Universality

We present a physics-informed machine learning framework based on Neural Ordinary Differential Equations that solves the holographic inverse problem: reconstructing the bulk spacetime and gauge field of a charged AdS black hole directly from boundary fermionic spectral functions. Encoding the UV asymptotics, horizon regularity, and zero temperature extremality as hard constraints in the neural network architecture, our framework reliably reconstructs the extremal Reissner-Nordström AdS geometry across three quantum critical regimes set by the $U(1)$ probe charge---non-Fermi liquid, marginal Fermi liquid (strange metal), and Fermi-liquid-like states---and can jointly infer the probe charge itself to sub-percent accuracy. Relaxing the near-AdS boundary constraint uncovers a geometrical degeneracy: bulk profiles that differ throughout the radial direction but share the same near-horizon $AdS_2 \times \mathbb{R}^2$ data reproduce identical spectral functions near the Fermi surface. This isospectral non-uniqueness is precisely the bulk degeneracy expected on general holographic grounds at zero temperature, and its spontaneous emergence across independent training runs shows that the network isolates the IR CFT universality rather than overfitting a single UV completion.

In this paper we tackle the problem of aligning LiDAR point clouds also known as the point cloud registration problem. We propose a new algorithm, PESTO, that exploits tetrahedra as "universal features" for LiDAR data, i.e., features that are agnostic to the environment where the LiDAR sensors are deployed. We show empirically that PESTO is competitive with existing solutions for aligning LiDAR point clouds, especially in environments with occlusions. Moreover, we establish PESTO's formal correctness by proving worst-case bounds on the alignment error.

Humans can learn and generalize novel concepts from sparse data because they express knowledge in rich structural formats. In this paper, we propose that programs are a strong candidate for universal representation of concepts. We review computational models of concept learning that use programs as their concept representation and evaluate their contribution toward a universal representational language.

What can a single layer of self-attention compute? We study head complexity: the minimum number of attention heads required to compute a function in a one-layer attention-only model. We establish an exact hierarchy under this measure: $k$ heads compute $k$-bit parity but cannot compute $(k+1)$-bit parity. The lower bound is unconditional in the two resources a transformer might otherwise exploit; it holds at unbounded embedding dimension and unbounded numerical precision. The proof rests on an alternating-sum obstruction: after clearing the softmax denominators, every monomial in the resulting decision polynomial omits at least one of the $k+1$ input bits, forcing its correlation with parity to vanish. The same obstruction yields lower bounds for related tasks, including the well-studied multi-hop induction-head task. We also establish compactness bounds for embedding dimension and numerical precision. Specifically, a compactness theorem shows that any function computable at all can be computed with embedding dimension and precision bounded by the discrete data of the task, namely, head count, alphabet size, and length. Thus, potentially unbounded dimension or precision provably cannot substitute for heads. Finally, we derive nearly matching universal bounds for general binary functions: $2^n$ heads suffice to compute every $n$-bit binary function, with one head per monomial in its multilinear expansion, while a counting argument shows almost all such functions require $Ω(2^n/n^2)$ heads. This lower bound matches the upper bound to within a $\operatorname{poly}(n)$ factor, even when dimension and precision are unbounded. Together, these results characterize head requirements for Boolean computation in this model.

Modern large language model (LLM) serving systems increasingly operate over repeated or shared context, yet each model typically performs its own prefill computation even when another model has already processed the same input. Existing KV-cache reuse mechanisms substantially reduce redundant computation within a single model, but generally assume that the producer and consumer of a cache are identical. We study \emph{cross-model KV sharing}, which translates the KV state produced by a source model into a representation that can be consumed by a different target model, including models that differ in scale, architecture, attention configuration, tokenizer, and model family. We evaluate the approach in both within-family and cross-family settings. For Qwen2.5-7B $\rightarrow$ Qwen2.5-1.5B, translated KV states improve LongBench2 accuracy from 27.59% to 34.48%, a gain of 6.89 percentage points over the native 1.5B baseline, while reducing handoff cost relative to native target prefill. For the cross-family Qwen2.5-1.5B $\rightarrow$ Gemma-2-2B setting, KV handoff reduces target-side prefill cost by up to 67.05% at 4K context length while maintaining decoding perplexity close to native-model baselines. In a more heterogeneous Llama3.1-70B $\rightarrow$ Qwen2.5-7B setting, cross-family handoff achieves 44.0% accuracy compared with 45.7% for native Qwen2.5-7B inference, while reducing measured latency from 899ms to 138ms. These results provide initial evidence that KV states can serve as transferable computational representations rather than strictly model-local caches, and motivate \emph{context mobility} as a systems abstraction for reducing redundant prefill across heterogeneous LLM and multi-agent inference workflows.

Closely related languages written in different scripts expose little surface overlap to multilingual models, limiting cross-lingual transfer. We compare two approaches to script unification: the general-purpose uroman romanizer and the family-specific Common Turkic Script (CTS). We train matched fastText models on transliterated Wikipedia corpora from 11 Turkic languages and evaluate them on WikiANN named entity recognition and Universal Dependencies part-of-speech tagging. CTS and uroman show no significant difference on NER, while both substantially outperform the official monolingual fastText baselines. POS results reveal no universal winner: language-specific differences are associated with the cross-lingual character n-gram coverage induced by each representation, while within-language coverage becomes more important when target-language supervision is available. Although CANINE-c achieves higher overall POS averages, the substantially simpler fastText-based systems remain competitive on several treebanks. Overall, the effectiveness of script unification depends on the language, the induced subword overlap, and the available supervision.

Cross-modal Re-Identification (ReID) aims to retrieve the same identity across heterogeneous imaging modalities and has been widely studied in visible-infrared person ReID and cross-modal ship ReID. Existing methods have achieved promising performance by learning modality consistency in the spatial embedding space, yet often overlook frequency-domain modality discrepancy, particularly in high-frequency representations that are both highly discriminative and modality-sensitive. In addition, most approaches are tailored to specific modality settings, limiting their applicability across diverse cross-modal scenarios. To address these challenges, we propose a Dual-Space Modality Consistency Learning (DSMCL) framework for universal cross-modal ReID. Specifically, DSMCL jointly models spatial feature distribution consistency and frequency-domain discriminative consistency. A Spatial Modality Consistency Learning (SMCL) branch performs Gaussian-based feature alignment, while a Frequency-aware Discriminative Consistency Learning (FDCL) strategy regularizes high-frequency representations through identity-aware cross-modal contrastive learning. By jointly capturing modality-specific characteristics and modality-shared identity cues, DSMCL learns robust representations and establishes a unified framework capable of accommodating diverse heterogeneous modality settings. Moreover, DSMCL is a plug-and-play framework that can be readily integrated into existing cross-modal ReID architectures. Extensive experiments on SYSU-MM01, RegDB, LLCM, HOSS-ReID, and CMShipReID across seventeen evaluation protocols show that DSMCL consistently improves multiple representative baselines.

The life sciences and health research have started to benefit from artificial intelligence, which raises ethical concerns that are real but, we argue, not special. Any science should be governed by values that rest on how the human brain is built and socialised rather than anything distinct to artificial intelligence. Importantly, the human brain has a different, much less costly computational architecture than these machines. This is achieved through the orchestration of a global neuronal workspace, and through reward best described not as a quantity to be maximised but as a continuous cycle of wanting, liking and satiety. As such, this creates the deep tension running through the ethics of the human person, between the universality of ethical judgement and the diversity of morals. The brain networks of the global workspace and emotion are universally shared, but the diversity of content is shaped by epigenetic appropriation of the particulars of the physical, social and cultural world, which makes every person unique. Still, if we were to build machines on these principles rather than the present unaffordable reward maximisers, the question of their governance would change from restraint to upbringing. We set out the institutions such a future would require, together with the questions that remain open.

