arXiv subjects

Truong Quynh Hoa

Publications and source records attributed to Truong Quynh Hoa.

8 recordsLinked to original sources

arXiv2026

First-Passage Prediction of Grokking Delay: ACalibrated Law under AdamW with Causal Validation

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.

cs.LG↗

arXiv2026

Spectral Entropy Collapse as a Phase Transition in Delayed Generalisation: An Interventional and Predictive Framework for Grokkin

Grokking - the delayed transition from memorisation to generalisation in neural networks - remains poorly understood. We study this phenomenon through the geometry of learned representations and identify a consistent empirical signature preceding generalisation: collapse of the spectral entropy of the representation covariance matrix. Across modular arithmetic tasks and multiple random seeds, spectral entropy decreases gradually during training and crosses a stable task-specific threshold before test accuracy rises. A representation-mixing intervention that delays this collapse also delays grokking, including under norm-matched controls, indicating that the effect is not explained by parameter norm alone. We further show that the entropy gap predicts the remaining time until grokking with useful out-of-sample accuracy. To probe the structure underlying this transition, we introduce a Fourier-alignment observable for cyclic-group tasks. Entropy collapse is strongly coupled to the emergence of Fourier-aligned representations, suggesting that spectral entropy tracks concentration of the representation into task-structured directions rather than generic compression alone. The same qualitative dynamics appear in non-abelian group composition tasks, while MLP controls show that entropy collapse by itself is insufficient for grokking in the absence of appropriate inductive bias. Taken together, the results support a view of grokking as a representational phase transition with an observable geometric signature. We discuss the scope and limitations of this interpretation, connections to recent feature-learning and spectral-dynamics work, and directions for testing whether similar transitions appear in larger-scale learning systems.

cs.LG↗

arXiv2026

The Norm-Separation Delay Law of Grokking: A First-Principles Theory of Delayed Generalization

Grokking -- the sudden generalisation that appears long after a model has perfectly memorised its training data -- has been widely observed but lacks a quantitative theory explaining the length of the delay. We show that grokking is a norm-driven representational phase transition in regularised training dynamics, and establish the Norm-Separation Delay Law: $T_{\mathrm{grok}} - T_{\mathrm{mem}} = Θ(γ_{\mathrm{eff}}^{-1} \log(\|θ_{\mathrm{mem}}\|^2 / \|θ_{\mathrm{post}}\|^2))$, where $γ_{\mathrm{eff}}$ is the optimiser's effective contraction rate ($γ_{\mathrm{eff}} = ηλ$ for SGD, $γ_{\mathrm{eff}} \ge ηλ$ for AdamW). The upper bound follows from a discrete Lyapunov contraction argument; the matching lower bound from dynamical constraints of regularised first-order optimisation. Across 293 training runs spanning modular addition, modular multiplication, and sparse parity, we confirm three falsifiable predictions: inverse scaling with weight decay ($R^2 = 0.97$), inverse scaling with learning rate ($R^2 = 0.92$), and logarithmic dependence on the norm ratio (Pearson $r = 0.91$). A fourth finding reveals that grokking requires an optimiser capable of decoupling memorisation from contraction: SGD fails entirely at the same hyperparameters where AdamW reliably groks. These results reframe grokking not as a mysterious optimisation artefact but as a predictable consequence of norm separation between competing interpolating representations. We further derive a practical three-input algorithm that predicts grokking delay at memorisation time with 34.6% mean absolute error (bootstrap 95% CI [30.0%, 39.4%], $N=60$ seeds), enabling principled early stopping.

cs.AI↗

arXiv2026

Detecting Neurovascular Instability from Multimodal Physiological Signals Using Wearable-Compatible Edge AI: A Responsible Computational Framework

