Papers

We study the generalized covering radii of binary primitive BCH codes, which measure how many parity-check columns suffice to span several prescribed syndromes. For the four-error-correcting family of length $2^m-1$, the second radius is exactly $11$ for $m\geq55$, and it is either $11$ or $12$ for $m\geq16$. For every fixed error parameter at least two, we give an explicit stable bound with two adjacent possible values for the second radius and an arithmetic criterion for exactness. At every higher order, we obtain explicit lower and upper bounds whose additive gap is bounded independently of the order for each fixed error parameter, once explicit field-size conditions hold. The bounds are therefore asymptotically tight as the order grows. The higher-order upper bound retains the common-core support count established by Xiong, Yip, and Zullo; our refinement reduces its sufficient field-size threshold at large order. The refinement combines componentwise mixed degrees with the ordinary degree of a multicone. The upper bounds come from constructing syndrome representations with a common set of parity-check columns.

While reinforcement learning (RL) allows generalist robot policies to continually improve during deployment, the large model size of modern generalist policies, such as VLAs, poses a fundamental obstacle to effective RL improvement. In particular, their severe inference latency—which can lead to pauses or jerky movements—can alter the effective environment dynamics and, if not correctly accounted for, break the Markov assumption that RL relies on, causing standard RL algorithms to fail completely. In this work, we introduce a latency-aware framework, Asynchronous RL with Intermediate Information (ARLI), that enables RL-based improvement of generalist policies under inference delays. Our framework builds on asynchronous inference approaches, which interleave action generation with execution to hide latency, and addresses its incompatibility with RL by providing a low-latency RL policy design that maximizes reactivity within the inference window through two contributions: state augmentations that restore near-Markovian structure by incorporating committed actions and a mid-inference observation. We evaluate our approach across simulated and real-world manipulation tasks, and find that it enables effective finetuning under inference delays where standard RL fails entirely, even matching or exceeding the performance of standard RL in idealized no-latency settings.

RL has emerged as a powerful paradigm for enhancing the instruction following capabilities of LLMs. While existing training recipes achieve substantial gains, we find that they suffer from exploration bias towards easy instructions when the training data has multiple instructions in a prompt. This bias is caused by two main reasons: 1) the policy model's initial ability to satisfy hard instructions is too low to trigger successful exploration during RL training, so the optimization is biased towards easy instructions; and 2) canonical RL training recipes typically employ a cumulative reward (the number of instructions fulfilled), treating all instructions equally, which biases the policy model towards fulfilling easy instructions to obtain the same amount of reward. To address these issues, we first propose two metrics to measure the exploration bias in instruction following and then introduce a two-stage framework to alleviate it: 1) Behavioral Bootstrapping, a lightweight rejection sampling fine-tuning stage before RL to activate hard instructions; and 2) Scarcity-Aware Rewards, a new RL reward function that assigns rewards to instructions based on their empirical scarcity. Experiments show that the proposed metrics are highly correlated with model performance, and our methods unleash the potential of RL training: our best models outperform the baselines by a significant margin across three verifiable instruction following benchmarks. We release codes at https://github.com/mianzhang/MulIF.

In this report, we recall Christiansen's [2011, Num. Math.] discrete elasticity complex that uses spaces of polynomials and distributions. Using the degrees of freedom of those spaces, we write a complex using vector-valued chains and co-chains that is isomorphic to Christiansen's complex. The operators of the new complex are algebraic, but use the geometry of the simplicial complex. Finally, we define a de Rham-like map from the smooth elasticity complex to this discrete complex.

We prove that exact Euclidean decision-CVP is $\mathsf{NP}$-complete on the coefficient lattices of nonzero principal ideals in the power-of-two cyclotomic rings $R_d:=\mathbb{Z}[y]/(y^d+1)$. Our deterministic reduction from Exact Cover by 3-Sets (X3C) produces a target and a squared threshold $\Delta$ such that the closest squared distance is exactly $\Delta$ in YES instances and at least $\Delta+4$ in NO instances. This also implies $\mathsf{NP}$-hardness of exact search-CVP under polynomial-time Turing reductions. We also transfer the resulting principal-ideal CVP instances to full-rank principal ideals of the cyclic quotient ring $\mathbb{Z}[X]/(X^D-1)$, where $D:=2d$. Their coefficient lattices are invariant under cyclic coordinate shifts. The lift preserves principality and multiplies corresponding squared distances by eight. Thus, on principal cyclic ideal lattices, exact decision-CVP is $\mathsf{NP}$-complete and exact search-CVP is $\mathsf{NP}$-hard. We also obtain uniformly computable fixed cyclotomic and cyclic families in which only the target and threshold depend on the X3C collection. Consequently, a polynomial-time solution to exact decision-CVPP on either family would imply $\mathsf{NP}\subseteq\mathsf{P}/\mathrm{poly}$ and collapse the polynomial hierarchy to $\Sigma_2^{\mathsf{P}}$. To our knowledge, the cyclic results answer Micciancio's questions of whether exact decision-CVP is $\mathsf{NP}$-hard on cyclic lattices and on a fixed family of cyclic lattices, even when restricted to full-rank principal cyclic ideals. Finally, under the coefficient embedding, we prove that exact decision-module-SIVP is $\mathsf{NP}$-complete on free rank-two modules over the same cyclotomic rings.

