arXiv subjects

Sebastian Pokutta

Publications and source records attributed to Sebastian Pokutta.

At least 19 recordsLinked to original sources

arXiv2026

Unified Toolbox for Multipartite Entanglement Certification

We present a unified framework for multipartite entanglement characterization based on the conditional gradient (CG) method, incorporating both fast heuristic detection and rigorous witness construction with numerical error control. Our method enables entanglement certification in quantum systems of up to ten qubits and applies to arbitrary entanglement structures. We demonstrate its power by closing the gap between entanglement and separability bounds in white-noise robustness benchmarks for a class of bound entangled states. Furthermore, the framework extends to entanglement robustness under general quantum noise channels, providing accurate thresholds in cases beyond the reach of previous algorithmic methods. These results position CG methods as a powerful tool for practical and scalable entanglement analysis in realistic experimental settings.

quant-ph↗

arXiv2026

Measuring Model-Specific Alignment Drift in LLM-Based Opinion Dynamics

Large language model (LLM) agents are increasingly used as synthetic participants in opinion-dynamics experiments, often assuming that an agent's behaviour is fully determined by its prompt. We test this assumption with a framework in which LLM agents discuss a contested policy issue over repeated rounds while their stance is quantified by a fixed psychometric instrument independent of any dynamics model. Across six LLMs, committed personas are intrinsically stable: in each of the five models tested without peer input, every agent keeps its assigned side for 20 rounds. The observed loss of alignment under discussion is therefore interaction-induced, we call it alignment drift, and model-specific: gpt-4.1 keeps opinion clusters apart, claude-sonnet-5 holds them partially, and gpt-5.6-sol and claude-opus-5 abandon them. Under selective attention, one LLM maintains separated opinion clusters under stance-homophilous attention. Qualitative profiles persist at doubled population and horizon and on a second issue. Such heterogeneity makes the LLM choice a first-class validity variable for social simulation.

cs.AI↗

arXiv2026

Tensor Decomposition for Non-Clifford Gate Minimization

Fault-tolerant quantum computation requires substantial resources for non-Clifford gates. Their count also enters exponentially into the runtime of several classical simulation methods. We present algebraic methods for minimizing the non-Clifford CCZ (Toffoli) count in {CNOT,CCZ} phase circuits using tensor decomposition over $\mathbb{F}_2$. On standard cubic benchmarks, these methods match or improve prior automated Toffoli counts, with most instances optimized in under a minute on a single CPU. With additional computation, the decompositions provide effective initializations for existing T-count methods, improving T counts on several circuits. We also present algebraic methods for CNOT-count optimization at fixed Toffoli count. This gives competitive ancilla-free finite-field multiplication circuits and reduces the CNOT count of XOR AES S-box circuits.

quant-ph↗

arXiv2026

The KV-Surgeon: Compensation-Aware Offline KV-Cache Compaction

Offline compaction of the key--value cache (KV-cache) reduces the cost of repeatedly querying a fixed context by constructing a smaller cache once and reusing it subsequently. The central challenge of compaction is deciding which cache entries to delete and which to retain. Existing methods score each candidate for deletion on its own, with the rest of the cache being held fixed. However, softmax renormalization of the attention operation couples these decisions in a nonlinear manner: removing one entry changes the attention weights of every remaining one. In this work, we introduce KV-Surgeon, which uses calibration data to take interactions into account in a tractable way. We derive a quadratic surrogate that admits closed-form expressions for jointly making the optimal greedy removal decision as well as compensation within the remaining entries. On QuALITY, LongHealth, and Long Code Arena, and at every evaluated compaction ratio, KV-Surgeon substantially advances the cost--accuracy Pareto frontier of dense and mixture-of-experts models from 4B to 30B parameters. At $50\times$ compaction, KV-Surgeon improves question-answering accuracy by up to four points over attention matching (Zweiger et al., 2026), the state of the art, at comparable cost. Lastly, we introduce an even faster variant, which also exceeds the state of the art while requiring only two fifths of its cost.

