arXiv:2602.10739v3 Announce Type: replace Abstract: Two-sided marketplaces embody heterogeneity in incentives: producers seek exposure while consumers seek relevance, and balancing these competing objectives through constrained optimization is now a standard practice. Yet practical platforms face interacting sources of heterogeneity that are often studied separately: multi-item recommendation, heterogeneous consumer groups, and business constraints beyond raw relevance. In this work, we present and study offline optimization framework for analyzing these trade-offs in an unified manner, extending prior two-sided formulations to represent more realistic discrete multi-item recommendations. Within this framework, we couple producer-side exposure guarantees with a consumer-group fairness objective and explicit business-oriented constraints. Our experiments show that the previously reported ``free fairness'' regime from highly stylized single-item recommendation settings disappears once each consumer receives multiple recommendations, and that moderate producer-fairness constraints can improve simulated business metrics by diversifying exposure away from saturated producers. We further show that reduction of inter-group disparity, preserves competitive overall utility.
Science Journals
arXiv:2607.00736v2 Announce Type: replace Abstract: Self-Supervised Monocular Depth Estimation (MDE) has garnered attention in recent years due to its independence from ground truth. However, most existing models are limited to a single scale and exhibit considerable performance degradation in complex driving environments. Networks specifically designed to handle dynamic traffic participants tend to be overly complex, hindering their deployment on resource-constrained automotive edge devices. To address these limitations and move towards robust driving perception, we propose FlexDepth, a scale-driven and flexible family of self-supervised MDE models tailored for challenging road scenarios. FlexDepth employs a two-stage static-dynamic decoupled training strategy, enabling the independent assessment of confidence for both static backgrounds and dynamic road objects. Furthermore, it introduces a meticulously designed Scale-Driven Decoder (SDD) to dynamically select components based on scale size, facilitating efficient feature fusion and the output of high-precision depth maps. Extensive experiments on standard driving benchmarks demonstrate that without any auxiliary information, our model achieves state-of-the-art performance across arbitrary scales with minimal computational overhead. Our smallest model, Flex-Nano, requires only 0.7 GFLOPs and achieves 37.6 FPS on mobile platforms, ensuring reliable real-time perception while maintaining excellent zero-shot generalization. Our source code is avalible: https://github.com/startnew/flexdepth
arXiv:2607.01515v1 Announce Type: new Abstract: We consider the problem of synthesizing robust feedback controllers for discrete-time linear systems that ensure the satisfaction of context-dependent linear temporal logic specifications in the presence of additive bounded disturbances. Building on existing results that reduce context-triggered temporal logic synthesis to the realization of context-dependent reach-avoid-stay (cRAS) objectives, we focus on the corresponding low-level control synthesis problem. We first employ certificate-based conditions for the almost-sure satisfaction of RAS specifications. Based on these conditions, we propose a switching control architecture that combines robust model predictive control (MPC) with a local invariant controller, and show that the resulting MPC value function serves as a reachability certificate while avoidance is enforced through robust constraints and the stay is enforced via the local controller. To obtain computationally tractable formulations for the resulting robust optimizations, we employ convex duality to reformulate the robust constraints into equivalent deterministic optimization problems, yielding convex quadratic and second-order cone programs for relevant geometric settings. The proposed framework is demonstrated on a robot navigation problem with context-triggered logical switches in both static and moving environments. The results show significantly larger feasible sets than Lyapunov-based approaches, while naturally accommodating dynamic environments and online task reconfiguration.
