arXiv:2606.15761v3 Announce Type: replace-cross Abstract: The saturation number $\mu^*(G)$ of a graph $G$ is the minimum cardinality of a maximal matching, and $H(G)$ is its harmonic index. TxGraffiti conjectured in 2023 that $\mu^*(G) \le H(G)$ for every nontrivial connected graph $G$, and B{\i}y{\i}ko\u{g}lu refuted this by showing that the ratio $\mu^*(G)/H(G)$ can be made arbitrarily large. Restricting to trees bounds the ratio sharply. Every nontrivial tree $T$ satisfies $\mu^*(T) < \frac{3}{2} H(T)$, with the constant $3/2$ best possible. A complementary bound $H(G) < 4\mu^*(G)$ holds for every graph with an edge, so on a nontrivial tree the saturation number is pinned to $\frac{1}{4} H(T) < \mu^*(T) < \frac{3}{2} H(T)$, both constants best possible. The friendship graph $F_4$ is a smallest counterexample to the conjecture, on nine vertices, and the smallest tree counterexample is the subdivided star on eleven vertices. For each positive integer $m$ a family of graphs with $m$ hubs has ratio approaching $m+1$, while the conjecture holds whenever all vertices have equal degree. Both invariants arise in applications, the harmonic index as a molecular descriptor and the saturation number as a measure of adsorption inefficiency, and the bounds estimate the latter, which is NP-hard to compute, by the former, which is computable in linear time.
Science Journals
arXiv:2606.19358v1 Announce Type: new Abstract: We introduceWorkBenchMark, a LEGO Duplo-based robotic assembly benchmark motivated by the RoboCup Smart Manufacturing League. Robotic assembly couples low-level manipulation with task-level symbolic reasoning under physical constraints, a combination that current end-to-end learning methods do not yet solve reliably. The benchmark provides 400 tasks across four complexity tiers. We provide an open-vocabulary perception, Assembly-by-Disassembly baseline solution. Our planning-based pipeline outperforms a modern vision-language-action approach across all tiers. The benchmark, simulation environment, and baseline implementation will be released openly to support the broader robotic assembly community.
arXiv:2606.19365v1 Announce Type: new Abstract: Diffusion models have become essential for high-fidelity 3D MRI synthesis, yet their deployment remains constrained by substantial GPU resource demands arising from hundreds of U-Net evaluations per sample and a highly heterogeneous kernel behavior. This paper performs a comprehensive performance analysis of the state-of-the-art medical diffusion model, Med-DDPM, across three generations of NVIDIA architectures to study kernel-level runtime breakdowns, instruction-mix characteristics, memory system utilization, warp-level activities, and profiler priority-score estimates. We show that training is overwhelmingly dominated by cuDNN convolution and implicit-GEMM kernels, with inefficiencies arising from memory-access patterns, tensor-layout conversions, and limited Tensor Core utilization. Guided by these insights, we evaluate two architecture-aware optimizations TF32 Tensor Core activation and a 3D channels-last layout and demonstrate that they reduce SM cycles by up to 100x, cut dynamic instructions by 100x, raise Tensor Core utilization from 1.45 to 9.98x, and increase IPC by 7% on A100, all without degrading synthesis quality.
arXiv:2606.19522v1 Announce Type: new Abstract: The retina offers a noninvasive window into neurodegenerative disease, capturing subtle structural patterns associated with a risk of future cognitive decline. Vision-language alignment frameworks such as REVEAL have shown that pairing retinal fundus images with structured clinical risk narratives improves early prediction of Alzheimer's disease (AD). A key design choice in these approaches is the use of phenotypic grouping, where individuals with similar risk profiles are treated as multi-positive pairs during contrastive learning. However, existing methods operationalize phenotypic similarity as a discrete construct, relying on hard group assignments that impose rigid supervision and decouple group formation from representation learning. We propose a continuous formulation of phenotypic structure within contrastive learning. Rather than assigning samples to fixed clusters, we model inter-subject similarity as a differentiable weighting function derived from intra-modality embedding similarities in both retinal images and risk profiles. These weights define soft multi-positive relationships through a continuous aggregation operator, enabling graded supervision that reflects the spectrum nature of disease risk. We further introduce a soft-target contrastive objective that jointly learns cross-modal alignment and phenotypic structure in an end-to-end manner. Evaluated on UK Biobank retinal imaging data for incident AD prediction, the proposed framework consistently outperforms discrete group-based contrastive learning and standard vision-language baselines. By treating phenotypic similarity as a learnable, continuous signal rather than a fixed grouping rule, our approach provides a principled and robust foundation for population-scale neurodegenerative risk modeling from multi-modal retinal and clinical data.