cs.LG↗

arXiv2026

AlphaDiana: A Measurement System for Agents in Verifiable Reasoning Tasks

Agents pair reasoning models with harnesses that organize model calls, execute tools, load skill instructions, and retain history in memory. Understanding agent performance requires linking execution conditions to outcomes, behavior, and resource use. We introduce AlphaDiana, a measurement system with modular interfaces for datasets, agents, environments, and scorers. It preserves harness-native control loops while controlling file reuse and memory retention separately. AlphaDiana supports macro analyses of complete agents and micro interventions on agent components such as tools, skills, and memory under matched conditions. We study three open-source models and three open-source harnesses on five answer-based benchmarks, with two models also tested on two interactive benchmarks. We find that harnesses do not consistently improve the accuracy of reasoning: gains on questions unsolved by the model alone can be outweighed by losses on questions it answers correctly without tools. This inconsistency extends to component interventions: neither skill guidance nor retained history reliably improves accuracy. Behavior and output-token use must be assessed with correctness: low token entropy can accompany wrong answers, and less output per execution can mean more output tokens per correct answer when accuracy falls. AlphaDiana links answer correctness and execution status to traces and resource records for comparing agents and diagnosing failures under shared task and resource policies.

cs.AI↗

arXiv2026

From Associations to Activations: Comparing Behavioral and Hidden-State Semantic Geometry in LLMs

We investigate the extent to which an LLM's hidden-state geometry can be recovered from its behavior in psycholinguistic experiments. Across eight instruction-tuned transformer models, we run two experimental paradigms -- similarity-based forced choice and free association -- over a shared 5,000-word vocabulary, collecting 17.5M+ trials to build behavior-based similarity matrices. Using representational similarity analysis, we compare behavioral geometries to layerwise hidden-state similarity and benchmark against FastText, BERT, and cross-model consensus. We find that forced-choice behavior aligns substantially more with hidden-state geometry than free association. In a held-out-words regression, behavioral similarity (especially forced choice) predicts unseen hidden-state similarities beyond lexical baselines and cross-model consensus, indicating that behavior-only measurements retain recoverable information about internal semantic geometry. Finally, we discuss implications for the ability of behavioral tasks to uncover hidden cognitive states.

cs.LG↗

arXiv2026

(Approximate) Symmetric Extension Complexity of the Spanning Tree Polytope

We prove a tight lower bound on symmetric LP formulations for the spanning tree polytope of the complete graph. More precisely, let $P_{ST}(K_n)$ be the spanning tree polytope of $K_n$. We show that, for all $n\ge13$, every symmetric extended formulation for $P_{ST}(K_n)$ has at least $\binom n3$ inequalities. Since the classical Martin formulation has a symmetric formulation of size $O(n^3)$, this gives \[ \operatorname{xcs}(P_{ST}(K_n))=Θ(n^3). \] We also study outer relaxations of the spanning tree polytope of $K_n$ for maximization with nonnegative edge weights. We show that for every fixed approximation factor below $3/2$, symmetric LP formulations still require $Θ(n^3)$ inequalities for all sufficiently large $n$, whereas factor $3/2$ admits a formulation of size $O(n^2)$. Moreover, we provide an exact symmetric SDP formulation of size $O(n^2)$, measured by PSD matrix order, which implies $\operatorname{xc}_{\mathrm{psd}}(P_{ST}(K_n))= Θ(n^2)$. Thus symmetric LP and SDP sizes already differ for exact formulations, and for every fixed approximation factor $1\leβ<3/2$ for all sufficiently large $n$.

math.CO↗

arXiv2026

The exact worst-case asymptotic rate of Nesterov acceleration for strongly convex optimization

