Computer Science (arXiv)

This paper reports on a locally motivated mixed-methods case study addressing a teaching-related suspicion held by software engineering instructors: that commit messages written by students frequently fail to serve their intended communicative role. To examine this suspicion empirically, we analyzed commit messages from student and industrial case-study projects using a partial replication of an established commit-message quality taxonomy. The results confirm that communication and quality issues occur recurrently in both contexts, substantiating the instructors' initial concern. Motivated by this finding, we devised What Do You Mean? (WDYM), a lightweight, role-based educational game intended to surface and address commit-message communication breakdowns within the constraints of university coursework. Analysis of gameplay observations and participant surveys shows that WDYM is effective in raising awareness and fostering reflection on commit-message communication issues, although it provides limited evidence of immediate or sustained improvement in commit-message writing practices. Taken together, the study presents WDYM as a useful, though imperfect, context-bound intervention for addressing a locally observed instructional problem, without claiming general applicability beyond the studied setting.

The cluster graphs on $n$ vertices, the disjoint unions of complete graphs, have the integer partitions of $n$ as their isomorphism classes, and the quotient edit distance $q^*(λ,μ)=\min_{σ\in S_n}|E(G_λ)\triangleσE(G_μ)|$ makes that set a metric space. Its metric geometry and its computational complexity both issue from one identity: $q^*$ is an affine function of the maximum of $\lVert X\rVert_F^2$ over the contingency tables with margins $λ$ and $μ$. Combinatorially, it yields two explicit $\ell_1$ models: the vertex-mass metric $δ_1$ on sorted degree sequences, with $\frac12δ_1\le q^*<\frac32δ_1$ and both constants optimal, and the block-energy metric $B$ on the vectors $\bigl(\binom{λ_i}2\bigr)_i$, with $q^*\le B\le2q^*-1$ by a per-table refinement measuring how far an alignment is from a block bijection. Hence $c_1(\mathcal K_n)\le2$, and an $O(n\log n)$-time algorithm returns an alignment of cost below $2q^*$ with the certificate $q^*\in[\lceil(B+1)/2\rceil,B]$. The Euclidean distortion of the class is $c_2(\mathcal K_n)=Θ(n^{1/4})$; against it we measure the weighted dyadic sums $F^{(γ)}$ of the Ferrers staircase, of dimension below $4n$ and computable in $O(n)$ time. The unweighted member has distortion exactly $Θ(n^{1/4}\sqrt{\log n})$, while the critical weight $γ=\frac14$ improves this unconditionally to $O(n^{1/4}(\log n)^{1/4})$ through an inverse energy inequality proved from the quantization of staircase jumps; removing the residual $(\log n)^{1/4}$ is reduced to one inverse inequality on the realizable cone. Computationally, the same identity gives a classification: deciding $q^*(λ,μ)\le Q$ is strongly NP-complete, evaluation is strongly NP-hard and admits no FPTAS unless $\mathrm P=\mathrm{NP}$, while the farthest alignment is polynomial-time solvable.

Many scalable latent 3D generators operate on structured tensors, whereas pre-optimized 3D Gaussian Splatting (3DGS) reconstructions are unordered, spatially irregular, and vary widely in primitive count. We present GS-Voxel, a fitting-free structured latent framework, and evaluate it for large-scale aerial 3D Gaussian scene generation. GS-Voxel deterministically converts a compatible pre-optimized 3DGS reconstruction into sparse active voxels without additional per-scene optimization, retaining the sub-voxel positions and rendering attributes of the selected primitives. A GS-specific factorized VAE then separately encodes voxel geometry and local Gaussian attributes into sparse 3D latents whose size grows with the number of occupied voxels rather than being limited by a fixed scene-wide primitive count. We train image-conditioned flow models in the GS-Voxel latent space to generate aerial 3DGS scenes. A key application enabled by GS-Voxel is large-area scene generation: overlap-aware tiled inference extends synthesis beyond a single training crop conditioned on satellite-view images. Our results show that GS-Voxel provides structured latents for pre-optimized aerial 3DGS reconstructions, with latent capacity that grows with the number of occupied voxels.

