arXiv subjects

Sebastian Pokutta

Publications and source records attributed to Sebastian Pokutta.

At least 19 recordsLinked to original sources

arXiv2026

Optimal Gradient-Norm Minimization in Non-Euclidean H\"older-Smooth Convex Optimization

Minimizing gradients of a convex function is an important problem across optimization and learning tasks. The gradient provides a directly computable certificate of approximate stationarity, and its minimization usually implies stronger results than those for minimization of function values. In this work, we study gradient-norm minimization for convex functions that are $(L,\kappa)$-H\"older smooth with respect to the $\ell_p$-norms, $p \geq 1$. We develop algorithms that achieve near-optimal gradient-oracle complexity for this problem. In the smooth case, our results resolve the previously open setting $p>2$. For H\"older-smooth objectives, we close the complexity gap throughout the full $p$-range, including to the best of our knowledge, a gap in the Euclidean case. We provide two families of algorithms: the first one comes with a simple iteration and generalizes a phenomenon known as mirror duality, exploiting dual behaviours of algorithms with errors and inexact computations. The second makes use of accumulating regularizers centered at different approximate solutions, which we sequentially minimize in order to provide our near-optimal rates.

math.OC↗

arXiv2026

Discrete eigenvalue optimization from entropic smoothing and first-order methods

We study the maximization of the minimum eigenvalue under combinatorial and integrality constraints. We propose a new approach based on branch-and-bound combines entropic smoothing of the minimum eigenvalue function and Frank-Wolfe methods over concave relaxations of the constraints, thereby exploiting combinatorial structure through linear optimization oracles. We establish approximation and convergence guarantees, including for truncated gradients computed from partial eigendecompositions, and introduce rank- and eigenvalue-based pruning and duality-based variable fixing. We evaluate the method on E-optimal experimental design and maximum algebraic connectivity problems and compare it with SCIP-SDP. The results show that our approach is particularly effective for large-dimensional instances and problems with additional combinatorial structure, whereas SCIP-SDP performs better on moderately sized instances with simpler constraints.

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 $(1-\mathrm{Tr}[\rho^2])/N_{\mathrm{traj}}$, 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

Joint-Range Inequalities for Nonconvex QCQPs

We study cutting planes for nonconvex quadratically constrained quadratic programs (QCQPs) through a project-then-lift approach inspired by mixed-integer rounding (MIR) inequalities. Given two base valid inequalities for the extended QCQP formulation, we project the associated two-row relaxation into a two-dimensional set and analyze the joint range of quadratic functions in two base inequalities. For the nonconvex joint range, we give a closed-form convex hull description of the projected set; for the convex joint range, we give its semidefinite representation. This yields a new family of joint-range inequalities, which can be lifted back to the extended QCQP formulation. MIR inequalities can handle ``mixed'' terms: continuous variables or fractional linear combinations of integer variables. Similarly, we propose more flexible secant mixed-joint-range inequalities, which better expose and exploit the nonconvex joint range. The proposed approach preserves sparsity, since the support of each lifted inequality is controlled by that of the base inequalities. In preliminary geometric experiments, the joint-range inequalities yield substantial area reduction of the projected relaxation constructed via reformulation-linearization-technique.

math.OC↗

arXiv2026

When Does LLM Orchestration Pay Off? A Controlled Evaluation of Accuracy, Cost, and Task Difficulty

LLM orchestration is often assumed to improve reasoning by allocating additional inference-time computation, yet its gains may not justify its cost. Existing comparisons also frequently overlook differences in optimization effort, making it difficult to isolate the value of orchestration itself. We conduct a controlled evaluation of Self-Refine, Best-of-$N$, and Debate against task-only and chain-of-thought (CoT) single-call baselines across five LLM backbones and three domains: competitive programming, chess puzzles, and mathematics. For comparability, we optimize each method with GEPA under the same optimization budget and evaluate all methods on the same difficulty-stratified benchmark items. Orchestration yields moderate but benchmark-dependent gains: averaged across backbones within each benchmark, the largest improvement is 4.6 percentage points over optimized CoT inference and 4.5 points over task-only inference, while requiring approximately 2 to 4 times the mean total tokens of task-only inference. Human-derived difficulty is associated with lower absolute accuracy in all three benchmarks, but within-benchmark analyses do not indicate that orchestration effects increase with task difficulty. By contrast, exploratory mixed-effects analyses reveal strong interactions between orchestration method and backbone model across all three benchmarks, showing that orchestration effectiveness depends substantially on the underlying model. Our results suggest that orchestration decisions should be model-specific and account for whether moderate accuracy gains justify the additional inference cost. More broadly, evaluations of LLM orchestrations should control optimization effort and report model-specific accuracy--cost trade-offs rather than treating additional inference-time structure as uniformly beneficial.