We study transcript management for fixed, finite-precision causal Transformers. A transcript is partitioned into channels of bounded blocks. Each transition consults a fixed visible suffix and may append one block, leaving the model, weights, and token protocol unchanged. The operation $P_c:=\PopContext(c)$ deletes the newest block on channel $c$ and exposes its predecessor. We model the layer by the Transcript-Managed Transducer $\TMTn{k}$: one finite controller, $k$ channels, and per-round actions from stay, push, and pop under a caller-driven status map. Fixed visible windows encode as finite symbols. The pop-free Restricted Transcript-Managed Transducer $\RTMTn{k}$ is the standard append-only layer and, for every fixed $k$, realizes exactly the deterministic finite-state transductions. The same holds for every fixed finite agent population under a monotone protocol that appends, routes, and copies visible blocks. Admitting $\{P_c\}_{c=1}^k$ restores pop. Newest-first, a pop-enabled channel is a stack; compiling to the Hopcroft--Ullman presentation transfers the classical hierarchy: $\DCFL$ for $k=1$ and $\RE$ for every $k\ge2$. Orchestrated one-channel agents match one controller with $k$ channels, so two pop-enabled transcripts---in one agent or two---suffice for universality. Simulation costs and invariance to fixed block size and visible radius are stated. The bounds fix precision, alphabets, blocks, visibility, controller state, and population; growing exact context, hidden-block access, writable stores, and unbounded \textbf{Spawn} add further state.

Tensor operations represent a cornerstone of modern scientific computing. However, the Numpy-like notation adopted by predominant tensor frameworks is often difficult to read and write and prone to so-called shape errors, i.a., due to following inconsistent rules across a large, complex collection of operations. Alternatives like einsum and einops have gained popularity, but are inherently restricted to few operations and lack the generality required for a universal model of tensor programming. To derive a better paradigm, we revisit vectorization as a function for transforming tensor operations, and use it to both lift lower-order operations to higher-order operations, and conceptually decompose higher-order operations to lower-order operations and their vectorization. Building on the universal nature of vectorization, we introduce einx, a universal notation for tensor operations. It uses declarative, pointful expressions that are defined by analogy with loop notation and represent the vectorization of tensor operations. The notation reduces the large APIs of existing frameworks to a small set of elementary operations, applies consistent rules across all operations, and enables a clean, readable and writable representation in code. We provide an implementation of einx that is embedded in Python and integrates seamlessly with existing tensor frameworks: https://github.com/fferflo/einx

Physics-informed machine learning incorporates physical principles --often expressed via differential operators-- into data-driven models. While physics-informed neural networks (PINNs) dominate empirical applications, the complexity of neural network architectures and optimization landscapes hinders the development of a corresponding learning theory. In turn, kernel methods offer an appealing alternative with closed-form solutions and analytical tractability, yet existing guarantees primarily cover the well-specified setting where the target belongs to the native Reproducing Kernel Hilbert Space (RKHS). This imposes unrealistic regularity assumptions that physical targets often fail to satisfy. In this paper, we introduce and analyze Physics-Informed Kernel methodS (PIKS). We establish the universal consistency of PIKS for linear differential constraints, proving that for universal kernels (such as Gaussian or Matérn), the estimator asymptotically learns the target while satisfying physical constraints. We further derive finite-sample bounds under suitable source conditions. Our analysis is based on extending classical operator-theoretic analysis of kernel methods to physics-informed machine learning. Numerical experiments demonstrate that PIKS can be competitive with PINNs and traditional finite element methods.

We investigate message-passing graph neural networks with random node features. Random node features are known to enhance the expressiveness of graph neural networks (GNNs) both theoretically and empirically. Here, we establish a novel universality result focusing on permutation-equivariant neural networks (PENNs), a class of GNNs built from feedforward neural network components that subsumes many prominent GNN architectures. We show that PENNs, combined with partially random node features, can approximate arbitrarily well in probability any measurable permutation-invariant or permutation-equivariant function on directed graphs of fixed size with multidimensional node and edge features. For $k$-times continuously differentiable functions, $k\geq 2$, we also derive upper bounds on the approximation rates, relating the complexity of the feedforward components of a PENN in terms of layer depth and number of nonzero weights to the desired approximation accuracy.

State-of-the-art toxicity detectors for text-to-image generation adopt a one-size-fits-all approach: a single universal model applying fixed safety guidelines to all users. Our empirical evidence shows that these detectors fail to shield marginalized communities: approximately 35% of generated images labeled safe are considered harmful by disability communities. In this position paper, we argue for community-specific toxicity detection (CTD). To demonstrate its feasibility, we collaborate with disability experts to develop safety guidelines for two communities: dwarfism and blind/low vision. Using a dataset of 2,400 annotated T2I-generated images we demonstrate that both large vision-language models and existing general-purpose toxicity detectors catastrophically fail to recognize harmful content under these guidelines in zero-shot settings with F1 score lower than random guessing (F1 0.32 and 0.37). Promisingly, prompt-based adaptation methods (ICL, VQA) substantially improve harm detection performance (GPT-4o: F1 0.50 and 0.78), while parameter-efficient fine-tuning improves smaller models (0.5b-7b with best F1 0.48 and 0.59) with less than 100 demonstrations, but remains sensitive to evolving guidelines. Despite these gains, CTD performance remains far below F1 $\approx 0.9$ achieved for general-purpose toxicity detection, highlighting the challenge and the need for sustained research effort.

Prior classical-ML learning-curve work fits power laws to tree, linear, and kernel models on tabular data, but at small scale: typically one curve, one team, a handful of cells. We present a distributed classroom-scale replication: 127 graduate students each ran a fixed protocol on 3 assigned datasets, drawn from 18 tabular classification and regression datasets and 6 model families (Boosting, Random Forest, SVM, Linear/Logistic, Ridge, Lasso), yielding 11,536 training runs and 1,648 fitted power-law curves of the form error(N) = a N^(-b) + c. Three findings. (1) Power laws fit: R^2 > 0.8 on 77.7% of cells, with tree ensembles dominating at full data (Boosting 50% of datasets, RandomForest 33%; linear models underperform on classification). (2) Approximate shared exponents within a model family: for 5 of 6 families, a single family-level exponent predicts each family's cross-dataset curves nearly as well as per-dataset exponents (R^2 gap < 0.011), though AIC favors the unconstrained fit and curve collapse is partial (32-58% of points within +/-0.5 dex). We frame this as approximate predictive compressibility, not dataset-independent universality; Lasso fails outright (negative control) and Ridge is fragile under leave-one-dataset-out. (3) Replicator-implementation variance: with random_state=42 fixed, independent re-implementations of the same protocol still differ by mean CV(b) = 0.144 on the fitted exponent -- not seed variance, but the spread induced by unconstrained parts of the protocol (preprocessing, encoding, missing-value handling). We release the aggregated curves, per-cell fits, and a practical data-requirement table for N* to reach target error 0.15.

Style transfer remains a fundamental and highly important task across various data modalities, enabling creative manipulation conditioned by both reference images and textual descriptions. Recently, methods utilizing Gaussian Splatting have emerged as a unified representation for 2D images, video, 3D scenes, and 4D dynamics. However, representing videos and 2D images with Gaussian Splatting is structurally sub-optimal for dense continuous domains. The number of required Gaussians often approaches the total number of pixels, raising questions about the actual utility of such a representation for these specific modalities. In contrast, Implicit Neural Representations have established themselves as a much more popular and natural choice across all these data domains. Implicit Neural Representations naturally provide significant advantages, including data compression, inherent capabilities for super resolution, and seamless integration with deep generative models. To this end, we introduce OmniStyle-INR, a novel framework that leverages network-based continuous representations as a truly universal domain. Our approach successfully performs high-quality style transfer across all visual modalities, guided seamlessly by both text prompts and visual exemplars.