The rapid growth of social media has greatly influenced political discourse, highlighting the need to understand individual political ideologies and their temporal dynamics. This task faces challenges such as data scarcity, abundant non-political content, costly and bias-prone manual annotation, and difficulty in modeling future ideological inclinations. To address these issues, we propose TSN4PI, a unified framework for tracking the evolution of political ideologies on social media. It includes two core modules. The PIDN uses large language models with style transfer and unsupervised domain adaptation to enable robust ideology detection and filter irrelevant content from noisy, cross-domain data. The PIPN employs temporal graph neural networks to predict future ideological shifts, enabling comprehensive analysis of ideology presence, intensity, and evolution. We release two large-scale datasets for noncommercial research use to facilitate further work. Extensive case studies on multiple platforms (X and Truth Social) validate the effectiveness of TSN4PI and provide empirical insights into political polarization and the evolution of online ideologies. Our findings offer a nuanced perspective, advancing both methodological development and empirical understanding in this field.

Ultrasound tongue contour segmentation remains challenging under cross-dataset domain shift, where limited annotations, probe variability, and acquisition noise often degrade model generalization. We present a source-free domain adaptation framework for robust ultrasound tongue segmentation built on a lightweight UltraUNet backbone. Starting from a checkpoint pretrained on only five labeled source images, simulating an underfitted constrained source model, the proposed method adapts to a fully-unlabeled target domain by iteratively refining pseudo-labels, filtering unreliable masks with a contour-based quality-control module, and generating target-style synthetic image-mask pairs through a segmentation-guided conditional GAN. The student model is then trained on a mixture of clean pseudo-labeled target images, noisy pseudo-labels with consistency regularization, and synthetic samples, enabling closed-loop adaptation without access to source data. We evaluate the method on 12 source-target transfer pairs across eight ultrasound tongue imaging datasets, and conduct source-size scaling experiments and ablation studies. Across all comparisons, the proposed framework improves segmentation overlap and contour accuracy over the baselines, including supervised ones. These results suggest that task-specific pseudo-label refinement and synthetic target-style augmentation can substantially improve source-free adaptation for ultrasound tongue imaging.

We describe an inference-time architectural enhancement for off-the-shelf foundation models that markedly reduces perplexity and boosts accuracy across generation and reasoning tasks. Our approach incurs essentially no additional latency during generation, though it requires serial processing in the prefill phase. Motivated by the fundamental limitation that state updates in feedforward transformers are bounded by model depth, our technique, recirculation, introduces a specific form of recurrence that allows the model to act as a dynamical system and track belief states. We distinguish this technique from chain-of-thought computation---which is better reserved for complex inferences rather than basic state tracking---as well as from popular depth-recurrence techniques (looping) and the costly training of recurrent transformers. We also propose and evaluate an adaptive variant of recirculation which requires only light tuning of hyperparameters while freezing the original model weights. Relative to the off-the-shelf baseline, adaptive recirculation achieves remarkable gains on the Gemma3 family, including a 23% reduction in perplexity on a suite of datasets, a 21% increase in accuracy on GSM8k, and reliable improvements in accuracy on other downstream tasks. Our training-free approach succeeds by leveraging the model itself to inform architectural modifications, suggesting a route to architectural evolution guided by a trained network's properties rather than forced, arbitrary design choices.