arXiv:2606.19620v1 Announce Type: new Abstract: We present G-Lox (group-adaptive Lox), a bridge-distribution system that preserves Lox-style distributor blindness while enabling hidden, stateful group-level adaptation. G-Lox places adaptive assignment logic behind a two-server privacy wall, so no single server learns group identifiers or group-to-bridge assignments. Private state access and state-dependent updates use two-server DPF/FSS protocols and secure two-party computation, supporting blockage reporting, transport-aware reassignment, and privacy-preserving group splitting. We evaluate G-Lox through system measurements and policy simulation. In our C++/EMP implementation over real TCP sockets, private state access has low client-visible overhead: across state sizes up to 2^16, communication remains in the low-KiB range per iteration. At M=1024, the client sends 1,968 bytes, receives 1,280 bytes, and completes an iteration in about 0.25 s. Simulations with group-specific blocking and Sybil enumeration show that G-Lox improves robustness over Lox- and rBridge-like baselines among systems that maintain broad issuance.
arXiv:2606.19654v1 Announce Type: new Abstract: ReDoS attacks constitute a critical class of resource-exhaustion vulnerabilities. In such attacks, adversaries exploit the pathological worst-case execution behavior of regular expression (regex) engines to induce highly asymmetric computational workloads, ultimately exhausting system resources and degrading service availability. To protect systems against ReDoS attacks, numerous detection techniques have been proposed that simulate the attack process by generating attack strings to proactively exploit ReDoS vulnerabilities at the early development stage and facilitate remediation. Existing techniques broadly fall into two classes: static analyses that search for pathological regex structures, and dynamic exploration methods that synthesize candidate attack strings. However, the generated attack strings are often impractical for real-world exploitation because they usually assume unrealistic input-length budgets and do not validate the effectiveness and efficiency of the attack at the program level. Therefore, many generated strings fail to trigger vulnerable regexes when applied to real-world programs, further limiting the practical utility. To address these shortcomings, we introduce an effective and efficient attack string generator, PUFFERDOS, designed to synthesize attack inputs that are both feasible within realistic length budgets and validated at the program level, enabling effective exploitation of ReDoS vulnerabilities in real-world programs. Specifically, we first define three vulnerable patterns based on our observation and formal verification. According to the patterns, PUFFERDOS conducts a synthesis technique to generate attack strings, and then refines and validates the strings with ReDoS-specific compositional concolic execution to guarantee real-world exploitability.
arXiv:2606.19703v1 Announce Type: new Abstract: Data visualization is essential for data analysis and communication, yet creating expressive visualizations remains labor-intensive. Recent AI-driven ``vibe coding'' tools enable users to generate visualizations through natural language interaction, lowering the barrier to entry. However, visualization implementation requires precise alignment between user intent and visual representation, which may differ from general software development practices. We present an empirical study with 16 participants of varying expertise to examine how users employ vibe coding tools for visualization implementation. Participants completed two visualization tasks and a semi-structured interview. Our findings characterize the diverse practices users adopt across prompting, evaluation, and iteration, and surface the challenges they encounter throughout the process.
arXiv:2606.20156v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have become a powerful framework for solving PDEs by embedding physical laws into differentiable objectives. Despite their advances, training PINNs remains fragile: recent conflict-averse optimization schemes alleviate gradient interference between residual and boundary losses, but we show that their effectiveness deteriorates as model capacity increases. In this paper, we identify a capacity-induced failure mode, where overparameterized networks undergo functional modularity, self-partitioning into task-exclusive modules that suppress cross-objective interaction and hinder convergence toward Pareto-stationary points. To address this issue, we propose a novel framework, Modular-Sparsity Synchronization (ModSync), which integrates structural optimization into conflict-averse training by penalizing task-exclusive connections while preserving interaction-promoting pathways. Extensive experiments across diverse PDE benchmarks demonstrate that ModSync consistently prevents capacity-driven failures, sustains robust cross-objective coupling, and achieves state-of-the-art accuracy. Codes are available at \url{https://github.com/heejokong/ModSync}.