Adaptive cruise control (ACC) vehicles are the first generation of automated vehicles. While fully automated vehicles are expected to benefit traffic flow, field experiments have shown that commercially available ACC vehicles may instead degrade it by reducing string stability and roadway throughput. To mitigate these effects, existing studies adjust the ACC control algorithm or introduce additional control inputs; however, few have examined the transition between the cruise control (CC) and ACC modes without modifying the ACC control algorithm itself, leaving the impacts of ACC vehicles incompletely understood. To address this gap, we propose a unified dynamical model of CC and ACC that interpolates continuously between the two modes through a sigmoid weighting function, and improve traffic flow by designing the mode switching. Based on this new model, we conduct an equilibrium and string stability analysis of the platoon, revealing the trade-off among safety, throughput, and string stability. The optimal switching threshold is designed under throughput-priority and safety-priority criteria, and compared against the threshold adopted by commercially available ACC vehicles. Numerical experiments show that, with a properly designed switching threshold, the throughput increases by up to 58.6% and the average speed variation, a measure of speed oscillations, decreases by up to 39.7% relative to the commercial baseline. We conclude that the excessively large switching threshold of commercially available ACC vehicles is a likely cause of their negative impact on traffic flow, and that this impact can be mitigated by properly reducing the threshold toward a safer and more string-stable regime.

Many support applications are developed to help users living through intimate partner abuse (IPA). However, many of those projects get abandoned, because the application was a prototype that never got turned into an actual product, funding ran out, or the people maintaining it moved onto other projects. This abandonment can have devastating consequences because the users of these applications are vulnerable by definition. In this ongoing research, we aim to measure the abandonment of intimate partner abuse support applications. Our preliminary results with a dataset of 197 support tools indicate that 58.9% of applications have lost support over time, either no longer receiving updates or not being available online at all.

Unmanned aerial vehicle (UAV)-mounted 5G New Radio base stations (gNBs) can augment terrestrial networks with an on-demand, repositionable Frequency Range 2 (FR2) capacity layer. This flexibility, however, couples the physical network topology with radio-resource management: UAV movement reshapes blockage, channel quality, and the set of effectively served users, while traffic demand, queues, and service requirements evolve at a much faster timescale. Existing Open Radio Access Network (O-RAN)-enabled UAV studies optimize trajectory, deployment, association, or resource allocation, but typically in isolation, without coordinating slow aerial control with fast per-user scheduling. We instead exploit O-RAN disaggregation, Key Performance Indicator (KPI) monitoring, and multi-timescale RAN Intelligent Controller (RIC) control to address this coupling: a Non-Real-Time RIC rApp uses aggregated KPIs and radio-environment context to jointly control tethered UAV placement and the enhanced Mobile Broadband (eMBB)/Ultra-Reliable Low-Latency Communication (URLLC) slice budget, while a Near-Real-Time RIC xApp allocates per-user resources within that budget. We realize this xApp as a permutation-equivariant DeepSets Soft Actor-Critic (D-SAC) scheduler that treats the users as an unordered set, trained in a Sionna RT ray traced channel. The resulting hierarchical controller improves eMBB SLA satisfaction by up to 17% and URLLC on-time delivery by up to 42% over classical and learned schedulers; the learned rApp further raises URLLC on-time delivery by up to 20% over baselines.