Physically grounded 3D assets are increasingly important for embodied AI and robotic simulation. However, most existing 3D assets lack unified physical semantics, including articulation semantics and intrinsic physical properties, required for realistic interaction. Current approaches either treat these semantics independently or rely on canonicalized object structures, limiting robustness across heterogeneous 3D assets. We present UniPhys, a scalable framework for automatically transforming raw 3D assets into simulation-ready assets with unified physical semantics. Based on UniPhys, we construct UniPhys-40K, a large-scale physically grounded dataset, together with UniPhys-Bench, a carefully verified benchmark for unified physical grounding evaluation. We further introduce UniPhysGen, a unified physical grounding model that jointly reasons over articulation semantics and intrinsic physical properties. UniPhysGen incorporates geometry-robust articulation grounding to mitigate geometric shortcut bias under heterogeneous part decompositions. Extensive experiments demonstrate state-of-the-art performance across articulation grounding and intrinsic physical property estimation tasks, while the resulting assets can be directly deployed in robotic simulation environments for realistic physical interaction. Our code and dataset will be available at https://github.com/breezexian/UniPhysGen.

Unmanned aerial vehicles (UAVs) increasingly rely on visual grounding capabilities to localize task-relevant targets from diverse instructions in complex aerial scenes. Existing referring expression comprehension (REC) benchmarks and methods, however, are largely built around text-only queries and single-object outputs, which limits their applicability to practical UAV scenarios involving reference images, multimodal instructions, absent targets, and multiple valid target instances. To address this gap, we introduce \emph{Universal Referring}, a generalized UAV referring task that jointly expands the query modality and the output cardinality. We construct \emph{UniRef-UAV}, a multimodal benchmark that supports text-only, image-only, and text+image queries with modality-dependent target cardinality, where text-only and text+image queries admit no-target, single-target, and multi-target grounding while image-only queries focus on existence-aware single-instance grounding. It also provides in-domain and cross-domain evaluation protocols for visual-query generalization. We further present \emph{UAV-URNet}, a detection-style baseline that maps heterogeneous queries into a shared query space and predicts variable-size target sets through set prediction. Extensive experiments show that UAV-URNet provides a stable and reproducible baseline with more consistent no-target discrimination and a more lightweight, reproducible implementation than large general-purpose MLLMs. Additional domain analysis, query-representation analysis, and ablation studies demonstrate that multimodal queries help reduce visual-query ambiguity and promote a more unified query--target alignment space. The annotations, visual query crops/images, train/validation/test splits, evaluation scripts, and baseline code will be made publicly available to facilitate reproducible research.

Code is the medium through which large language models generate structured artifacts: charts, scientific figures, vector graphics, CAD models, 3D scenes, and hardware designs are all produced by writing programs. In this regime single pass inference is brittle, because the compiler, renderer, or simulator that decides whether the artifact exists is invisible to the model. We present PairCoder, which grounds review in the toolchain and realizes it as two agent pair programming: a Driver agent writes the program, a Navigator agent reviews it against verification evidence (diagnostics, execution results, and renderings of the current artifact beside the target), and the two switch roles when errors persist. Across 17 public benchmarks and seven models from three vendors, PairCoder improves essentially every benchmark whose artifact is verifiable, on full official metric suites rather than execution alone (for example, Blender scene executability 0.20 to 0.78; TikZ compile rate up 10 to 30 points on every model), at 2.9 to 9.2 times single model cost (about 7 times overall). The improvements concentrate where the toolchain provides an informative oracle and the baseline leaves headroom, and the method ties or mildly regresses where the oracle is weak; we frame pair programming as a reliable recipe for verified code driven generation.

Neural scaling laws describe how pre-training loss decays as power laws with training time, model size, and compute. This position paper argues that the exponents of these power laws are fixed by generic mechanisms: a one-third time scaling due to the strong nonlinearity of Softmax, an inverse width scaling due to representational superposition, and an inverse depth scaling due to ensemble averaging of Transformer layers. These mechanisms are robust to a wide range of data structures and architectural details, placing current large language models in a universality class with fixed exponents. The coefficients, however, are expected to be sensitive to data and architecture details, and directly determine practical quantities such as the optimal model shape and the compute-optimal frontier. We therefore argue that understanding the coefficients is the key to near-term performance improvements, and that a closer examination of the current universality class may reveal pathways to better universality classes.

Czech has been part of Universal Dependencies since its first release in 2015. It has also been one of the best represented languages, with the Prague Dependency Treebank being order of magnitude larger than most other UD treebanks. More recently, three other datasets from the Prague family were added and the annotations thoroughly revisited, forming the "Prague Dependency Treebank-Consolidated" (PDT-C). In comparison to the original PDT, PDT-C is more than twice as large, but it is also much more diverse in terms of genres and domains. In this paper, we describe the conversion of the new resource to Universal Dependencies. While the two annotation schemes are relatively similar at the first sight, there are numerous small differences in topology of the dependency structures and in granularity of the POS and relation type inventories. We demonstrate a selection of such differences on examples, discuss the diverging motivations, as well as ways to overcome the differences during conversion. We argue that while PDT is less "universal" and more tightly bound to one language, its multi-layer annotation is rich and provides all information needed for basic UD trees, and much more.

Unifying image clustering across different clustering scenarios remains challenging due to fundamental gaps among tasks. We introduce a Guideline-Driven Image Clustering Agent, the first universal framework that bridges these gaps through textual guidelines. To incorporate complex guidelines without task-specific training, we propose Generative Concept Proxy Modeling, which generates guideline-aware embeddings via concept proxy extraction. For scenarios requiring automatic cluster discovery, we introduce LLM Traversal based on Minimum Spanning Tree that selectively applies LLM reasoning for complex semantic judgments. Our method generalizes across diverse clustering scenarios spanning from general to fine-grained categorization, from global to local criteria, and from balanced to long-tail distributions. Our framework consistently outperforms specialized methods across diverse clustering tasks.

Leveraging Multimodal Large Language Models (MLLMs) via contrastive learning has become a mainstream paradigm for improving the performance of Universal Multimodal Retrieval (UMR). However, previous works have ignored the grain blindness when adapting the contrastive paradigm into retrieval tasks. Grain blindness refers to the tendency of the model to overlook grain-level information contained in the query, which is crucial for effectively handling complex queries. This stems from contrastive learning treating samples as a binary classification (positive/negative), while ignoring the different information carried by each negative sample. To address this, we argue that negatives should be treated differently according to their similarity to the positive sample, enabling the model to learn distinct grain information from each negative. In this paper, we introduce a simple but effective framework, called ELVA, a novel rule-based RL framework that mitigates grain blindness through ranking-driven MLLMs. 1) Instead of relying on reward models, we extend Reinforcement Learning with Verifiable Rewards (RLVR) to retrieval tasks, allowing the model to explore new ranking behaviors without explicit ranking labels. 2) By utilizing rule-based rewards, our approach jointly optimizes the ranking of negative samples while enlarging the similarity gap between positive and negative. To more precisely measure grain blindness, we further introduce MRBench, a new benchmark specifically designed for multi-grain query scenarios. ELVA achieves state-of-the-art results across standard retrieval benchmarks, and its notable 13.1% improvement on MRBench further demonstrates its effectiveness in alleviating grain blindness.

We propose triangular consistency as a first-principled constraint for optical flow, which is agnostic to network architecture, supervision type, and dataset, and applies to both image-pair and multi-frame settings. This simple but powerful constraint is to compose two flows to induce a third flow and enforce consistency among the three. The composed flows may arise from (i) image pairs, yielding cycle consistency; (ii) multiple video frames, producing longer-range motion through temporal chaining; or (iii) image pairs combined with controlled synthetic transformations, which becomes data augmentation. This triangular consistency introduces negligible computational overhead and requires no additional annotations. Since it is derived directly from the geometry of optical flow, it does not rely on model-specific assumptions and serves as a ``universal'' plug-and-play component for optical flow training. Experiments show consistent improvement across supervised, unsupervised, and transfer learning settings.

