arXiv:2507.11234v3 Announce Type: replace
Abstract: The Skolem Problem asks to determine whether a given linear recurrence sequence (LRS) $\langle u_n \rangle_{n=0}^\infty$ over the integers has a zero term, that is, whether there exists $n$ such that $u_n = 0$. Decidability of the problem is open in general, with the most notable positive result being a decision procedure for LRS of order at most 4.
In this paper we consider a bounded version of the Skolem Problem, in which the input consists of an LRS $\langle u_n \rangle_{n=0}^\infty$ and a bound $N \in \mathbb N$ (with all integers written in binary), and the task is to determine whether there exists $n\in\{0,\ldots,N\}$ such that $u_n=0$. We give a randomised algorithm for this problem that, for all $d\in \mathbb N$, runs in polynomial time on the class of LRS of order at most $d$. As a corollary we show that the (unrestricted) Skolem Problem for LRS of order at most 4 lies in $\mathsf{coRP}$, improving the best previous upper bound of $\mathsf{NP}^{\mathsf{RP}}$.
The running time of our algorithm is exponential in the order of the LRS -- a dependence that appears necessary in view of the $\mathsf{NP}$-hardness of the Bounded Skolem Problem. However, even for LRS of a fixed order, the problem involves detecting zeros within an exponentially large range. For this, our algorithm relies on results from $p$-adic analysis to isolate polynomially many candidate zeros and then test in randomised polynomial time whether each candidate is an actual zero by reduction to arithmetic-circuit identity testing.
Science Journals
arXiv:2607.17916v1 Announce Type: new
Abstract: 3D Gaussian Splatting (3DGS) and recent compression schemes such as HAC++ enable high-fidelity real-time neural rendering, but their bitstreams are fragile under packet loss during network streaming. Existing compression methods often separate correlated anchor attributes into independent streams, so losing one packet can create attribute-inconsistent broken anchors and severe rendering artifacts. We propose a packet-loss robust 3DGS transmission and error concealment framework. On the encoder side, anchor-level atomic packaging jointly encapsulates all attributes of each anchor, converting corrupted-attribute failures into clean missing-anchor erasures. Stratified random grouping further disperses packet losses across the spatial domain to avoid large contiguous voids. On the decoder side, we formulate recovery as prior-aware attribute inpainting. A Context-Aware Residual Interpolation (CARI) branch uses hash-grid prior predictions and neighboring residuals to build a robust baseline, while a lightweight two-layer graph neural network with cross-attention over hash-grid priors refines high-frequency attribute residuals. Attribute-wise confidence control falls back to interpolation when learned predictions are unreliable. Experiments under 20 percent random packet loss on BungeeNeRF, Mip-NeRF 360, and Tanks and Temples show that the proposed method substantially improves over no-concealment transmission and limits average PSNR degradation to about 3 dB relative to the lossless HAC++ reference.
arXiv:2607.18130v1 Announce Type: new
Abstract: Most parameter-efficient finetuning (PEFT) methods adapt weights or activations, thus leaving one of the key Transformer components unchanged: residual connections. This paper investigates Manifold-Constrained Hyper-Connections (mHC), a generalisation of residual connections, as a novel PEFT approach, wrapping frozen OLMo-2 backbones with learned residual routing modules. We find that mHC can finetune frozen Transformers, but that its role differs fundamentally from the original pre-training setting: in finetuning, fixing the residual mixing matrix to identity often improves performance. As a standalone PEFT method, mHC does not consistently outperform LoRA. However, at matched trainable parameter budgets, mHC+LoRA combinations improve language-modelling loss and show task-dependent benchmark gains at both 1B and 7B scale. Overall, our results identify residual routing as a distinct and promising novel PEFT axis.