The ultra-weak variational formulation (UWVF) is known to be the Trefftz discontinuous Galerkin scheme obtained from the standard PWDG flux family by setting \(\alpha=\beta=\delta=1/2\). We give a short structural explanation of this fact. On every interior mesh edge, the two PWDG jump terms at these parameter values are exactly one half of the sum of the squared norms of the two oriented impedance-transmission defects used by the UWVF. Thus the Trefftz-DG norm is the natural Riesz norm of the global transmission defect. In PWDG coordinates its Gramian is the anti-Hermitian part of the discrete matrix, and Riesz normalization puts the operator in the normal form \(K+\ii I\), with \(K\) Hermitian. The same argument applied directly to the discrete UWVF yields the complementary normal form \(\tfrac12 I+\ii K_{\rm U}\). This identifies the classical equivalence as a relation between broken-field and impedance-trace coordinates for the same edge-coupling problem, rather than only as a particular choice of penalties.

On a 3D-printed tactile map, a building felt under the finger is an anonymous shape: touch alone cannot tell which footprint is which, and a spoken description cannot reliably point to one shape at one place. We present a web-based tool that lets a sighted helper click to add on-shape Braille labels to an already-generated map model, downstream of the geometry generator so that whoever knows the reader and the local Braille standard does the labeling. The tool offers click-based OpenStreetMap matching, hand-editable abbreviation that shrinks a name to fit a footprint, and print-safe dot geometry with a review step that catches anomalies before printing. We demonstrate it on five printed maps of different place types, from a downtown core to a college campus and a small dining mall. In formative sessions in which ten BLV readers compared an unlabeled print with an annotated one, four read Braille fluently, so we treat Braille as one output among several rather than the only one. The tool's core is the link between coordinates, geometry, and a place's semantics, which can drive an audio readout or a non-Braille code. The tool is available at https://leolee7.github.io/Annotate_Braille/.

Transformer-based language models are widely used as models of human language processing, yet their attention mechanisms allow lossless access to the full preceding context, unlike the limited memory systems of humans. We hypothesize that installing memory constraints into transformers' attention mechanisms can improve their fit to human behavioral data. While previous work has explored individual constraints in isolation, we conduct a systematic comparison of multiple attention-based memory mechanisms across different model sizes and training corpora, evaluating both psychometric predictive power for human reading times and grammatical competence. We additionally compare static constraints, in which the constraint strength is fixed throughout training, to dynamic memory curricula. We find that constraints that are sensitive to the content of intervening tokens consistently achieve the highest alignment with human reading times, outperforming distance-based constraints. We observe a dissociation between psychometric fit and grammatical competence under dynamic memory curricula, suggesting that Transformers cannot serve as a one-size-fits-all cognitive model.

SHAP and LIME are now standard tools for interpreting black-box predictions, yet their outputs can vary substantially when the input is perturbed by small amounts of noise–a problem we observed firsthand in our previous work on food security in Madagascar (Ralinirina et al., 2025). This variability raises the question of whether such explanations can be trusted at all. We address it by constructing an auditing protocol that measures two properties of any post-hoc explainer: robustness (how stable the explanation is under input perturbation) and fidelity (whether the features deemed important actually drive the model's prediction). These two quantities are combined into a single Trust Score. We run the protocol on a multi-sectoral dataset from Madagascar (83 features, 253 records, 4 malnutrition classes) using three classifiers and two explainers, plus their regularized counterparts. The results are sobering: models with AUC above 0.99 can produce numerically degenerate or flatly uninformative explanations, and fidelity scores lose discriminative power when the model is overfitted. These findings suggest that auditing XAI outputs is not optional but necessary, particularly when they inform decisions in sensitive domains.

Quantized fine-tuning (QLoRA) saves memory but not time. It dequantizes every 4-bit weight on the fly, so it trains more slowly than fp16 LoRA. We present AQLoRA (Adaptive-Quantization LoRA), a recipe that buys part of that time back. One CPU pass ranks layers by NF4 reconstruction error, with no search and no calibration data, and keeps a fixed fraction of them in fp16. Those layers skip dequantization, which is where the speed comes from. A quality setting adapts every layer. A speed setting adapts only the top blocks, so the backward pass stops early. The selection matches the accuracy of Unsloth's hand-curated dynamic-4bit list. We evaluate on Commonsense-170K across six models and four architecture families, from 1.4B to 14B. The speed setting trains 11.3 +/- 2.3% faster than well-tuned QLoRA and gives up 0.1 to 1.5 accuracy points. It was faster in all thirteen independent timing sessions, at worst by 7%. The quality setting trains 4.8 +/- 2.0% faster, matches QLoRA's accuracy on every model, and is within a point of fp16 LoRA. The memory premium depends on the architecture: 0.06 to 0.8 GiB on the 1-4B models, 0.5 GiB at 7B, 1.9 GiB at 14B. These error bars are measured between independent sessions, not within one. Timing on shared hardware needs three rules: fix the measurement duration, not the step count; measure the noise floor from a duplicated arm; and repeat whole sessions, since on one model three sessions that each passed the floor test spread over 8.2 points. We validate the recipe with controls and report the two that failed. Choosing adapter layers by weight density is no better than random. Choosing protected layers by quantization error is not either, on five models at three budgets with memory-matched controls and downstream on two. The number of protected layers sets the speed; which layers they are does not measurably change accuracy.