We study Nesterov's accelerated gradient method with its standard constant parameters for smooth strongly convex optimization. We characterize the exact worst-case asymptotic factor for the squared distance to the minimizer. To this end, we construct candidate worst-case trajectories by combining planar spirals with a common contraction factor that satisfy a self-similarity condition. Each component rotates by a fixed angle at every iteration. The exact factor is the optimal value of a linear optimization problem over probability measures on a fixed disk, with constraints derived from smooth strongly convex interpolation. Every optimal measure has a common contraction factor, which is also the largest factor for which the angular interpolation conditions are feasible. We also show that this worst-case asymptotic rate can be realized by a \emph{single} function in a finite-dimensional space whose iterates attain this factor. A matching upper bound holds uniformly over all functions in the class and all finite dimensions. Consequently, allowing the function, dimension, and initial point to vary with the iteration horizon does not increase the worst-case asymptotic factor. We also show that the exact factor is $1-4/(3\sqrtκ)+o(κ^{-1/2})$ as $κ\to\infty$, where $κ=L/μ$ is the ratio of the gradient Lipschitz constant to the strong convexity parameter.

math.OC↗

arXiv2026

Lower Bounds for Randomized Linear-Oracle Optimization over Strongly Convex Sets

Recent results [arXiv:2602.04378, arXiv:2602.22608] have established worst-case objective-error lower bounds of order $1/T^2$ after $T$ linear minimization oracle (LMO) calls, matching the upper bound [arXiv:1406.1305] in its dependence on $T$ and thereby resolving a long-standing open question. Upon close inspection, however, both lower bounds are somewhat brittle. The first [arXiv:2602.04378] applies only to the standard Frank--Wolfe algorithm, and, as we show, its prescribed slow exact-line-search trajectories can amplify sufficiently small initialization errors exponentially, corresponding to roughly one additional bit of initialization accuracy per iteration. The second [arXiv:2602.22608] obtains lower bounds for any deterministic LMO-based first-order method via a resisting oracle that adversarially adapts to the queries of the algorithm. In both cases it is conceivable that randomization may circumvent these lower bounds; in particular, neither establishes a lower bound for unrestricted randomized first-order LMO methods. We close this gap by proving an $Ω(L\operatorname{diam}(S)^2/T^2)$ distributional lower bound for randomized first-order linear minimization oracle methods over strongly convex sets. While our construction reuses the family of [arXiv:2602.22608], our proof characterizes the conditional distribution of the hidden permutation after adaptive queries and bounds the expected decrease of a combinatorial statistic controlling optimizer variance. We further show that the same error threshold holds with probability at least $3/4$ and yields a stopping-time tail bound.

math.OC↗

arXiv2026

LinearPFN: Amortized Variable Selection for Linear Models with Interactions

Spike-and-slab regression is a standard Bayesian formulation of variable selection: it returns a posterior distribution over which candidate effects are active rather than a single selected subset, so that every candidate effect carries an inclusion probability. Its cost grows exponentially with the number of candidate effects, so the posterior can be enumerated exactly only when the number of predictors is small. Beyond that reach, the posterior has to be approximated, typically by Markov chain Monte Carlo over the model space, which requires a fresh run for every dataset and, within a fixed budget of steps, may fail to converge. We present LinearPFN, a prior-data fitted transformer network that amortizes spike-and-slab inference for linear models with main effects and pairwise interactions. The network is pretrained once on synthetic datasets, drawn from an explicitly specified prior, and a single forward pass over a new dataset returns posterior inclusion probabilities, posterior-mean coefficients and posterior predictive distributions with no per-dataset fitting. The prior is conjugate by design, so that the posterior for each fixed set of active effects has a closed form, and wherever the exact posterior is still computable by enumeration we verify the network's outputs against it. On real predictor matrices from published social-science datasets, with outcomes drawn from the prior so that the true active set is known, LinearPFN attains a higher per-dataset selection AUC and a higher F1 under the median probability model rule than five classical baselines. The lead holds when the coefficients, the interactions or the noise depart from the prior. Code: https://github.com/schiekiera/LinearPFN. Trained model: https://huggingface.co/schiekiera/LinearPFN.