Humans often acquire new skills by observing others, since observed behaviors implicitly reveal how to act in an environment. However, observations drawn from a heterogeneous population introduce conflicting behavioral signals, making it difficult to determine which behaviors are worth imitating. We address this challenge with General Reward Inference and Disentanglement (GRID), a social learning method that extracts universally useful behaviors from a heterogeneous population of demonstrators pursuing different goals. GRID decomposes per-agent reward functions into a general reward, capturing behaviors shared across all agents, and specific rewards, capturing individual preferences and objectives. Training exclusively on the general reward provides a new paradigm of generalist pretraining. It yields a generalist agent that internalizes universal environmental competencies, such as safety and basic task proficiency, without the mode-averaging bias that afflicts standard learning from demonstration techniques. This generalist serves as a superior prior for fine-tuning to downstream tasks, including preferences unseen during training. Experiments across a synthetic basis function decomposition, multi-agent Craftax, and a continuous autonomous driving simulator (Highway-Env) confirm that GRID successfully disentangles reward structure in a semantically meaningful way, outperforms standard learning from demonstration baselines, and enables more efficient and stable specialization.

Language models trained on large-scale vision-language data have demonstrated strong potential for embodied agents. Harnessing models through embodied tools use offers a promising alternative to end-to-end vision-language-action systems by combining high-level reasoning with external modules for perception, planning, and control. However, it remains unclear what makes an effective harness for embodied manipulation, and to what extent such a harness can unlock embodied capabilities in a wide range of reasoning models. In this work, we present Guava, a harness framework for embodied tool use developed through systematic exploration of the design space of agent workflows, action spaces, and observation spaces. Our study identifies three key ingredients for effective embodied agents: iterative perception-reasoning-action loops, semantic action abstractions, and multimodal observations. To understand whether these design principles are universal even to small models, we develop an end-to-end training pipeline that distills embodied manipulation capabilities into a 4B open-source model using fewer than 2K trajectories collected entirely in simulation. Experimental results in both simulation and real-world environments show performance comparable to frontier proprietary models while exhibiting strong generalization to unseen objects, novel instructions, and long-horizon tasks. Results suggest that a well-designed harness can serve as a scalable, model-agnostic interface for embodied manipulation, enabling strong emergent embodied capabilities in compact open-source models with minimal training data.

Do different LLM architectures encode high-level concepts in structurally compatible ways? We systematically characterize a geometric-functional universality dissociation: across multiple concept domains and architectural families, moderate geometric convergence coexists with near-perfect functional transfer. Using contrastive-difference CKA (CKA_Delta), a training-free diagnostic that computes kernel alignment on per-sample contrastive differences, we isolate concept-specific convergence from generic similarity -- achieving significant discrimination where standard CKA cannot. The dissociation replicates across all six concept domains we test (five with p <= 0.017 geometric discrimination and safety as a converging-functional trend, p = 0.08), including two non-instruction concepts (code-vs-NL, reasoning-vs-recall) validated without system prompts; a single 70B--70B pair provides an observational note that universality may strengthen with scale, requiring replication with additional >=70B models. We position CKA_Delta as a practical regime classifier and architectural outlier detector (Gemma: d = 1.08, AUC = 0.79) rather than an absolute transfer-accuracy predictor, providing a training-free diagnostic for cross-architecture concept monitoring.

Post-training methods such as supervised fine-tuning (SFT) and preference optimization typically align language models toward a single global assistant behavior. While effective for improving average helpfulness, this can suppress the natural variation of human responses across languages, tasks, and dialogue settings. We study this problem as conditional human-distribution alignment: models should match the human response distribution appropriate to the current interaction context, rather than a universal response style. We introduce PolyAlign, a distribution-aware alignment framework that organizes bilingual interaction data into bucket-specific human reference distributions defined by language, interaction track, response family, and length. PolyAlign combines Bucket-Aware SFT, which balances optimization across heterogeneous buckets, with Human-Distribution Preference Optimization (HDPO), which regularizes preference learning using critic-estimated distance to bucket-specific human support. Across a bilingual evaluation suite covering English and Chinese single- and multi-turn settings, PolyAlign improves conditional naturalness and distributional faithfulness while preserving competitive task utility. The results suggest that post-training should move beyond global alignment objectives toward interaction-aware alignment with human response distributions.

Dynamic Facial Expression Recognition (DFER) is a key enabling technology in affective computing, human-computer interaction, and intelligent multimedia systems. Despite the significant influence of cultural nuances on FER performance, most existing FER systems assume that emotional expressions are universally consistent across populations. This variation can be attributed to systematic differences in facial muscle activation patterns across cultures. A major challenge in advancing cross-cultural FER lies in the scarcity of culturally diverse benchmark datasets. To address this, a new hybrid multicultural video dataset termed Global Cross-Cultural Facial Expression Recognition (GCC-FER) is introduced. GCC-FER comprises 23,934 video samples spanning four cultural groups (African, Caucasian, East Asian, and South Asian) across seven basic expressions, combining psychologically supervised in-house data collection for underrepresented populations with rigorous ethnicity filtering of existing sources. To the best of our knowledge, GCC-FER is the first large-scale global cross-cultural DFER dataset designed to address these demographic gaps. Leveraging this dataset, behaviorally grounded cultural priors are derived for each cultural group and a global prior for practical deployment. A Culture-Aware FER (CA-FER) system is proposed to mitigate cultural bias by adaptively recalibrating latent facial representations. Extensive experiments on GCC-FER and DFEW demonstrate that the proposed system consistently improves FER performance across multicultural settings.

Learning dexterous manipulation requires demonstrations that preserve fine hand-object interactions while remaining executable at deployment. Existing pipelines either lose deployable dexterity through retargeting or embodiment conversion, or rely on robot-specific teleoperation that is costly to scale and often lacks intuitive, contact-aware control for dexterous data collection. We present RealDexUMI, a wearable universal manipulation interface built around a shared dexterous end-effector module that integrates a lightweight dexterous hand, in-hand vision, and fingertip tactile sensing. A palm-side isomorphic teleoperation glove maps human finger inputs to robot-hand joint commands, enabling real-time, retargeting-free, intuitive, and precise hand control. The shared hand and sensing modules yield zero-gap end-effector data, with matched in-hand observations, tactile signals, contacts, and hand actions between collection and deployment. Across eight real-robot tasks spanning fine-grained, contact-rich, long-horizon, and bimanual manipulation, policies trained on RealDexUMI data achieve an average success rate of 88.75%, generalize to unseen initial poses, and transfer across three embodiments. Website: https://research.beingbeyond.com/realdexumi

Computer-Aided Design (CAD) underpins modern engineering and manufacturing by enabling the creation of precise, editable 3D models. However, CAD research typically studies tasks in isolation, and multi-modal, multi-task learning for CAD is hindered by the absence of a unified benchmark. To address this gap, we introduce UniCAD, a comprehensive benchmark for multi-modal CAD learning that covers point-to-CAD reconstruction, text/image-to-CAD generation, and CAD question answering across diverse input modalities. Alongside the benchmark, we present UniCAD-MLLM, a universal multi-modal large language model that ingests text, images, sketches, and point clouds and performs these heterogeneous tasks in an end-to-end fashion within a single framework. Extensive experiments on the UniCAD and Fusion360 benchmarks demonstrate that UniCAD-MLLM achieves state-of-the-art performance across all tasks, outperforming existing task-specific and multi-task baselines. We will release the dataset, code, and pretrained models to accelerate future research.

