arXiv subjects

Rubén Darío Guerrero

Publications and source records attributed to Rubén Darío Guerrero.

10 recordsLinked to original sources

arXiv2026

Directions That Don't Drift: Stiefel Manifold Routing for Transformer Attention

The query and key projections $\WQ,\WK$ in attention are almost always trained by Euclidean optimizers with no geometric constraint. We constrain them to the Stiefel manifold and optimize with a Riemannian Adam carrying one scalar second moment per frame---the form of \citet{becigneul2019}, here extended to the compact, non-Hadamard $\St(d,r)$ with a tangent projector, step-norm cap, and polar retraction. Four propositions prove steepest descent in the embedded metric, gradient-scale independence, well-conditioning, and exact $\mathrm{O}(d)$-equivariance. A fifth records that weight decay has \emph{identically zero} Riemannian gradient on $\St(d,r)$ ($W{=}WI_r$ lies in the normal space), so decay cannot act on the constrained frames. On a CIFAR-10 patch benchmark at $n{=}10\mathrm{k}$ this rule gains $\mathbf{+6.79}$\,pp over AdamW across 12 paired starts ($t{=}38.33$, $12/12$); earlier fixed-step Riemannian SGD gains $+1.97$\,pp, of which $+1.69$\,pp comes from frozen orthonormal initialization alone. The corrected Adam's lead grows with data: $+1.9$\,pp at $n{=}1\mathrm{k}$ to $+6.7$\,pp at $n{=}50\mathrm{k}$. A 12-seed ablation credits all gain to the scale-free step ($+4.63$\,pp, $12/12$), nothing to the projector or equivariance; a targeted $\varepsilon$-sweep causally confirms the mechanism ($-2.6$\,pp at $\varepsilon{=}0.1$, $p{<}0.001$). Two five-seed grokking studies confirm the constrained arm does not grok better than the baseline ($p{=}0.019$, A2 wins): the weight-decay exemption has no grokking consequence. A single-seed pilot exploiting this localization achieves the first stable grokking under slingshot conditions---Stiefel + targeted circuit regularization keeps routing-frame isometry error $10^6\times$ lower than the unconstrained ablation through every collapse.

cs.LG↗

arXiv2026

Analytic Gradients and Nonadiabatic Couplings for Device-Resident DMRG-QD-NEVPT2 Through Conical Intersections on a Consumer GPU

Nonadiabatic dynamics through a conical intersection requires both static and dynamic correlation and, at every geometry, an excited-state gradient and interstate nonadiabatic coupling (NACME). Analytic multireference derivatives at this level have been confined to datacenter-scale hardware. We report device-resident \mbox{DMRG-QD-NEVPT2} with analytic gradients and NACMEs within the $8$\,GB of a consumer GPU: a density-matrix-renormalization-group (DMRG) active-space reference supplies the static correlation, and quasi-degenerate SC-NEVPT2 dresses it through a multi-state effective Hamiltonian that remains valid \emph{through} a conical intersection, where single-state perturbation theory develops a vanishing denominator and fails. Every gradient and NACME is one reverse-mode transpose of a single contraction graph: the DMRG sweep enters as a gauge-free differentiable node, and all two-electron work is AO-direct through Cholesky factors. The DMRG reference is exact within the active space ($\sim\!10^{-15}$\,Ha). The corrected adiabats close smoothly to a real $S_0/S_1$ conical intersection with a non-vanishing, $1/ΔE$-divergent NACME---where linear-response TDDFT returns zero identically---and the dressing restores the differential dynamic correlation that ionic $ππ^*$ states require. DMRG-NEVPT2 and quasi-degenerate NEVPT2 are each established; what is new is the combined stack---multi-state and through a conical intersection, with analytic gradients and couplings---realized device-resident on commodity hardware.

physics.chem-ph↗

arXiv2026

Density-Functional Excited-State Gradients and Nonadiabatic Couplings on a Consumer GPU from a Contraction-DAG