cs.AI↗

arXiv2026

Bounded-Support Additive Latin Transversals

We consider the following additive Latin transversal problem. Given a multiset $A=(a_1,\dots,a_k)$ of elements of $\mathbb Z_m$ and a set $B\subseteq\mathbb Z_m$ of cardinality $k$, the task is to order $B$ as $b_1,\dots,b_k$ so that the sums $a_i+b_i$ are pairwise distinct. When $k=m$, Hall proved that a solution exists if and only if $\sum_{i=1}^m a_i\equiv 0 \pmod m$; moreover, his theorem yields a polynomial-time construction. Alon proved that a solution always exists when $m$ is prime and $k<m$, but no polynomial-time construction is known in general. Our main algorithmic contribution is a direct randomized algorithm for Color-Counted Matching: given an edge-colored graph and prescribed target counts for the colors, find a matching using exactly the prescribed number of edges of each color. If $q$ is the sum of the target counts and $h$ is the number of colors, our base-$(q+1)$ reduction to Exact Red Matching, combined with the algorithm of Mulmuley-Vazirani-Vazirani, gives a randomized algorithm with running time $\left(|V|^2+|E|(q+1)^{h-1}\right)^{O(1)} $ for an input graph $(V,E)$. Thus the dependence on the target matching size is $q^{O(h)}$, up to polynomial factors in the graph size. In contrast, applying the general matching-ILP theorem of Lassota and Ligthart as a black box yields a $q^{O(h^2)}$ dependence for the corresponding fixed-size color-counted instances. Applying this primitive to additive Latin transversals with $s=|\operatorname{supp}(A)|$, we obtain an algorithm in randomized time $(k+\log m)^{O(s)}$. In particular, additive Latin transversals are randomized polynomial-time constructible for every fixed support size.

cs.DS↗

arXiv2026

The Weight Distribution of the Third-Order Reed-Muller Code of Length 2048

We compute the weight distribution of the third-order Reed--Muller code RM(3,11) of length 2048. The weight enumerator is assembled from the coset weight enumerators of f+RM(2,10), evaluated for representatives of all 3691560 nonzero GL(10,2)-orbits of Boolean cubic forms in ten variables. The computation rests on a structural theorem: a nondegenerate Boolean cubic form admits a nondegenerate hyperplane restriction, except for a single orbit in each odd dimension. The same pass determines the second-order nonlinearity of every cubic form: the relative covering radius of RM(2,10) in RM(3,10) is 408, attained on 179 orbits. This raises the best known lower bound on the covering radius of RM(2,10) from 400 to 408. A complementary heuristic search shows that the relative covering radius of RM(6,10) in RM(7,10) is at most 32, improving the previous bound of 50.

cs.IT↗

arXiv2026

A Counterexample to Ziegler's Cross-Polytope Conjecture for Simplicial 0/1-Polytopes

Ziegler proved that every simplicial $d$-dimensional $0/1$-polytope has at most $2d$ vertices, and asked whether equality forces the polytope to be centrally symmetric and hence, equivalently, a $0/1$-realization of the $d$-dimensional cross polytope. In this note, we give a negative answer, exhibiting an explicit set of $14$ vertices in $\{0,1\}^7$ whose convex hull is a simplicial $7$-polytope and is not centrally symmetric. Moreover, via exhaustive enumeration we show that up to the symmetries of the cube, there are precisely five such polytopes in dimension $7$ (of two combinatorial types) that are not centrally symmetric.

math.CO↗

arXiv2026

Classification of Boolean Cubic Forms in Ten Variables

We classify Boolean cubic forms in ten variables up to GL(10,2)-equivalence. The catalog contains all 3691560 nonzero orbits. For every orbit we provide a representative with small monomial count, the stabilizer order, and the alternating rank together with an explicit decomposition. The classification is obtained by rank-stratified enumeration. We verify completeness by the Burnside orbit count and independently by the orbit--stabilizer identity. We also provide a fast, complete GL(10,2)-invariant. By polarization, this gives the first complete classification of alternating trilinear forms in dimension 10 over GF(2).