Authorship verification (AV) assumes that an author's writing style remains sufficiently stable to distinguish it from that of other writers. In practice, however, this assumption is challenged by distribution shifts caused by changes in genre, time, and AI-assisted writing. Existing AV benchmarks typically study these factors in isolation and focus predominantly on English, limiting our understanding of model robustness under realistic conditions. We introduce AVShift, the first German benchmark for systematically evaluating AV under multiple distribution shifts. AVShift comprises over 150,000 text pairs spanning three genres and 21 years, enabling controlled evaluation of cross-genre, temporal, and AI-era shifts within a unified framework. We benchmark representative feature-based, embedding-based, and LLM-based approaches. Our experiments show that fine-tuned LLMs generalize best across genres and benefit substantially from stylistically diverse training data. We further demonstrate that temporal drift is one of the strongest factors affecting AV, with performance degrading significantly as the time gap between documents increases. In contrast, we find no evidence of a measurable AI-era distribution shift within AVShift. Finally, our feature analysis reveals stylistic features that remain stable across genres, while their relative importance varies depending on the specific genre transition. We release AVShift and our code for future research.

Uncertainty visualisation is important for data transparency, especially for map visualisations where data is often aggregated. Despite the importance of this area, studies evaluating uncertainty visualisation lack consensus and produce conflicting results. This work introduces a new evaluation approach for uncertainty visualisation that attempts to assess uncertainty as noise, rather than signal. We evaluate five methods of visualising uncertainty: standard choropleth maps, value/variance bivariate maps, value-suppressing uncertainty palettes, overlaid sampling, and pixelated sampling maps. Built on principles of implicit testing, we put an 'uncertainty visualisation' spin on the classic Ishihara colourblind test to create a novel test that is able to evaluate uncertainty as noise. We compare signal visibility to conventional hypothesis tests at various levels of group separation. By building our experimental design on top of established graphics theory, we isolate the plot components that facilitate successful signal suppression and establish foundational theory for the perception of uncertainty visualisation.

Programmatic representations provide a compelling paradigm for 3D content creation, enabling fine-grained edits, interpretability, and explicit structural control. Yet, agentic workflows that rely on large language models (LLMs) to author 3D programs remain brittle, often failing to translate high-level intent into consistent low-level geometry. We attribute this fragility to a mismatch between existing programmatic interfaces and the reasoning strengths of LLMs, which favor semantic structure and spatial relations over fragile numeric choices. In this paper, we jointly design an Agent-centric Domain-Specific Language (aDSL) and a role-specialized multi-agent system to close this gap. aDSL bridges semantic logic and geometric constraints by emphasizing composability and spatial reasoning; it enables agents to manipulate geometry through relational operators instead of brittle absolute coordinates. Building on aDSL, our training-free multi-agent system follows a Plan-Execute-Critic loop to decompose requests, synthesize code, and iteratively repair errors and constraint violations using execution feedback. Experiments show that this co-design improves robustness, controllability, and faithfulness to user intent. Our method outperforms prior LLM-based baselines on text-to-shape and image-to-shape tasks while preserving explicit structure, editability, and interpretability. It also enables downstream applications such as articulated object creation and structured scene composition. Our code is available at https://github.com/sig-pku/aDSL.

Diffusion models have achieved remarkable success in image and video generation, yet the high computational cost of iterative sampling remains a critical bottleneck for practical deployment. Feature caching has emerged as a promising acceleration paradigm by reusing or predicting intermediate features across timesteps. However, existing training-free methods apply uniform prediction strategies that cannot adapt to the heterogeneous feature dynamics, causing significant quality degradation under high acceleration ratios. We propose LinCa, a feature caching framework based on learnable invertible networks. LinCa decomposes cached features into sub-components with distinct continuity properties via a lightweight invertible network and applies differentiated prediction orders matched to each component. The strict invertibility guarantees lossless reconstruction back to the original feature space, forming a unified Decompose-Predict-Reconstruct pipeline. By training separate predictors for different models and timestep segments, LinCa adapts to heterogeneous feature dynamics. Experiments on FLUX, Qwen-Image, and HunyuanVideo demonstrate that LinCa, with less than 0.2% additional parameters, significantly outperforms existing methods and maintains near-lossless quality at 5-7x speedup. Code: https://github.com/QHR69/LinCa