arXiv:2607.01431v1 Announce Type: new Abstract: We introduce ISOSCI, a benchmark of isomorphic cross-domain science problem pairs that separates reasoning ability from domain knowledge retrieval in LLM evaluation. Each pair shares identical logical structure but requires different domain-specific knowledge, enabling controlled attribution of reasoning-mode gains. Across five model pairs spanning four model families, we find that 91.3% of reasoning-mode gains are knowledge-dependent rather than structure-invariant (63/69 gains; Wilson 95% CI [82.3%, 96.0%]), directly challenging the assumption that chain-of-thought reasoning improves short-horizon procedural scientific problem-solving. Reasoning toggles on highly capable models provide less than 5 percentage points accuracy gain across all domains, and a reasoning-specialized model (o3-mini) that outperforms its standard counterpart on GPQA Diamond (+19.2 percentage points) underperforms on ISOSCI (-24.7 percentage points), showing that benchmark choice determines conclusions about reasoning utility. We release ISOSCI at https://huggingface.co/datasets/isosci/isosci
arXiv:2607.00780v2 Announce Type: replace Abstract: Most adaptive-inference techniques for foundation models change what the model does - early exit, MoE routing, KV-cache compression, dynamic attention sparsity. The input that hits the backbone, however, remains a fixed-grid tokenisation indifferent to image content. We argue that this is a missed lever. We present SpiralFovea, a parameter-free, input-adaptive tokeniser in which token identity, location, scale, and count are all functions of local visual entropy and selection completes before any backbone parameter is queried. Around content-driven hotspot anchors, multi-scale spiral rings produce <= 78 patches that replace the standard 196-patch ViT grid at the input stage. Across four canonical fine-grained benchmarks, SpiralFovea yields +1.7-2.1 pp accuracy with a 60% reduction in input tokens, an 84% reduction in self-attention FLOPs at every transformer layer, and 18-29% throughput gains over the matched static tokenisation baseline. A controlled ablation on CUB-200-2011 Genus across four backbones reveals a clean diagnostic: the gain magnitude tracks inversely with the strength of the backbone's whole-image positional prior, isolating self-supervised foundation models as the regime where input-adaptive tokenisation is most valuable.
arXiv:2607.01477v1 Announce Type: new Abstract: Photonic integrated circuits on the silicon-on-insulator (SOI) platform typically interface with free space via grating couplers, but scaling these to collimated beams with diameters beyond 100 $\mu$m requires a fundamentally different regime of extremely weak, spatially distributed coupling. While such large-area couplers have been demonstrated, their beam quality has remained largely uncharacterized, even though applications such as coupling into high-finesse resonators or trapping of cold atoms require both a large aperture and a near-Gaussian profile. This article presents an SOI meta-grating coupler that emits collimated, near-Gaussian beams of approximately 300 $\mu$m waist diameter. The design synthesizes the required emission profile from a spatially tailored coupling strength, realized by locally varying a sub-wavelength unit cell while independently setting the local emission angle. This approach achieves the very low coupling strengths required for large beams and yields a measured beam quality of $M^2 \leq 1.10$. The scheme extends directly to other target profiles, such as flat-top or higher-order modes, rendering meta-grating couplers a practical chip-to-free-space interface for mode-matching-sensitive applications.
arXiv:2607.01556v1 Announce Type: new Abstract: Standard MipNeRF360-style 3D Gaussian Splatting (3DGS) evaluation holds out every N-th frame -- but these frames have trained neighbors on both sides, so the metric measures near-trajectory interpolation rather than spatial generalization. We introduce a fair matched-count protocol that isolates this effect: both arms train on the same number of images and differ only in whether the holdout is spread evenly (interpolation) or forms a contiguous spatial sector (extrapolation). Our primary finding is a large, consistent interpolation-extrapolation gap of 3~12dB -- several times the differences typically reported between competing methods. The gap is robust to training noise, is in two cases large enough to flip a method ranking under multi-seed confirmation, and -- crucially -- persists across three representation families, including a non-Gaussian volumetric neural radiance field (NeRF), so it reflects spatial coverage rather than any one representation. Diagnostically, it is dominated by a diffuse/geometry-proxy component and tracks each view's angular distance to its nearest training view, a zero-cost signal that also guides capture planning; loss-side regularization yields only marginal gains. Standard holdouts remain useful for near-trajectory rendering but should not, alone, be read as evidence of spatial generalization. Prior work notes protocol sensitivity; ours is, to our knowledge, the first to combine matched-count paired holdout, cross-representation quantification, and a diagnostic analysis Table 1. We describe a spatial-holdout benchmark toolkit with standardized splits and baselines for 16 scenes, which we are preparing for public release.
arXiv:2607.01656v1 Announce Type: new Abstract: The interaction between brain structure and genetic influences is key to understanding neuropsychiatric disorders. However, most large-scale datasets are unimodal, providing either neuroimaging or genetics data. We propose CALM, a framework that learns interpretable associations between brain ROIs and genetic pathways from completely disjoint populations. CALM aligns the two modalities in a shared latent space via linear projections that simultaneously match the class-conditional latent distributions and ensure group separability. These projections provide interpretable pathway--ROI associations. When trained on unimodal imaging and genetics datasets, CALM generalizes to an unseen paired dataset, outperforming several state-of-the-art methods and ablation baselines. We also demonstrate stability of the learned associations against a paired baseline. Our experiments on autism spectrum disorder reveal immune and metabolic pathways linked to specific cortical regions and are consistent with established literature. Thus, CALM opens the door to leveraging large unimodal repositories for studying cross-modal interactions in brain disorders across disparate datasets.
