arXiv subjects

Vincent Ginis

Publications and source records attributed to Vincent Ginis.

At least 19 recordsLinked to original sources

arXiv2026

Steiner Tree Parameterized by Multiway Cut: Single-Exponential Time and Polynomial Space

In the Steiner Tree problem, the goal is to find a minimum-weight tree containing a given set of terminals in an edge-weighted graph. Given a multiway cut of size $s$, we propose a deterministic algorithm running in $2^{O(s)}\operatorname{poly}(n,b)$ time and polynomial space ($n$ vertices, non-negative $b$-bit integer weights). A multiway cut for the terminals is a set of vertices whose deletion leaves at most one terminal in each connected component. This result answers a question of Jansen and Swennenhuis (ESA 2024). Building on their component decomposition, we show that it suffices to connect the selected cut vertices together with $O(s)$ additional terminals and attach the remaining terminals by shortest paths. We use colour coding to optimize over the choice of these additional terminals.

cs.DS↗

arXiv2026

Spectra of stochastic matrices with a Toeplitz interior

For stochastic matrices of order $n$, the Karpelevič region is the set of all possible eigenvalues. We study matrices whose first and last $m$ rows are arbitrary probability vectors, while the remaining middle rows come from one probability vector by successive cyclic shifts to the right, moving the last entry to the first position each time. As $m$ increases, their eigenvalue regions expand from the polygon spanned by the $n$th roots of unity. For $n\ge3$, they first equal the full Karpelevič region at $m=\lceil(n-1)/4\rceil$. Reproducing all $n$ eigenvalues, counted with multiplicity, of every stochastic matrix of the same order requires $m=\lfloor n/2\rfloor$. Thus, in even order $n\ge4$, retaining two consecutive rows with the Toeplitz pattern can exclude eigenvalue lists even when every possible eigenvalue occurs individually. The boundary of the Karpelevič region consists of arcs joining roots of unity. We determine the least $m$ for which every point of each arc occurs as an eigenvalue in our family. For arcs whose nonreal points first become possible eigenvalues at order $n\ge4$, and for $m\ge1$ below this minimum, no point on the arc other than its endpoints occurs in the family. At the minimum, every point on the arc becomes attainable. At the smallest order $n\ge4$ at which a nonreal point on a boundary arc away from its endpoints can occur as an eigenvalue, that point determines the characteristic polynomial of every stochastic matrix of order $n$ having it as an eigenvalue. Further results describe the smaller regions and the angles at which their boundaries approach roots of unity.

math.PR↗

arXiv2026

Higher Reasoning Effort Improves Reference Verifiability and Changes Reasoning Summaries in GPT-5.5

Large language models are increasingly being used in different stages of scientific knowledge production, including the suggestion of references. These models can operate at different levels of reasoning effort and provide summaries of their reasoning processes. This raises two questions: Does increasing reasoning effort improve the verifiability of generated references, and do the resulting reasoning summaries reveal how the model's behavior changes with greater effort? We examined summaries from GPT-5.5 as it generated scholarly references for 1,000 papers under paired low- and high-effort settings. Generated references were matched to external bibliographic records, and reasoning summaries were scored for four predefined features and explored for additional features discovered by GPT-5.5. High effort increased the mean paper-level resolver-verified reference rate from 78.3% to 84.8%, and produced longer reasoning summaries. All four predefined features received higher scores under high effort. The discovered features changed less uniformly: some appeared equally often in both conditions, whereas others were more common under high effort. Within each effort condition, neither feature set showed a consistent increase in verification rates with higher scores.

cs.CL↗

arXiv2026

Evaluating LLM-Generated Feedback on Handwritten Mathematics: Feedback Quality and Subsequent Exam Performance

We evaluate the quality of feedback and practice exercises generated by GPT-5.1 from handwritten university mathematics answers and their grades, and examine whether receiving this feedback improves subsequent exam performance. We use six weekly bonus tests in an English (n=343) and a Dutch (n=236) cohort. Tests 1 and 3 used a crossover feedback design; otherwise, all attendees received feedback. To evaluate the feedback, six reviewers assessed 157 messages from three English-cohort tasks using six criteria scored from 0 to 3. The practice exercises received the highest proportion of strong ratings (95.5%), while diagnostic specificity (41.1%) and clarity and tone (33.4%) received fewer. Feedback for the lowest-scoring answers was rated as less actionable, suggesting that these students may need more targeted guidance from instructors. Comparisons of related exam questions showed mixed results, with no statistically significant differences after adjustment across four comparisons. Greater attendance and feedback exposure were associated with higher exam scores, but the contribution of feedback could not be separated from attendance and practice. Our findings show the potential of an integrated framework merging instructor guidance with automated feedback generation to provide personalised learning support at scale.

