arXiv subjects

Artus Krohn-Grimberghe

Publications and source records attributed to Artus Krohn-Grimberghe.

8 recordsLinked to original sources

arXiv2026

Certified exact identification of the I3322 quantum value

We determine the quantum value of the three-setting, two-outcome Bell functional I3322. The value is the unique intersection $q_\dagger$ of an analytic A-high stable curve of the exact Jacobi characteristic map with a central reverser curve. A computer-assisted proof isolates this intersection in a rational interval of width $10^{-55}$, beginning 0.2508753845139765356173366109459512989013219739714764755. We prove that the supremum over finite-dimensional tensor-product strategies, the unrestricted spatial value and the commuting-operator value all equal $q_\dagger$. No finite-dimensional strategy attains the value, whereas a normal infinite-dimensional spatial strategy and a commuting GNS strategy do. The proof combines an exact Bellman/path variational reduction, extraction of a positive bilateral calibrated Jacobi fibre from a maximizing weak-star state, a reflected-fibre central-incidence theorem and interval certificates for the unique stable/central intersection. A separate operator-positive three-remainder decomposition gives the commuting upper bound. The complete verification record is archived at DOI 10.5281/zenodo.22160086.

quant-ph↗

arXiv2026

Exact certification of a positive-order Rényi additivity violation for an explicit channel pair

Cubitt, Harrow, Leung, Montanaro, and Winter (CHLMW) exhibited an explicit pair of quantum channels whose minimum output Rényi entropy is nonadditive at order zero, and reported numerical violations at positive orders close to zero. Their paper states that a semidefinite-programming argument yields a rigorous positive-order interval for the same example, without printing the endpoint or a verifiable certificate; a recent paper by Leung, Lovitz, and Wu records that for this pair "no rigorous endpoint was obtained". We close that gap for the trace-preserving normalization of the printed pair fixed in Section 2. Small rational witness matrices prove that every output of either channel has all eigenvalues between $301/100000$ and $2/3$; a single explicit entangled input has an exact rational joint output spectrum of rank eight; and two independent elementary interval arguments turn these three facts into a proof of strict additivity violation, $S_p^{\min}(\mathrm{N}_R\otimes\mathrm{N}_{\bar S}) < S_p^{\min}(\mathrm{N}_R)+S_p^{\min}(\mathrm{N}_{\bar S}),$ for every real order $0<p\le 1/22$. Every step of the verification reduces to comparisons of integers, and the complete certificate is a few small rational matrices that a reader can check with a short program -- or, for any single order, by hand. To our knowledge, consistent with the assessment of Leung, Lovitz, and Wu, this is the first printed, computer-verifiable certified positive-order endpoint for this explicit pair. We claim no novelty for the phenomenon or for the eigenvalue-floor mechanism, both due to CHLMW, and no optimality of the endpoint.

quant-ph↗

arXiv2026

The entanglement of purification is not additive

The entanglement of purification $E_P$, introduced by Terhal, Horodecki, Leung, and DiVincenzo in 2002, measures the total correlations of a bipartite state by the entanglement needed to purify it; whether it is additive on tensor powers has been open since its introduction. In 2012 Chen and Winter argued "beyond reasonable doubt", from numerical evidence, that the two-qubit Werner state at singlet fraction $f = 1/200$ is a counterexample, and explicitly left a completely rigorous proof to future work. To our knowledge we give the first rigorous proof: for this state $W$, $E_P^\infty(W) \le 0.9663\ldots < 97/100 < E_P(W)$, hence the entanglement of purification is strictly nonadditive at some finite tensor power. The lower bound is a finite certificate: analytic reductions send the Schmidt spectrum of every purification in the complete complex Stiefel domain to a point satisfying explicit necessary inequalities in a three-dimensional box, and an exact-rational subdivision of that box has 25,383 leaves, each of which either excludes nonphysical points or proves the entropy bound. The upper bound combines an exact symmetric-support endpoint, an explicit feasible isometry, and a convexity theorem for the regularized quantity, closed by two directed rational logarithm certificates. Every computer-assisted certificate reduces to integer comparisons; a dependency-free program verifies all of them from the supplementary artifact.

quant-ph↗

arXiv2026

A certified lower bound on the quantum-capacity threshold of the depolarizing channel