math.NT↗

arXiv2026

Symmetric Extension Complexity of the Spanning Tree Polytope

In this note, we prove a tight lower bound on symmetric extended 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 \[ \operatorname{xcs}(P_{ST}(K_n))=\Theta(n^3). \]

math.CO↗

arXiv2026

Neural Field Tokenizations with Hierarchy and Spatial Locality Priors

Neural fields parameterize data as functions from coordinates to values, providing a unified framework for representation learning across modalities. Existing approaches are dominated by per-sample meta-learning, which scales poorly due to memory-intensive inner-loop optimization. The natural alternative -- feed-forward encoding -- typically introduces modality-specific assumptions, sacrificing the generality that makes learning with neural fields attractive. We argue that locality and hierarchy are useful priors for learning field representations that can be injected without compromising modality-agnosticism. We propose LH-NeF, a framework to learn general-purpose tokenized representations of continuous signals. A locality-preserving hierarchical encoder maps raw coordinate-value field observations to structured tokens, from which the field is reconstructed during training. By replacing meta-learning's inner loop with a single forward pass, LH-NeF uses 42x less memory and supports 133x larger batches than the strongest modality-agnostic baseline. Across images, 3D shapes, and climate fields, our learned representations match or exceed performance of modality-agnostic, modality-specific, and specialized generative neural field baselines on both reconstruction and downstream tasks.

cs.LG↗

arXiv2026

Random-Subspace Frank--Wolfe over Strongly Convex Sets

Frank--Wolfe methods avoid projections, but over curved feasible regions the full-space linear minimization oracle (LMO) can itself become the computational bottleneck. We introduce random-subspace Frank--Wolfe (RSFW), the first Frank--Wolfe framework, to our knowledge, that replaces the ambient LMO by exact LMOs over random low-dimensional affine sections of a general feasible set, while preserving feasibility in the original space. For smooth convex objectives over compact strongly convex feasible sets, we prove a dimension-explicit approximate-oracle inequality and derive the standard $O(1/k)$ open-loop rate, with high-probability and almost-sure counterparts. Under short steps and a gradient lower bound, the same geometric control yields linear convergence, and we extend the sublinear theory to finite-sum stochastic gradients. We also show that random sections can improve the local curvature model controlling short steps: for smooth objectives, the quadratic model along a sampled section is governed by the compressed Hessian, yielding computable $d\times d$ curvature constants for quadratic objectives over balls and ellipsoids. These results provide a geometric theory of oracle-side randomization in projection-free optimization.

math.OC↗

arXiv2026

Abs-Smooth Frank-Wolfe Method: Primal-Dual Analysis, Heavy Ball Momentum, and Inexact Oracles

We study projection-free optimization for convex objectives that satisfy abs-smoothness, a structural property that captures many non-smooth yet piecewise smooth functions arising, e.g., in modern machine learning models. We develop a unified framework for Abs-Smooth Frank-Wolfe methods, establishing a clean primal-dual analysis that guarantees convergence without requiring classical smoothness assumptions. Our framework extends the available results in two important directions. First, we introduce a heavy ball momentum variant and show that momentum can be incorporated naturally under abs-smoothness while preserving convergence guarantees. Second, we analyze inexact minimization oracles, demonstrating robustness to approximate inner solutions. Moreover, we relax the full convexity assumption and study the case where convexity holds only for the piecewise linear approximations of the objective, further broadening the applicability of conditional gradient methods to a wider class of non-smooth problems.

math.OC↗

arXiv2026

What Do Evolutionary Coding Agents Evolve?

Recent work pairs LLMs with evolutionary search to iteratively generate, modify, and select code using task-specific feedback. These systems have produced strong results in mathematical discovery and algorithm design, yet a fundamental question remains: what do they actually evolve? Progress is typically summarized by the best score a run reaches under a task-specific evaluator, but that score can reflect several different mechanisms: new algorithmic structure, re-tuning an existing strategy, recombining ideas already in the model's internal knowledge, or overfitting to the evaluator. Distinguishing these mechanisms requires inspecting the search process itself, not only its final outcome. We introduce EvoTrace, a dataset of evolutionary coding traces spanning four evolutionary frameworks, reasoning and non-reasoning models, and 16 tasks across mathematics and algorithm design. To analyze these traces, we develop EvoReplay, a replay-based methodology that reconstructs the local search states behind high-scoring solutions and tests controlled interventions, including adjusting constants, removing program components and substituting models or prompting contexts. We annotate every code edit in EvoTrace with one of nine recurring edit types using an LLM-as-judge pipeline validated against blind human re-annotation. Across EvoTrace, most score gains come from a small subset of these edit types. We further find a deterministic cycling pattern: about 30% of code lines added during search are byte-identical re-introductions of previously-deleted lines, present throughout nearly every run. These results show that benchmark gains in evolutionary coding agents can arise from qualitatively different mechanisms, only some of which correspond to new algorithmic structure. EvoTrace enables more diagnostic evaluation of evolutionary coding agents beyond final benchmark scores.