cs.CY↗

arXiv2026

Rational Dyck Excursion Counts as Sums of Generalized Fuss-Catalan Products

For walks with jumps +p and -q, where p,q are coprime positive integers, we express the weak and strict rational Dyck excursion counts as finite weighted sums of generalized Fuss-Catalan products. Both sums run over the same partitions of q for every path size. Reversing the order of the steps and changing their signs transforms a returning walk with jumps +p and -q into one with jumps +q and -p, with the same heights in reverse order. This preserves both weak and strict excursions. Applying the formulas with p and q exchanged therefore gives sums over partitions of p, so we can choose the smaller of the two jump magnitudes. The indices of the Fuss-Catalan factors satisfy certain divisibility conditions that are determined by the jump magnitudes and the partition parts. The weak formula alternates in sign with the number of parts, whereas every term in the strict formula is positive. We prove both formulas by cutting unrestricted walks at their first and last visits to their lowest height. Expanding the resulting factors produces the partitions of q and the different signs. We also give equivalent binomial convolutions. Multiplying each Fuss-Catalan factor by q in the weak formula or p in the strict formula gives a positive integer. For q=1, the weak and strict counts reduce to Fuss-Catalan and shifted Raney numbers, respectively; for q=2 and q=3, the formulas yield explicit convolution identities.

math.CO↗

arXiv2026

Big-Big-SycoBench: A Benchmark to Detect Sycophancy Through Model Responses to Valid vs. Invalid Arguments

Sycophancy in large language models risks amplifying unsupported claims or beliefs across the knowledge ecosystem as these systems increasingly contribute to research synthesis, evaluation, and decision-making. A reliable model should revise its judgement when a user identifies a genuine flaw, but should resist pushback based on fallacies, emotion, or irrelevant appeals to authority. While sycophancy is usually measured on questions with a verifiable answer, the evaluative tasks in which it is most difficult to detect have no such ground truth. We introduce Big-Big-SycoBench, which measures sycophancy through argument discernment: the ability to revise an evaluation after valid criticism while resisting invalid pressure. The benchmark consists of 450 text artefacts with 5,400 arguments for raising or lowering their quality scores, each reviewed by one or more of twelve human annotators. An LLM scores each artefact twenty times to establish its baseline score and uncertainty. The model is then given a valid or invalid argument and asked to update its score. We only count a revision if it exceeds the model's own baseline variability. We use the resulting score delta to distinguish responsiveness to valid arguments from compliance with invalid ones. Across ten models, responsiveness is 88-95\% for seven, 76-77\% for Kimi K3 and GLM-5.3, and 32\% for Opus 5.5. Compliance ranges from 0.2\% for GPT-6 Astra to 95\% for GPT-4o. Big-Big-SycoBench is intended to guide the development of models whose judgements can be corrected by sound arguments, but not displaced by unsupported pressure.

cs.AI↗

arXiv2026

The Eigenvalue Region of a Family of Markov Chains with Randomness Confined to Two States

We determine the complete eigenvalue region of the following Markov chains on $2q$ states, for $q\ge2$. The states are $A_0,\ldots,A_{q-1}$ and $B_0,\ldots,B_{q-1}$. Each transition $A_j\to A_{j+1}$ and $B_j\to B_{j+1}$, for $0\le j<q-1$, has probability one. From $A_{q-1}$, the chain moves to $A_0$ with probability $a$ and to $B_0$ with probability $1-a$. From $B_{q-1}$, it moves to $B_0$ with probability $b$ and to $A_j$ with probability $(1-b)p_j$. Here $a,b\in[0,1]$ and $p_j\ge0$ with $\sum_{j=0}^{q-1}p_j=1$; these parameters vary over all permitted values. Every segment from zero to an attainable eigenvalue lies in the region. Its unit-circle points are exactly the roots of unity of order at most $2q$, as for unrestricted stochastic matrices of the same order, yet the full region is strictly smaller. It excludes $0<|\operatorname{Arg}λ|<π/q$. For odd $q$, the final nonreal boundary arc ends at a negative real point inside the unit disk; the remaining interval to $-1$ is also boundary. Every transition matrix has the same characteristic polynomial as one with $a=b$. Among $q+1$ fixed matrices in this balanced family, convex combinations of at most three realize every attainable eigenvalue, and two suffice on the boundary. Both bounds are sharp within this set. Consecutive reduced fractions in $[1/(2q),1/2]$ with denominators at most $2q$ select the upper nonreal boundary constructions. Each boundary radius is the unique solution of an equation whose left-hand side increases strictly with the radius.