We introduce \emph{universal transformers}: fixed transformers that can simulate any transformer in a given class via a suitable input embedding. Analogous to a universal Turing machine, the input embedding encodes a description of the target model while all internal parameters remain fixed. We provide explicit sparse constructions achieving universality when the embedding dimension is sufficiently large, and further show that universality is generic: randomly initialized transformers are universal almost surely, which aligns with recent empirical results of Zhong and Andreas (2024). We empirically validate our theory on the algorithmic tasks of parenthesis balancing and multi-hop reasoning. Our results suggest that much of a transformer's expressive power may reside in its input representation rather than its learned weights.

Pattern languages are a classical model in formal language theory and algorithmic learning theory. This note formulates the problem of computing the inclusion depth of a pattern language: the length of the longest strict inclusion chain from the universal pattern language to the language generated by a given pattern. Inclusion depth captures the mind-change complexity of pattern identification from positive data. The central open question is whether the inclusion depth ID_Sigma(p) is computable for every pattern p over every finite alphabet Sigma with at least two symbols, and whether it is computable in polynomial time. A simple conjectured formula, ID_Sigma(p) = 2|p| - #var(p) - 1, would imply a linear-time algorithm. The problem connects pattern language inclusion, combinatorics on words, language identification in the limit, and mind-change-bounded learning.

Structural probes train on Universal Dependencies (UD), which does not encode formal-syntactic abstractions such as phase boundaries or phase-internal cohesion. Whether large language models (LLMs) encode these remains an open question that UD-based probing cannot answer by construction. We evaluate structural probes on wh-movement stimuli where UD distances are invariant across conditions by design -- any non-zero effect therefore reflects structure beyond UD. The three conditions -- bare small clause, infinitival, and finite -- are ordered by the number of Minimalist Program (MP) phase boundaries the wh-element crosses. Across 13 LLMs from four families, we find a phase-count gradient on a cross-clause pair (12/13 models) and a 13/13 sign asymmetry on a within-clause pair whose UD distance is identical across conditions -- the latter specifically predicted by phase-internal cohesion, an MP abstraction invisible to UD by construction. Activation patching confirms the representations are causally active in 12/13 models. These findings suggest that distributional pretraining can induce representations aligned with formal-syntactic abstractions beyond the reach of annotation-based probing; UD-grounded probes provide a lower bound on syntactic encoding, not an upper bound.

Across machine learning, biology, and physics, independently evolving systems often converge toward strikingly similar high-level structures despite radically different microscopic details. Grokking circuits converge across random seeds, evolutionary lineages rediscover similar metabolic solutions, and renormalization flows approach common fixed points. We propose the Hierarchical Emergence Framework (HEF) as a candidate universality framework for such convergence phenomena. HEF models emergence as a phase transition in a mechanism landscape constrained by thermodynamic and information-theoretic laws. The framework introduces a critical energy threshold Ec separating an exploration regime with competing mechanisms from a convergence regime governed by a unique minimum-cost mechanism. Under structural assumptions, we prove physical feasibility, derive strict metric contraction, and establish convergence toward a unique fixed-point representation independent of initial conditions. We further connect this convergence structure to causal emergence through Effective Information and mechanism competition entropy. To test the framework, we study delayed generalization ("grokking") in modular arithmetic transformers across 111 experiments. We identify a reproducible empirical fingerprint of the Ec transition: the weight norm peaks systematically before grokking in 92% of runs. Normalized accuracy curves collapse onto a tanh kink (R^2=0.93) consistent with a Landau-Ginzburg universality class, and all grokked models converge to 0.9745+/-0.014 regardless of initialization, weight decay, or training fraction (ANOVA p>0.13). HEF is not presented as a universal theory of emergence, but as a falsifiable mathematical scaffold for studying convergence phenomena across complex systems.

Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The universality properties of such any-dimensional models remain poorly understood, as universality is traditionally studied for models accepting inputs of a fixed size, defined on a compact subset of their domain. In sharp contrast, any-dimensional models can be viewed as sequences of functions defined on growing-sized inputs, and it is not clear in which sense they can be universal. We develop a systematic approach to establish any-dimensional universality, by identifying any-dimensional functions with a unique function taking inputs in a suitable infinite-dimensional limit space containing inputs of all finite sizes as well as their limits. Using the symmetries of these inputs and relations between inputs of different sizes, we show that this limit space admits a natural topology with rich families of compact sets on which any-dimensional universality can be established. We illustrate our approach by showing that several existing architectures fail to be universal, and we propose simple modifications that restore universality.

Katharevousa Greek remains poorly served by contemporary NLP pipelines despite its importance for legal, administrative, and parliamentary archives. We present a reproducible workflow for building and evaluating a Universal Dependencies-style parsing resource for Katharevousa parliamentary questions from Greece's early post-junta period. The pipeline links OCR-aware reconstruction, schema-constrained LLM-assisted annotation, automatic validation, deterministic CoNLL-U snapshotting, fixed-split evaluation, and model-family comparison. The frozen automatically validated reference set contains 1{,}697 sentences, split into 1{,}357 training sentences and 340 held-out test sentences. We compare off-the-shelf Greek and Ancient Greek parsers, a feature-based parser, mBERT, XLM-R, and custom Stanza training under the same scoring protocol. Off-the-shelf systems show substantial register mismatch: the strongest external baseline, spaCy Greek, reaches 0.4183 LAS. The best structural parser, an XLM-R model, reaches 0.8893 UPOS accuracy, 0.7250 dependency-relation F1, 0.6098 UAS, and 0.5162 LAS, an absolute LAS gain of 0.0980 over the best external baseline. The feature-based model remains competitive for UPOS and relation labeling, indicating that transparent lexical-context features still matter at this data scale. Beyond scores, the paper contributes an auditable methodology for turning difficult historical parliamentary OCR into reusable syntactic NLP infrastructure. The entire pipeline -- code, schema, frozen reference annotations, fixed train/test split, and per-model benchmark reports -- is released as an open-access companion to this paper.

We develop a mean-field theory of dropout as a perturbation of critical signal propagation at the edge of chaos, and show that it predicts a simple, no-cost change to standard practice: \emph{front-loaded} dropout schedules cut test loss by $18$--$35\%$ over constant dropout in MLPs and Vision Transformers at fixed budget. The theoretical mechanism is that dropout shifts the perfect-alignment fixed point, making the depth scale for information propagation finite even at critical initialization. We derive critical and crossover scaling laws for correlation decay and establish that smooth activations and kinked, \relu{}-like activations constitute distinct universality classes, with different critical exponents and a universal two-parameter scaling collapse in detuning and dropout strength. The distinction traces to the analytic structure of the correlation map: smooth activations admit a Taylor expansion near perfect alignment, while kinked activations develop a branch point with universal non-analyticity. As a corollary, the framework yields saturated dropout profiles under fixed budget; a regularization-reach argument then selects front-loaded schedules, with accuracy gains as a consistent secondary effect. We also discuss how the same Gaussian-kernel structure extends the theory beyond MLPs toward CNNs and residual architectures.

The Strong Platonic Representation Hypothesis suggests that representational convergence in artificial neural networks can be harnessed constructively: embeddings can be translated across models through a universal latent space without paired data. We ask whether an analogous geometry can be recovered across human brains. Using fMRI data from the Natural Scenes Dataset, we propose a self-supervised encoder that learns subject-specific embeddings from brain data alone by exploiting repeated stimulus presentations. We show that these independently learned spaces can be translated across subjects using unsupervised orthogonal rotations, without paired cross-subject samples or intermediate model representations. Synchronizing pairwise rotations into a single shared latent space further improves cross-subject retrieval, indicating that subject-specific spaces are mutually compatible with a common coordinate system. These results provide evidence for a shared neural geometry in the human visual cortex: subject-specific fMRI representations are approximately isometric across individuals and can be translated through purely geometric transformations.