We present a real-time pipeline of open source, pretrained models for streaming identification of a target speaker, motivated by hearing-aid applications where latency as low as 10 ms can be perceptible. We formulate a two-step approach in which incoming audio is first segmented by speaker using low-latency streaming diarization, followed by speaker verification against a registered target speaker. To emulate conversational speech while minimizing overlap, we use the This American Life Podcast Transcripts dataset and select the host as a consistent target speaker. We benchmark offline diarization with Pyannote and LIUM using diarization error rate (DER) and select Pyannote based on baseline performance and compatibility with streaming. We then evaluate speaker verification using Pyannote and TitaNet-Large and generate ROC curves to select an operating region. We integrate Diart and tune clustering parameters to reduce DER while maintaining real-time operation. We pair Diart with Pyannote verification and evaluate system-level performance by converting predicted and ground-truth speech regions into 100 ms binary masks. Across 17 evaluation episodes, the system achieves greater than 0.90 median accuracy with high specificity (0.95-0.98) at cosine distance thresholds of 0.7-0.75, demonstrating a practical proof of concept for downstream low-latency selective amplification.

The impact of climate variability on food production has led to the creation of various forecasting models that uses machine learning (ML), numerical weather predictors (NWP) or a hybrid of ML-NWP models to identify structural and physical relationships between meteorological drivers and crop growth, in order to predict crop yield. Droughts, for example the 2012 Midwestern US (Corn Belt) drought, are extreme events that affect crop production and test the limits of these forecasting models. Using 16 meteorological drivers as predictors, we compare ML (non-deep learning) and deep learning forecasting models to predict the county-level corn yield for the extreme drought year, 2012. This forecasting problem is characterized by a dissimilarity between the feature distributions of the training and test data, where the meteorological conditions of the extreme drought year fall outside the range of historically observed values. Additionally, the dataset consists of spatial and temporal irregularities where counties with missing yields introduce spatial sparsity and the use of only a subset of daily values per year introduce temporal sparsity. To overcome this, we use sample weighting and feature selection as modifications to improve our forecasting models. These modifications lead to an improvement for ML models; however, the deep learning model VITA shows little to no improvement. While VITA outperforms the ML models with or without modifications, our current study sheds light on the effect of dissimilarity between train and test feature distributions on forecasting models, compares deep learning versus non-deep learning models, and introduces modifications that are effective for non-deep learning models.

This paper examines the growing role of AI in scientific discovery. It first surveys the rapid rise of AI capabilities, especially in reasoning, abstraction, planning, and long-horizon task execution, before turning to scientometric evidence of AI's diffusion across the sciences. It then proposes a typology of AI systems used in research, ranging from specialized scientific AI through scientific AI assistants and agents to hybrid experimental systems that combine computation and physical experimentation. On this basis, it offers a selective overview of recent achievements in mathematics and computer science, physics, chemistry, the life sciences, and the behavioural and social sciences. It argues that, despite these advances, current systems remain constrained by important technical, epistemic, and institutional limitations, and that their growing use introduces both near-term and longer-term risks. The conclusion further suggests that the advancement of AI in science raises broader questions concerning the division of cognitive labour between human researchers and machines.

Point-Based Neural Rendering (PBNR) is emerging as a promising class of rendering techniques, which are permeating all aspects of society, driven by a growing demand for real-time, photorealistic rendering in AR/VR and digital twins. However, achieving real-time PBNR on VR/AR devices is challenging. This paper proposes MetaSapiens v2, a PBNR system that delivers real-time neural rendering on VR/AR devices while maintaining human visual quality. MetaSapiens v2 combines four techniques. First, we present an efficiency-aware pruning technique to optimize rendering speed. Second, we introduce a Foveated Rendering (FR) method with an efficient primitive for PBNR, leveraging humans' low visual acuity in peripheral regions to relax rendering quality and improve rendering speed. Third, we leverage the redundancy between the two eyes and propose a selective warping method to further reduce the computation overhead in AR/VR binocular rendering. Finally, we propose an accelerator design for binocular FR, addressing the load imbalance issue in (FR-based) PBNR and supporting warping for efficient binocular rendering. Our evaluation shows that MetaSapiens v2 achieves an order of magnitude speedup over existing PBNR models while maintaining the visual quality.

