Claude Skills by VectorSpaceLab

Run bounded scaled L-BFGS optimization with two-loop directions, memory updates, and backtracking safeguards.

Compute L-BFGS search directions with the two-loop inverse-Hessian recursion and scalar scaling.

Compute Algorithm 1 PINN loss weights from NTK trace ratios with degeneracy checks and diagnostics.

Compute PINN neural tangent kernel block traces, eigenvalue summaries, and dominance diagnostics from empirical Jacobians.

Build deterministic PINN residual problem fixtures with boundary and PDE residual targets for NTK recovery experiments.

Run bounded proxy PINN training comparisons that exercise residual construction, NTK weighting, and optimizer updates.

Compute Burgers-style PINN residual values and derivative diagnostics from differentiable or analytic surrogate predictions.

Define auditable PINN PDE recovery items with separate observations, collocation points, coefficients, provenance, and target metadata.

Convert PINN traces into numeric proxy metrics and mechanism checks for validator-ready recovery evidence.

Combine PINN supervised and residual losses and execute bounded optimizer updates with validator-compatible traces.

Compares curvature metrics across architecture-style variants and records qualitative sharper/flatter conclusions.

Defines model, loss, parameter, gradient, and Hessian-vector product contracts for PyHessian-style curvature analysis.

Packages reduced recovery evidence, source-boundary checks, mechanism checks, metrics, and validation-ready logs.

Builds a Lanczos tridiagonal matrix from HVP calls and extracts eigenvalue-weight pairs as a compact ESD proxy.

Implements power iteration and Hutchinson trace estimation over an HVP oracle for fast curvature summaries.

Solve regularized PSD systems with randomized Nyström preconditioned conjugate gradients and log convergence evidence.

Build and apply the inverse action of the Nyström preconditioner for regularized PSD linear systems.

Compute a stable randomized Nyström PSD low-rank eigendecomposition from a dense PSD matrix or matrix-vector product interface.

Compute effective dimension, choose a bounded Nyström rank, and evaluate recovery traces for condition-number and PCG iteration improvements.

Maintain and sample Go-Explore archive entries using score, length, and exploration metadata.

Build stable Go-Explore archive cell keys from structured or grid observations for bounded recovery experiments.

Execute a bounded Go-Explore return-then-explore Phase 1 loop in resettable sparse-reward environments.

Evaluate Go-Explore archived trajectories with deterministic replay and bounded perturbation checks for recovery evidence.

Evaluate Integrated Gradients experiments against completeness, sensitivity, implementation invariance, and symmetry axioms.

Build and validate absence baselines and straight-line interpolation paths for Integrated Gradients recovery experiments.

Compute Integrated Gradients with Riemann-summed path gradients and completeness diagnostics for attribution recovery.

Validate a Jump-Start Reinforcement Learning guide-policy interface and better-than-random progress assumptions before using it for roll-in.

Evaluate Jump-Start Reinforcement Learning recovery evidence with mechanism checks for guide roll-in, curriculum handoff, value update, and proxy metric validity.

Build Jump-Start Reinforcement Learning rollouts that switch from guide-policy control to exploration-policy control under curriculum or random guide-step schedules.

Apply a minimal value-based exploration-policy update to Jump-Start Reinforcement Learning trajectories and record optimizer evidence.

Execute a reduced PPO actor-critic update with clipped surrogate, value loss, and optimizer-step evidence.

Compute and validate PPO clipped probability-ratio surrogate objectives and trust-region-style diagnostics.

Validate reduced PPO recovery evidence with mechanism checks, source-boundary checks, and pass-rate metrics.

Compute PPO fixed-segment rollout returns and generalized advantage estimates with auditable terminal handling.

Compute Random Network Distillation novelty bonuses from frozen deterministic target features and trainable predictor mean-squared error.

Compute separate extrinsic and intrinsic return streams for Random Network Distillation dual-value-head policy optimization.

Scale Random Network Distillation intrinsic rewards with running discounted-return statistics for stable exploration bonuses.

Normalize observations for Random Network Distillation with running statistics and clipping before target and predictor feature computation.

Run a bounded Random Network Distillation proxy recovery experiment with executable evidence and generated-skill invocation logs.

Compute Soft Actor-Critic maximum-entropy value and actor objective terms for bounded recovery experiments.

Build and sample validated off-policy replay batches for Soft Actor-Critic recovery harnesses.

Score reduced Soft Actor-Critic recovery traces for mechanism fidelity and source boundary compliance.

Execute one deterministic reduced Soft Actor-Critic critic actor and target update for recovery evidence.

Run a bounded actor-critic Self-Imitation Learning update and log trainable parameter evidence.

Compute Self-Imitation Learning policy and value losses using the paper's positive-advantage gate.

Validate Self-Imitation Learning recovery evidence for source boundaries, executable metrics, and mechanism-faithful proxy checks.

Build Self-Imitation Learning replay records by converting completed agent episodes into discounted state-action-return tuples.

Allocate high-priority traffic first and iteratively increase low-priority shaper rates while residual estimated capacity permits objective improvement.

Estimate overlay load and safe available bandwidth from existing delay or packet-loss measurements using M/M/1/K equations.

Represent flow groups, overlay links, priorities, SLA thresholds, and per-flow measurements for QoS optimization experiments.