cs.NE↗

arXiv2026

Simulating Eating Disorder Patients with LLMs: Evaluating Psychological Persona Stability in Multi-Turn Conversations

Large language model (LLM)-based simulations of clinical patients are increasingly used for research and training, yet their validity requires persona stability: coherent maintenance of an assigned psychological profile across and within conversations. We evaluate this prerequisite using eating disorder personas grounded in five published case vignettes, a dual-assessment framework (self-report + independent observer ratings), and validated psychometric instruments (EDE-Q) with known ground-truth scores. Across six LLMs and two experiments (between-conversation stability (Exp. I) and within-conversation stability (Exp. II)), we find that LLMs are paradoxically too stable and too inaccurate: variability is negligible, yet all models systematically overshoot ground-truth severity by 12-30% of the scale range (0.7-1.8 points on a 0-6 scale). The mechanism is selective stereotyping: models differentiate cases on behavioural items (dietary restraint) but maximise cognitive-affective items (body dissatisfaction, weight preoccupation) at ceiling regardless of case severity. Additional conversational context does not improve accuracy; it compounds the overshoot. LLMs can portray severe eating pathology but lack a representation of moderate clinical presentations, a "missing middle".

cs.CY↗

arXiv2026

Curvature-Dependent Lower Bounds for Frank-Wolfe

The Frank-Wolfe algorithm achieves a convergence rate of $\mathcal{O}(1/T)$ for smooth convex optimization over compact convex domains, accelerating to $\mathcal{O}(1/T^2)$ when both the objective and the feasible set are strongly convex. This acceleration extends beyond strong convexity: Kerdreux et al. (2021a) proved rates of $\mathcal{O}(T^{-p/(p-1)})$ over $p$-uniformly convex feasible sets, a class that interpolates between strongly convex sets and more general curved domains such as $\ell_p$ balls. In this work, we establish a matching $\Omega(T^{-p/(p-1)})$ lower bound for every $p\ge 3$ under exact line search or short steps, and extend the lower bound to objectives satisfying a H\"olderian error bound. The proofs analyze the dynamics of Frank-Wolfe iterates on simple instances and hence are not limited to the high-dimensional setting, unlike information-theoretic lower bounds.

math.OC↗

arXiv2026

Agentic MIP Research: Accelerated Constraint Handler Generation

Mixed-integer programming (MIP) research is both mathematically sophisticated and engineering-intensive: testing an algorithmic hypothesis within a branch-and-cut solver requires substantial implementation, debugging, tuning, and large-scale benchmarking. We propose an agentic MIP research framework that shortens this feedback loop by embedding LLM agents into a solver-aware harness for generating, verifying, and evaluating plugins for the open-source solver SCIP. Propagation methods play a central role in accelerating MIP solving by exploiting global constraints. We instantiate our framework on the semantic lifting of MIP formulations into global constraints and the automatic construction of propagation-only SCIP constraint handlers. On the MIPLIB 2017 benchmark set, the framework successfully recovers global constraint structures from constraint programming and generates executable constraint detectors and propagation-only constraint handlers. Furthermore, the framework naturally extends to in-context learning within a sandboxed environment, enabling agents not only to tune and debug generated constraint handlers on real instances, but also to explore global constraint patterns in MIP problems and discover novel propagation strategies not yet implemented in SCIP. This framework allows us to systematically distinguish meaningful algorithmic improvements from low-value or overly costly candidates: the novel propagation methods successfully solved five additional instances within the explored benchmark. Overall, this framework demonstrates that LLM agents can autonomously navigate the complex MIP research loop, paving the way for a more automated solver development process.

cs.AI↗

arXiv2026

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

Student simulation with Large language models (LLMs) offers a scalable alternative for educational research and teacher training. Yet, its validity depends on whether models maintain stable personas across extended interactions. We test this prerequisite using a dual-assessment framework measuring self-reported characteristics and observer-rated behavioral expressions. Across two experiments testing four clinically-grounded ADHD persona conditions, five LLMs, and three prompt designs, we quantify between-conversation stability (N=4,968) and within-conversation stability (N=3,952 across 9 turns). Self-reported characteristics remain stable for high intensities, constituting a necessary prerequisite for valid behavioral simulation. Observer-rated behavioral expression reveals selective instability: within-conversation drift occurs in unscripted dialog for high and moderate ADHD personas. Scripted interactions with explicit task prompts eliminate this drift entirely. Stable, persona-aligned simulated learners benefit from a structured interaction design to maintain behavioral coherence, which holds significant implications for teacher training, adaptive tutoring, and any application requiring sustained, path-dependent learner interactions.

cs.HC↗