Sparse attention mechanisms, which score all token pairs but propagate only the strongest, now underpin the most efficient Transformers for lightweight image super-resolution. This paper observes that sparsification changes what it means to improve such a network. A dense attention layer has one place where representation quality matters: the aggregation of attended features. A sparse layer has two, because the top-k operator first decides which tokens survive and only then decides what to do with them, and a token discarded at the selection stage cannot be recovered downstream. Selection quality and aggregation quality are therefore separable targets, addressed by modules placed before and after the attention respectively. We test this by pairing a dual-branch spatial enhancement on the input of a progressive focused attention with a wavelet-domain modulation on its output, forming SFMformer. Measuring each module alone and jointly over all fifteen benchmark-scale pairs, we find their gains are not additive: the joint gain exceeds the sum of the individual gains on nine pairs, and the sign of the discrepancy is predicted by how much the weaker module contributes on its own (r = -0.72), so the two compound when they relieve different constraints and overlap when they relieve the same one. Enabling spectral modulation once per block rather than once per layer retains the effect at roughly one-sixth of its cost, keeping the model below one million parameters at every scale. SFMformer ranks first on 28 of 30 PSNR/SSIM entries across five benchmarks and three upscaling factors. We report the cases where the pairing does not help, and deploy the model on a Raspberry Pi 5 to confirm the design is practical under tight resource budgets.

Online log anomaly detection is critical for maintaining the reliability of large-scale computing systems. Although recent language model-based log anomaly detectors achieve strong detection performance, their confidence estimates remain poorly calibrated. We show that these detectors frequently assign excessive confidence to incorrect predictions, particularly for anomalous logs under severe class imbalance. Moreover, confidence on erroneous predictions remains persistently high even when conventional calibration metrics indicate good calibration, creating a critical reliability gap for operational monitoring systems. To address this issue, we propose Log Reconstruction and Distance (LoRD), a lightweight post-hoc calibration framework for reliable log anomaly detection. LoRD learns prediction-route-specific reliability models from latent representations of correctly classified validation samples and estimates prediction reliability through route-wise reconstruction distances. Based on the estimated reliability, LoRD selectively recalibrates high-risk predictions to suppress overconfident errors while preserving reliable predictions. Extensive experiments on four large-scale log benchmark datasets and multiple language model-based detectors demonstrate that LoRD consistently improves confidence reliability and substantially reduces overconfident anomaly-related errors without sacrificing anomaly detection performance.

To address challenges such as gray elements and material overlaps, this paper extends the level set-based negative-mapping interpolation method to the multi-material proportional topology optimization of macro-scale structures in two and three dimensions. The approach utilizes an alternating active-phase algorithm to decompose M-phase problems into simplified two-phase subproblems described by level set functions. By integrating an evolutionary strategy, the method circumvents complex sensitivity calculations. A negative-mapping interpolation then removes the material overlaps at the interfaces. Numerical experiments on 2D cantilever and MBB beams and on a 3D cantilever beam demonstrate that the present method eradicates gray elements, produces smooth boundaries and ensures overlap-free material distributions at a compliance comparable to that of the classical SIMP method, lower than the SIMP value in four of the eight two-dimensional test cases and higher by 0.3%, 0.4%, 4.8% and 12.7% in the other four; the influence of the material properties, of the interface treatment and of the number of iterations on the results is also discussed.