The noise threshold below which the qubit depolarizing channel retains positive quantum capacity has been studied since 1996. The classic constructions come with exact finite formulae, but in every reported threshold to date -- most recently the record of Agarwal et al. -- the final step, the sign of the coherent information at the reported point, is a floating-point evaluation. We give the first exact-arithmetic, independently machine-checkable positivity proofs in this regime: an explicit 45-copy rank-two input state $A$, published as a 1,472-byte witness, with certified $I_c > 0$ at the exact rational $p = 16239/250000 = 0.064956$ (per-Pauli convention; total error rate $3p = 0.194868$) -- beyond both the best value printed in the Agarwal et al. paper ($0.064657$) and the strongest state in the same authors' public repository ($\approx 0.064911$), both numerical. Because the depolarizing family is a semigroup under composition, fixed-input coherent information is nonincreasing in $p$ on $[0,1/4]$, so a single certified point extends to the entire interval below it. The same machinery confines the positivity boundaries of $A$ and of the strongest public state of Agarwal et al. to disjoint rational intervals separated by more than $1/25000$ -- to our knowledge the first proven ordering of the positivity boundaries of two explicit competing code states. Every computational claim in the paper reduces to a finite list of big-integer comparisons, checkable by a dependency-free few-hundred-line verifier whose soundness rests on three self-contained half-page lemmas. Payloads, certificates, and verifier accompany the paper as a supplementary artifact.

quant-ph↗

arXiv2026

MedCalc-Bench Doesn't Measure What You Think: A Benchmark Audit and the Case for Open-Book Evaluation

MedCalc-Bench is a widely used benchmark for evaluating LLM performance on clinical calculator tasks, with state-of-the-art direct prompting scores plateauing around 35% on the Verified split (HELM MedHELM leaderboard) and the best published approach-RL with verifiable rewards-reaching 74%. We present three contributions that challenge the benchmark's current framing. First, we conduct a systematic audit of the benchmark's calculator implementations, identifying and fixing over 20 errors ranging from critical formula inaccuracies to runtime bugs in a NeurIPS-published dataset. Second, we show that a simple intervention-providing the model with the calculator specification at inference time ("open-book" prompting)-raises accuracy from ~52% to 81-85% on GLM-4.6V and GLM-4.7, surpassing all published results including RL-trained systems, without any fine-tuning. Third, we establish an upper bound of 95-97% using GPT-5.2-Thinking, with residual errors attributable primarily to ground-truth issues and dataset ambiguities. Our findings suggest that MedCalc-Bench predominantly measures formula memorization and arithmetic precision rather than clinical reasoning, and would be better framed as a tool-use evaluation.

cs.LG↗

arXiv2018

Multi-Stage Reinforcement Learning For Object Detection

We present a reinforcement learning approach for detecting objects within an image. Our approach performs a step-wise deformation of a bounding box with the goal of tightly framing the object. It uses a hierarchical tree-like representation of predefined region candidates, which the agent can zoom in on. This reduces the number of region candidates that must be evaluated so that the agent can afford to compute new feature maps before each step to enhance detection quality. We compare an approach that is based purely on zoom actions with one that is extended by a second refinement stage to fine-tune the bounding box after each zoom step. We also improve the fitting ability by allowing for different aspect ratios of the bounding box. Finally, we propose different reward functions to lead to a better guidance of the agent while following its search trajectories. Experiments indicate that each of these extensions leads to more correct detections. The best performing approach comprises a zoom stage and a refinement stage, uses aspect-ratio modifying actions and is trained using a combination of three different reward metrics.

cs.CV↗

arXiv2017

Facial Key Points Detection using Deep Convolutional Neural Network - NaimishNet

Facial Key Points (FKPs) Detection is an important and challenging problem in the fields of computer vision and machine learning. It involves predicting the co-ordinates of the FKPs, e.g. nose tip, center of eyes, etc, for a given face. In this paper, we propose a LeNet adapted Deep CNN model - NaimishNet, to operate on facial key points data and compare our model's performance against existing state of the art approaches.

cs.CV↗

arXiv2015

AutoCompete: A Framework for Machine Learning Competition

In this paper, we propose AutoCompete, a highly automated machine learning framework for tackling machine learning competitions. This framework has been learned by us, validated and improved over a period of more than two years by participating in online machine learning competitions. It aims at minimizing human interference required to build a first useful predictive model and to assess the practical difficulty of a given machine learning challenge. The proposed system helps in identifying data types, choosing a machine learn- ing model, tuning hyper-parameters, avoiding over-fitting and optimization for a provided evaluation metric. We also observe that the proposed system produces better (or comparable) results with less runtime as compared to other approaches.

stat.ML↗