Science & Mathematics

We study inverse and consensus analysis for PROMETHEE II ranking problems when the performance table is fixed. Existing approaches in PROMETHEE-based sensitivity and consensus analysis usually focus on deviations of criteria weights while treating preference functions as fixed. Nevertheless both sets of parameters jointly determine the outranking flow scores. We introduce a linear reparametrization of the PROMETHEE II net flow scores based on weighted preference increments over the observed differences of performances. This representation yields a linear expression of the net flows and clarifies how weights and preference functions interact. Building on this result, we derive linear optimization models for three settings: minimizing weight deviations while allowing preference functions to vary; minimizing deviations over the full set of preference parameters; and multiple decision-maker consensus analysis (with objectives based either on total deviation or on the maximal individual deviation to promote fairness). An illustrative example shows that allowing preference functions to vary can dramatically change the inverse-analysis conclusions obtained from weight-only models, and that the proposed group formulations distinguish efficient consensuses from fairer ones.

Broad classes of deep generative models (DGMs) operate by learning to map a simple source distribution, such as a standard Gaussian, to a complex high-dimensional target distribution. Despite their success, DGMs often empirically struggle to accurately represent distributions with heavy tails or well-separated modes. In this work, we show that these difficulties reflect intrinsic properties of the underlying transport problem rather than particular neural network architectures or training procedures. We establish quantitative lower bounds on the gradients and Jacobians of pushforward mappings that transport log-concave source distributions to such targets. For heavy-tailed target distributions, the required gradient magnitude grows as the target develops increasingly large moments. For multimodal target distributions, the low-probability regions between well-separated modes similarly force large gradients in the transport map. We discuss how such large derivatives relate to trade-offs between expressivity and numerical stability. Our results hold under substantially weaker regularity conditions than previous analyses and remain stable under perturbations of the target distribution. Finally, we show that these obstructions can be mitigated when the goal is approximation of a given density rather than generative modeling. Specifically, we propose simple classes of bijective reparametrizations that can alleviate the difficult geometric structure and reduce the gradient burden placed on the learned generative map. Numerical experiments support our theoretical analysis.

Materials improvements in transmon qubits have yielded remarkable advances in qubit lifetimes (T1)and coherence times (T2). However, state-of-the-art superconducting qubits experience temporal fluctuations in their performance, which limit gate fidelities and quantum processor performance. We observe correlated increases in qubit relaxation and dephasing rates that last for minutes to hours, which we call T1 and T2 excursions. Using interleaved lifetime and coherence time measurements, noise spectroscopy, and two-level-system (TLS) spectroscopy, we find that these excursions are caused by single or few strongly-coupled TLS defects that spectrally diffuse into resonance with the qubit frequency. Our measurement protocol provides a powerful tool for understanding the noise sources that cause temporal fluctuations in superconducting qubit performance.

A property-based test (PBT) checks a property of a program on many generated inputs, but writing one takes a property, a generator of valid inputs, and an oracle. LLM-based PBT writers produce all three, yet they have been evaluated only on Python libraries. We study how two of them, Proptest-AI and Agentic-PBT, generalize to ten programs in five domains: deep learning libraries, databases, system software, compilers, and LLM serving engines. Most of these programs take text in their own language, such as queries, configurations, and programs. Agentic-PBT covers more branches than Proptest-AI on seven of the ten programs with Opus 5 and on all ten with GLM-5.3-Flash. Domain-specific fuzzers cover more of the compilers and of PostgreSQL and less of PyTorch than Agentic-PBT. We filed 180 bug reports, 44 of which duplicate reports that others filed after the models' knowledge cutoffs; maintainers have confirmed 65 of the others, in all five domains, and fixed 23. We draw lessons for building and evaluating such writers: low observability hurts them, and mature fuzzers paired with LLM-written properties could check that each feature behaves as documented.