Large Language Models (LLMs) demonstrate strong capabilities in automated essay scoring (AES), but contemporary approaches typically employ fixed prompt selection, failing to address operational cost concerns and evolving optimal configurations. We propose a novel cost-aware approach that treats each prompt type as an arm in a multi-armed bandit (MAB) controller, enabling adaptive selection of optimal prompting strategies during inference. Our experiments on IELTS Writing Task 2 essays show that the MAB framework achieves comparable scoring accuracy to exhaustive grid search while reducing LLM calls by 78.4% to find the best grading approach. We implemented four distinct grading recipes (multi-step vs. single-step assessment, with vs. without calibration examples) and found that the multi-step approach with examples achieves the highest accuracy. By tracking token usage and latency alongside agreement metrics, we produce the first cost-reliability learning curves for essay scoring, providing actionable insights for educational technology platforms that must balance operational costs against assessment validity. This work represents the first application of online control mechanisms to adaptively select prompting strategies in AES, transforming prompt selection from an offline hyperparameter optimization problem into an efficient online learning task.

Designing effective reward signals for open-domain question answering is challenging because high-quality responses must simultaneously satisfy multiple aspects of answer quality that are difficult to capture with a holistic scalar objective. We introduce a rubric-based reward framework that generates query-specific rubrics grounded in retrieved evidence and decomposed into multiple quality dimensions, providing fine-grained supervision during post-training. Averaged across three evaluation axes (composition, grounding, and instruction-following), our approach improves over the instruction-tuned baseline by 6.5% and over flat rubric variants by 4%, with consistent gains across all evaluation datasets. Conditioning rubrics on retrieved evidence improves factual support, while decomposing rubrics into quality-specific dimensions further improves coherence, organization, and adherence to query requirements. Our results show that grounded, multi-dimensional rubrics provide more effective reward supervision for complex open-domain question answering.

Automated fact-checking is essential for ensuring the reliability of public health information, yet the biomedical domain poses unique challenges. Validating biomedical claims requires rigorous interpretation of scientific literature, assessment of retrieved evidence, and comprehensive justification toward the conclusion. Although Large Language Models (LLMs) enhanced by Retrieval-Augmented Generation (RAG) and agentic search perform automated fact-checking in a retrieve-then-verify paradigm, current methods still output isolated prediction labels, lacking explanatory depth and offers limited utility for human understanding. To bridge this gap, we introduce an LLM-based agent named BioCheck Agent that generates structured biomedical fact-checking reports with agentic search. Rather than merely outputting supported or refuted labels, our agent synthesizes final conclusions with retrieved evidence and rigorous analysis. To ensure domain-specific accuracy, BioCheck Agent exclusively searches high-quality scientific literature in PubMed, utilizing advanced Boolean search operators. Recognizing that direct prompting often results in hallucinations and low-quality reports, especially for lightweight open-source models, we further propose the Evidence-Grounded Group Relative Policy Optimization (EG-GRPO) to perform reinforcement learning on BioCheck Agent with a task-specific reward that incentivizes advanced search behavior and high-quality evidence retrieval while penalizing hallucinations. Our experimental results show that compared to the base model Qwen3.5-4B, BioCheck Agent with EG-GRPO improves label prediction accuracy on SciFact by 9.95%. Furthermore, it achieves a 3.7% higher evidence quality score and a 19.63% lower evidence hallucination rate, demonstrating its ability to generate biomedical fact-checking reports with improved accuracy and quality.