arXiv:2606.20205v1 Announce Type: new Abstract: Psychological instruments designed for humans are increasingly used to assign large language models (LLMs) stable psychological profiles that affect their usability, safety assessment, and use as proxies for human participants in research. Using a formal psychometric framework, we show that these profiles are largely a measurement artifact. Administering a battery of personality and risk-preference instruments spanning self-reports and behavioral tasks to 56 instruction-tuned LLMs alongside large human reference samples, we report four findings. First, differences between models are driven not by the traits an instrument targets but by a directional response bias, a tendency to respond toward one end of the scale, or one labeled option, regardless of item content; a variance decomposition attributes 81-90% of between-model variation to this bias, against 9-16% in humans. Second, the bias declines with model capability but is not eliminated by it. Third, because bias rather than trait drives responding, an instrument's apparent reliability is almost entirely predicted by its response orthogonality, a term we coin for the proportion of items for which trait and bias point in opposite directions. Fourth, the profile a model appears to have shifts with the items used and can be manufactured through item selection. These results demonstrate that the apparent psychological profiles of LLMs are artifacts of the instrument used to measure them, not properties of the models themselves. As instruments borrowed from human psychology are rarely fully orthogonal and may inherently lack validity for LLMs, we call for dedicated assessments centered on response orthogonality.
arXiv:2606.19354v1 Announce Type: new Abstract: Test-time scaling (TTS) has emerged as a powerful paradigm for improving the reasoning performance of large language models (LLMs) by investing additional compute at inference time. A central component of TTS is the \emph{verifier}, which selects or scores candidate solutions to guide the search process. While prior work has explored the benefit of verification, a fundamental question remains underexplored: \emph{what is the optimal granularity of verification under a given compute budget?} Coarse-grained outcome reward models (ORMs) and fine-grained process reward models (PRMs) represent two extremes, yet neither alone achieves compute-optimality across all regimes. In this paper, we establish a unified theoretical framework, called \textbf{GRACE} (\underline{G}ranularity-\underline{R}egulated \underline{A}daptive \underline{C}omputational \underline{E}fficiency), that characterizes the optimal verification granularity as an explicit function of problem difficulty, verifier accuracy, and compute budget. We prove that there exists a phase transition: fine-grained verification dominates when either the compute budget is large or the problem is hard, whereas coarse-grained verification is preferred in the low-budget, easy-problem regime. Our theory unifies Best-of-$N$, beam search, and step-level MCTS within a single Pareto-optimality framework, and motivates an adaptive granularity strategy that provably achieves the compute-performance Pareto frontier. Empirical results on MATH-500, GSM8K, and AIME benchmarks corroborate all four theoretical claims, with our adaptive strategy outperforming fixed-granularity baselines by up to 3.1\% accuracy at matched compute.
arXiv:2606.20399v1 Announce Type: new Abstract: Ambiguity-bounded versions of $\mathrm{NP}$, denoted $\mathrm{UP}_{\leq f(n)}$, bound by $f(n)$ the number of accepting paths the nondeterministic polynomial-time Turing machine can have on inputs of length $n$. Such classes range from Valiant's completely unambiguous ($f(n)=1$) class $\mathrm{UP}$ to $\mathrm{NP}$ itself, where there is no bound or, equivalently, there is the toothless exponential bound ($f(n) = 2^{n^{O(1)}}$). This paper seeks to understand which of these classes stand and fall together as to whether they equal deterministic polynomial time. Informally put, what ranges of ambiguities have linked fates? That is, for which pairs of nondecreasing functions, $(f_1 ,f_2)$, satisfying $(\forall n)[f_1(n) \leq f_2(n)]$, does it hold that $\mathrm{P} = \mathrm{UP}_{\leq f_1(n)} \implies \mathrm{P} = \mathrm{UP}_{\leq f_2(n)}$. More particularly, for which pairs does that hold robustly, i.e., it holds in the real world and every relativized world? And for which pairs does that implication fail to hold robustly, i.e., there is an oracle $A$ such that $\mathrm{P}^A = \mathrm{UP}_{\leq f_1(n)}^A \subsetneq \mathrm{UP}_{\leq f_2(n)}^A$? The only previously known positive result is Watanabe's 1988 result that $ \mathrm{P} = \mathrm{UP}_{\leq 1} \implies (\forall k \geq 1)[\mathrm{P} = \mathrm{UP}_{\leq k}]$, which even holds robustly. His result, though lovely, applies only to constant-bounded ambiguities. As our positive result, we present a new class of cases (Theorem 3.8) that apply (and even robustly apply) at greater ambiguity levels. To give our class of cases, we leverage two approaches: a novel path-poisoning approach that works even on superconstant ambiguities (Theorem 3.5) and a new application of the power of padding (Theorems 3.3/3.4). As negative results, we show that for essentially all other cases, no linkage holds robustly.