cs.LG↗

arXiv2026

Better bounds on finite-order Grothendieck constants

Grothendieck constants $K_G(d)$ bound the advantage of $d$-dimensional strategies over $1$-dimensional ones in a specific optimisation task. They have applications ranging from approximation algorithms to quantum nonlocality. However, apart from $d=2$, their values are unknown. Here, we exploit a recent Frank-Wolfe approach to provide good candidates for lower bounding some of these constants. The complete proof relies on solving difficult binary quadratic optimisation problems. For $d\in\{3,4,5\}$, we construct specific rectangular instances that we can solve to certify better bounds than those previously known; by monotonicity, our lower bounds improve on the state of the art for $d\leqslant9$. For $d\in\{4,7,8\}$, we exploit elegant structures to build highly symmetric instances achieving even greater bounds; however, we can only solve them heuristically. We also recall the standard relation with violations of Bell inequalities and elaborate on it to interpret generalised Grothendieck constants $K_G(d\mapsto2)$ as the advantage of complex $d$-dimensional quantum mechanics over real qubit quantum mechanics. Motivated by this connection, we also improve the bounds on $K_G(d\mapsto2)$.

math.OC↗

arXiv2026

Symmetric multipartite Bell inequalities via Frank-Wolfe algorithms

In multipartite Bell scenarios, we study the nonlocality robustness of the Greenberger-Horne-Zeilinger (GHZ) state. When each party performs planar measurements forming a regular polygon, we exploit the symmetry of the resulting correlation tensor to drastically accelerate the computation of (i) a Bell inequality via Frank-Wolfe algorithms, and (ii) the corresponding local bound. The Bell inequalities obtained are facets of the symmetrised local polytope and they give the best known upper bounds on the nonlocality robustness of the GHZ state for three to ten parties. Moreover, for four measurements per party, we generalise our facets and hence show, for any number of parties, an improvement on Mermin's inequality in terms of noise robustness. We also compute the detection efficiency of our inequalities and show that some give rise to activation of nonlocality in star networks, a property that was only shown with an infinite number of measurements.

quant-ph↗

arXiv2026

Improved local models and new Bell inequalities via Frank-Wolfe algorithms

In Bell scenarios with two outcomes per party, we algorithmically consider the two sides of the membership problem for the local polytope: constructing local models and deriving separating hyperplanes, that is, Bell inequalities. We take advantage of the recent developments in so-called Frank-Wolfe algorithms to significantly increase the convergence rate of existing methods. As an application, we study the threshold value for the nonlocality of two-qubit Werner states under projective measurements. Here, we improve on both the upper and lower bounds present in the literature. Importantly, our bounds are entirely analytical; moreover, they yield refined bounds on the value of the Grothendieck constant of order three: $1.4367\leqslant K_G(3)\leqslant1.4546$. We also demonstrate the efficiency of our approach in multipartite Bell scenarios, and present the first local models for all projective measurements with visibilities noticeably higher than the entanglement threshold. We make our entire code accessible as a Julia library called BellPolytopes.jl.

quant-ph↗

arXiv2026

A Unifying Perspective on Descent Directions for Constrained Minimization and Switching Criteria

Descent directions are fundamental to first-order methods for constrained convex optimization. In this work, we provide a unified perspective of these directions as they arise within the projected and conditional gradient methods. We show that the directional derivative of the Euclidean projection of the negative gradient is the steepest feasible descent direction, and induces a natural optimality measure independent of polytope-specific geometric constants. We characterize the properties of the projection of the gradient over the polytope, and show that Frank-Wolfe vertices are essentially the limit of this projection curve. Motivated by these insights, we develop hybrid algorithms that interpolate between projected gradient descent and conditional gradients, using computable switching criteria. The proposed methods achieve linear convergence without relying on the pyramidal width or similar constants. We further show that the number of breakpoints in the projection curve over the simplex and the hypercube is linear in the dimension.