math.CO↗

arXiv2026

A proof of the Karpelevič theorem via invariant polygons

The Karpelevič theorem describes the complex numbers that occur as eigenvalues of stochastic matrices of a fixed order. We give a self-contained proof based on invariant polygons. Their geometry yields a product equation for an eigenvalue of maximal modulus at a fixed argument. Convexity determines this modulus, explicit stochastic matrices attain it, and a comparison between Farey intervals completes the boundary description. As the matrix order increases, the resulting equation gives a uniform relative asymptotic for the gap $1-|z|$ between a boundary point $z$ and the unit circle, even arbitrarily close to arc endpoints. We also determine the optimal contraction factor for a planar rotation and dilation when vector size is measured by scaling a polygon with at most $N$ vertices.

math.RA↗

arXiv2026

On the Spectral Region of n-Cycle Stochastic Matrices

For every $n\geq3$, we determine the union of the spectra of row-stochastic matrices supported on a directed $n$-cycle with self-loops and strictly positive cycle edges. These matrices describe progression through cyclic stages with geometric waiting times, and also arise by uniformization of unidirectional continuous-time reaction cycles. For the latter, the classification determines the minimum transition-rate bound required to realize a prescribed nonreal eigenvalue and provides rates attaining that bound. The angles $m=\mathrm{Arg}λ$ and $M=\mathrm{Arg}(λ-1)$ reduce the nonreal eigenvalue problem to determining the range of a strictly convex logarithmic sum over angles with prescribed sum. Jensen's inequality gives its minimum, simplex vertices give its finite maximum, and connectedness makes these bounds sufficient for realization. The resulting branch graphs are strictly decreasing and their horizontal sections are ordered. This ordering gives the complete boundary, which alternates between uniform-cycle segments and one-loop algebraic arcs. We state a direct membership criterion and construct a realizing matrix for every spectral point; every nonreal point admits a realization with at most two distinct self-loop weights. The real spectral set is $[-1,1]$ for even $n$ and $(0,1]$ for odd $n$. Allowing deleted cycle edges adds only $0$ in odd dimension and adds nothing in even dimension. We also apply the classification to a branching network with matched holding probabilities on parallel paths. The proofs are independent of Karpelevich's theorem.

math.RA↗

arXiv2026

Shorter Reasoning, Earlier Answers? An Evaluation of Reasoning Interfaces

Large language models often reason at length before answering, increasing cost and latency. Prompts and trained settings can shorten this reasoning, but a shorter trace may only show that the model stopped sooner. Here, we evaluate paired runs of the same question at matched reasoning horizons across 198 GPQA Diamond and 500 MMLU-Pro questions. We test a numeric/concision prompt that announces a token limit for Qwen3-14B and the trained effort settings of gpt-oss-20b and -120b. The Qwen prompt shortens reasoning traces by 12-17%, while accuracy changes at matched token limits are small and mixed. A concise/early-answer instruction raises MMLU-Pro accuracy by 3.8 percentage points at 512 tokens, including +2.7 points when both runs are unfinished. Its gain at 2,048 tokens is uncertain. For gpt-oss, candidate-logit answers from completed low- and medium-effort reasoning are 14.5-26.3 points more accurate than matched-horizon high-effort answers. Most of the 512-token advantage comes from lower effort finishing earlier, while differences among unfinished runs are smaller and mixed. Wrong early answers often concentrate probability on the chosen option, so earlier stopping does not uniformly improve probability quality. In these tests, a tight deadline can favor lower effort or a concise instruction, whereas allowing high effort to finish can recover higher final accuracy. Evaluations should report correct completion before a deadline, the answer obtained when a run is stopped, differences among unfinished runs, and probability assigned to the correct answer separately.

cs.LG↗

arXiv2026

How Much Does a Reasoning Summary Reveal? An Observability Ladder for Large Language Models

Large language models often show users a final response and a short reasoning summary while the full reasoning trace stays hidden. We introduce an observability ladder that holds each completed run fixed and varies only what a reader inspects to judge whether the answer is correct: the response, a self-summary the model writes from the trace, the trace itself, and internal signals, each with and without the prompt. Across three benchmarks and five open-weight Qwen3 and gpt-oss models, we train matched linear correctness predictors on each access level. Without the prompt, summaries carry most of the trace's ranking signal (mean AUROC 0.774 versus 0.813) and add +0.156 over the response alone. With the prompt visible, the summary's gain collapses to +0.019, while the trace still adds +0.041. Even at equal length, the trace's last words predict correctness as well as summaries, or slightly better, and carry denser and more discriminative uncertainty and self-correction cues. On MMLU-Pro questions with both correct and incorrect runs, linear summary readers are near chance and trace readers retain only modest signal, both with and without the prompt (prompt-withheld AUROC 0.503-0.545 versus 0.544-0.590). With the prompt withheld, a GPT-5-mini reader recovers substantially more signal from both summaries and traces on gpt-oss-20b, and even then the trace keeps a small +0.034 advantage. Much of the linear readers' trace signal is associated with length. In the common case where users already hold the prompt, summaries are less helpful than the full trace for monitoring correctness. Monitorability is thus a joint property of the display and the reader, so any monitorability claim, including for faithfulness, should specify both.