Recent progress in robotic learning has been fueled by large-scale datasets collected in everyday environments. However, most existing datasets emphasize short-horizon, low-contact tasks such as pick-and-place, and therefore do not capture the precision control, force/torque or tactile regulation, and multimodal feedback required for industrial assembly. To address this gap, we introduce PRISM, a large-scale multimodal dataset for contact-rich industrial operations. The dataset spans more than 25 manipulation tasks (e.g., electronic components plug/unplug, conveyor-based sorting) and covers diverse mechanical constraints. PRISM includes more than 5,000 trajectories totaling 45 hours of teleoperated demonstrations, recorded using synchronized multi-view RGB-D, force/torque, tactile, and robot-state measurements. In contrast to datasets collected in household or laboratory settings, PRISM provides a realistic benchmark for multimodal perception and control under high-precision industrial constraints, and serves as a foundation for contact-rich, generalizable manipulation in real-world manufacturing environments. The dataset is open-sourced at: https://tengbo-yu.github.io/PRISM/

Every document a security copilot retrieves can be true, instruction-free, and non-contradictory --- and the copilot can still be driven to assess a critical, exploitable vulnerability correctly and then recommend a remediation that leaves it open. We study this failure in retrieval-augmented generation (RAG) backing analyst-facing copilots in Security Operations Centers, and identify a class of attacks, \emph{\compmis{}} (COMA), in which every adversarial document is factually correct, instruction-free, non-contradictory, and distributionally benign --- yet the answer is misled by their \emph{composition}. We realize \compmis{} through \emph{action-corruption}, which steers a correctly-diagnosed vulnerability toward an inferior remediation, and \emph{verdict-flip}, which destabilizes the exploitability verdict via an undecidable reachability chain. Action-corruption bites all five tested models --- including frontier reasoning models --- on every run, on two synthetic domains and a real CVE (CVE-2021-33813); verdict-flip bites stochastically, decreasing with model capability but never vanishing. A single principle governs both: the attack succeeds when the disambiguating fact must be \emph{inferred} rather than \emph{read}. We propose \ccd{} (Causal Counterfactual Defense), an audit that measures the leave-one-out causal influence of each retrieved document and flags answers whose influence concentrates on low-trust documents. \ccd{} localizes the attack to attacker-controlled documents with no false positives on four benign multi-document controls; an adaptive influence-spreading adversary is caught by an \emph{aggregate} variant. We release attack seeds and a \ccd{} reference implementation.

State-of-the-art model-based reinforcement learning methods learn neural world models that allow policy improvement by planning in a latent space, without assumptions on the structure of the underlying environment. While expressive, these models are generally task-dependent: they learn uninterpretable latent representations that are tied to the training task and thus hard to generalize to new tasks. In this work, we present a novel world model formulation where the reward prediction only depends on a subset of structured, symbolic components of the whole latent state. Decoupling observation reconstruction and reward prediction allows us to learn world models that can adapt zero-shot, i.e. without further environment interactions, to new reward functions defined over the same symbolic state space. We discuss the main advantages and challenges of learning these neurosymbolic world models and demonstrate the strong generalisation properties of our approach over purely neural methods.

Let $W_N$ be an exact length-$N$ block from a strictly positive i.i.d. source $\mathbf p$ on a fixed finite alphabet. We prove that the canonical T-complexity $c_T$ satisfies \[ \frac{c_T(W_N)}{e^{-γ}h(\mathbf p) N/\log N}\longrightarrow1 \] in probability and in $L^r$ for every fixed $1\le r<\infty$, where $h(\mathbf p)$ is the source entropy in nats and $γ$ is the Euler-Mascheroni constant. The proof combines an exact length budget for canonical recovery, a critical-scale $E_1$ estimate for an ideal backward chain, and an exact finite-block boundary representation. An exact Doob-transform identity expresses the finite-boundary law relative to the ideal law conditioned at each step to avoid the current history-dependent successor codeword. A history-uniform renewal estimate then makes the telescoping endpoint density uniformly asymptotic to one, so no one-step approximation errors accumulate.