arXiv:2606.20418v1 Announce Type: new Abstract: Acoustic environments often contain multiple overlapping sound events, and the same acoustic scene can be described using diverse textual expressions, making audio-text alignment inherently ambiguous. This paper proposes a probabilistic audio-language pretraining framework to model many-to-many correspondence ambiguity in audio-text alignment. Unlike conventional contrastive methods that learn deterministic point embeddings, our approach represents each modality as a distribution and learns uncertainty-aware cross-modal alignment. Rather than relying on masking-based uncertainty simulation, we mix audio-text pairs to create overlapping sounds that better reflect real acoustic mixtures and capture semantic inclusion relations among sound events. We further introduce a multi-level inclusion loss to enforce representations consistent with these relations. Experiments on audio-text retrieval benchmarks show that the proposed method outperforms deterministic baselines.
arXiv:2606.20459v1 Announce Type: new Abstract: IVF pregnancy rates are routinely modeled using patient-level variables, while high-resolution laboratory environmental data remain underutilized. We show that this is a missed opportunity. Rather than relying on raw sensor averages, we engineer 55 context-aware temporal features, including rolling thermal stability, simultaneous temperature-humidity adherence, peak stress duration, and post-stress recovery speed, that capture the dynamics of incubator microenvironments. On 61 weeks of data from an Asian IVF clinic, these features reduce cross-validated prediction error to 1.27%, compared to 3-5% for raw averages. We then train a hierarchical Bayesian Beta regression model that shares environmental effects across an Asian and a Northern European clinic via partial pooling, while preserving site-specific baselines. On held-out data from the Northern European clinic, the model achieves R2 = 0.86 and a 64% error reduction for the 35-39 age group over a naive baseline, demonstrating that structured environmental monitoring contains clinically meaningful, transferable signal.
arXiv:2606.19367v1 Announce Type: new Abstract: Building on a two-parameter Weibull framework for diagnosing transformer weight distributions, we study why the Weibull weight-scale parameter $\lambda$ grows, overshoots, and then relaxes during AdamW training. We derive a leading-order three-force decomposition of the squared weight norm from the AdamW update: an alignment force measuring the correlation between weights and the adaptive update direction, an injection force from adaptive step magnitude, and a decay force from decoupled weight decay. On self-trained Pythia-70M models with ground-truth optimizer moments, alignment dominates the rise phase, contributing 88-94% of the absolute force budget across four random seeds and remaining robust to super-weight removal. Near saturation, alignment and decay approach balance, explaining the transition from weight-scale growth to relaxation. These force dynamics directly govern the squared-norm component underlying $\lambda(t)$; the remaining RMS-to-Weibull reconstruction offset is measurable and decomposes into bridge and integration components, totaling approximately 5-6% in densely sampled regions. To extend the analysis to real models where optimizer moments are unavailable, we introduce a spline displacement method that recovers the alignment force from sparse checkpoints with approximately 92-94% accuracy, about twice the naive two-point baseline. We further observe that the peak value of $\lambda(t)$ varies with training-data coherence in our experiments, suggesting a data-dependent component of weight-scale growth that we leave to a controlled follow-up study. Code and data are available at https://github.com/tiexinding/NPM-Weibull-public.