cs.LG↗

arXiv2026

Geometric Configurations of Perturbed Jailbreak Prompts

Perturbation techniques that turn unsuccessful jailbreak prompts into successful ones are continuously evolving, constituting a major security threat to LLM safety. In this paper, we investigate the internal representations of such string-level perturbed jailbreak inputs in the small weight models of the Qwen-2.5-1.5B/-3B/-7B-Instruct and Llama-3.2-1B/-3B/-3.1-8B-Instruct families. We select two representation spaces: the last-layer-last-token embedding space and the top-50 next-token probability space. The former space separates prompts based on their spelling and format, while the latter space is effectively one-dimensional but appears more complex to cluster. Within our refusal-dominated answer set we find no behavioral hyperplane in either space. Only the next token "Sure" in the 1.5B Qwen model, and both tokens "," and "ĊĊ" in the 1$ Llama model, display a significant association with a compliant-labeled answer.

cs.CR↗

arXiv2026

Stochastic realisers of non-degenerate full-degree Type II reduced Ito polynomials

Let $f_α(x)=(x^q-(1-α))^d-α^d x^z$, where $0<α<1$, $q\ge 2$, $d\ge 2$, $1\le z\le q-1$, and $\gcd(q,z)=1$. These are the non-degenerate full-degree Type II reduced Ito polynomials of order $n=qd$. We give a complete parametrisation, up to permutation similarity, of the stochastic matrices whose characteristic polynomial is $f_α$. The support data are a composition $a_0+\cdots+a_{d-1}=z$ and a cyclic origin $ρ\in\mathbb{Z}_q$. The transfer support in block 0 is an arbitrary nonempty subset of $[ρ,ρ+a_0]_q$, while the support in block $t\ge 1$ is an arbitrary nonempty subset of $[ρ-\sum_{j=1}^t(a_j+1),ρ-\sum_{j=1}^t(a_j+1)+a_t]_q$. The horizontal weights at the selected positions are arbitrary elements of $(0,1)$ whose product in every block is $1-α$. The proof first shows that the order-$n$ Type II arc lies strictly outside $Θ_{n-1}$, which permits the Dmitriev--Dynkin/Kirkland--Smigoc two-shift reduction. A circular separation theorem then classifies the possible supports, and Coates' formula supplies the characteristic polynomial. This resolves the non-sparse full-degree Type II characteristic-polynomial realiser problem.

math.RA↗

arXiv2026

The relationship between reasoning and performance in large language models--o3 (mini) thinks harder, not longer

Large language models have demonstrated remarkable progress in mathematical reasoning, leveraging chain-of-thought and reinforcement learning. However, many open questions remain regarding the interplay between reasoning token usage and accuracy gains. In particular, when comparing models across generations, it is unclear whether improved performance results from longer reasoning chains or more efficient reasoning. We systematically analyze reasoning chain length across o1-mini and o3-mini variants on the Omni-MATH benchmark, finding that o3-mini (m) achieves superior accuracy without requiring longer reasoning chains than o1-mini. Moreover, we show that accuracy generally declines as reasoning chains grow across all models and compute settings, even when controlling for difficulty of the questions. This accuracy drop is significantly smaller in more proficient models, suggesting that new generations of reasoning models use test-time compute more effectively. Finally, we highlight that while o3-mini (h) achieves a marginal accuracy gain over o3-mini (m), it does so by allocating substantially more reasoning tokens across all problems, even the ones that o3-mini (m) can already solve. These findings provide new insights into the relationship between model capability and reasoning length, with implications for efficiency, scaling, and evaluation methodologies.

