Expressivity

Linear RNNs based on the delta-rule enable efficient sequence modeling, but their linear updates with a low-rank correction constrain their expressivity. Prior work has shown that composing two delta-rule transitions in a single recurrent update can model a 2D rotation, but this increases the rank and the cost of the updates compared to a single transition. We show that Kimi Delta Attention (KDA) can realize 2D rotations by combining a single delta-rule transformation with a second reflection supplied by its channel-wise gate. This requires extending the parameter ranges of KDA by combining two existing range extensions: allowing gates in $[-1,1]$ and the delta-rule coefficient $β$ in $[0,2]$. We call the resulting model Complex KDA (CKDA). It preserves KDA's stability and efficiency, with transitions that remain diagonal-plus-rank-one and non-expansive, while reaching the state-tracking expressivity of DeltaProduct$_2$. We characterize the expressivity of CKDA and prove that every orthogonal diagonal-plus-rank-one matrix is exactly a CKDA transition matrix. A single CKDA layer can track every finite group isomorphic to a subgroup of $\mathrm{SO}(3)$, and many state-tracking results use one fewer layer for CKDA compared to other diagonal-plus-rank-one Linear RNNs. Empirically, combining both extensions yields the strongest length extrapolation among tested KDA range settings on $S_3$, $S_4$, and periodic audio continuation. In language modeling, CKDA outperforms Transformers and other linear RNNs, obtains similar results to a KDA baseline, and shows promising scaling behavior. Our code is open source at https://github.com/OpenEuroLLM/ComplexKDA and our models are available at https://huggingface.co/collections/openeurollm/complexkda.

In previous papers, we began the study of sequence prediction algorithms adapted to stringological word complexity measures. In particular, we defined a complexity measure called Arithmetic Repetition Complexity (ARC) which admits a polynomial-time prediction algorithm with a mistake bound quasilinear in the complexity. Here, we show a weaker complexity measure related to ARC that admits an especially efficient prediction algorithm: an algorithm that runs in quasilinear time and polylog space for appropriate highly-structured sequences. The complexity measure is defined via a restricted class of "zipline programs" (a variant of straight-line programs), which we call layered. We thus get a less expressive measure with a more efficient algorithm (compared to our results for ARC), demonstrating a possible tradeoff.

Large language models are increasingly used to generate and evaluate online content, yet it remains unclear whether the qualities they associate with higher engagement match what real users respond to. We study this question using 1.17 million answers to 25,978 questions from Zhihu, Quora, and Reddit, comparing real platform answers and AI-generated answers across four within-question engagement levels. We introduce Ontological Preference Measurement, which represents answers along three dimensions: logic, affect, and expression. We find a systematic gap between AI preference and real user engagement: as target engagement increases, LLMs add more explicit logical structure, while real user engagement is more strongly associated with affective and expressive salience. We call this tendency logic overbinding. Based on this diagnosis, we propose Ontology-Masked Reasoning Autoencoding (OMRA), a controlled intervention that masks and reconstructs over-explained spans while preserving stance, factual content, and coherence. Across four LLM families, OMRA reduces the measured gap by an average of 54.4%. In human evaluation, OMRA wins 62.4% of pairwise preference judgments against matched real platform answers, even though the real answers are more often judged to be human-written.

Whitney's theorem allows isomorphism testing for connected simple graphs, apart from $K_3$ and $K_{1,3}$, to be formulated as distinguishing their line graphs. However, the relation between fixed-dimensional Weisfeiler--Leman (WL) expressivity on line graphs and on their roots remains unresolved. We study this relation through Implicit Line-Graph WL (ILG-$k$-WL), which is exactly $k$-WL on $L(G)$, executed over the edges of $G$ with line-graph relations derived from endpoint incidence and without explicitly constructing $L(G)$. On the Whitney-general class, the relation between root-domain and line-graph WL depends on $k$. For $k=1,2$, ILG-$k$-WL adds no distinguishing power beyond root-domain $1$-WL and misses some pairs that $1$-WL separates. For $k=3$, we prove the backward containment $L(G)\equiv_{3\text{-WL}}L(H)\Rightarrow G\equiv_{3\text{-WL}}H$. Strongly regular witness pairs, including the Shrikhande/rook pair, show that ILG-$3$-WL is strictly more expressive than $3$-WL. The backward containment also extends to disconnected graphs with no isolated vertices when every connected component is Whitney-general. Deterministic ILG-$3$-WL separates all three substructure-counting witness pairs, all $105$ pairs in SR25, and $359$ of $400$ BREC pairs. An untrained dense ILG-$3$-GNN gives the same pairwise verdicts on these evaluations.

