Truong Xuan Khanh

Truong Quynh Hoa, Hoang Dinh Cuong, Truong Xuan Khanh

We propose Melaguard, a multimodal ML framework (Transformer-lite, 1.2M parameters, 4-head self-attention) for detecting neurovascular instability (NVI) from wearable-compatible physiological signals prior to structural stroke pathology. The model fuses heart rate variability (HRV), peripheral perfusion index, SpO2, and bilateral phase coherence into a composite NVI Score, designed for edge inference (WCET <=4 ms on Cortex-M4). NVI - the pre-structural dysregulation of cerebrovascular autoregulation preceding overt stroke - remains undetectable by existing single-modality wearables. With 12.2 million incident strokes annually, continuous multimodal physiological monitoring offers a practical path to community-scale screening. Three-stage independent validation: (1) synthetic benchmark (n=10,000), AUC=0.88 [0.83-0.92]; (2) clinical cohort PhysioNet CVES (n=172; 84 stroke, 88 control) - Transformer-lite achieves AUC=0.755 [0.630-0.778], outperforming LSTM (0.643), Random Forest (0.665), SVM (0.472); HRV-SDNN discriminates stroke (p=0.011); (3) PPG pipeline PhysioNet BIDMC (n=53) -- pulse rate r=0.748 and HRV surrogate r=0.690 vs. ECG ground truth. Cross-modality validation on PPG-BP (n=219) confirms PPG morphology classifies cerebrovascular disease at AUC=0.923 [0.869-0.968]. Multimodal fusion consistently outperforms single-modality baselines. Code: https://github.com/ClevixLab/Melaguard

Truong Xuan Khanh, Truong Quynh Hoa, Luu Duc Trung et al.

We give the first quantitative prediction of grokking delay under AdamW. Treating the delay as a first-passage time, we derive a closed-form law T_grok - T_mem = (1 / 2 kappa_LL eta lambda) log(V_mem / V_star), where V_t = ||theta_t||^2 is the squared parameter norm, V_star is an architecture-dependent threshold, and kappa_LL absorbs the AdamW correction to the clean-SGD contraction rate 2 eta lambda. Calibrating (kappa_LL, V_star) on a single hyperparameter cell predicts grokking delays on 26 held-out runs with MAPE 17.7% over a 41x delay range; the law generalises to MLPs (MAPE 18.0%, N=34) and degrades to 23.3% on cross-task extension (N=46, 43.5x range), with a structured residual in which V_star / V_mem stays comparatively stable within architecture (CV about 14% on the 1L transformer). First-passage of V_t is necessary but not sufficient. A quantile-margin theorem establishes that positive delay requires both norm separation V_mem > V_post and angular reachability of a threshold alpha_star = arcsin(C / V_T_mem^(1/2)), where C is computable from the empirical NTK feature map and the validation-margin quantile. Calibrating C on modulus p=89 predicts alpha_star = 47.2 degrees at p=97 (observed 47.8 degrees, error 1.3%) as a prior cross-cell prediction. Causal interventions that freeze the norm or remove weight decay at memorisation eliminate grokking (0/6 vs. 3/3 baseline), trapping the angular displacement near 12 degrees. kappa_LL is empirically measured per architecture rather than derived from (beta_1, beta_2, epsilon); within-architecture CV stays at most 15% across four architectures, but values differ by about 2x between architectural variants beyond depth alone. Empirical scope is algorithmic tasks (modular arithmetic, sparse parity) under AdamW; whether the law transfers to natural-language scale models is open.

Truong Xuan Khanh

Phase-transition phenomena in deep learning (grokking, emergent capabilities, and ontological reorganization under context shift) have been studied through several lenses, including representational compression, singular learning theory, and information-theoretic progress measures. Independently, non-equilibrium statistical physics has identified phase transitions in driven chemical reaction networks underlying prebiotic selection, with empirical signatures that are difficult to reproduce within single-field gradient accounts. We propose a perspective in which both classes of phenomena admit a common description as driven informational systems: stochastic processes governed by two gradient fields, an entropy production rate Sigma and an information quasi-potential Phi_I := -ln p*, where p* is the stationary density. Within this framework we introduce two candidate order parameters: an adversarial breakdown threshold alpha_dagger and a self-referential coupling threshold kappa_c. The joint scaling of (alpha_dagger, kappa_c) defines a candidate universality class with exponents (gamma_1, gamma_2). We outline the geometric structure of this framework, identify falsifiable predictions distinguishing it from single-field alternatives, and show consistency with recent empirical findings (2024--2026) on alignment transitions, adversarial breakdown scaling, and partial introspection in large language models.

Truong Xuan Khanh, Truong Quynh Hoa, Luu Duc Trung et al.