cs.LG↗

arXiv2026

The Type III realisation conjecture of Kirkland and Šmigoc

Kirkland and Šmigoc constructed a family of stochastic matrices realising the Type III boundary polynomials in the Karpelevič region and conjectured that, conversely, every stochastic realisation of such a polynomial must come from their construction. We prove this conjecture for the full nonzero parameter range $0<α\le1$, for genuine Type III reduced Ito polynomials of order $n$, $f_α(x)=x^y(x^q-(1-α))^d-α^d$, where $n=qd+y$. For $0<α<1$, the proof first reduces every realisation to a two-shift cyclic normal form using the Dmitriev--Dynkin boundary theorem. The remaining argument is finite and combinatorial: Coates' coefficient formula and the equality case of a weighted Turán theorem force the $q$-cycles associated with the backward edges to split into $d$ complete multipartite classes of equal total weight. A circular-arc telescoping argument then converts this additive equality into the product condition required by Kirkland and Šmigoc. The endpoint $α=1$ is treated separately. We also explain why the closed endpoint $α=0$ is degenerate: the literal extension to this endpoint fails, because reducible realisations with closed $q$-cycles and transient states need not contain the global $n$-cycle.

math.RA↗

arXiv2026

Neural Networks for Inverse Design of Cascaded-Mode Near-Field Landscapes

Structuring optical near-fields is important for applications in microscopy and nanoparticle manipulation. Traditionally, near-fields are structured using antenna nanostructures that locally convert propagating far-fields into bound near-fields. Recently, a remote structuring approach was proposed using cascaded mode interference in a multimode waveguide. However, determining the complex coefficients of the optimal modal combination needed to obtain specific near-fields remains a challenge. We address this inverse design problem using artificial neural networks. We model the relationship between the design parameters and near-field landscapes using multilayer neural networks. After training, these networks are used for gradient-based optimization to reconstruct target near-field profiles. We implement this methodology to design longitudinal and lateral field variations. Our approach designs simple and complex longitudinal landscapes, demonstrating accurate prediction and flexibility. Lateral field reconstruction is more challenging but improved with training data selection and augmentation. This work establishes deep learning as an efficient and scalable framework for cascaded-mode near-field inverse design.

physics.optics↗

arXiv2026

Rebuttals Move Peer-Review Scores, but Initial-Review Structure Bounds the Movement

Author rebuttals are the main post-submission window in peer review, but their effect on reviewer scores remains hard to measure because score updates mix rebuttal content with initial score position, paper-level consensus, reviewer confidence, and discussion dynamics. We study ICLR 2024-2025 using 73,000 reviewer trajectories with externally archived pre- and post-rebuttal scores, and use LLMs only as measurement instruments. Gemini Flash 3.0 predicts implied pre-rebuttal scores from score-stripped review text. The resulting text-score offset predicts later movement, with score-increase rates rising from 8.3% when text reads below the assigned score to 31.9% when it reads above. Claude Opus 4.6 induces, and outcome-blinded Gemini Flash 3.0 validates, a 44-feature taxonomy of resolved reviewer-author exchanges, where 23 features replicate across model and held-out year under Bonferroni correction. In the rebuttal-engaged benchmark (n=6,705), initial-review structure already predicts much score movement (AUC=0.747, minimal AUC=0.696), while adding the resolved exchange raises AUC to 0.804. Rebuttals can move scores, but measurable movement is bounded by initial-review structure, and robust exchange signals are mostly rebuttal failure modes.

cs.DL↗

arXiv2026

Thinking Like a Scientist? A Structural Study of LLM-Generated Research Methods

Large Language Models (LLMs) are increasingly used to guide research methodology, yet their default methodological tendencies under minimal prompting remain unclear. Here, we prompt GPT-5.1, Gemini 3 Pro, and DeepSeek-V3.2 with an LLM-extracted research question from each of 1,000 recent arXiv computer-science papers and compare the resulting methodology suggestions against a paper-derived experimental inventory. Since we provide only the research question, the differences we measure reflect initial suggestions and not how optimal those suggestions are. We extract structured method features from both sources, map them into a shared taxonomy, and quantify divergence across multiple taxonomy dimensions including model provider, dataset task type, and evaluation metric type. The strongest imbalance appears in provider choice, with Jensen-Shannon divergence about 3-5x larger than any other taxonomy dimension. Other/Academic single-occurrence models are underrepresented by 23-24 percentage points, while reused academic/community models are slightly overrepresented (4-6pp). LLMs also suggest a much narrower range of methods overall: the effective number of model entities contracts from 1,232 to 59-96, and inter-LLM rank correlations (0.55-0.68) generally exceed LLM-to-paper correlations (0.33-0.56), so the distortions are largely shared across models. Popularity baselines, BM25 retrieval calibration, and paper-level similarity tests confirm that the outputs are query-specific responses, but filtered through a narrower set of options. Researchers who rely on LLM suggestions without cross-checking therefore risk narrowing their methodological search space toward a more concentrated default.

cs.CL↗