arXiv subjects

Abdeljalil Sakat

Publications and source records attributed to Abdeljalil Sakat.

5 recordsLinked to original sources

arXiv2026

Fresh at Decision, Stale at Action: Routing New Information to LLM Decisions Already Made

Freshness shapes an LLM decision at the moment it is made; the action it commits to is latent, carried out later, in a changing world. We therefore introduce a timestamp theory of decision validity and a decision ledger that realises it. Six timestamps define a decision; a freshness ceiling bounds what up-to-date evidence guarantees at action time, placing the remaining risk in information published afterwards. Accuracy then factorises into two capabilities: routing, which delivers that information to affected decisions before their revision deadlines, and temporal judgment, which reads it for the time of action. The ledger is persistent state holding each decision's times, evidence and background knowledge, indexed by watch conditions written at decision time. Controlled decision streams with exact labels confirm four predictions across five LLMs, from 8B to frontier scale: freshness alone yields exactly the accuracy the ceiling predicts; models act on decisive news once it arrives, so accuracy follows routing; the ledger's index sets what routing reaches, and watch conditions reach indirect dependencies at low exposure; and the remaining errors concern when a change takes effect. Freshness makes a decision right when it is made; routing and temporal judgment keep it right when it is carried out.

cs.AI↗

arXiv2026

Reference-free logged energy-oracle recovery for neural approximations of symmetric coercive variational problems: conforming Riesz reconstruction and archive-level selection

Neural PDE training yields a finite checkpoint archive, yet its logged energy errors are inaccessible without the exact solution, while loss-based selection does not necessarily recover the logged energy oracle. For admissible neural approximations of symmetric coercive variational problems, we introduce a reference-free selection rule based on minimizing a computable conforming Riesz monitor. The exact residual-energy identity and conforming projection make the monitor an unconditional lower bound converging monotonically to each logged energy error under nested conforming refinement; under saturation, hierarchical enrichment yields a computable upper estimate and hence a lower-upper bracket. A key finding is that archive selection is order-sensitive: unresolved checkpoint-dependent components can reverse the oracle-non-oracle ranking at finite resolution, so checkpointwise recovery alone is insufficient. For finite archives, we prove uniform recovery, yielding convergence to the logged-oracle error and, without saturation, logged-oracle selection at sufficiently fine auxiliary resolution. Under saturation, the bracket gives a computable near-oracle bound and certifies unique logged-oracle selection upon interval separation. We also bound logging-resolution loss and certify oracle inclusion over prescribed comparison trajectories. The resulting criterion replaces inaccessible exact-error minimization by computable, training-independent post-training selection on the intrinsic energy-error scale, requiring only the computed candidates and the variational problem. Experiments on diffusion and elasticity, including a non-manufactured perforated plate, demonstrate energy-scale calibration, oracle-level selection, and modest post-processing cost.

cs.LG↗

arXiv2026

Intrinsic perturbation scale for certified oracle objectives with epigraphic information

We introduce a natural displacement control for minimizer sets of oracle objectives equipped with certified epigraphic information. Formally, we replace the usual local uniform value control of objective perturbations - uncertifiable from finite pointwise information without additional structure - by the strictly weaker requirement of a cylinder-localized vertical epigraphic control, naturally provided by certified envelopes. Under set-based quadratic growth (allowing nonunique minimizers), this yields the classical square-root displacement estimate with optimal exponent 1/2, without any extrinsic assumption.

math.OC↗

arXiv2026

A Mosco sufficient condition for intrinsic stability of non-unique convex Empirical Risk Minimization

Empirical risk minimization (ERM) stability is usually studied via single-valued outputs, while convex non-strict losses yield set-valued minimizers. We identify Painlevé-Kuratowski upper semicontinuity (PK-u.s.c.) as the intrinsic stability notion for the ERM solution correspondence (set-level Hadamard well-posedness) and a prerequisite to interpret stability of selections. We then characterize a minimal non-degenerate qualitative regime: Mosco-consistent perturbations and locally bounded minimizers imply PK-u.s.c., minimal-value continuity, and consistency of vanishing-gap near-minimizers. Quadratic growth yields explicit quantitative deviation bounds.

cs.LG↗

arXiv2025

KD-PINN: Knowledge-Distilled PINNs for ultra-low-latency real-time neural PDE solvers

This work introduces Knowledge-Distilled Physics-Informed Neural Networks (KD-PINN), a framework that transfers the predictive accuracy of a high-capacity teacher model to a compact student through a continuous adaptation of the Kullback-Leibler divergence. In order to confirm its generality for various dynamics and dimensionalities, the framework is evaluated on a representative set of partial differential equations (PDEs). Across the considered benchmarks, the student model achieves inference speedups ranging from x4.8 (Navier-Stokes) to x6.9 (Burgers), while preserving accuracy. Accuracy is improved by on the order of 1% when the model is properly tuned. The distillation process also revealed a regularizing effect. With an average inference latency of 5.3 ms on CPU, the distilled models enter the ultra-low-latency real-time regime defined by sub-10 ms performance. Finally, this study examines how knowledge distillation reduces inference latency in PINNs, to contribute to the development of accurate ultra-low-latency neural PDE solvers.

cs.LG↗