Multilingual language models can solve the same mathematical problem in different languages, but it remains unclear whether they rely on shared features or on language-specific computations that only produce similar outputs. We study this question in five models from four families using the Multilingual Grade School Math (MGSM) dataset, with problems solved in English, German, French, Spanish, Russian, and Chinese, retaining problems with valid reasoning traces in all six languages and replaying those traces through the model to record representations at multiple layers. For each model, we first use Centered Kernel Alignment (CKA) to identify layers with cross-language alignment. At each selected layer, we train two sparse autoencoders (SAE): a baseline reconstruction-only model and a contrastive variant introduced in this work, the Geometry-Invariant SAE (GI-SAE). GI-SAE supplements the reconstruction loss with an Information Noise-Contrastive Estimation (InfoNCE) loss that trains the encoder to produce similar activations for traces of the same problem, regardless of language or token position. We then test whether the resulting shared features are functionally interchangeable by swapping their values between languages during the model's forward pass and measuring the resulting change in output, quantified by Kullback-Leibler (KL) divergence per feature. Although GI-SAE yields higher CKA and Jaccard similarity at nearly every layer, higher geometric similarity does not consistently imply greater functional interchangeability. We find that cross-language feature sharing is model- and architecture-dependent in this sample and appears at different depths in different models. GI-SAE primarily amplifies cross-language structure already present: the pattern is model-specific, with strengthening in Qwen, no functional benefit in Gemma, and mixed layer-dependent effects in Llama and Phi.

Masked diffusion language models (dLLMs) can in principle generate text faster than autoregressive (AR) models, since they denoise many tokens at once. Recent systems have begun building serving infrastructure for dLLMs, but none first measure how these models behave under real, concurrent serving load. Serving systems built without this grounding risk carrying over assumptions from AR serving that may not hold for dLLMs. We characterize dLLM serving to close this gap, using LLaDA-8B-Instruct with a D2F (Discrete Diffusion Forcing) LoRA adapter on a single NVIDIA H200 GPU, evaluated on GSM8K and HumanEval. We report three findings. First, request difficulty, the number of denoising steps a request needs, is discrete rather than continuous: requests fall into 11 fixed step-count levels (178 + 29k), and no signal we test predicts the level before generation starts (best R2 = 0.150). Second, benchmarks with short generation budgets below 320 tokens understate serving variance, since requests are cut off before the latency spread appears. Third, only 24% of single-request wall-clock time is GPU computation; the rest is CPU-side dispatch overhead. Batching mainly helps by amortizing this overhead: sharing one forward pass per denoising step improves throughput by 16.0x at batch size 16 over a per-request-dispatch baseline. We also argue structurally that output quality should not degrade with batch size, stating three assumptions this rests on; we measure 74 to 76% GSM8K accuracy at single-request scale. Finally, we derive a batch-timeout rule for fixed-fill synchronized batching under Poisson arrivals. Together, these results show that serving diffusion language models needs parallelism at the level of each denoising step, which differs from AR serving in how admission and eviction interact with an already shared forward pass.

We introduce Giga-Embeddings, a family of text embedding models designed to combine strong retrieval quality with efficient serving. Its largest member is a sparse 10B-parameter Mixture-of-Experts encoder with approximately 1.8B active parameters per token. Across English, Russian, multilingual, and code MTEB benchmarks, this model achieves the strongest aggregate performance within the family on all four evaluated suites. In our vLLM benchmark with 1024-token inputs, it processes 114.5k tokens per second, providing 25 percent higher throughput than the dense 3B model and 1.56-2.65x the throughput of the evaluated external systems. The family also includes a dense 3B encoder and a distilled 480M encoder for tighter compute and memory budgets. We train the compact model using a dimension-agnostic objective that aligns teacher and student similarity distributions. The resulting 480M model scores 70.98 on Russian MTEB, surpassing FRIDA while using 42 percent fewer parameters. We release all three model checkpoints.

Storage-backed inference is easy to overclaim: process RSS excludes charged page cache, process-local device readings exclude board-wide use, and successful generation does not establish correct asynchronous reuse. We present a falsifiable certificate separating representation, semantic demand, scheduler requests, and traffic while naming resource authorities, exactness horizons, and tested reuse transitions. At one Qwen3-Next identity, the stock router selects all 48 x 512 managed layer-expert objects during 32K prefill. Their duplicate-free, overlap-free canonical union gives a 43.59375 GiB semantic-demand lower bound, exceeding the declared 34 GiB full-residency envelope and the 11 GiB host-hard plus physical 24 GiB-device envelope. LRU64 execution stays within its host-hard/GPU-audited contract. Against one prespecified zero-cache oracle, all 64 token IDs, every byte of 64 complete 151,936-float logit rows, 3,408 route events, response bytes, and recorded consumer and destination identities are exact. Recurrent-state and upstream-runtime equality are excluded. In a matched source campaign, the buffered path completes exactly but reaches the 11 GiB host ceiling and records 33,481 memory.max events. The blocking one-window direct path and complete eight-window asynchronous component are exact with positive margin and zero limit events. Across six counterbalanced pairs, the complete asynchronous component takes 32.3% of the blocking direct path's wall time at identical physical source bytes per output; the comparison jointly changes queue depth, overlap, and lifecycle implementation. Separately, fourteen prespecified control/fault cells pass across later Qwen3-Next and Gemma 4 binaries, supporting fail-closed behavior only for the named transitions. The principal experiment is one fixed model, workload, runtime, device, and 64-output horizon.