arXiv:2607.01858v1 Announce Type: new Abstract: Automata on linear orderings are finite-state automata introduced by Bruy\`ere and Carton as a broad generalization of finite, infinite and transfinite-word automata. In this context, a word is defined as a function from a linear ordering to a finite alphabet. This general definition can make automata on linear orderings difficult to reason about. In this work, we introduce constructible words as an intuitive way of tackling this difficulty. These words can be obtained by a finite number of applications of simple operators and thus admit a finite notation. We show that a rational language of words indexed by scattered (countable and uncountable) linear orderings is characterized by its constructible words. Our proof of this result relies on an interesting theorem of semigroup theory due to Colcombet. We expect this property to be useful in future theoretical developments about automata on scattered linear orderings.
arXiv:2607.02477v1 Announce Type: cross Abstract: We study the mixing times of stochastic spin systems corresponding to nearest-neighbour Glauber dynamics on dynamical percolation, defined on $d$-dimensional torus of side-length $N$. In this model, the status of each edge (open or closed) updates independently at rate $\lambda>0$, according to $\mathrm{Ber}(p)$ samples. Simultaneously, the spin of each site updates at rate $1$ according to Glauber dynamics on the environment restricted to open edges. We show that for a relatively general class of nearest-neighbour systems, as long as $p<p_c(d)$, for any temperature, if $\lambda$ is sufficiently small, the mixing time is of order $\frac{\log N}{\lambda}$. This Markov chain is non-reversible, and the proof is obtained by developing a particular coupling that couples together local configurations whenever the environment behaves well.
arXiv:2605.27898v2 Announce Type: replace Abstract: As LLMs are increasingly deployed as agents, reliable assessment of their agentic capabilities has become essential. However, reported benchmark scores often jointly reflect model capability and the implementation choices each benchmark is packaged with, making cross-benchmark results difficult to interpret as clean measurements of the underlying model. In this work, we present a unified framework for the fair evaluation of LLM agentic capabilities. Driven by a unified configuration system, the framework integrates diverse benchmarks into a standardized instruction-tool-environment format, executes agents through a fixed ReAct-style architecture within a controllable sandbox, and provides an optional offline setting that replaces volatile live environments with curated snapshots, so that framework effects and environment effects can be analyzed separately. Building on this, we unify the evaluation methodology under each benchmark's original task-success criteria, while introducing unified metrics for resource consumption and a taxonomy for decision- and execution-level failure attribution. Within this framework, we adapt 7 widely used benchmarks spanning 24 domains across single-agent, multi-agent, and safety-critical scenarios, and conduct a large-scale empirical analysis over 400K rollouts and 5B tokens on 15 models. The results show that scaffold choice and environmental volatility materially shift benchmark outcomes in both directions, allowing our framework to disentangle intrinsic LLM capabilities from framework- and environment-induced artifacts. We further demonstrate its extensibility as a secure testbed for safety-critical domains. Codes and benchmarks at are available at https://github.com/whfeLingYu/A-Unified-Framework-for-the-Evaluation-of-LLM-Agentic-Capabilities, https://huggingface.co/datasets/whfeLingYu/Unified_Agent_Framework.
arXiv:2607.01530v1 Announce Type: new Abstract: Understanding user intent is fundamental to delivering relevant search results in e-commerce. However, substantial fraction of real-world queries are under-specified (e.g., "watch" or "shirt"), lacking explicit attributes such as gender or age group. This ambiguity poses a significant challenge for query intent detection models in e-commerce search systems, which must accurately infer latent user intent (e.g., age, gender) to support effective downstream retrieval. We introduce IntentTune, a framework for resolving ambiguous or under-specified query intents by leveraging either (1) user-specific behavioral signals including search history, browsing activity, and profile attributes or (2) population-level demand patterns aggregated across all users. Through experiments on real-world e-commerce data, we first demonstrate that population-level demand patterns alone are insufficient to reliably infer intent in under-specified queries. We then demonstrate that user-specific behavioral signals -- particularly prior search queries -- outperform both population-level statistics and static profile information for inferring gender, age group, product category, and size intent from underspecified queries.