arXiv:2607.17219v1 Announce Type: new
Abstract: Human survey respondents exhibit question-order effects that satisfy the QQ (quantum question) equality, an a priori, parameter-free prediction of the projective quantum question-order model. We develop the QQ equality into an audit criterion for sequential judgments of autoregressive large language models (LLMs). Theoretically, we characterize which mechanism classes satisfy it robustly: marginal-independent kernels satisfy QQ iff all four mismatch transition rates coincide (a class containing the 2D rank-1 projective model with a fixed measurement pair under state variation); a polarity- and position-dependent repetition family is characterized by an exact cross-symmetry condition with closed-form violations; QQ-satisfying behaviors are closed under order-matched mixing; and the rank-2 Contextuality-by-Default criterion translates into audit coordinates as $|\qQQ|\le\OSS$, where $\OSS$ (the order-sensitivity score) totals the order sensitivity of the two marginals. Methodologically, we develop a pre-specified, audit-logged pipeline applicable to any model exposing next-token log-probabilities; it combines worst-case robustness envelopes, sampling-consistency spot checks, full label counterbalancing, and a saturation diagnostic. Empirically, in a first-signal pilot on an open-weight instruction-tuned model under two framings, all pre-specified health gates passed, yet 17/18 and 7/8 item pairs, respectively, were saturated (near-deterministic), and no item was certified residually contextual. Forced-binary next-token log-probabilities were thus inadequate for distribution-level QQ audits under the tested model and prompting conditions; we recommend pre-specified saturation diagnostics whenever next-token distributions are treated as survey-response distributions.
arXiv:2509.14230v2 Announce Type: replace
Abstract: While structured pruning presents a highly effective pathway for accelerating Large Language Model (LLM) inference, existing methods frequently suffer from significant performance degradation and demand computationally retraining to recover capabilities. To overcome these barriers, we present NIRVANA, a novel, hardware-aware structured pruning framework designed to preserve both zero-shot performance and the optimization landscape for downstream fine-tuning. Departing from traditional loss-based heuristics, our approach evaluates structural importance through a first-order function-space saliency inspired by the Neural Tangent Kernel (NTK), effectively safeguarding the model's critical training dynamics. To prevent structural collapse at high compression rates, we introduce a global unit-ranking strategy coupled with an analytically derived allocation mechanism, which optimally balances the pruning aggressiveness between attention heads and MLP neurons. Furthermore, we eliminate the instability typically associated with random data sampling by employing a lightweight, KL-divergence-driven calibration data selection process. Extensive evaluations across Llama3, Qwen, and T5 architectures demonstrate that NIRVANA consistently establishes new state-of-the-art results on different benchmarks, providing a theoretically sound and practical approach to LLM compression. The code is available at https://github.com/iDEA-iSAIL-Lab-UIUC/NIRVANA.
arXiv:2509.14357v4 Announce Type: replace
Abstract: The Freeze-Tag Problem (FTP) asks for the minimum time needed to activate a swarm of robots, starting from a single active robot. When an active robot reaches a frozen robot, the latter becomes active; both robots may then move independently and activate further robots. We prove that FTP is strongly NP-hard in the plane under every fixed rational $L_p$ distance, $1 \le p < \infty$, and under $L_\infty$. The geometric argument also applies to every fixed real $p > 1$ for which the metric admits an effective specification. For $L_1$ and $L_\infty$, the integer-coordinate decision problems are strongly NP-complete. The reduction starts from Numerical 3-Dimensional Matching with distinct integers and also yields NP-completeness for unweighted planar grid graphs.
arXiv:2509.20174v2 Announce Type: replace
Abstract: Higher-order interactions, where groups of nodes interact collectively rather than pairwisely, are central to many complex systems, from neural and ecological networks to social contagion. However, simulating dynamical processes on such higher-order structures remains computationally challenging due to the combinatorial growth of possible interactions. Here, we develop efficient and statistically exact Gillespie algorithms for Markovian spreading dynamics on large and heterogeneous hypergraphs. By incorporating phantom processes $-$events that advance time without altering the system's state$-$, we drastically reduce the computational complexity of standard algorithms ($\mathcal{O}(N^2)$), achieving up to linear scaling with system size. Relying on the susceptible-infected-susceptible model with critical mass thresholds as a benchmark, we show that the optimized algorithms outperform standard approaches by several orders of magnitude, enabling simulations of networks with millions of nodes and broad heterogeneity in both degree and interaction order. Efficient sampling methods, needed to overcome the bottlenecks imposed by either a high maximum order or number of interactions, and other dynamical processes on higher-order networks are tackled. These results establish a general framework for scalable, continuous-time simulations of higher-order contagion and related dynamical processes.