Nonadiabatic dynamics needs an excited-state gradient and an interstate nonadiabatic coupling matrix element (NACME) at every nuclear geometry, and a double-hybrid functional's accuracy has been unavailable for the coupling. We report the first analytic derivative NACME for a double-hybrid excited state---deferred in the original hh-TDA method and supplied for hybrids only by Yu \emph{et al.}---derived, with the hole-hole and particle-particle Tamm--Dancoff (\hhTDA/\ppTDA) gradients and NACMEs, as a single reverse-mode transpose of one contraction graph closed under a non-symmetric atomic-orbital-direct $J/K$ kernel. Its double-hybrid excitation energy lowers the vertical-excitation mean absolute deviation from bare-\hhTDA\ $0.86$ to $0.47$~eV and removes the $+0.53\!\rightarrow\!+0.05$~eV over-excitation bias, improving seven of ten states while over-correcting the ionic $ππ^*$ states---the expected perturbative-doubles failure, reported not trimmed. Every coupling is validated to $\sim\!10^{-4}$ against an independent \emph{literal many-electron wavefunction-overlap} oracle that shares no code path with the method, and is physically meaningful at the ammonia $n\!\rightarrow\!σ^*$ \emph{covalent} conical intersection, where the \hhTDA/\ppTDA manifolds recover the $F\!-\!2$ seam and adiabatic linear-response TDDFT gives $τ\!\equiv\!0$ by construction. Gradients, NACMEs, and the double-hybrid coupling all run device-resident and AO-direct through one shared Cholesky-decomposed $J/K$ engine within the 8\,GB of a consumer RTX~4060 (a profile-guided $\sim\!10^2\times$ launch collapse preserving double-precision bit-identity)---placing on a commodity desktop card a correlated excited-state derivative capability that has until now required datacenter hardware.

physics.chem-ph↗

arXiv2026

EOM-CC Excited-State Gradients and Nonadiabatic Couplings on a Consumer GPU from a Contraction-DAG with Laplace-Transform J/K Kernels

We present a unified, memory-bounded GPU realization of equation-of-motion coupled-cluster (EOM-CC) excited-state gradients and interstate nonadiabatic couplings (NACMEs) on a single 8\,GB consumer GPU. Both are built from one contraction directed acyclic graph: the EOM-CC relaxation is the reverse-mode transpose of the forward density build rather than a per-state re-derivation, and an atomic-orbital-direct Laplace-transform $J/K$ kernel, made non-symmetric ($J^x(A,B)\neq J^x(B,A)$) by the transition densities, resolves every energy denominator with no four-index molecular-orbital tensor; a two-sided Davidson returns both eigenvectors from one device-resident, spin-pure solve. The pipeline is \emph{validated end to end at small scale}: gradients and NACMEs match finite differences across four spin multiplicities and full configuration interaction to $<\!10^{-12}$ for two electrons, and the excited-state gradient matches the independent \textsc{Psi4} code to $\le\!4.6\times10^{-7}~E_h/a_0$ from \ce{H2O} to aromatic benzene. The kernels and the ground-state solve reach chromophores ($\le\!730$ AO) in 8\,GB, and a frozen-natural-virtual compression lets the eigensolver \emph{execute} a complete excited-state gradient and $Q$--$B$ NACME of the chlorophyll-core chromophore \ce{Mg}-porphine (def2-SVP, $439$ AO) on the card. We present that run as a \emph{capability demonstration} -- executed and translationally invariant to machine zero, but anchored only piece-wise and bounded by a direct convergence study at ${\sim}10^{-2}~E_h/a_0$ -- not a converged spectroscopic result. The validated small-scale capability and the memory-bounded implementation are the contribution.

physics.chem-ph↗

arXiv2026

Game-Theoretic Discovery of Quantum Error-Correcting Codes Through Nash Equilibria