arXiv:2607.01553v1 Announce Type: new Abstract: Transformers have become general-purpose architectures, but their all-to-all self-attention is poorly matched to graph data, whose interactions are sparse, structured and multi-scale. Existing Graph Transformers address this mismatch through structural encodings, hybrid message-passing modules or learned attention constraints, often introducing additional complexity and limited interpretability. Here we introduce X-LogSMask, an explainable multi-head logarithmic structural mask that injects symmetrically normalized graph topology directly into attention logits. The logarithmic transform converts structural connectivity into a topology-aware gating signal, suppressing unsupported node interactions while preserving feature-dependent attention. By assigning different powers of the normalized adjacency matrix to different attention heads, X-LogSMask gives each head a defined structural radius and supports multi-hop information propagation within a single layer. We further show that a standard Transformer encoder can be interpreted as one-step message passing on a complete graph, motivating X-LogSMask as a topology-constrained alternative to unrestricted self-attention. Across 20 node-, edge- and graph-level benchmarks, Transformers equipped with X-LogSMask achieve state-of-the-art performance on 13 datasets and remain competitive in a lightweight one-layer configuration. These results show that simple, interpretable structural masks can make self-attention an effective graph-learning operator without changing the Transformer architecture. The code is available at https://github.com/LiLeyan-0120/X-LogSMask.
arXiv:2607.01585v1 Announce Type: new Abstract: Predicate invention (PI), the creation of new predicates to extend the hypothesis space, remains a critical bottleneck in Inductive Logic Programming (ILP). Existing methods rely on domain expertise and produce semantically opaque predicates, hindering adaptation to unfamiliar domains and cross-task reuse. We present ADVENT, an LLM-driven PI mechanism for ILP. ADVENT pairs LLM abductive generation with Prolog deductive verification, forming an iterative loop in which concrete execution results guide the LLM to refine candidate predicates. The mechanism leverages Large Language Models to identify implicit patterns in structured relational data and invent auxiliary predicates with meaningful names and definitions. Invented predicates and learned rules accumulate in a knowledge pool for cross-task reuse. Experiments on nine poker-hand concepts across seven LLMs show that LLM-driven PI achieves 58% success rate where ILP alone fails entirely, formal verification raises this to 80%, and the knowledge pool yields gains up to +31 percentage points, while producing human-interpretable rules. These results suggest that ADVENT offers a promising direction for automating predicate invention and enabling cross-task knowledge reuse in ILP.
arXiv:2510.19709v2 Announce Type: replace-cross Abstract: Noncollinear antiferromagnets exhibit anomalous Hall and magneto-optical Kerr effects driven by Berry curvature despite negligible net magnetization, promising ultrafast spintronic applications. While both effects are theoretically expected to reveal the intrinsic Berry curvature that serves as a spintronic memory bit, their quantitative interpretation is complicated by additional temperature-dependent contributions superimposed on the magnetic order parameter: extrinsic skew scattering in dc Hall transport, and optical-resonance effects in visible-wavelength Kerr measurements. Here we perform polar Kerr measurements at the infrared telecommunication wavelength (1550 nm) on epitaxial, stoichiometric Mn3NiN single crystal films, revealing for the first time a spontaneous Kerr signal that remains stable within a few percent over a 200 K range below the N\'eel temperature. This temperature-invariant intrinsic Kerr response contrasts with the strongly temperature-dependent anomalous Hall effect in the same sample dominated by extrinsic skew scattering. Our findings establish infrared Kerr effect as a robust, local probe of Berry curvature in noncollinear antiferromagnets, enabling quantitative characterization and advancing antiferromagnetic spintronic technologies.
arXiv:2604.01874v2 Announce Type: replace-cross Abstract: We exhibit nontrivial transversal logical multi-controlled-$Z$ gates on $[\![N,\Theta(N),\tilde\Theta(N)]\!]$ quantum low-density parity-check (qLDPC) codes with soundness $\tilde\Theta(1)$, combining nearly optimal code parameters with fault-tolerant non-Clifford gates on qLDPC and quantum locally testable codes for the first time. Remarkably, our proofs proceed through highly general algebraic arguments. Building on insights from [Li et al.,~arXiv:2603.25831], we develop a general covering space framework for constructing and computing a rich family of cohomological invariant forms on sheaf codes that induce transversal logical multi-controlled-$Z$. To certify their nontriviality, we further demonstrate the existence of two-way product-expanding punctured Reed--Solomon codes, which is striking in light of the many negative examples for the product expansion behavior of ordinary Reed--Solomon codes. This approach directly overcomes the previous obstruction to realizing nontrivial logical operations while simultaneously preserving the code parameters. The claimed almost-good code results follow immediately as examples.