arXiv:2509.20593v3 Announce Type: replace
Abstract: This paper presents an uncertainty-aware framework for the active tracking of marine pollution sources using Unmanned Surface Vehicles (USVs). The proposed framework employs an Informative Path Planning (IPP) strategy driven by Bayesian inference, modelling the belief of source location as a categorical distribution. This work presents a high-fidelity simulation pipeline, coupling Computational Fluid Dynamics (CFD) for realistic pollutant dispersion with Gazebo-based hydrodynamics and ArduPilot for USV control. Furthermore, this paper introduces the Smallest Credible Interval (SCI) as a metric to quantify estimation uncertainty and to serve as an autonomous termination criterion. Extensive simulations across diverse wave conditions and source locations demonstrate that the proposed framework achieves a 95.8% success rate, significantly outperforming baseline methods in both localisation accuracy and environmental adaptability. This framework provides a scalable and ROS-compatible foundation for fully autonomous environmental monitoring and rapid incident response.
arXiv:2607.17228v1 Announce Type: new
Abstract: Prior work on LLM-generated text has demonstrated quantitative and qualitative departures from text produced by humans. LLM-generated texts differ from human writing in style, resulting in a characteristic textual "feel," while the semantic range of LLMs is much restricted compared to that of humans. In this contribution, I note simple but consistent patterns in the statistical distribution of n-grams within LLM-generated text. Via qualitative analysis of these n-grams, I reveal deficiencies in LLM style. Because higher-order n-grams correlate to semantic content, I conclude that questions of style and semantics are not cleanly separable.
arXiv:2607.17440v1 Announce Type: cross
Abstract: Models of unification predict additional $Z'$ boson, which contributes to parity non-conservation (PNC) in atoms. If $Z'$ boson is light, ratio of $Z'$ boson contribution to the Standard Model $Z$ boson contribution to atomic PNC increases with decreasing nuclear charge $Z$ faster than $1/Z^2$. This motivated our previous study of PNC in hydrogen and deuterium proportional to the weak interaction matrix elements $<s|W|p> $. An enormous additional relative enhancement appears in the matrix elements between higher waves, such as $<p_{1/2,3/2} | W | d_{3/2,5/2}> $, since $p_{3/2}$ and $d_{3/2,5/2}$ wave functions vanish at $r \to 0$, suppressing matrix elements of the contact $Z$ boson mediated contact electron-nucleus interaction. Measurements of $<p_{1/2,3/2} | W | d_{3/2,5/2}> $ will simplify disentanglement of the $Z'$ contribution from the Standard Model background.
arXiv:2607.17447v1 Announce Type: cross
Abstract: Language models produce probabilities over words, but professional decisions require uncertainty over meaningful states such as diagnoses, hypotheses or operational conditions. A model's printed numerical confidence does not establish reliability. We introduce a semantic map: a prespecified, testable bridge from probabilities over verbal responses to probabilities over declared states, formulated as semiparametric inference for a finite-valued latent state. A reference model defines the target posterior, the language model supplies an unrestricted conditional distribution over verbal responses, and held-out calibration connects them. We derive posterior-error bounds and conditions for existence, uniqueness, stability and sequential Bayesian updating. Crucially, language probabilities depend on the prompt's lexical form, whereas the target posterior is unchanged by information-equivalent rewording. We test the method on professional market text compiled from Federal Reserve economic and financial series and on controlled simulations with exact posteriors. Across two fitted language models, language-derived probabilities outperform printed numerical probabilities, recover held-out posteriors with valid uncertainty coverage, remain largely stable under paraphrasing, and respond appropriately to altered evidence. The broader implication is that prompt engineering optimizes a wording-dependent response, whereas scientific and professional use requires validated stability of application-relevant meaning. The semantic map turns this general concern into a testable statistical problem and, when its acceptance conditions hold, yields an auditable posterior estimate. The same principle offers a template for auditing classifications, recommendations and other fluent responses that may conceal semantic instability.