Ask a model "how many settlements did the Normans control?" and it answers that the passage does not say. Tell it "given that the Normans controlled 12 settlements of 400 inhabitants, what is the total?" and it computes 4,800. Nothing was added to the passage; the unsupported fact merely became usable. Benchmarks for unanswerable questions are built almost entirely by omission, deleting the fact a question needs and scoring refusal, so they never probe this. Holding source support fixed and varying only whether an unsupported premise is usable, flagging drops 8-30 points and commitment to an answer rises 1.5-2.3x on GSM8K across four models spanning two families and 2B-26B; all 16 paired contrasts remain significant after Holm correction. Two further manipulations reproduce it, one also on SQuAD: a fact asserted rather than asked about, and a corrupted intermediate value rather than a removed one. Models articulate the exact gap they then ignore, stating that "there is no financial information provided" for an inert premise and silently adopting a fabricated price for the same item. We read these as one behaviour: whether a model checks depends substantially on whether usable material is present, even when source support is held fixed. Because the main design never instructs models to reject premises introduced in the question, adopting such a premise can also be read as conditional reasoning, and we delimit what the design does and does not show. In the judging seat the pattern differs: asked whether the answer follows, judges pass solutions with a required step deleted 78-99% of the time at every scale tested. A natural prompt-level mitigation lowers accuracy by 22 points without improving detection.

Non-Classical Logics. Theory and Applications (NCL) is an international conference aimed at presenting novel results and survey papers in the broad field of non-classical logics and their applications. The first two editions were held in Ł{ó}d{ź}, Poland, in September 2008 and 2009. Subsequent editions were organised in Toru{ń} (2010, 2012, 2015, 2018) and Ł{ó}d{ź} (2011, 2013, 2016, 2022, 2024). The tenth edition of the conference, organised by the University of Ł{ó}d{ź} in 2022, was the first to have its proceedings published in EPTCS. We are honoured and pleased to continue this practice and, for the third time, include all accepted long papers in an EPTCS volume. Furthermore, for the first time, we have also included all accepted extended abstracts in the volume.

In formal systems such as Lean 4, efficiently finding answers to mathematical problems and generating verifiable proofs is an important task in automated mathematical reasoning. In the traditional way where an upstream solver provides multiple candidate answers, the common workflow requires searching for proofs for each candidate separately, incurring redundant computational cost. To this end, we propose a joint proof framework that integrates candidate answer selection, answer supplementation, and formal proof generation into a unified reasoning process. At its core is a trained prover that selects given or proposes new answers and generates a proof for at least one answer in a single call. Joint proof can also reuse generated proofs to check for faithfulness errors. For problems with a unique answer, if two distinct answers both obtain verifiable proofs under the same formal statement, this confirms the statement does not faithfully preserve the original problem semantics. On MATH-500, AMC 2023, and AIME 2024/2025/2026, our framework achieves the same formal proof success rate as per-candidate proof generation with about one sixth of the token cost, and identifies at least 6.1% of the formalized statements as unfaithful without requiring additional judges. Our model and code are available at https://github.com/Linppz/Gobble-Prover.

Generative models increasingly expose a reasoning effort setting that lets users scale inference-time compute, trading higher cost for potentially improved performance. Users must choose an effort level before knowing whether extra reasoning will help, and even a successful run does not reveal whether the effort purchased was necessary. Reasoning effort is therefore a credence good: buyers observe the outcome but cannot assess the marginal value of the computation they paid for. In this work, we measure the counterfactual effect of effort levels on both proprietary and open-weight models on four benchmarks, spanning single-call reasoning and long-horizon agentic tasks. Effort, it turns out, does not consistently preserve tasks that lower effort solves, can overspend, and can change trajectory behavior. First, we find that although higher effort can raise accuracy in aggregate, it frequently fails on tasks that lower effort solved. Second, on the subset of easy tasks that every effort level solves, higher effort is generally more costly, with the highest effort level costing up to 42x as much as the lowest. Lastly, effort changes not only how many tokens are used, but also how agents solve tasks: at higher effort, agents verify their own work more heavily and more often search for solutions than work through problems directly, both of which lengthen trajectories without necessarily altering the outcome. These findings show that naively choosing the highest level is not only cost-inefficient but also offers no guarantee of the best instance-level performance. A simple alternative, starting at the lowest effort and escalating only after a verified failure, matches or improves on fixed top effort across all models and benchmarks at lower cost for most proprietary models.