arXiv:2607.01600v1 Announce Type: new Abstract: As large language models (LLMs) are deployed as communicating agents, does inter-agent communication cause outputs to converge? We introduce BOUNDARY_SYNC, a protocol measuring representational coupling via the Coupling Amplification Factor (CAF = JSD_cond / JSD_baseline), where CAF < 1 indicates homogenization and CAF > 1 indicates diversification. In controlled GPT-4o experiments (N=30, ~9,900 API calls), we measure coupling in text and image communication. Key findings: (1) text communication causes significant homogenization (CAF=0.803 [0.740, 0.873], d=1.30, p<0.001), confirmed by no-communication ablation and prompt-perturbation controls; (2) image communication also homogenizes under within-modality baselines (CAF=0.834 [0.811, 0.858]), with comparable proportional effect; (3) group size moderates coupling direction -- K=5 produces homogenization while K=3 yields CAF > 1.0 (point estimates 1.14 and 1.06, CI pending), suggesting a directional shift toward diversification; (4) cross-model replication shows extreme variation (CAF 0.034-0.803), with DeepSeek dominated by format artifacts; (5) coupling is stateless -- driven by prompt context rather than cumulative updating, with continuous consensus producing monotonic convergence. These results establish LLM agent coupling as real, measurable, and controllable at the prompt level, with direct implications for multi-agent system design.
arXiv:2607.02153v1 Announce Type: new Abstract: We improve significantly the Nart-Montes algorithm for factoring polynomials over a complete discrete valuation ring $\mathbb{A}$. Our first contribution is to extend the Hensel lemma in the context of generalised Newton polygons, from which we derive a new divide and conquer strategy. Also, if $\mathbb{A}$ has residual characteristic zero or high enough, we prove that approximate roots are convenient representatives of types, leading finally to an almost optimal complexity both for irreducibility and factorisation issues, plus the cost of factorisations above the residue field. For instance, to compute an OM-factorisation of $F\in\mathbb{A}[x]$, we improve the complexity by a factor $\delta$, the discriminant valuation of $F$.
arXiv:2607.01607v1 Announce Type: new Abstract: Large language model (LLM) inference suffers from growing inefficiency across the prefill and decode phases, especially under weight-only quantization, where activations remain in FP8 while weights are compressed to low-bit integers. Existing LUT-based accelerators mainly target FP8-INT4 computation and still rely on separate floating-point (FP) datapaths for attention GEMM operations, leading to redundant hardware and non-unified mixed-precision execution. Moreover, their static dataflows are poorly matched to the distinct prefill and decode phases. To address these challenges, we propose MxGLUT, a reconfigurable LUT-centric broadcast (RLB) dataflow accelerator built on mixed-precision LUT-based processing elements (MxLPEs). Guided by a unified LUT-based execution framework, MxGLUT organizes both FP8-INT4 and FP8-FP8 GEMMs under a single LUT-based compute mechanism without dedicated FP multipliers or additional FP datapaths, and further adopts the RLB dataflow that localizes heavy partial-sum accumulation during the prefill phase and exploits weight reuse in the decode phase. Synthesized in UMC $28\,\mathrm{nm}$ CMOS at $200~\mathrm{MHz}$, MxGLUT reduces multiplier area by up to $56.92\%$ and power by up to $77.07\%$ and $78.35\%$ in FP8-INT4 and FP8-FP8 modes, respectively. At the accelerator level, MxGLUT achieves an area efficiency of $0.492~\mathrm{TFLOPS/mm^2}$ and an energy efficiency of $11.58~\mathrm{TFLOPS/W}$, while adding native FP8-FP8 support incurs only $2.57\%$ and $3.34\%$ reductions in area and energy efficiency, respectively, relative to the FP8-INT4-only FIGLUT baseline. Across the Llama family, MxGLUT achieves up to $2.16\times$ and $1.49\times$ latency speedup, and reduces normalized energy to $0.44\times$ and $0.71\times$ in prefill and decode, respectively, with at most $1.70\%$ perplexity increase.