arXiv:2509.22337v2 Announce Type: replace
Abstract: Belief Propagation (BP) is a widely used approximate inference algorithm in probabilistic graphical models (PGMs), but is computationally expensive when applied to large-scale program analysis. Existing GPU-based approaches are unable to support flexible update strategies and have yet to integrate logical constraints with GPU acceleration, leading to challenges in both generality and efficiency.
We present FastLBP, a GPU-accelerated BP framework for program analysis. We propose a unified representation for specifying flexible update strategies required in program analysis, along with a dependency analysis algorithm to enable parallel execution. Furthermore, we implement BP with local structures on GPUs by assigning individual threads to message computations and utilizing a memory-efficient representation. Experiments on SmartFL and BINGO show that FastLBP achieves average speedups of $17.42\times$ and $2.82\times$ over CPU-based approaches on SmartFL and BINGO, respectively, and $6.14\times$ over GPU-based approach on SmartFL, while preserving accuracy. Moreover, FastLBP supports update strategies that existing GPU-based approaches cannot support, demonstrating its improved generality for real-world program analysis.
arXiv:2509.23071v2 Announce Type: replace
Abstract: Retrieval-augmented generation (RAG) agent development is hindered by the lack of executable ground-truth agent-environment interaction trajectories. Existing datasets provide questions, answers, and evidence, but lack fine-grained supervision for retriever invocation, dynamic planning, and stepwise decision-making. Reinforcement learning offers a potential solution, but often suffers from sparse rewards and cold-start failures when base large language models (LLMs) lack sufficient reasoning capability. Meanwhile, existing data synthesis methods mainly generate post-hoc rationales rather than executable environment-interaction trajectories. In this paper, we propose EviPath, an evidence-anchored reasoning path synthesis paradigm for RAG agent development. EviPath reverse-engineers executable trajectories from question-answer pairs and supporting evidence through three stages: (i) Abductive Subtask Planning, which decomposes questions and plans dependency-aware solution paths; (ii) Faithful Sub-question Answering, which uses supporting evidence as a proxy environment to generate grounded intermediate thoughts and answers; and (iii) Conversational Fine-Tuning, which converts complete trajectories into a dialogue format for supervised fine-tuning. Experiments on widely used question-answering benchmarks show that an 8B model trained on our synthetic corpus significantly and consistently outperforms state-of-the-art baselines, achieving a 14.7% absolute Exact Match gain in open-domain question answering.
arXiv:2509.23185v2 Announce Type: replace
Abstract: We present an integrated planning framework for quadrupedal locomotion over dynamically changing, unforeseen terrains. Existing methods often depend on heuristics for real-time foothold selection-limiting robustness and adaptability-or rely on computationally intensive trajectory optimization across complex terrains and long horizons. In contrast, our approach combines reactive synthesis for generating correct-by-construction symbolic-level controllers with mixed-integer convex programming (MICP) for dynamic and physically feasible footstep planning during each symbolic transition. To reduce the reliance on costly MICP solves and accommodate specifications that may be violated due to physical infeasibility, we adopt a symbolic repair mechanism that selectively generates only the required symbolic transitions. During execution, real-time MICP replanning based on actual terrain data, combined with runtime symbolic repair and delay-aware coordination, enables seamless bridging between offline synthesis and online operation. Through extensive simulation and hardware experiments, we validate the framework's ability to identify missing locomotion skills and respond effectively in safety-critical environments, including scattered stepping stones and rebar scenarios.