This work proposes a self-attention mechanism based on the fully connected quantum Boltzmann machine (FC-QBM), and further constructs a fully connected quantum Boltzmann machine language model (FC-QBM-LM) using the mechanism as the core engine. By performing unitary evolution on semantic quantum states, the mechanism implicitly implements positional encoding and self-attention computation, eliminating the need to decompose continuous semantic streams into discrete matrices for explicit matrix multiplication, with the measurement results naturally satisfying the normalization condition. Specifically, this work rigorously derives the computational principle of the self-attention mechanism based on FC-QBM, and demonstrates that this mechanism is mathematically equivalent to the classical self-attention mechanism. The mathematical principles governing the training and generation of FC-QBM-LM are thoroughly derived, and the two corresponding algorithms are subsequently developed. An 8-qubit FC-QBM-LM is finally constructed and trained on the corpus of Tang poetry. Under the 8-qubit setting, the quantum layer implements the entire positional encoding and self-attention computation pipeline with only 44 parameters. In the noiseless scenario, the model exhibits favorable convergence. Furthermore, the quantum circuit proposed in this work, which terminates with Y-axis rotation gates, achieves better convergence than the counterpart terminating with X-axis rotation gates. Under the small-sample regime and across eight distinct noise intensity levels, the model demonstrates strong noise robustness, retaining over 99% of its noiseless convergence performance. Experiments on five-character quatrain generation reveal that the model preliminarily exhibits three core capabilities: associative and divergent thinking, content generation across imagery and human-aligned word ordering.

A scalar measurement can determine a robust decision without identifying the latent covariance or every decision risk. We study finite Gaussian projection experiments with a fixed mean-plus-standard-deviation target. The observation laws define a set of indistinguishable moment models. We exhibit decisions that agree throughout that set despite unidentified risk values, and give a confidence-set certificate that returns a decision or an unresolved outcome. We prove soundness, necessary abstention for indistinguishable models with incompatible optima, and a fixed-checkpoint certification guarantee. A scalar profile reduces nonlinear risk comparisons to convex inner problems. Across seven synthetic instances, jointly calibrated moment regions give sufficient budgets 21 to 52 times explicit expected-sample information lower bounds. Separately measured stopping times are lower, with zero decision errors in 1,900 simulated streams. These comparisons do not constitute matching bounds, and the guarantees require Gaussian replication.

The recent data and AI regulations and governance needs have highlighted the need for removing specific data even from models trained on or with them. While retraining the entire model is a theoretically trivial solution, it is computationally expensive, thereby motivating research in Machine Unlearning. This paper introduces a robust approximate unlearning technique for the family of prototype-based classifiers called Generalized Learning Vector Quantization, aimed at removal of effects of specified samples, either due to deletion request or due to them being identified as noisy or corrupt. We first show the impact of the different sizes of the forget set, as well as the characteristics of the data in this set, on the unlearned model. To address the sources of instabilities detected in this unlearning method we propose an adapted version of this technique, such that the unlearning is robust to the characteristics of the forget set. Thereafter using the intrinsic interpretability property of GLVQ and appropriate metrics defined in unlearning literature, we show the efficacy (approximately 0 deviation of parameters and performance of unlearned model relative to retrained model) and efficiency (6X for smallest dataset to 10^(5)X in the largest dataset) of the proposed unlearning techniques compared to naive retrained, on six benchmark datasets for tabular data recommended by literature. Although in this work we investigated only binary class problems, the proposed robust unlearning strategy can be readily applied for removing sample effects from any trained GLVQ model, i.e., it does not require any modification in the training scheme of GLVQ.

The Voynich manuscript is a fifteenth-century book in a script that no one can read. One account holds that its text means nothing and that a scribe made it by copying his own words and changing them a little. The other holds that a real language lies hidden behind a cipher. We write each account as a program that fills the pages of the manuscript, fit every program with the same budget, and check it on statistics the fit never saw. The copying process of Timm and Schinner predicts these statistics far better than any cipher with one key. But ciphers that switch keys between the manuscript's two dialects, or that encode only the word classes of a real text, predict them equally well. Word statistics alone cannot decide. We look for a trace of language that needs no decipherment. In 28 texts in 16 languages the same word pairs keep sharing a line. The manuscript shows this pattern at half the strength of the weakest of these texts. A word code keeps the pattern above the manuscript unless its plaintext has a weak pattern or many words are miscopied. Solvers that decipher control texts find no readable text in the manuscript under a letter cipher, a word code or 28 codes with one letter, letter pair or syllable per word. Word codes of abbreviated Latin, the plaintext their fits prefer, show which word follows which more clearly than the manuscript unless two words in five are miscopied. One cipher remains possible, a nomenclator with a second key whose scribe miscopies more than half of the words, and our solvers cannot exclude it in 9 of 16 languages. Most of the structure a solver finds comes from how the end of one word shapes the start of the next, which reflects how tightly glyphs are bound to each other. Planted messages are found reliably only when they are long, each letter always becomes the same word and these words are adjacent, so other messages could hide.