Lung cancer tissue diagnostics is complex, as therapy decisions in precision oncology rely on the integration of histomorphological, immunohistochemical, and molecular features. Yet pathological assessment remains largely visual and semi-quantitative and shows interobserver variability, while existing artificial intelligence (AI) tools cover only selected tasks, rarely reach generalizable expert-level performance, and lack prospective clinical validation. To address these challenges, we developed and clinically validated LUCAID, an agentic AI system for precision lung cancer pathology. An integrative agent couples diagnostic reasoning with nine modules that cover the full routine workflow, from quality control, tumor detection and segmentation, histological subtyping, tumor microenvironment profiling, tumor cellularity quantification, and predictive biomarker scoring (PD-L1, MET, TROP-2) to automated structured report generation. LUCAID enables users to interactively query the module outputs and generate reports that contextualize the results. Against large-scale expert ground-truth annotations, the analysis modules achieved F1 scores of 0.82-0.95. In prospective clinical validation, LUCAID reached 93.0% concordance with an expert-panel adjudicated reference standard across clinically actionable decisions, compared with 68.3-81.1% for five experienced thoracic pathologists.

Recent progress in image restoration has converged on all-in-one architectures that jointly handle multiple degradations within a single network. These methods are effective on static benchmarks but target a closed-world setting that assumes simultaneous access to every target degradation at training time. In practice, degradations are encountered sequentially as field-deployed systems progressively face new environmental conditions, and historical training data is often unavailable due to privacy or storage constraints. Accommodating a new degradation then requires either retraining on the union of all prior data, which is often costly or infeasible, or fine-tuning, which causes catastrophic forgetting. We formulate multi-degradation image restoration as a continual domain-incremental learning problem, in which degradations arrive incrementally and prior data is unavailable. Our proposed Restoring without Forgetting (RwF) framework learns a lightweight adapter for each new degradation, eliminating forgetting by construction at a fraction of the cost of dedicated per-domain networks. To isolate degradation learning from dataset variation, we construct a benchmark spanning five degradation domains under shared image content. At test time, an unsupervised routing mechanism identifies the appropriate restoration path for unknown inputs without requiring domain labels. Across the five-domain sequence, RwF improves final average PSNR over naive sequential fine-tuning by 15.25 dB and 11.83 dB on the Restormer and NAFNet backbones, respectively. The framework transfers to eleven canonical real-degradation benchmarks (3,465 images) at 89.5% routing accuracy with only a +0.94 dB oracle PSNR gap, establishing, to our knowledge, the first systematic baseline for continual multi-degradation image restoration.

Speciation in generative diffusion models denotes the emergence of distinct stable branches during denoising, through which initially undifferentiated trajectories progressively commit to different data classes. In this work we develop an intrinsic theory of speciation for diffusion models supported on compact Riemannian manifolds: the aim is to go beyond existing theoretical descriptions, which usually identify speciation with a symmetric pitchfork bifurcation and assume to work in a large-dimensional space. We characterize speciation by bifurcations of the critical points of the evolving probability density. A spectral heat-kernel representation makes explicit the role of the manifold geometry, while Poincaré-Hopf and Morse theory impose global constraints on the number and type of score equilibria and reveal topologically-imposed geometrical modes. For mixtures of heat kernels, we prove that generic speciation events have a one-dimensional critical kernel and admit an A2 fold normal form; pitchforks and simultaneous multidirectional transitions arise from nongeneric symmetric configurations. We derive geometry-dependent estimates of speciation times for bimodal mixtures and Riemannian regular simplices. We further establish structural stability of nondegenerate folds under score perturbations and show that the first-order time shift is determined solely by the component of the score error along the critical direction. The theory is illustrated on the sphere using mixtures of von Mises-Fisher distributions, where pitchfork and saddle-node bifurcations, topological modes, and hierarchical multiple speciations are observed. Finally, a chart-based intrinsic score-learning scheme based on neural networks contrasts the theoretically predicted transitions on prototypal and more complex datasets.