arXiv:2607.17136v1 Announce Type: new
Abstract: Agentic computer-use RL is reported in single runs, and those numbers mislead. Using verifier-guided repair of a 35B computer-use agent (CUA) across five oracle-graded environments, we show a repaired policy's success rate is dominated by upstream variance: a variance-components decomposition across three cells (crossed data-draw $\times$ seed grid, bootstrap CIs) finds evaluation variance negligible ($\sigma_{\mathrm{eval}} \approx 0$) and the training-seed effect small everywhere ($\leq 10\%$); instead it splits between the data draw and run-to-run nondeterminism, the data draw's share rising to dominant ($48\%$) on the hardest cell. There the run-to-run distribution is bimodal (Hartigan dip $p=0.07$, $k=10$), so a single run has roughly a 30% chance of the failure mode and mean$\pm$std is the wrong summary. On that footing, two findings hold. First, repairability is two-tier in how constrained the corrective action is: a single fixed token installs reliably (done-detection $0.97\pm0.06$), while open-ended corrections are only partial -- spatial-coordinate clicks (grounding $0.53\pm0.35$) and a generative field-fill ($0.14\pm0.04$). Second, the frame-level repair transfers to task success only when the corrective action is the task's sole remaining blocker (LinkedIn 8/20 vs. base 0/15, Fisher $p=0.006$). We caught two of our own over-claims -- a sample-efficiency curve and a 'grounding cannot be bought' boundary -- only by replicating across seeds; a stress test makes the stakes external: a single-run improvement of the size this field publishes would have the wrong sign roughly one-third of the time in a comparable regime. We release a library (cua_reliability) for routine k-seed reporting. The apparatus is, to our knowledge, the first multimodal segment-aggregated on-policy self-distillation (SA-OPSD) update on a real 35B CUA policy.
arXiv:2509.24511v2 Announce Type: replace
Abstract: Retractions have increased sharply in recent years, alongside a growing number of papers that receive post-publication comments questioning their reliability (commented papers). Together, retracted and commented papers undermine the credibility of scientific research and may also threaten public health. In this study, we examine problematic papers in the field of non-coding RNA (ncRNA) from multiple perspectives to identify common patterns and inform strategies for addressing large-scale fraudulent publications. We find that studies on under-investigated ncRNAs are more likely to become problematic papers. These papers often show substantial textual similarity, and many additional papers with similar text also display suspicious image duplication. Healthcare institutions, particularly those with lower publication output, appear especially vulnerable to producing such papers. Most problematic papers are concentrated in a small set of journals, many of which do not adequately address concerns raised after publication. Overall, our findings indicate that a substantial number of problematic papers may remain undetected and that their shared characteristics can support more effective strategies for identifying and curbing large-scale fraudulent publications.
arXiv:2607.17563v1 Announce Type: new
Abstract: Many fine-grained recognition tasks contain hierarchical labels such as order, family and species. Although this supervision should be beneficial, jointly optimising all levels often leads to unstable training because coarse and fine classifiers impose inconsistent gradients on the shared backbone. This hierarchical gradient conflict prevents the model from learning a coherent coarse-to-fine representation. In this paper, we propose FlexiGrad, a simple and parameter-free method that regulates gradient interactions during backpropagation. FlexiGrad removes only the harmful conflicting component when tasks disagree and reinforces the shared direction when they partially agree through a smooth hierarchy-aware weighting function. This produces stable optimisation and preserves both global structure and fine-grained discriminative cues. FlexiGrad integrates into existing architectures without modification while improves multi-granularity accuracy on CUB-200-2011, FGVC-Aircraft and Stanford Cars. The code will be available at PRIS-CV/FlexiGrad.