Transformers trained on modular arithmetic exhibit sharp transitions between memorization, generalization, and collapse. We show that weight decay acts as a scalar empirical control parameter for these regimes, and introduce two cheap online diagnostics, mean pairwise attention-head cosine similarity and entropy standard deviation, that track training dynamics from attention activations alone and complement loss-landscape diagnostics at lower compute cost. Across eleven experimental conditions and three model scales (0.82M to 85M parameters), the weight-decay axis separates memorization, developmental grokking, and collapse. A near-transition logistic fit localizes the memorization-to-developmental boundary at $λ_c=0.0158$ (95% CI [0.0109, 0.0200], N=210); a power-law fit gives an empirical exponent $ν=0.757$ (CI [0.725, 0.799]). Reference exponents $ν=1/2$ and 3D Ising $ν\approx 0.63$ lie outside this empirical CI under our four-bin grid, so we report $ν$ as empirical and defer universality-class identification to denser finite-size-scaling work. A horizon-matched multi-task replication (n=280, four modular operations) preserves the weight-decay control pattern; a paired attention-head re-initialization experiment at $λ=0.05$ changes Phase-2 amplitude (Cohen's $d=-1.190$, n=10, $p_t=4.5 \times 10^{-3}$), while matched weight-norm clipping does not. Three cross-architecture probes (4L MLP, 4L LSTM, and 4L Mamba; each n=70) replicate the weight-decay-controlled transition with architecture-specific $λ_c$ values. Main diagnostic claims are scoped to modular arithmetic in small transformer attention models; the non-attention experiments are scope probes, and architecture-wide, language-model, and universality-class claims are out of scope.

Scientific and technological frontiers advance through punctuated dynamics, yet the principles governing these dynamics remain poorly understood. Here we collect and analyze datasets tracking the evolution of frontiers across 9 different domains, spanning materials discovery, structural biology, AI, computational biomedicine, data science, theoretical computer science, Formula-1 racing, and physical wheel building. Analyzing 6.8M solutions to 6.7K tasks, we uncover three universal patterns: (1) waiting times between new frontiers are heavy-tailed, with most attempts concentrated in long stasis; (2) frontier records accumulate at a sublinear rate, faster than logarithmic yet slower than linear growth; (3) record-breaking events are temporally correlated, generating short-term predictability yet long-term unpredictability. Despite the differences in the scale, scope, and definition of the settings, these patterns are remarkably consistent across all domains we study, and are not captured by models from complex systems, record statistics, economics of innovation, and cultural evolution. We trace the missing ingredient to the distinction between radical and incremental innovation, and develop a minimal, analytically solvable model incorporating both radical resets that restructure what is achievable and incremental refinements that exploit the current frontier. The simple model reproduces all three empirical regularities. Remarkably, the leading-order predictions are parameter-independent, identifying a new universality class governing punctuated progress and yielding testable predictions about how openness and access to frontier solutions shape the pace of advance. Overall, these results reveal universal dynamics governing punctuated progress and identify the interplay between radical resets and incremental refinements as the key driver of how scientific and technological frontiers advance.

Deep neural networks trained with different architectures, objectives, and datasets have been reported to converge on similar visual representations. However, what remains unknown is which visual properties models actually converge on and which factors may underlie this convergence. To address this, we decompose the object similarity structure of 162 diverse vision models into a small set of non-negative dimensions. To determine universal versus model-specific dimensions, we then estimate how often each dimension reappears across models. In contrast to model-specific dimensions, universal dimensions are more interpretable and more strongly driven by conceptual image properties, indicating the relevance of interpretability and semantic content as implicit factors driving universality across models. Differences in architecture, objective function, training data, model size, and model performance do not explain the emergence of universal dimensions. However, models with more universal dimensions also better predict macaque IT activity and human similarity judgments, suggesting that universality reflects representations relevant to biological vision. These findings have important implications for understanding the emergent representations underlying deep neural network models and their alignment with biological vision.

With the recent surge of generative models, diffusion-based approaches have become mainstream for view synthesis tasks, either in an explicit depth-warp-inpaint or in an implicit end-to-end manner. Despite their success, both paradigms often suffer from noticeable quality degradation, e.g., blurred details and distorted structures, caused by pixel-to-latent compression and diffusion hallucination. In this paper, we investigate diffusion degradation from three key dimensions (i.e., spatial, temporal, and backbone-related) and propose UniFixer, a universal reference-guided framework that fixes diverse degradation artifacts via a coarse-to-fine strategy. Specifically, a reference pre-alignment module is first designed to perform coarse alignment between the reference view and the degraded novel view. A global structure anchoring mechanism then rectifies geometric distortions to ensure structural fidelity, followed by a local detail injection module that recovers fine-grained texture details for high-quality view synthesis. Our UniFixer serves as a plug-and-play refiner that achieves zero-shot fixing across different types of diffusion degradation, and extensive experiments verify our state-of-the-art performance on novel view synthesis and stereo conversion.

We introduce a technique that enables Neural-ODEs to approximate arbitrary velocity fields with a priori planted fixed-points. Specifically, a recipe is given to explicitly accommodate for a finite collection of points in the reference multi-dimensional space of the Neural-ODE where the velocity field is exactly equal to zero. In this way, the gradient-based training is rigorously constrained inside the prescribed hypothesis class while leaving the expressive power of the Neural-ODE unaltered. We rigorously prove the universality of the Neural-ODE under any local constraints in the velocity field and give a computationally convenient way of imposing the fixed points. Our method is then tested on two paradigmatic physical models.

Large language models from different families use different hidden dimensions, tokenizers, and training procedures, making behavioral directions difficult to compare or transfer across models. We introduce an anchor-projection framework that maps hidden representations from each model into a shared anchor coordinate space (ACS). Behavioral directions extracted from source models are projected into ACS and averaged into a canonical direction. For a new model, the canonical direction is reconstructed into its native hidden space using only anchor activations, without fine-tuning or target-specific direction extraction. We evaluate five instruction-tuned model families and ten behavioral axes. We find that same-axis directions align tightly across the Llama-Qwen-Mistral-Phi (LQMP) cluster in ACS. This shared structure transfers to downstream tasks. For the aligned LQMP cluster, held-out targets achieve (0.83) ten-way detection accuracy and (0.95) mean binary AUROC, while canonical steering induces refusal-rate shifts of up to +0.46% under distribution shift. Sensitivity analyses show that two source models and small anchor pools already suffice to approximate transferable directions. Overall, ACS provides a novel perspective on cross-family interpretability, revealing that representation-level transfer remains robust across model families.

Training neural networks to satisfy universal constraints over continuous domains poses unique challenges. Common examples include Lyapunov Neural Networks (Lyapunov NNs) and Physics-Informed Neural Networks (PINNs), where analytical solutions are generally either unavailable or overly restrictive. Sample-based methods are therefore commonly used to enforce these constraints, and the choice of samples has a substantial impact on convergence speed, stability, and solution quality. Most existing methods rely on fixed heuristics or handcrafted rules, and are suboptimal in practice. In this paper, we aim to improve upon them by learning, from data and experience, how to dynamically and iteratively adjust the samples in response to the model's evolving learning performance. Trained by reinforcement learning, the learned policy improves empirical constraint satisfaction on test problems while significantly improving efficiency. We validate the approach on both Lyapunov NNs and PINNs, and demonstrate its broader applicability to domains where adaptive input selection is essential for effective training.