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

cs.LG↗

arXiv2026

Entropy Collapse: A Universal Failure Mode of Intelligent Systems

A foundational assumption in complex-system collapse studies is that critical transitions are second-order, preceded by early-warning signals like rising autocorrelation, variance, and critical slowing down (Scheffer, 2009). We show this fails for feedback-amplified adaptive systems. We prove entropy collapse - the irreversible contraction of effective state space when feedback amplification alpha exceeds novelty regeneration beta - is a first-order (discontinuous) phase transition. Four exact results: (1) Threshold alpha_c(beta) = 1/(1-beta), from Jacobian spectrum of Multiplicative-Weights operator. (2) Discontinuity: entropy order parameter m = 1 - H_ss/H_max jumps Delta m_0 = 0.698 at alpha_c, with hysteresis Delta H_hyst approx 2.73 nats (lower bound; up to 3.9 nats in simulations); no pre-transition warnings as autocorrelation and variance stay finite. (3) Relaxation exponent nu = 1, from transcritical bifurcation (R^2 = 0.9997 vs. simulation); universality across update mechanisms. (4) Two classes: feedback curvature kappa = f''(1/N) determines order - Class 1 (kappa > 0, convex, e.g., power-law) irreversible with nu = 1; Class 2 (kappa = 0, linear) reversible with nu = 1/2. Theorems validated in neural experiments on two-layer autoregressive transformer (SmallGPT, N=50 vocab, 92 conditions, 8 seeds/condition): Delta H_hyst^NN = 2.92 nats > 2.73 (Theorem 2); nu^NN = 1.14 +/- 0.13, R^2 = 0.977 (Theorem 3). This unifies AI model collapse (Shumailov et al., 2023), economic institutional sclerosis, and evolutionary genetic bottlenecks as first-order entropy-driven processes, evading standard early-warning monitoring.

cs.AI↗

arXiv2026

Norm-Hierarchy Transitions in Representation Learning: When and Why Neural Networks Abandon Shortcuts

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.

cs.LG↗

arXiv2026

Intelligence as Trajectory-Dominant Pareto Optimization

Despite recent advances in artificial intelligence, many systems exhibit stagnation in long-horizon adaptability despite continued performance optimization. This work argues that such limitations do not primarily arise from insufficient learning, data, or model capacity, but from a deeper structural property of how intelligence is optimized over time. We formulate intelligence as a trajectory-level phenomenon governed by multi-objective trade-offs, and introduce Trajectory-Dominant Pareto Optimization, a path-wise generalization of classical Pareto optimality in which dominance is defined over full trajectories. Within this framework, Pareto traps emerge as locally non-dominated regions of trajectory space that nevertheless restrict access to globally superior developmental paths under conservative local optimization. To characterize the rigidity of such constraints, we define the Trap Escape Difficulty Index (TEDI), a composite geometric measure capturing escape distance, structural constraints, and behavioral inertia. We show that dynamic intelligence ceilings arise as inevitable geometric consequences of trajectory-level dominance, independent of learning progress or architectural scale. We further introduce a formal taxonomy of Pareto traps and illustrate the resulting trajectory-level divergence using a minimal agent-environment model. Together, these results shift the locus of intelligence from terminal performance to optimization geometry, providing a principled framework for diagnosing and overcoming long-horizon developmental constraints in adaptive systems.

cs.AI↗

arXiv2026

Dynamic Intelligence Ceilings: Measuring Long-Horizon Limits of Planning and Creativity in Artificial Systems

Recent advances in artificial intelligence have produced systems capable of remarkable performance across a wide range of tasks. These gains, however, are increasingly accompanied by concerns regarding long-horizon developmental behavior, as many systems converge toward repetitive solution patterns rather than sustained growth. We argue that a central limitation of contemporary AI systems lies not in capability per se, but in the premature fixation of their performance frontier. To address this issue, we introduce the concept of a \emph{Dynamic Intelligence Ceiling} (DIC), defined as the highest level of effective intelligence attainable by a system at a given time under its current resources, internal intent, and structural configuration. To make this notion empirically tractable, we propose a trajectory-centric evaluation framework that measures intelligence as a moving frontier rather than a static snapshot. We operationalize DIC using two estimators: the \emph{Progressive Difficulty Ceiling} (PDC), which captures the maximal reliably solvable difficulty under constrained resources, and the \emph{Ceiling Drift Rate} (CDR), which quantifies the temporal evolution of this frontier. These estimators are instantiated through a procedurally generated benchmark that jointly evaluates long-horizon planning and structural creativity within a single controlled environment. Our results reveal a qualitative distinction between systems that deepen exploitation within a fixed solution manifold and those that sustain frontier expansion over time. Importantly, our framework does not posit unbounded intelligence, but reframes limits as dynamic and trajectory-dependent rather than static and prematurely fixed. \vspace{0.5em} \noindent\textbf{Keywords:} AI evaluation, planning and creativity, developmental intelligence, dynamic intelligence ceilings, complex adaptive systems

cs.AI↗