arXiv:2510.01483v3 Announce Type: replace
Abstract: Vision-language models (VLMs) demonstrate strong image-level scene understanding, but reasoning over long egocentric video remains costly: because VLMs maintain no persistent memory or explicit spatial representation, all sampled frames must be re-processed for every new query. We present VL-KnG, a training-free framework that constructs spatiotemporal knowledge graphs from monocular egocentric video, bridging fine-grained scene graphs and global topological graphs without 3D reconstruction. VL-KnG processes video in chunks, maintains persistent object identities via large language model (LLM)-based Spatiotemporal Object Association (STOA), and answers questions through Graph-Enhanced Retrieval (GER), which combines subgraph retrieval with visual grounding. Once constructed, the knowledge graph removes the need to revisit raw video at query time, decoupling query latency from video length. Across three embodied question answering benchmarks -- OpenEQA, NaVQA, and our newly introduced WalkieKnowledge -- VL-KnG achieves accuracy competitive with frontier VLMs while answering queries at substantially lower latency and with explainable, graph-grounded reasoning; it further surpasses prior persistent-representation baselines and open-weight VLMs in several settings. Deployment on a real robot demonstrates practical applicability, with query latency remaining stable as observation history grows. As a persistent, queryable scene memory, VL-KnG provides a concrete substrate for memory maintenance and knowledge updating in embodied AI agents.
arXiv:2510.05969v3 Announce Type: replace
Abstract: Large language models (LLMs) are increasingly deployed on complex reasoning tasks, yet little is known about their ability to internally evaluate problem difficulty, which is an essential capability for adaptive reasoning and efficient resource allocation. In this work, we investigate whether LLMs implicitly encode problem difficulty in their internal representations. Using a linear probe on the final-token representations of LLMs, we demonstrate that the difficulty level of math problems can be linearly modeled. We further locate the specific attention heads of the final Transformer layer: these attention heads have opposite activation patterns for simple and difficult problems, thus achieving perception of difficulty. Our ablation experiments prove the accuracy of the location. Crucially, our experiments provide practical support for using LLMs as automatic difficulty annotators, potentially substantially reducing reliance on costly human labeling in benchmark construction and curriculum learning. We also uncover that there is a significant difference in entropy and difficulty perception at the token level. Our study reveals that difficulty perception in LLMs is not only present but also structurally organized, offering new theoretical insights and practical directions for future research. Our code is available at https://github.com/Aegis1863/Difficulty-Perception-of-LLMs.
arXiv:2510.09171v2 Announce Type: replace
Abstract: Instance-level recognition (ILR) focuses on identifying individual objects rather than broad categories, offering the highest granularity in image classification. However, this fine-grained nature makes creating large-scale annotated datasets challenging, limiting ILR's real-world applicability across domains. To overcome this, we introduce a novel approach that synthetically generates diverse object instances from multiple domains under varied conditions and backgrounds, forming a large-scale training set. Unlike prior work on automatic data synthesis, our method is the first to address ILR-specific challenges without relying on any real images. Fine-tuning foundation vision models on the generated data significantly improves retrieval performance across seven ILR benchmarks spanning multiple domains. Our approach offers a new, efficient, and effective alternative to extensive data collection and curation, introducing a new ILR paradigm where the only input is the names of the target domains, unlocking a wide range of real-world applications. The code and pretrained models are publicly available at https://github.com/yankungou/ILGen.
arXiv:2607.17313v1 Announce Type: new
Abstract: We study the graph Laplacian operator as a regularizer in a generalized Tikhonov framework for linear ill-posed problems. The Laplacian is updated iteratively from the current reconstruction, so that progressively sharper structural information about the solution is fed into the regularization term. We introduce three schemes: a standard one that rebuilds the Laplacian from each new iterate; an error-equation scheme that, following the error-based formulation of iterated Tikhonov regularization, builds the Laplacian from an estimate of the reconstruction error rather than of the image itself; and a mixed scheme combining the two. We establish convergence of all three schemes for noisy data under a priori parameter and stopping rules as the noise level tends to zero. Numerical experiments in two-dimensional computed tomography and image deblurring show consistent gains in reconstruction quality and sharper recovery of fine details.