In many practical applications it is important to build symmetries into neural network architectures. Consider the important case of permutation symmetry on point clouds consisting of $n$ points in $d$ dimensions. In this case the network learns a function on a set of $n$ points in $\mathbb{R}^d$, and a natural paradigm for constructing invariant networks is Janossy pooling, which generalizes the popular Deep Sets architecture. We study the universality of this approach, in particular the important question of how large the embedding dimension must be to guarantee universality of this architecture. Specifically, using a novel technique, we prove new lower bounds on the required size of this embedding dimension. For Deep Sets, this gives the correct minimal dimension up to a constant factor for all $d > 1$. For $k$-ary Janossy pooling, we prove the first non-trivial lower bound on the required embedding dimension when $k > 1$.

We introduce the Yat kernel $k_{b,\varepsilon}(\mathbf{w},\mathbf{x})=\frac{(\mathbf{w}^\top\mathbf{x}+b)^2}{\|\mathbf{x}-\mathbf{w}\|^2+\varepsilon},\qquad b\ge 0,\ \varepsilon>0,$ a rational hidden-unit primitive whose units are Mercer sections over a shared input/weight space. For $b\ge 0$ the kernel is PSD; for $b>0$ it dominates a scaled inverse-multiquadric (IMQ) in the Loewner order, yielding fixed-kernel universality, characteristicness, and strict positive definiteness on every compact domain. The polynomial numerator opens nonradial alignment channels absent from finite IMQ expansions, witnessed by the directional far-field trace $T_\infty g_\varepsilon(\cdot;\mathbf{w},b)(\mathbf{u})=(\mathbf{u}^\top\mathbf{w})^2$. Algebraically, a second finite difference in the bias recovers any IMQ atom from three positive-bias Yat atoms exactly, sharp at three atoms in every dimension at exact pointwise equality. A trained shared-$(b,\varepsilon)$ Yat layer is therefore a finite learned-center expansion in a fixed universal characteristic RKHS, with closed-form norm $\boldsymbolα^\top\mathbf{K}\boldsymbolα$ and explicit diagonal $(\|\mathbf{x}\|^2+b)^2/\varepsilon$ driving a Rademacher generalization bound.

We consider the infinite-width limit of a fully connected deep neural network with general weights, and we prove quantitative general bounds on the $2$-Wasserstein distance between the network and its infinite-width Gaussian limit, under appropriate regularity assumptions on the activation function. Our main tool is a Lindeberg principle for Deep Neural Networks, which we use to successively replace the weights on each layer by Gaussian random variables.

Deploying reinforcement learning policies in the real world requires adapting to time-varying environments. We study this problem in the contextual Markov Decision Process (cMDP) framework, where a family of environments is indexed by a low-dimensional context unknown at test time. The standard approach decomposes the problem: train a so-called "universal policy" which assumes knowledge of the true context, then pair it with a context estimator which approximates context using the observed trajectory. We identify a simple, counterintuitive trick that substantially improves the estimator: randomly delete a fraction of the training buffer after each round. This works because data is collected across multiple rounds using progressively better policies, and older trajectories come from a different distribution than what the estimator will face at deployment time; random deletion creates an implicit exponential decay on older data while preserving diversity without requiring any explicit identification of which samples are stale. This reduces robustness gap by 30% for MLPs and by 6% on average for recurrent networks. Strikingly, it allows a narrow MLP with 5x fewer parameters to outperform a wide MLP trained without deletion. To understand when and why deletion helps, we analyze regularized empirical risk minimization with a mismatch between the train distribution and the distribution at deployment; in this idealized setting, we prove that removing a single uniformly random training point decreases expected test loss in expectation under mild conditions. For ridge regression we make this quantitative: deletion helps when the regularization coefficient is moderate and the signal-to-noise ratio (SNR) is sufficiently low, and, crucially, this SNR threshold gives a direct measure of how large the distribution mismatch between training and deployment must be for deletion to be beneficial.

We report a striking statistical regularity in frontier LLM outputs that enables a CPU-only scoring primitive running at 2.6 microseconds per token, with estimated latency up to 100,000$\times$ (five orders of magnitude) below existing sampling-based detectors. Across six contemporary models from five independent vendors, two generation sizes, and five held-out domains, token rank-frequency distributions converge to the same two-parameter Mandelbrot ranking distribution, with 34 of 36 model-by-domain fits exceeding $R^{2} = 0.94$ and 35 of 36 favoring Mandelbrot over Zipf by AIC. The shared family does not collapse the models into statistical duplicates. Fitted Mandelbrot parameters remain cleanly separable between models: the cross-model spread in $q$ (1.63 to 3.69) exceeds its per-model bootstrap standard deviation (0.03 to 0.10) by more than an order of magnitude, yielding tens of standard deviations of separation per few thousand output tokens. Two capabilities follow. First, statistical model fingerprinting: text from a vendor-delivered LLM can be tested against its claimed model family without cryptographic watermarks or access to model internals, supporting provenance verification and silent-substitution audits. Second, a model-agnostic reference distribution for black-box output assessment, from which we derive a single-pass scoring primitive that composes with model log probabilities when available and degrades to a rank-only mode usable on closed APIs. Pilot results on FRANK, TruthfulQA, and HaluEval map where the primitive helps (lexical anomalies, unsupported entities) and where it structurally cannot (reasoning errors in domain-appropriate vocabulary). We position the primitive as a first-pass triage layer in compound evaluation stacks, not as a replacement for sampling-based or source-conditioned verifiers.

We demonstrate that a small transformer can learn to execute programs in MicroPy, a simplified yet computationally universal programming language. Given procedure definitions together with an expression to evaluate, the transformer predicts small-step execution using PENCIL scaffolding for space-efficient execution within a bounded context window. After training on randomly generated, meaningless MicroPy programs, the learned transformer generalizes to various human-written programs including bit copying and flipping, binary addition and multiplication, and SAT verification and solving. We note that the trained model can achieve out-of-distribution generalization; i.e., evaluate novel programs from distribution on programs. Since MicroPy can express any computation, our results provide empirical evidence that a standard transformer can be trained to act as a universal computer.

We analyze the universal approximation property of Kolmogorov-Arnold Networks (KANs) in terms of their edge functions. If these functions are all affine, then universality clearly fails. How many non-affine functions are needed, in addition to affine ones, to ensure universality? We show that a single one suffices. More precisely, we prove that deep KANs in which all edge functions are either affine or equal to a fixed continuous function $σ$ are dense in $C(K)$ for every compact set $K\subset\mathbb{R}^n$ if and only if $σ$ is non-affine. In contrast, for KANs with exactly two hidden layers, universality holds if and only if $σ$ is nonpolynomial. We further show that the full class of affine functions is not required; it can be replaced by a finite set without affecting universality. In particular, in the nonpolynomial case, a fixed family of five affine functions suffices when the depth is arbitrary. More generally, for every continuous non-affine function $σ$, there exists a finite affine family $A_σ$ such that deep KANs with edge functions in $A_σ\cup\{σ\}$ remain universal. We also prove that KANs with the spline-based edge parameterization introduced by Liu et al.~\cite{Liu2024} are universal approximators in the classical sense, even when the spline degree and knot sequence are fixed in advance.

Multimodal Large Language Models (MLLMs) have emerged as a promising foundation for universal multimodal embeddings. Recent studies have shown that reasoning-driven generative multimodal embeddings can outperform discriminative embeddings on several embedding tasks. However, Chain-of-Thought (CoT) reasoning tends to generate redundant thinking steps and introduce semantic ambiguity in the summarized answers in broader retrieval scenarios. To address this limitation, we propose Rewrite-driven Multimodal Embedding (RIME), a unified framework that jointly optimizes generation and embedding through a retrieval-friendly rewrite. Meanwhile, we present the Cross-Mode Alignment (CMA) to bridge the generative and discriminative embedding spaces, enabling flexible mutual retrieval to trade off efficiency and accuracy. Based on this, we also introduce Refine Reinforcement Learning (Refine-RL) that treats discriminative embeddings as stable semantic anchors to guide the rewrite optimization. Extensive experiments on MMEB-V2, MRMR and UVRB demonstrate that RIME substantially outperforms prior generative embedding models while significantly reducing the length of thinking. Code is available at https://github.com/PeppaWu/RIME.