Data curation is a first-order design choice in machine learning, yet tailoring training data to a downstream model and task remains costly in labor, expertise, and compute. Datasets are therefore often processed through fixed pipelines and reused across applications. We show that this assumption is fragile: across 55 dataset--model tasks spanning biological domains, the same curation recipe can help one model while hurting another. Effective curation must adapt to the downstream setting, motivating automated search over data recipes. We first build an agentic system that searches for curation policies at deployment, improving data utility via \textit{test-time curation (TTC)}. Although achieving performance gains, its search is driven largely by recent feedback and remains local. Adding persistent memory helps the agent retain evidence across iterations and reveals a deeper problem: it forms claims that extend beyond the conditions in which they were observed, sometimes abandoning an entire strategy after a single unsuccessful trial. To address this problem, we introduce CaliMem, a calibrated-memory agentic loop that requires the agent to predict the outcome of each proposed policy before executing it. Comparing this prediction with the observed result gives the agent a \textit{reality check} on the claims behind its proposal. It uses the prediction error to retain supported claims, revise mistaken ones, and specify the conditions under which a conclusion holds. This makes the agent's beliefs testable, reduces overgeneralization, and supports more effective long-horizon exploration. Across biological and LLM post-training tasks, CaliMem consistently outperforms fixed curation baselines and published methods, and exceeds full-data training by up to 19.4\%. Code is open-sourced.

Reinforcement learning commonly exhibits non-monotonic performance dynamics in single-task settings. During learning, a sequence of policies is generated whose true performance is unknown and may oscillate significantly across iterations. Despite this well-known phenomenon, standard experimental practice typically reports either the final visited policy or the best among periodically evaluated ones, implicitly assuming that these selection criteria reliably approximate the best-performing policy visited throughout the entire sequence. In this work, we present an empirical study on the implications of non-monotonicity for policy selection in single-task policy-based reinforcement learning. We introduce post-hoc diagnostic metrics to characterize performance degradation and assess the accuracy and efficiency of different selection criteria. These metrics allow us to evaluate commonly used selection strategies across standard continuous-control benchmarks using a well-established on-policy actor-critic method. Our results show that, in this representative experimental setting, widely adopted selection practices can deviate considerably from the best policy encountered during learning, leading to underperforming estimates and suboptimal use of computational resources. As an alternative, we recommend a validation-based policy selection strategy constrained by computational cost, which provides a more consistent and accurate approximation of the best visited policy while improving selection efficiency. Overall, our findings highlight policy selection as an underexplored factor in the evaluation protocols of reinforcement learning and motivate further study on explicit and standardized validation-based selection procedures.

Requirements traceability links support activities such as change-impact analysis, coverage checking, and validation. Industrial requirements can include traceable images, which text-only approaches cannot process directly. For a fixed classifier configuration, binary decisions alone offer no direct way to adjust the balance between missed and incorrect links. We extend a retrieval-augmented generation (RAG) approach for inter-requirements traceability link recovery (TLR). Our extension retrieves text and image candidates separately, classifies each retrieved pair with a vision-language model, and filters the predicted links by verbalized confidence. We evaluate our approach on three non-overlapping industrial requirement sets and six public text-only datasets. On the industrial test sets, our approach achieves an F1 score of 0.310, compared with 0.114 for our replication of the baseline approach by Hey et al. Our approach recovers links in all four modality combinations while improving text-only F1 on the industrial data and maintaining similar performance on the public datasets, but recovery remains limited by failures to retrieve related text requirements for image queries. Confidence filtering produces link sets with different precision and recall, removing false positives and some correctly recovered links from the unfiltered link set. This study provides industrial evidence on the potential and limitations of a current RAG-based TLR approach for multimodal requirements and identifies cross-modal retrieval as the component to prioritize in further optimization.