arXiv:2510.09344v2 Announce Type: replace
Abstract: Elderly speech poses unique challenges for automatic processing due to age-related changes such as slower articulation and vocal tremors. Existing Chinese datasets are mostly recorded in controlled environments, limiting their diversity and real-world applicability. To address this gap, we present WildElder, a Mandarin elderly speech corpus collected from online videos and enriched with fine-grained manual annotations, including transcription, speaker age, gender, and accent strength. Combining the realism of in-the-wild data with expert curation, WildElder enables robust research on automatic speech recognition and speaker profiling. Experimental results reveal both the difficulties of elderly speech recognition and the potential of WildElder as a challenging new benchmark. The dataset and code are available at https://github.com/NKU-HLT/WildElder.
arXiv:2607.17654v1 Announce Type: cross
Abstract: Multidimensional graded response models (MGRMs) are widely used for analyzing ordinal questionnaire data in psychological and educational assessments. A central challenge in applying these models is determining the number of latent dimensions. Conventional approaches usually fit multiple fixed-dimensional models and select among them using post-hoc criteria such as AIC, BIC, or cross-validation, which can be computationally demanding and ignore uncertainty in dimensionality during estimation. We develop an adaptive Bayesian dimension selection framework for probit MGRMs. Building on the cumulative shrinkage process, we assign a cumulative ordered spike-and-slab (COSS) prior to the column-specific variances of the item loading matrix. This prior induces increasing shrinkage across latent dimensions, allowing redundant dimensions to be shrunk toward zero while preserving flexibility for active dimensions. Albert--Chib latent response augmentation is used to handle the ordinal probit likelihood, yielding conditionally Gaussian updates for item loadings and latent traits. These updates are combined with Gibbs updates for threshold and shrinkage parameters in an efficient adaptive sampler.
Simulation studies evaluate the proposed
method in terms of dimension recovery, parameter
estimation accuracy, and computational efficiency, with comparisons to conventional fixed-dimensional estimation and model selection procedures. The results show that the proposed approach accurately recovers the latent structure while avoiding repeated model fitting over multiple candidate dimensions. We further illustrate the method using real psychological assessment data, demonstrating its practical utility for uncovering interpretable latent structures in ordinal item responses.
arXiv:2607.17634v1 Announce Type: new
Abstract: Recent advances in text-to-image (T2I) generation have enabled controllable image synthesis by incorporating conditions beyond text. However, most existing diffusion-based methods are limited to a single type of control condition (e.g., bounding boxes or keypoints), which restricts their flexibility. To address this limitation, we propose MixDiffusion, a training-free diffusion framework for multi-condition T2I generation. MixDiffusion theoretically supports an arbitrary number of control conditions, including bounding boxes, keypoints, sketches, depth maps, reference images, and text, by collaboratively integrating multiple pre-trained uni-condition diffusion models. The key insight of the proposed approach is to derive the predicted noise distribution in each denoising step of the diffusion-based multi-condition image generation model from the predicted noise distributions of multiple diffusion-based uni-condition models with a derived integration formula, which is supported by rigorous theory proof. Owing to its training-free nature, MixDiffusion is easy to deploy and readily extensible to new control modalities.
arXiv:2607.17494v1 Announce Type: new
Abstract: Linear probing hash tables classically use a \emph{greedy} insertion strategy, placing a key $u$ in the first available position out of $h(u), h(u) + 1, h(u) + 2, \ldots$. If the hash table is filled to $1 - 1/x$ full, this results in $\Theta(x^{2})$ worst-case expected insertion time.
In this note, we show that there is a simple \emph{non-greedy} insertion strategy that does better, and without requiring elements to be reordered within the table over time. Given $x$ in advance, the strategy is able to bring the worst-case expected insertion time down to $O(x \log x)$.