math.OC↗

arXiv2026

Scalable Lindblad Noise Learning via Stochastic Tensor-Network Simulation

Learning dissipation rates in large-scale open quantum systems is a major obstacle for near-term quantum technologies, as existing Lindblad estimation methods are typically limited to small system sizes due to the computational complexity of repeatedly solving the Lindblad equation during optimization. Here, we propose a scalable noise-learning framework for Lindblad dissipation rates that combines a stochastic simulation method, the Tensor Jump Method (TJM), with gradient-free optimization of a least-squares cost-function defined on time series of local-observable expectation values. We demonstrate the approach on two noise models in the Ising model: a site-resolved (local) model, in which independent dissipation rates are learned for each site up to $N_{\mathrm{site}}=16$, and a spatially homogeneous (global) model with only seven parameters, scaled to $N_{\mathrm{site}}=160$ sites.We complement these numerical results with a series of exact, provable guarantees: the Frobenius variance of the TJM density-matrix estimator is shown to equal $(1-\mathrm{Tr}[ρ^2])/N_{\mathrm{traj}}$, an exact purity-based characterization of the stochastic estimation error; the corresponding purity evolution is proven to be monotonically non-increasing for Hermitian jump operators; and, under a finite covariance distance assumption, the standard deviation of the cost-function is shown to decrease with system size, so that fewer trajectories are needed to reach a fixed target accuracy as the system grows. Together, this combination of scalable numerics and rigorous theoretical guarantees positions TJM-based noise learning as a practical foundation for characterizing dissipation in large quantum devices and for guiding future work on error mitigation and quantum error correction.

quant-ph↗

arXiv2026

Robot Programming with Augmented Reality: The Role of Spatial Ability

Programming a robot arm requires users to interpret coordinate frames, joint rotations, and trajectories that are not directly visible. Augmented reality (AR) can make these spatial relations visible, but its benefits may depend on users' spatial ability. We conducted a randomized between-subjects experiment ($N=71$) in which participants learned to program a physical UR5e robot using either conventional teach-pendant controls with PDF instructions or a head-mounted AR interface that displayed joints, coordinate frames, and waypoints. We measured users' spatial ability with the Mental Rotation Test and assessed subjective cognitive load and system usability. Overall, AR did not significantly improve cognitive load or usability compared with conventional instruction. However, exploratory analyses revealed a compensatory effect: spatial ability predicted higher usability and lower extraneous cognitive load in the control group, but not in the AR condition, suggesting AR mitigated the disadvantage typically faced by users with lower spatial ability. These findings point to a compensatory function of AR that should be explored to guide the design of personalized AR interfaces for human-robot interaction.

cs.RO↗

arXiv2026

LLM-Based Educational Simulation: Evaluating Temporal Student Persona Stability Across ADHD Profiles

Large language model (LLM)-based student simulation offers a scalable alternative for educational research, teacher training, and learner practice. However, its validity depends on whether LLMs maintain stable personas across and within interactions. We test this using a dual-assessment framework measuring self-reported characteristics and observer-rated behavioral expressions. Across three ICD-11-informed ADHD-related intensity conditions and a default condition, five LLMs, and three prompt designs, we quantify between-conversation (Exp. I; N=$4,962$) and within-conversation stability (Exp. II; N=$3,952$). Experiment I shows that self-reports and observer ratings are more stable at high than moderate intensities across the tested models, prompts, and independent runs. Experiment II shows that self-reports remain stable throughout extended interactions, but observer-rated behavior drifts in unscripted dialog for high- and moderate-intensity personas. Scripted interactions with recurring task-relevant prompts eliminate this drift almost entirely (up to 97\% reduction). Structured interaction design helps simulated learners maintain behavioral stability in sustained, path-dependent interactions.

cs.HC↗

arXiv2026

Prompting Against Persona Drift: Comparing Intervention Timing and Content in LLM-Simulated Conversations

Simulating student personas with large language models (LLMs) enables scalable evaluation of educational systems. However, behavioral drift, a progressive decline in persona consistency, can emerge over extended conversations, limiting the validity of such simulations. We evaluate five prompt-level mechanisms using separate monitoring and intervention pipelines. Across 1,200 28-turn conversations spanning four LLMs and two ADHD persona intensities, we varied when to intervene (static vs. adaptive) and what to inject (reinjection vs. reflective reminder), plus a novel adaptive condition in which a monitor generates behavior-specific instructions. Relative to no intervention, reinjection reduced the modeled rate of LLM-rated drift by 35--38\%, reflective reminders by 22--27\%, and behavior-specific instruction by 87\%. None eliminated drift. We found no evidence that adaptive timing outperformed static scheduling. Monitoring therefore appears more useful for deciding \textit{what} to correct than \textit{when} to intervene, although behavior-specific instruction requires component-level testing.

cs.HC↗