arXiv:2607.01609v1 Announce Type: new Abstract: Recent advances in Artificial Intelligence (AI) have revolutionized Electronic Design Automation (EDA), particularly through Large Language Models (LLMs) for circuit design tasks. However, their application to analog and mixed-signal domains remains limited by the lack of machine-readable representations of existing circuit design knowledge. Circuit schematic images found in research manuscripts, textbooks, and websites constitute a vast repository of validated designs; however, these visual representations cannot be directly processed by EDA tools. Converting them into machine-readable netlists is essential for enabling simulation, verification, and building comprehensive databases for AI-based models. Current conversion methods lack generalization across both Integrated Circuit (IC) and Printed Circuit Board (PCB) level schematics. Moreover, they struggle with component recognition and connectivity inference, and fail to distinguish between connected junctions and crossing wires. In this paper, we propose SINA, an open-source circuit schematic image-to-netlist generator. SINA is a fully automated pipeline that integrates deep learning for robust component detection, connected-component labeling for accurate connectivity inference, Optical Character Recognition (OCR) for component reference designator extraction, and a Vision-Language Model (VLM) for reliable reference designator assignment. SINA handles both IC- and PCB-level schematics and incorporates dedicated crossing-wires detection to differentiate wire intersections from connections. We validate the correctness of the generated netlists using graph isomorphism techniques. Our experiments demonstrate an overall netlist generation accuracy of 96.67%, which is 2.72x higher compared to state-of-the-art approaches.
arXiv:2607.01610v1 Announce Type: new Abstract: Counterfactual explanation (CE) is widely used to enhance the interpretability of machine learning models and support data-driven decision-making based on model predictions. However, existing CE methods typically require two exogenously specified inputs: a desired output value (target) and a distance function that quantifies changes in explanatory variables. In regression settings, neither the validity of target specification nor the practical interpretation of the distance metric has been sufficiently addressed. Furthermore, most existing CE methods focus on altering predictions rather than optimizing a decision objective, even though real-world decision-making often requires explicit objective maximization. To address these limitations, we formulate CE as a profit maximization problem in management and marketing contexts and propose a framework termed profit-based counterfactual explanation (PBCE). PBCE eliminates the need for exogenous target specification by directly maximizing profit as the primary optimization objective. Concurrently, the distance term is reinterpreted as the cost of modifying product attributes, providing a clear and economically grounded interpretation.
arXiv:2607.01980v1 Announce Type: new Abstract: Automated authoring of Gherkin Behavior-Driven Development (BDD) acceptance criteria remains a manual bottleneck in requirements engineering. This study investigates whether epic-organized LLM-generated Gherkin produces higher quality and coverage than requirement-aligned generation. We compare our Timeless (an epic-organized LLM pipeline) approach against a naive large language model (LLM) baseline on four requirements documents (107 requirements) from the PURE dataset. Evaluation covers structural metrics, automated requirement coverage via TF-IDF and dense embeddings, and blind expert assessment by four researchers. In our evaluation, the JSON-constrained pipeline produced structurally valid scenarios across all generated outputs, while the zero-shot baseline achieved 99% structural validity. Semantic coverage was comparable to the baseline, with Timeless achieving 94.3% semantic Requirement Coverage Rate compared with 92.9% for the baseline. TF-IDF produced lower coverage scores for the epic-organized output, suggesting that lexical metrics may miss coverage when scenarios paraphrase requirements at a higher level of abstraction. Expert raters prefer the epic-organized strategy on Correctness (4.61 vs 4.14), Executability (4.61 vs 4.07), and Completeness (4.31 vs 3.50). Overall, the results suggest that epic-organized generation can improve perceived Gherkin quality while maintaining comparable semantic coverage, although broader replication is needed before generalizing this finding.