arXiv:2606.20490v1 Announce Type: new Abstract: To address the challenges of interoperability in computational science, we present the latest updates to the software package MaRDI Open Interfaces. This software package aims to decrease the time and coding/testing efforts spent by computational scientists on tasks such as writing bindings to numerical solvers and adapting experiment codes to the varying interfaces of solvers for the same problem type (e.g., for benchmarking, which solver is better). By streamlining these tasks, this software package helps researchers focus on the actual essence of their computational projects. Here, we demonstrate a recently developed interface for nonlinear optimization and illustrate how it can be applied for computational experiments with optimization problems. As an example of such problem, we consider training of physics-informed neural networks to predict the solutions of viscous Burgers' equation.
arXiv:2606.19398v1 Announce Type: new Abstract: Self-supervised speech encoders are predominantly trained by predicting discrete hard cluster IDs at masked positions, a recipe that collapses acoustic ambiguity at category boundaries and requires interrupting training to re-cluster the entire corpus between iterations. We introduce S-JEPA, a JEPA-style encoder-predictor pair trained to match the soft posteriors of a Gaussian Mixture Model at masked positions via KL divergence. Training runs as one continuous optimization trajectory in two phases: a fixed GMM over MFCC features, then an online GMM over encoder features, with the input layer selected adaptively from a label-free signal, removing both the offline re-cluster step and the hand-tuned choice of which transformer layer to cluster on. Under the SUPERB protocol, S-JEPA achieves the lowest WER among evaluated SSL methods below 90M parameters and matches HuBERT-Base on emotion recognition at roughly half its parameter count, establishing a new Pareto frontier without offline re-clustering or teacher distillation. An analysis of the predictor's per-frame entropy on held-out speech reveals a bimodal distribution with a substantial minority of frames near the entropy of a perfect two-cluster tie, providing direct empirical evidence that the soft-target objective preserves the acoustic ambiguity that hard targets would collapse. Code is available at https://github.com/gioannides/s-jepa.
arXiv:2606.19468v1 Announce Type: new Abstract: The narrative composition of web-scale LLM pretraining corpora remains largely unexplored even though narrative is a fundamental mode of human communication. We present the first fine-grained study of narrative features in Dolma, a 3-trillion-token open pretraining corpus. Drawing on narrative theory, we design a framework spanning three core narrative elements (agency, setting, and events) operationalized as 11 interpretable dimensions. After sampling and annotating a diverse set of 400 passages, we finetune and validate NarraBERT, a RoBERTa-based model for fine-grained narrative prediction. We apply NarraBERT to 3M passages, resulting in a new dataset, NarraDolma. We find (i) narrative structure is measurable at scale across extremely heterogeneous data, (ii) we uncover a continuous, multidimensional narrative structure underlying web text, and (iii) narrative qualities are unequally distributed across pretraining sources and topics in ways that current curation practices neither measure nor account for. Our framework, dataset, and analyses provide a foundation for understanding how narrative qualities are distributed in LLM pretraining data and for studying how data composition affects narrative reasoning tasks. We publicly release NarraDolma and NarraBERT.
arXiv:2606.19777v1 Announce Type: new Abstract: We estimate that data centers caused average retail electricity rates to fall modestly in the United States from 2015 to 2024 using an instrumental variables approach. Despite prevailing sentiment, the finding is consistent with economic reasoning: existing large power system fixed costs, economies of scale in transmission and distribution, and declining unit costs for generation imply that durable demand growth lowers average prices. We find patterns of economies of scale for transmission, distribution, and generation costs as well as within and across retail customer classes. We caution that future supply constraints could reverse the effect.