Quantum error correction code discovery has relied on algebraic constructions with predetermined structure or computational search lacking equilibrium-topology analysis. We introduce a game-theoretic framework recasting code optimization as strategic interactions between competing objectives, where Nash equilibria systematically generate codes with desired properties. We validate the framework by demonstrating it rediscovers the optimal $[\![15,7,3]\!]$ quantum Hamming code in 20\% of independent runs (Calderbank-Shor-Steane 1996) from competing objectives without predetermined algebraic structure, with equilibrium analysis providing transparent mechanistic insights into why this topology emerges. Applied across seven objectives -- distance maximization, hardware adaptation, rate-distance optimization, cluster-state generation, surface-like topologies, connectivity enhancement, and maximization of the quantum Fisher information $\mathcal{F}_Q$ (which quantifies, via the Cramér--Rao bound, the metrological sensitivity of the encoded codespace) -- the framework generates distinct code families through objective reconfiguration rather than algorithm redesign. Scalability to hardware-relevant sizes is demonstrated at $n=100$ qubits, discovering codes including $[\![100,50,4]\!]$ with distance-4 protection and 50\% encoding rate, with tractable $O(n^3)$ per-iteration complexity enabling discovery in under one hour. This work opens research avenues at the intersection of game theory and quantum information, providing systematic, interpretable frameworks for quantum system design.

quant-ph↗

arXiv2026

Bond-dimension scaling of a local-refinement advantage over hyperoptimized tensor-network contraction on Sycamore like topologies

We identify a missing local-refinement stage in the cotengra tensor-network contraction pipeline and show that its impact grows monotonically with bond dimension on the \emph{connectivity graph} of Sycamore-like topologies. Appending a nearest-neighbor interchange (NNI) search to the \cotengra{} output at matched 8-s wallclock yields a median \emph{predicted} cost-model gap $Δ\fT$ at $n{=}500$ that grows monotonically and approximately linearly in $χ$, from $\sim\!15$~bits at $χ{=}2$ to $\sim\!116$~bits at $χ{=}16$ (Fig.~\ref{fig:chi_sweep}), with the refiner winning on $25/25$ seeds at every tested $χ$. Two control families -- random $3$-regular and QAOA $p{=}2$ interaction graphs -- show median $|Δ\fT| \leq 0.71$~bits across both controls at every $χ$, with refiner win rate falling toward chance as $χ$ grows; the signal is topology-specific, not a generic refinement-budget effect. An ablation establishes that refinement itself, not the four-axis Pareto acceptance rule, drives the gain ($|Δ\fT| \lesssim 0.1$ bits between scalar and Pareto arms at $χ{=}2$). The Sycamore-circuit envelope (App.~\ref{em:sec:results:syccirc}) reports the corresponding refinement on actual random circuits at depths $m \in \{4, 6, 8, 10, 12\}$, where the refiner wins on $5/5$ instances at every depth. The advantage is therefore largest precisely in the bond-dimension regime relevant to physical contraction.

quant-ph↗

arXiv2026

A four-player potential game for barren-plateau-aware quantum ansatz design

We cast the design of parameterized quantum circuits as a four-player potential game whose state is a circuit directed acyclic graph (DAG) and whose players encode trainability, non-stabilizerness, task performance, and hardware cost. Per-player restricted action sets factorize the move space into append, remove, retype, and rewire operations; a block-coordinate $\varepsilon$-Nash residual $δ_\text{Nash}$ certifies that no single player can improve unilaterally. A single weight sweep on MaxCut $K_4$ traces a Pareto frontier from a Clifford endpoint $(M_2/n,\langle H\rangle)=(0,4.00)$ to a non-Clifford endpoint $(0.48,3.30)$. On three four-qubit hardware topologies (heavy-hex, $2\times 2$ grid, Rydberg all-to-all), Nash search achieves the highest mean potential; on the $2\times 2$ grid Nash reaches the theoretical ceiling $Φ_\text{max}=4.10$ on two of five seeds while the simulated-annealing baseline does so on one; paired Wilcoxon tests over five seeds cannot reject the null on any single topology ($p\ge 0.22$). On LiH/STO-3G, seeding Nash from a 58-gate Givens-doubles ansatz produces a 48-operation, depth-25 circuit retaining $97.7\%$ of the correlation energy while simultaneously reducing gate count, increasing non-stabilizerness, and controlling trainability. The framework is complementary to energy-only searches such as ADAPT-VQE and k-UpCCGSD, which reach chemical accuracy with fewer operations but do not optimize the other three axes.