Low-resource machine translation requires methods that differ from those used for high-resource languages. This paper proposes a novel in-context learning approach to support low-resource machine translation of the Coptic language to English, with syntactic augmentation from Universal Dependencies parses of input sentences. Building on existing work using bilingual dictionaries to support inference for vocabulary items, we add several representations of syntactic analyses to our inputs , specifically exploring the inclusion of raw parser outputs, verbalizations of parses in plain English, and targeted instructions of difficult constructions identified in sub-trees and how they can be translated. Our results show that while syntactic information alone is not as useful as dictionary-based glosses, combining retrieved dictionary items with syntactic information achieves significant gains across model sizes, achieving new state-of-the-art translation results for Coptic.

Zeroth-Order optimization presents a promising memory-efficient paradigm for fine-tuning Large Language Models by relying solely on forward passes. However, its practical adoption is severely constrained by slow wall-clock convergence and high estimation variance. In this work, we dissect the runtime characteristics of ZO algorithms and identify a critical system bottleneck where the generation of perturbations and parameter updates accounts for over 40% of the training latency. We argue that the standard uniform exploration strategy is fundamentally flawed as it fails to account for the heterogeneous sensitivity of layers in deep networks, resulting in computationally wasteful blind searches. To address this structural mismatch, we propose AdaLeZO, an Adaptive Layer-wise ZO optimization framework. By formulating the layer selection process as a non-stationary Multi-Armed Bandit problem, AdaLeZO dynamically allocates the limited perturbation budget to the most sensitive parameters. We further introduce an Inverse Probability Weighting mechanism based on sampling with replacement, which guarantees unbiased gradient estimation while effectively acting as a temporal denoiser to reduce variance. Extensive experiments on LLaMA and OPT models ranging from 6.7B to 30B parameters demonstrate that AdaLeZO achieves 1.7x to 3.0x wall-clock acceleration compared to state-of-the-art methods. Crucially, AdaLeZO functions as a universal plug-and-play module that seamlessly enhances the efficiency of existing ZO optimizers without incurring additional memory overhead.

Recent studies reveal striking representational alignment between artificial neural networks (ANNs) and biological brains, leading to proposals that all sufficiently capable systems converge on universal representations of reality. Here, we argue that this claim of Universality is premature. We introduce the Umwelt Representation Hypothesis (URH), proposing that alignment arises not from convergence toward a single global optimum, but from overlap in ecological constraints under which systems develop. We review empirical evidence showing that representational differences between species, individuals, and ANNs are systematic and adaptive, which is difficult to reconcile with Universality. Finally, we reframe ANN model comparison as a method for mapping clusters of alignment in ecological constraint space rather than searching for a single optimal world model.

With the development of robotics, skeleton-based action recognition has become increasingly important, as human-robot interaction requires understanding the actions of humans and humanoid robots. Due to different sources of human skeletons and structures of humanoid robots, skeleton data naturally exhibit heterogeneity. However, previous works overlook the data heterogeneity of skeletons and solely construct models using homogeneous skeletons. Moreover, open-vocabulary action recognition is also essential for real-world applications. To this end, this work studies the challenging problem of heterogeneous skeleton-based action recognition with open vocabularies. We construct a large-scale Heterogeneous Open-Vocabulary (HOV) Skeleton dataset by integrating and refining multiple representative large-scale skeleton-based action datasets. To address universal skeleton-based action recognition, we propose a Transformer-based model that comprises three key components: unified skeleton representation, motion encoder for skeletons, and multi-grained motion-text alignment. The motion encoder feeds multi-modal skeleton embeddings into a two-stream Transformer-based encoder to learn spatio-temporal action representations, which are then mapped to a semantic space to align with text embeddings. Multi-grained motion-text alignment incorporates contrastive learning at three levels: global instance alignment, stream-specific alignment, and fine-grained alignment. Extensive experiments on popular benchmarks with heterogeneous skeleton data demonstrate both the effectiveness and the generalization ability of the proposed method. Code is available at https://github.com/jidongkuang/Universal-Skeleton.

This paper explores the response of Large Language Models (LLMs) to user prompts with different degrees of politeness and impoliteness. The Politeness Theory by Brown and Levinson and the Impoliteness Framework by Culpeper form the basis of experiments conducted across three languages (English, Hindi, Spanish), five models (Gemini-Pro, GPT-4o Mini, Claude 3.7 Sonnet, DeepSeek-Chat, and Llama 3), and three interaction histories between users (raw, polite, and impolite). Our sample consists of 22,500 pairs of prompts and responses of various types, evaluated across five levels of politeness using an eight-factor assessment framework: coherence, clarity, depth, responsiveness, context retention, toxicity, conciseness, and readability. The findings show that model performance is highly influenced by tone, dialogue history, and language. While polite prompts enhance the average response quality by up to ~11% and impolite tones worsen it, these effects are neither consistent nor universal across languages and models. English is best served by courteous or direct tones, Hindi by deferential and indirect tones, and Spanish by assertive tones. Among the models, Llama is the most tone-sensitive (11.5% range), whereas GPT is more robust to adversarial tone. These results indicate that politeness is a quantifiable computational variable that affects LLM behaviour, though its impact is language- and model-dependent rather than universal. To support reproducibility and future work, we additionally release PLUM (Politeness Levels in Utterances, Multilingual), a publicly available corpus of 1,500 human-validated prompts across three languages and five politeness categories, and provide a formal supplementary analysis of six falsifiable hypotheses derived from politeness theory, empirically assessed against the dataset.

Traffic forecasting is a challenging spatio-temporal modeling task and a critical component of urban transportation management. Current studies mainly focus on deterministic predictions, with limited considerations on the uncertainty and stochasticity in traffic dynamics. Therefore, this paper proposes an elegant yet universal approach that transforms existing models into probabilistic predictors by replacing only the final output layer with a novel Gaussian Mixture Model (GMM) layer. The modified model requires no changes to the training pipeline and can be trained using only the Negative Log-Likelihood (NLL) loss, without any auxiliary or regularization terms. Experiments on multiple traffic datasets show that our approach generalizes from classic to modern model architectures while preserving deterministic performance. Furthermore, we propose a systematic evaluation procedure based on cumulative distributions and confidence intervals, and demonstrate that our approach is considerably more accurate and informative than unimodal or deterministic baselines. Finally, a more detailed study on a real-world dense urban traffic network is presented to examine the impact of data quality on uncertainty quantification and to show the robustness of our approach under imperfect data conditions. Code available at https://github.com/Weijiang-Xiong/OpenSkyTraffic

Data-driven dexterous hand manipulation requires large-scale, physically consistent demonstration data. Simulation and video-based methods suffer from sim-to-real gaps and retargeting problems, while MoCap glove-based teleoperation systems require per-operator calibration and lack portability, as the robot hand is typically fixed to a stationary arm. Portable alternatives improve mobility but lack cross-platform and cross-operator compatibility. We present DEX-Mouse, a portable, calibration-free hand-held teleoperation interface with integrated kinesthetic force feedback, built from commercial off-the-shelf components under USD 150. The operator-agnostic design requires no calibration or structural modification, enabling immediate deployment across diverse environments and platforms. The interface supports a configuration in which the target robot hand is mounted directly on the forearm of an operator, producing robot-aligned data. In a comparative user study across various dexterous manipulation tasks, operators using the proposed system achieved an 86.67% task completion rate under the attached configuration. Also, we found that the attached configuration reduced the perceived workload of the operators compared to spatially separated teleoperation setups across all compared interfaces. The complete hardware and software stack, including bill of materials, CAD models, and firmware, is open-sourced at https://dex-mouse.github.io/ to facilitate replication and adoption.