arXiv:2606.20506v1 Announce Type: new Abstract: Style-content dual-reference generation aims to synthesize an image that preserves the structure and semantics of a content reference while adopting the style of a separate style reference.Despite recent progress, this setting remains challenging because models must balance content fidelity, style alignment, and instruction following avoiding semantic leakage from the style reference.A key bottleneck is the lack of large-scale triplet data with clean content-style separation and broad long-tail style coverage.In this work, we propose FreeStyle, a scalable dual-reference generation framework based on community LoRA mining.We treat community LoRAs as compositional anchors for style and content, and design a rigorous generation and filtering pipeline to construct large-scale Style-Reference and Content-Reference triplets across multiple base models.To address content leakage, we adopt a two-stage curriculum with stage-specific disentanglement mechanisms: an attention-level enrichment constraint that suppresses style-reference leakage in the style-transfer stage, and a frequency-aware RoPE modulation strategy that targets positional-correspondence-based leakage in the harder dual-reference stage.We also introduce a benchmark covering both style-reference and dual-reference generation, with evaluations on style similarity, content preservation, aesthetics, instruction following, and leakage rejection. The benchmark incorporates a style-invariant Content Alignment Score (CAS) and introduces a calibrated VLM-based Rejection Score for evaluating generation reliability and leakage suppression.Extensive experiments show that our model achieves a strong balance among style alignment, content preservation, and leakage suppression.
arXiv:2606.19469v1 Announce Type: new Abstract: Undergraduate computer science is governed by international curricular guidelines revised about once a decade, yet programs lack a reliable, reproducible way to measure how completely they cover the current guidelines and how that coverage shifts when the guidelines are restructured. We address this with a human-in-the-loop pipeline that measures a program's coverage of an external body of knowledge, applied longitudinally to one accredited BSc in Computer Science against Computer Science Curricula 2013 (CS2013) and 2023 (CS2023). The pipeline represents the program and each guideline as structured corpora, generates candidate course-to-knowledge-unit matches by semantic retrieval, and confirms them through human judgment under an explicit coverage definition. Of seven benchmarked retrievers, a reciprocal-rank-fusion ensemble was strongest, and a reputed long-context model underperformed a small sentence model, so retriever choice must be measured. Both maps were validated by an independent second rater (Cohen's kappa 0.64 for CS2023, 0.69 for CS2013). The program covers 49.7% of CS2023 and 50.9% of CS2013 knowledge units, near-constant across a decade. Extending the same retrieve-then-confirm design to competency articulation and cognitive depth shows that the program articulates the competency for ~88% of covered units under each guideline, yet delivers it at the recommended depth for 76% of present units under CS2023 against 95% under CS2013, a gap reflecting the newer guideline's raised expectations, not the program. The longitudinal comparison separates persistent structural gaps (parallel and distributed computing, foundations of programming languages, systems fundamentals), uncovered against both guidelines and ABET, from differences that reflect the standard's evolution. The instrument is reusable and available from the authors on request.
arXiv:2606.19480v1 Announce Type: new Abstract: When stochastic field dynamics are cast into a path-integral formulation, perturbation theory becomes systematic but the resulting expansion quickly grows combinatorially large. The setting targeted here includes multi-component, multi-dimensional fields with matrix propagators, tensor-valued couplings, and non-Gaussian driving noise specified by arbitrary $n$-point cumulants. Wick pairings grow factorially, and component indices must be routed through the tensor-valued vertices. The useful output is not a raw contraction list, but a diagram table: one entry per topology, with multiplicities, coupling sums, signs, and causal constraints resolved. We present sft-wick, an open-source Python package that constructs these diagram tables and computes their integrals numerically. Given an action and an observable, it enumerates topologically distinct Feynman diagrams, derives their algebraic coefficients, and evaluates the resulting diagram integrals from user-supplied response and cumulant functions. The core algorithm enumerates spatial topologies before routing component indices, avoiding contraction-by-contraction Wick expansion. Response-field constraints, including vanishing response-response contractions, the ito prescription, and the absence of causal response loops, are enforced during enumeration. Predictions are validated against direct Langevin simulation, agreeing to within the simulation's statistical noise.