arXiv:2607.01993v1 Announce Type: new Abstract: The silhouette is one of the most widely used measures to assess the quality of a $k$-clustering of a dataset of $n$ elements. Its evaluation requires no information beyond the clustering assignment. In addition, the silhouette is extremely easy to interpret, providing a score to measure the quality of a clustering as a whole or for each element. The exact computation of the: (i) silhouette of each element of a dataset; and (ii) the global silhouette of the clustering; require $\Theta(n^2)$ distance calculations, under general metrics. The quadratic complexity $\Theta(n^2)$ is extremely prohibitive, especially on massive modern datasets. Surprisingly, existing approximate methods using $O(n^2)$ distance calculations are heuristics not offering provable and controllable guarantees on the quality of their results. We introduce the first rigorous and efficient algorithms to estimate: (i) the (local) silhouette of each element of a dataset; and (ii) the (global) silhouette; of any metric $k$-clustering. Our methods, based on sampling, perform $O(nk\varepsilon^{-2}\ln (nk/\delta))$ distance computations, and provide estimates with additive error $O(\varepsilon)$ with probability at least $1-\delta$. That is, parameters $\varepsilon$ and $\delta$ in $(0,1)$ control the trade-off between accuracy and efficiency. We also introduce a scalable and distributed design of our methods for the MapReduce and Massively Parallel Computing (MPC) frameworks. Our distributed algorithms use a constant number of rounds and sublinear local memory. Finally, we perform extensive experiments against state-of-the-art approaches. The results show that our new techniques yield the best trade-off between accuracy and efficiency for both local and global silhouette estimation. In addition, our methods scale efficiently to massive datasets for which an exact computation of the silhouette is not practical.
arXiv:2605.00275v2 Announce Type: replace Abstract: Background: Conversational AI chatbots are emerging as scalable mental health tools, but little is known about real world engagement or its relationship to clinical outcomes. Objective: To characterize engagement phenotypes among users of Ash, a purpose-built AI mental health chatbot, and examine associations with clinical change and working alliance. Methods: K-means clustering across eight behavioral features identified engagement phenotypes among 102,684 users. Subsamples completed the PHQ-9 (n=298), GAD-7 (n=298), and MSPSS (social support; n=194) baseline and 3 weeks; 11,437 users completed baseline Working Alliance Inventory (WAI). Results: Five engagement phenotypes emerged: Early Dropouts (52.2%), Power Users (1.6%), Intensive Users (4.1%), Weekly Users (25.3%), and a novel Concentrated User pattern (16.8%); across users, 66.9% had at least one overnight session (9pm-5am). Significant pre-post improvements occurred in depression (d = -0.51), anxiety (d = -0.57), and social support (d = 0.22). An observed dose-response gradient in self-reported depression improvement was replicated in a larger sample using model-predicted PHQ-9 (n = 23,813), with the largest improvements among high-engagement Power and Intensive Users (d = -0.40 and -0.43) and the smallest among Early Dropouts (d = -0.11). Higher working alliance predicted depression improvement and moderated the engagement-social support relationship. Conclusions: Engagement with AI mental health tools is multidimensional, and different clinical outcomes respond to different dimensions of use. Findings caution against treating session counts as a primary engagement metric and offer naturalistic evidence for the clinical value of purpose-built conversational AI.
arXiv:2607.01902v1 Announce Type: new Abstract: Reliable confidence estimates are essential in semantic segmentation, especially in safety-critical settings where overconfident errors can mislead downstream decisions. Yet modern segmentation models often remain miscalibrated. Post-hoc calibration offers a practical way to correct confidence estimates without retraining the segmentation model, but its use in dense prediction raises structural issues that are often overlooked. We study two such issues. First, adding a constant to all logits leaves the softmax probabilities unchanged, but several standard calibrators can still depend on this arbitrary offset. As a result, two logit representations encoding the same predictive distribution may yield different calibrated probabilities. We define translation-invariant (TI) calibrators as those whose outputs are unchanged under such shifts, characterize which common calibrators satisfy this property, and construct TI counterparts of shift-sensitive calibrators to isolate the effect of removing representation dependence. Second, post-hoc calibration is typically fitted by minimizing a likelihood-based objective, whereas segmentation models are trained with task-specific metrics such as Dice. This mismatch can cause calibration to alter class orderings and degrade the deployed segmentation map. We study decision-preserving calibration under argmax- and order-preservation constraints. Since enforcing these constraints collapses affine softmax calibrators to temperature scaling, we introduce class-conditional affine calibrators that can be made argmax- or order-preserving while retaining greater expressivity, allowing us to quantify the calibration-segmentation trade-off induced by decision preservation. Across natural-image and medical segmentation benchmarks, and under corruption-based covariate shift, matched comparisons show that TI variants generally improve calibration metrics, while decision-preserving variants prevent…