Tabular Foundation Models (TFMs) increasingly rely on in-context learning, where a model receives labelled examples at inference time and predicts labels for new inputs without updating its weights. Existing TFMs are typically trained on either massive synthetic corpora or very large collections of real datasets. In contrast, we show that surprisingly strong transfer can emerge from self-supervised pre-training on just a single real table. In this setting, we also find that tables tend to be either broadly useful or broadly poor regardless of downstream prediction task, and that the strongest predictor of usefulness is the number of features rather than the number of instances. This leads to a task-centric interpretation of tabular pre-training: the number and the quality of tasks are essential for the pre-training of TFMs. We show that the same task-centric perspective can help corpus design at scale: fine-grained column-level pre-processing consistently improves downstream performance, while no improvements are observed when we filter or deduplicate at the dataset level. Finally, we offer a new perspective for how TFMs generalize: we believe that tabular in-context generalization is largely retrieval-based, and good models are those that learn to identify relevant examples in the provided context and aggregate them well. The mechanics of TFMs have been relatively understudied; our task-centric, retrieval-based perspective offers a new framework to guide future model and corpus design.

In the Code World Model paradigm an LLM synthesizes an executable world model that a classical planner searches, and the model is accepted when it reproduces sampled transitions. We ask what that acceptance certifies in continuous control. We define the pipeline's danger as an expected risk and isolate its exact factor: the probability that N i.i.d. gate rollouts all miss a critical event of probability r is exactly (1-r)^N; an independent acceptance sample adds its budget to the exponent. On three hybrid instruments the accepted mode-blind model is exploited: the planner is pinned at the mode boundary at a regret of nearly the whole attainable return. We prove a localization budget, valid at boundary points: models with Lipschitz constant at most L differing by eta at a point disagree above tolerance eps on a region of volume at least kappa((eta-eps)/L)^(d+m); the discontinuous reset modes studied pay no such budget. With real LLM synthesis, GPT-5.x repairs an omitted 1D clamp in 105 of 111 mode-containing draws -- every attempt exact on 50 of 56 instrument-stream blocks (95% CI [0.781, 0.960]). On 2D regions no artifact recovers the rule (0/156); eight targeted interventions leave the failure in place, and positive controls locate it: a located rule is not induced, while given form and location the constants follow exactly. A version-space certificate proves identification is class-relative: at the widest dose the declared fit succeeds in 20/20 blocks and every sample-consistent circle is within tolerance in 18/20. We prove a class of entry rules exactly consistent with every sample yet harmless at play, so identifiability is a measurable property of the instrument. Re-scoring all 1034 artifacts on independent samples confirms acceptance certifies sample consistency and no more: where the gate is provably informative it covers about two percent of the exploited planner's queries.

Large Language Models (LLMs) demonstrate remarkable multi-hop reasoning capabilities over long contexts, yet the internal mechanisms enabling these distant cognitive leaps remain poorly understood. Traditional attention-based interpretability often fails to capture true semantic proximity due to routing artifacts like attention sinks. In this paper, we bypass attention weights to directly analyze the dynamic geometry of the hidden state manifold, proving that deep LLM latent spaces natively organize into Small-World networks. By sparsifying the continuous similarity matrices of long-context representations into unweighted graphs, we trace the connectivity between highly disjoint semantic anchors across two distinct architectures. Our findings reveal a sharp topological phase transition: while early syntactic layers remain entirely fractured, deep reasoning layers abruptly compress massive conceptual distances into highly navigable pathways strictly bounded by the "Six Degrees of Separation" limit (=< 6 semantic hops). Furthermore, we demonstrate the practical efficacy of this framework by applying it to zero-shot hallucination detection within Retrieval-Augmented Generation (RAG) using the RAGognize dataset. We show that factually grounded generations maintain structural integrity with their source context (approximately 3 hops), whereas hallucinations induce severe topological collapse. Ultimately, this work mathematically formalizes how transformers execute abstract reasoning and provides a novel, strictly geometric signature for evaluating factual reliability.

We study the problem of guessing a realization of an i.i.d. random sequence given element-wise correlated side-information. We use type-counting to provide estimates of the tail probabilities of the number of guesses for the case without side-information, which was shown earlier through large-deviation techniques. We then extend the same counting argument to the conditional setting, obtaining new explicit expressions for the corresponding guesswork exponents as divergences involving conditional tilted distributions. Finally, we provide an application of these exponents to brute-force password guessing with side-information.