arXiv:2606.19483v1 Announce Type: new Abstract: Vision Foundation Models (VFMs) with Vision Transformer (ViT) backbones, such as DINOv2, have become essential for downstream tasks like object recognition and semantic segmentation. The immense computational requirements of backbones often necessitate distillation into smaller architectures for edge deployment. Feature-based knowledge distillation (KD) often suffers from the teacher-student gap; the student struggles to imitate teacher's complex feature map due to its limited capacity. To mitigate this bottleneck, we propose LEAP: Layer-skipping Efficiency via Adaptive Progression, a training curriculum for ViT feature-based knowledge distillation. By utilizing the teacher's intermediate feature maps as a sequence of progressively more difficult targets, our curriculum allows the student to build a foundational representation before tackling higher-level abstractions. Our results demonstrate that this paradigm significantly accelerates convergence through adaptive difficulty selection across various student model sizes and dataset scales. With our curriculum, the LEAP-distilled ViT-S achieves 90.1% accuracy on ImageNet-100, a +12.24% improvement compared with baseline. On ImageNet-1K, LEAP achieves +3.84% and +7.75% improvement for the instance retrieval task on the Oxford and Paris datasets, respectively. Furthermore, the curriculum enables 25.1% savings in training FLOPs and 21% savings in training time on ImageNet-100 by implementing early-stopping for teacher inference during the initial stages of training. Code is available at https://github.com/KevinZ0217/LEAP
arXiv:2606.19491v1 Announce Type: new Abstract: Pretrained transformers sit near singular minima of the loss, where the Fisher information metric degenerates along dead directions: directions in parameter space along which the directional Fisher vanishes. Locating such a direction normally needs a forward pass and an eigendecomposition of activations, or a sampling-based complexity estimate; none returns a direction computable from the network's parameters alone. We give one, for LayerNorm transformers. The inverse-scale direction $\gamma^{-1}/\|\gamma^{-1}\|$ of the LayerNorm affine is an exact algebraic kernel of the post-final-norm centred activation covariance, for any input distribution, and induces a corresponding dead direction in parameter space. It is read from the LN scale parameter alone, with no forward or backward pass and no eigensolve: the cheapest dead-direction read, specific to LayerNorm. We test it on $14$ pretrained transformers ($9$ LayerNorm, $5$ RMSNorm; $160$M-$35$B; language and vision objectives). At random initialisation the predicted direction matches the measured bottom singular direction (one forward pass, direct SVD) to four decimal places on $9/9$ LayerNorm models, and is correctly absent on $5/5$ RMSNorm models, which lack the mean-subtraction projector that creates it. On the trained checkpoint the covariance eigenvalue along this direction deepens by ${\sim}10^3\times$ and further dead directions open; the random-init-to-trained gap is a one-forward-pass, per-checkpoint readout of singular structure along the predicted coordinate. Two consequences follow in closed form: the residual stream's smallest singular value is preserved block-to-block on $13/14$ transformers measured on their own input distribution, the one exception (Gemma$4$-$31$B) a genuine dead direction the same read pinpoints; and the kernel direction's presence classifies a transformer's normalisation from the parameters alone.
arXiv:2606.20563v1 Announce Type: new Abstract: Creating 3D visual illusions, a single 3D mesh that reveals entirely different semantics from various viewing angles, is a fascinating but tough challenge. Existing optimization-based methods are slow and can produce oversaturated colors. In contrast, naive stitching approaches fail to produce geometrically coherent objects. This results in visible unnatural seams and semantic leaks. In this paper, we present a fast and training-free framework for generating text-driven 3D visual illusions. Our approach decouples the generation into two stages. First, we propose a cross-space dual-branch denoising process. This process dynamically decodes 3D latents into voxel space for CLIP-guided orientation alignment and Signed Distance Field (SDF) blending, which ensures seamless geometric fusion. Second, we introduce a view-conditioned texture synthesis module that projects and aggregates view-specific 2D diffusion priors onto the fused geometry. Extensive experiments demonstrate that our method generates highly realistic, dual-semantic 3D illusions in just 3-5 minutes. It significantly outperforms existing methods in geometric integrity, semantic recognizability, and efficiency. Project page: https://siang1105.github.io/JanusMesh.github.io/
arXiv:2606.19519v1 Announce Type: new Abstract: The predominant formal models for blockchain systems, particularly smart contracts, have largely been drawn from the classical theory of computation, with the finite state machine (FSM) or labeled transition system serving as the primary conceptual tool. However, the FSM relegates the most difficult and novel aspect of a blockchain -- the achievement of consensus in a decentralized environment -- to a complex, often messy, implementation detail that lies outside the formal model itself. But the process of consensus is not an ancillary feature; it is the very essence of the computational phenomenon. To model it faithfully, a new mathematical language is required. The central thesis of this work is that topos theory, the theory of categories of sheaves, provides the native mathematical language for systems defined by local consistency and the construction of global truth.