Grokking is the sudden generalization that appears long after a model has perfectly memorized its training data. Although this phenomenon has been widely observed, there is still no quantitative theory explaining the length of the delay between memorization and generalization. Prior work has noted that weight decay plays an important role, but no result derives tight bounds for the delay or explains its scaling behavior. We present a first-principles theory showing that grokking arises from a norm-driven representational phase transition in regularized training dynamics. Training first converges to a high-norm memorization solution and only later contracts toward a lower-norm structured representation that generalizes. Our main result establishes a scaling law for the delay: T_grok - T_mem = Theta((1 / gamma_eff) * log(||theta_mem||^2 / ||theta_post||^2)), where gamma_eff is the effective contraction rate of the optimizer (gamma_eff = eta * lambda for SGD and gamma_eff >= eta * lambda for AdamW). The upper bound follows from a discrete Lyapunov contraction argument, and the matching lower bound arises from dynamical constraints of regularized first-order optimization. Across 293 training runs spanning modular addition, modular multiplication, and sparse parity tasks, we confirm three predictions: inverse scaling with weight decay, inverse scaling with learning rate, and logarithmic dependence on the norm ratio (R^2 > 0.97). We further find that grokking requires an optimizer that can decouple memorization from contraction: SGD fails under hyperparameters where AdamW reliably groks. These results show that grokking is a predictable consequence of norm separation between competing interpolating representations and provide the first quantitative scaling law for the delay of grokking.

Truong Xuan Khanh, Truong Quynh Hoa, Luu Duc Trung et al.

Grokking -- delayed generalisation long after memorisation -- lacks a predictive mechanistic explanation. We identify the normalised spectral entropy $\tilde{H}(t)$ of the representation covariance as a scalar order parameter for this transition, validated on 1-layer Transformers on group-theoretic tasks. Five contributions: (i) Grokking follows a two-phase pattern: norm expansion then entropy collapse. (ii) $\tilde{H}$ crosses a stable threshold $\tilde{H}^* \approx 0.61$ before generalisation in 100% of runs (mean lead: 1,020 steps). (iii) A causal intervention preventing collapse delays grokking by +5,020 steps ($p=0.044$); a norm-matched control ($n=30$, $p=5\times10^{-5}$) confirms entropy -- not norm -- drives the transition. (iv) A power-law $ΔT = C_1(\tilde{H}-\tilde{H}^*)^γ+C_2$ ($R^2=0.543$) predicts grokking onset with 4.1% error. (v) The mechanism holds across abelian ($\mathbb{Z}/97\mathbb{Z}$) and non-abelian ($S_5$) groups. Crucially, MLPs show entropy collapse without grokking, proving collapse is necessary but not sufficient -- architecture matters. Code: https://anonymous.4open.science/r/grokking-entropy

Truong Xuan Khanh, Truong Quynh Hoa

Neural networks often rely on spurious shortcuts for many epochs before discovering structured representations. However, the mechanism governing when this transition occurs and whether its timing can be predicted remains unclear. Prior work shows that gradient descent converges to low norm solutions and that neural networks exhibit simplicity bias, but neither explains the timescale of the transition from shortcut features to structured representations. We introduce the Norm-Hierarchy Transition (NHT) framework, which explains delayed representation learning as the slow traversal of a hierarchy of parameter norms during regularized optimization. When multiple interpolating solutions exist with different norms, weight decay gradually moves the model from high norm shortcut solutions toward lower norm structured representations. We derive a tight bound showing that the transition delay grows logarithmically with the ratio between shortcut and structured norms. Experiments on modular arithmetic, CIFAR-10 with spurious features, CelebA, and Waterbirds support the predictions of the framework. The results suggest that grokking, shortcut learning, and delayed feature discovery arise from a common mechanism based on norm hierarchy traversal during training.

Truong Xuan Khanh, Truong Quynh Hoa

Intelligent systems are widely assumed to improve through learning, coordination, and optimization. However, across domains -- from artificial intelligence to economic institutions and biological evolution -- increasing intelligence often precipitates paradoxical degradation: systems become rigid, lose adaptability, and fail unexpectedly. We identify \emph{entropy collapse} as a universal dynamical failure mode arising when feedback amplification outpaces bounded novelty regeneration. Under minimal domain-agnostic assumptions, we show that intelligent systems undergo a sharp transition from high-entropy adaptive regimes to low-entropy collapsed regimes. Collapse is formalized as convergence toward a stable low-entropy manifold, not a zero-entropy state, implying a contraction of effective adaptive dimensionality rather than loss of activity or scale. We analytically establish critical thresholds, dynamical irreversibility, and attractor structure and demonstrate universality across update mechanisms through minimal simulations. This framework unifies diverse phenomena -- model collapse in AI, institutional sclerosis in economics, and genetic bottlenecks in evolution -- as manifestations of the same underlying process. By reframing collapse as a structural cost of intelligence, our results clarify why late-stage interventions systematically fail and motivate entropy-aware design principles for sustaining long-term adaptability in intelligent systems. \noindent\textbf{Keywords:} entropy collapse; intelligent systems; feedback amplification; phase transitions; effective dimensionality; complex systems; model collapse; institutional sclerosis