limitation Description Future Extension Phase boundaries Thresholds between phases are empirical Automatic phase boundary optimization Stochasticity Random noise introduces minor variability Advanced uncertainty modeling Generalization Tested mainly on COVID-19 data Multi-domain testing (finance, climate) 📜 SCIENTIFIC CONTRIBUTION # Contribution 1 Complete mathematical formalization of 33 philosophical principles into a functional predictive system 2 Introduction of the XEPTQLRI index as a measurable quantity of dialectical tension 3 Ten-phase typology (τ₀–τ₉) for describing system dynamics 4 The 33rd Principle as a qualitative jump operator 5 Proof that a philosophically grounded system can outperform statistical models with millions of parameters 💡 CONCLUSION Aspect XENOPOULOS Advantage Performance 98.31% accuracy — superior to all compared models Cost Zero training cost, runs on any computer Energy 0.001 kWh per prediction (vs 200 kWh) Environment Zero carbon footprint (vs 100+ tons CO₂) Transparency Full interpretability through 33 principles Philosophical foundation Dialectics meets computation — a paradigm shift 📥 CODE AVAILABILITY The system's source code is available upon request for academic collaboration.Please contact the author for further information. 🙏 ACKNOWLEDGMENTS This work is dedicated to the memory of my father, Epameinondas Xenopoulos, whose work Epistemology of Logic (1998, 2nd ed. 2024) provided the foundation for this entire endeavor. I warmly thank my family for their support, and my granddaughter who, at 9 years old, reminded me daily that dialectics is not theory but a way of life. 📚 REFERENCES # Reference 1 Xenopoulos, E. (2024). Epistemology of Logic (2nd ed.), https://www.researchgate.net/publication/359717578_Epistemology_of_Logic_Logic-Dialectic_or_Theory_of_Knowledge 2 Hegel, G.W.F. (1812). Science of Logic 3 Piaget, J.
EVs live and die by their batteries. To keep drivers safe and confident in their vehicles, we need efficient, accurate, and private ways to track each battery's SoH. But, EV labelled data is scarce, sharing raw data raises privacy flags, and big models strain on-board hardware. This thesis tackles all three problems through a two-step remedy in one shot. 1. Learn data representations without needing labels: Each car trains a small autoencoder to reconstruct its own collected sensor data after randomly hiding parts of the signal. 2. Share knowledge, not data: Instead of uploading the raw collected data, every car sends only its trained model parameters to a remote cloud server. The server aggregates parameters from all cars and sends the improved model back. Four simple questions guide our work: 1. Does this usage of unlabelled data improve the model's performance? 2. How much of the signal should be hidden to get the best representation learning? 3. What is the optimal strategy for incorporating the limited labelled data available into the model? 4. Does this aggregation of separately trained models hurt accuracy compared with a fully centralized approach? Our experiments show a 17% lower average MAE, with up to a 60% improvement in the best cases, when we make use of the available unlabelled data versus training exclusively on labelled data. Hiding 30-40% of signals strikes the balance between challenge and clarity. Finally, aggregation of models on average stays within 0.05Ah of centralized training, virtually no loss, with zero raw-data exposure. This thesis incorporates cloud computing, SSL, and FL to present a light, privacy-friendly pipeline for fleet-wide SoH estimation, evidence that unfrozen fine-tuning outshines frozen variants, the first systematic look at how masking ratio shapes battery time-series representation learning, and practical proof that sharing model weights instead of data keeps accuracy basically untouched and privacy intact.
This paper proposes a two-stage approach to parametric nonlinear time series modelling in discrete time with the objective of incorporating uncertainty or misspecification in the conditional mean and volatility. At the first stage, a reference or approximating time series model is specified and estimated. At the second stage, Bayesian nonlinear expectations are introduced to incorporate model uncertainty or misspecification in prediction via specifying a family of alternative models. The Bayesian nonlinear expectations for prediction are constructed from closed-form Bayesian credible intervals evaluated using conjugate priors and residuals of the estimated approximating model. Using real Bitcoin data including some periods of Covid 19, applications of the proposed method to forecasting and risk evaluation of Bitcoin are discussed via three major parametric nonlinear time series models, namely the self-exciting threshold autoregressive model, the generalized autoregressive conditional heteroscedasticity model and the stochastic volatility model. Supplementary Information: The online version contains supplementary material available at 10.1007/s00181-022-02255-z.
In econophysics, statistical-physics techniques are used to model economical systems. In this thesis, we investigate the entropy and the Computational Information Density (CID) of the Bitcoin blockchain. The CID is defined as the compression ratio of some particular algorithm when applied to the raw data of the state of the system. It is related to entropy as both CID and entropy are measures of information.\nWe find a strong correspondence between the CID and entropy for the Bitcoin blockchain, where features are similar, but without one being a clear function of the other. This can be explained by intercorrelations between one agent and the next, which the entropy does not count. We also calculate some correlations to see if the CID and the entropy have some predictive power for the price, and we find a small correlation, but very small in comparison to the predictive power of the price itself.\nThese results the power of the CID-entropy correspondence and how the Bitcoin blockchain may be used as a useful large-scale toy model for econophysics. We anticipate that these results can be used for a further look into the CID-entropy relation, as the similarities are visible but there is no exact correspondence. Besides this, these results can form a basis for a further look into the predictive power of the CID or the entropy for the price.