Problem definition: Solar electricity generation is a strategic component of energy portfolios designed to meet growing demand and reduce carbon emissions. Governments and municipalities encourage household photovoltaic (PV) adoption through upfront rebates and tax credits. Limited budgets require principled, data-driven policies that account for the drivers of adoption and the effects of incentives on adoption rates. Methodology/results: We develop a dynamic structural model of residential PV diffusion based on adoption decisions by forward-looking households that weigh the economic trade-offs between installing now and later. Adoption depends on return on investment and influence from neighboring adopters. The model segments households by home value and urbanization level, incorporates unobserved heterogeneity, and captures spatiotemporal installation dynamics. We estimate the model using Bayesian methods and detailed household-level data from Austin, Texas. In out-of-sample tests, it predicts installations more accurately than contemporary alternatives. We simulate counterfactual policies within the dynamic equilibrium of PV diffusion to evaluate rebate designs. The framework can also be adapted to study the adoption of other durable technologies. Managerial implications: A rebate offered for a limited period generates more adoption and emissions reductions than a prolonged, costlier program. This counterintuitive result arises from forward-looking behavior, neighbor influence, and accelerated adoption before the rebate expires. We also evaluate phased reductions and rebates differentiated by household segment. A two-step reduction outperforms multiple small reductions. Geographic differentiation improves policy performance, whereas differentiation by home value offers little advantage over a uniform rebate.

Mixture-of-Experts (MoE) scales language models by routing each input through a small set of independently parameterized experts. We show that copying this design into convolutional networks fails for a structural reason: parallel convolutional experts that read the same input channels learn nearly identical filters. We therefore move the expert axis from operator duplication to channel selection. We introduce Mixture of Channel Experts (MoCE), a structured sparse channel-mixing layer, inspired by MoE, that replaces pointwise (1x1) channel-reduction projections. In MoCE, an expert is a single output channel with a learned sparse support of k << C input channels. The selected channels are combined by a softmax whose temperature is predicted per input, so each expert can move between mean-like and max-like aggregation. A residual expert summarizes the unselected channels, and a load-balancing loss keeps channel coverage complete. MoCE replaces a dense projection whose cost is quadratic in C with a mechanism whose relative cost scales as k/C, and the predicted savings hold in measured wall-clock time. Across ResNet backbones on ImageNet-1K and CIFAR-100, transfer learning, EfficientViT, and a strong modern training recipe, MoCE matches or exceeds dense baselines and prior channel-selection methods while reducing MACs by 16.7% and end-to-end latency.

Psychological research on emotion dynamics has established that human affect is a continuous, evolving process: emotions rise, decay, and transition within seconds. Current emotional text-to-speech (TTS) systems, however, condition on a single discrete label or static embedding per utterance, fundamentally misaligning with the temporal nature of affect. While recent LLM-based TTS systems may implicitly vary prosody through text understanding, such variation is neither explicitly controllable nor precise enough for targeted intra-utterance transitions. We address three challenges: (1) a multi-pass flow blending pipeline synthesizes frame-aligned transition audio, circumventing the scarcity of natural intra-utterance transitions; (2) dual-stage Valence-Arousal-Dominance (VAD) conditioning guides prosodic planning in the LLM and acoustic realization in the flow decoder via frame-level VAD embeddings; (3) direction-magnitude decoupled injection structurally separates emotion direction from injection magnitude, preventing content degradation. EmoTra-TTS adds only +0.43% parameters with no latency overhead, achieves 30%-87% relative improvement on emotion transition quality, corroborated by 64.4%-79.5% overall win rates in pairwise preference tests against four SOTA baselines and two commercial systems.

How does an intelligent visual system combine what objects look like with how they move while remaining robust as appearance changes? We addressed this question by comparing human perception and neural activity in macaque inferior temporal cortex with representations from image- and video-based neural networks spanning recognition, segmentation, optic-flow processing and predictive world modeling. Temporal integration improved object representations, but most video recognition models generalized poorly when appearance was disrupted while motion structure was preserved. Humans and macaque IT remained robust. Notably, predictive world models combined strong cross-appearance generalization with the closest correspondence to IT, outperforming other video-modeling approaches in neural fidelity. Yet no model reproduced the cortical transformation from early appearance-dominated responses toward later appearance-invariant motion coding. These results identify progressive integration of motion into object representations as a principle of robust dynamic vision and implicate predictive learning as a promising route toward realizing this computation in artificial systems.