quant-ph↗

arXiv2026

RECURSUM: Automated Code Generation for Recurrence Relations Exceeds Expert Optimization via LayeredCodegen

Automated code generation can systematically exceed expert hand-optimization for recurrence relations-computational primitives ubiquitous in orthogonal polynomials, special functions, numerical integration, and molecular integral evaluation. We present RECURSUM, a Python-based domain-specific language generating optimized C++ for arbitrary recurrence relations via three backends: template metaprogramming for compile-time evaluation, a novel LayeredCodegen backend with architectural optimizations, and runtime loop-based evaluation. The DSL uses einsum-inspired notation to specify recurrences, validity constraints, and base cases in 10-30 lines of Python, generating 650+ lines of production C++. LayeredCodegen achieves 9.8x speedup over expert hand-written implementations and 1.9x over template metaprogramming for McMurchie-Davidson Hermite coefficients. Architecture analysis reveals three quantifiable effects: (1) zero-copy output parameters eliminate return-by-value overhead (70-80% of speedup), (2) guaranteed function inlining eliminates compiler-refused overhead (15-20%), (3) exact-sized stack buffers achieve 100% cache efficiency vs 27% for MAX-sized arrays (5-10%). We validate on 24 recurrence types spanning pure mathematics (Legendre, Chebyshev, Hermite, Laguerre polynomials), numerical analysis (Clenshaw, Golub-Welsch), and quantum chemistry (McMurchie-Davidson, Rys quadrature, Boys function). Production benchmarks show speedups propagate to complete algorithms, with generated code matching expert baselines within 3.3%. RECURSUM demonstrates that systematic code generation serves as the performance ceiling for recurrence algorithms. By eliminating the dual expertise barrier (domain knowledge + C++ metaprogramming), the framework democratizes high-performance scientific computing-establishing a paradigm where automated generation systematically exceeds manual optimization.

cs.PL↗

arXiv2025

Physics-Constrained Adaptive Neural Networks Enable Real-Time Semiconductor Manufacturing Optimization with Minimal Training Data

The semiconductor industry faces a computational crisis in extreme ultraviolet (EUV) lithography optimization, where traditional methods consume billions of CPU hours while failing to achieve sub-nanometer precision. We present a physics-constrained adaptive learning framework that automatically calibrates electromagnetic approximations through learnable parameters $\boldsymbolθ = \{θ_d, θ_a, θ_b, θ_p, θ_c\}$ while simultaneously minimizing Edge Placement Error (EPE) between simulated aerial images and target photomasks. The framework integrates differentiable modules for Fresnel diffraction, material absorption, optical point spread function blur, phase-shift effects, and contrast modulation with direct geometric pattern matching objectives, enabling cross-geometry generalization with minimal training data. Through physics-constrained learning on 15 representative patterns spanning current production to future research nodes, we demonstrate consistent sub-nanometer EPE performance (0.664-2.536 nm range) using only 50 training samples per pattern. Adaptive physics learning achieves an average improvement of 69.9\% over CNN baselines without physics constraints, with a significant inference speedup over rigorous electromagnetic solvers after training completion. This approach requires 90\% fewer training samples through cross-geometry generalization compared to pattern-specific CNN training approaches. This work establishes physics-constrained adaptive learning as a foundational methodology for real-time semiconductor manufacturing optimization, addressing the critical gap between academic physics-informed neural networks and industrial deployment requirements through joint physics calibration and manufacturing precision objectives.

cs.LG↗

arXiv2024

Bee-yond the Plateau: Training QNNs with Swarm Algorithms

In the quest to harness the power of quantum computing, training quantum neural networks (QNNs) presents a formidable challenge. This study introduces an innovative approach, integrating the Bees Optimization Algorithm (BOA) to overcome one of the most significant hurdles -- barren plateaus. Our experiments across varying qubit counts and circuit depths demonstrate the BOA's superior performance compared to the Adam algorithm. Notably, BOA achieves faster convergence, higher accuracy, and greater computational efficiency. This study confirms BOA's potential in enhancing the applicability of QNNs in complex quantum computations.

quant-ph↗