We develop a Monte Carlo lattice Boltzmann method to compute statistical solutions to the three-dimensional incompressible Navier–Stokes and Euler equations. Entropic space-time adaptive relaxation of the higher order kinetic moments yields stable numerical solutions with decreasing viscosity. We provide a convergence analysis that is conditional on four explicitly stated assumptions regarding the discrete dynamics. Under diffusive scaling, the laws of the discrete ensemble converge along a subsequence to a limit satisfying the Foias–Temam Liouville formulation of the Navier–Stokes equations. Consequently, provided the structure function scaling holds uniformly, the vanishing viscosity limit of these measures satisfies the multi-point statistical Euler hierarchy of Fjordholm, Mishra, and Weber. The limit measures inherit the known weak-strong uniqueness principle on the interval of existence of a strong Euler solution. Under explicit scaling assumptions, a Kuznetsov-type argument yields a fractional 1-Wasserstein convergence rate. We present three-dimensional computations of time-dependent statistical solutions along the inviscid limit of the incompressible Navier–Stokes equations together with convergence measurements in the Wasserstein metric. Numerical experiments on a randomized Taylor–Green vortex with 24-dimensional initial uncertainty recover Kolmogorov's K41 scaling for energy spectra and structure functions, exhibit the failure of pathwise strong convergence, and yield Wasserstein convergence rates of about $0.5$ at the onset of turbulence. Finally, error measurements with respect to spectral hyperviscosity computations indicate that the computed limit measure is independent of the numerical regularization.

This paper evaluates quantum and AI-accelerated risks to TLS 1.3 cryptographic dependencies under an evidence-tiered model, distinguishing mechanism-backed threats (Shor algorithm against RSA and ECC) from contingency-backed risks to lattice-based post-quantum cryptography (PQC) and hypothesis-only risks to hash-based and symmetric primitives. We do not identify any known breaks of ML-KEM, ML-DSA, SLH-DSA, or AES-256. Instead, we use explicit scenario assumptions, organized as a four-scenario capability model with parameters and pseudocode for reproducibility, to stress-test migration timelines accompanied by parameter sensitivity analysis and explicit falsification analysis. The primary methodological contribution is a reproducible scenario-estimation instrument together with its explicit update mechanics: every parameter is a named, anchored quantity that can be varied and the model rerun; a stated protocol maps observed conformance to, or deviation from, the modeled curves onto revisions of specific parameters, so progressive refinements can be tested against accumulating historical data. The paper is a methodological companion to quantum resource-estimation studies and to expert-elicitation timeline surveys such as the Global Risk Institute quantum threat reports, with its revision rules stated explicitly. As of mid-2026, the model does not show any NIST-approved algorithms as broken. Instead, the vulnerability spectrum under different scenarios shows RSA risk crossing the 50% threshold between 2030-2032 and the PQC risk becoming a non-zero risk after 2032-2035 under contingency scenarios conditional on the unproven dimension-collapse. We urge PQC migration as mandatory per the 2030 and 2031 federal deadlines and by Mosca HNDL reasoning, and that crypto-agility and hybrid cryptographic deployment be considered necessary complements to any PQC migration efforts.

LLM-as-a-judge methods are widely used for evaluating the quality of generated open-ended text. Such evaluations are generally multi-dimensional, since the error patterns in texts can be different for different dimensions. Therefore, reliable LLM judges should evaluate each target dimension independently. To quantify the extent to which LLM judges depend on non-target dimensions when evaluating a target dimension, i.e., inter-dimension dependence, we propose CorrGap. To measure this, CorrGap uses the difference in correlations between LLM-predicted scores and ground truth scores across different groups of texts. Using CorrGap, we show that inter-dimension dependence is pervasive across LLM judges in open-ended text evaluation tasks. To mitigate inter-dimension dependence, we propose DimCheck, a method that iteratively removes unrelated evidence from COTs generated by LLM judges in a step-wise way. We show that DimCheck mitigates inter-dimension dependence and outperforms strong baselines across three LLMs and four tasks. We also show that smaller trained LLMs can approximate larger LLMs in DimCheck, with much lower inference costs.