Training data constrains optimizer geometry through the covectors visible to a declared information channel. We study how such partial information determines a full positive cometric relative to a reference and which degrees of freedom remain unidentified. Our central result resolves full-column-rank positive-definite compression under affine-invariant Riemannian geometry. The compression map is a split-Hadamard metric submetry and admits an explicit unique completion that is the affine-invariant nearest full geometry realizing a visible target and yields exact full-to-visible variational reduction. When the channel moves, the completions form a gauge-invariant rank stratification of the positive-definite cone. Its closed-form pullback pair metric separates visible-metric motion from subspace rotation through a reference-mismatch weight, yields an explicit positive-semidefinite multi-direction Gram matrix, and exposes the precise singularity of reference-valued modes. The mechanism is explained by a metric theorem equating ball submetry, attained fiber distance, and lossless reduction of every monotone radial visible decision problem. A smooth split-Hadamard theorem supplies coherent information sheets, proximal commutation, and solution-wise gradient-flow lifting. The positive-definite realization also gives closed-form prior-data shrinkage. Diagonal and block optimizer families reduce to relative-interior conic image tests with valid facial certificates, while deterministic and finite-sample bounds quantify recovery of the visible geometry and its subspace. Together these results characterize exact reduction, reference-dependent completion, and structured expressivity for the stated finite-dimensional affine-invariant model.

We present DuplexDrama, the first synthesized spoken dialogue dataset that simultaneously covers four dimensions: (i) complete persona and scenario settings; (ii) three full-duplex behaviors (interruption, backchannel, incomplete); (iii) expressive speech with persona-aligned emotion labels; and (iv) script-aware sound events. DuplexDrama is built via a 4-stage pipeline; quality validation on both scripts and synthesized audio confirms its quality. We have produced more than 2,000 hours audio data with a 64-voice timbre pool spanning 13 personas and 5 age buckets; 3.8% of all turns carry at least one full-duplex behavior. This data has been validated through internal full-duplex model training. We will release a curated subset of 6,400 bilingual dialogues (800 h, Chinese ~500 h + English ~300 h) to advance full-duplex spoken dialogue model research. Data samples are available at our demo page and LLM-judge evaluation prompts will be released with the dataset.

Computational recognition of verbal humour remains a challenging task, requiring an understanding of language, delivery style, emotions, and cultural context. Most existing approaches focus on binary classification and lack datasets that capture psychological dimensions of humour alongside variations in expression. We introduce MultiHuSE, a multimodal dataset comprising 2,407 high-definition videos of 50 demographically diverse actors performing 1,463 text samples across four psychological humour styles (affiliative, aggressive, self-enhancing, and self-deprecating), as well as neutral content. A subset is additionally annotated for underlying emotions. The dataset uniquely captures multiple actor interpretations of the same texts, enabling systematic analysis of expressive diversity. Baseline experiments show that multimodal fusion outperforms unimodal approaches (80.1% vs. 77.4% accuracy) in humour style classification, with particularly strong gains for affiliative humour (66% to 74%). While text provides the strongest individual signal, fusion models deliver meaningful improvements. We hope that MultiHuSE provides empirical support for psychological theories linking humour and emotion, while also opening new avenues for research in human communication, well-being, and AI-driven interaction. The dataset is available for academic use under an End-User Licence Agreement.

Enabling robots to perform musical instruments with human-level expressivity represents a frontier in bridging the gap between mechanical precision and artistic interpretation. Despite advances in robotic dexterity, replicating the fluid finger transitions and nuanced dynamic control characteristic of human pianists remains a significant challenge. Through a reinforcement learning-based control framework, we demonstrate that a dexterous robotic hand can achieve high-fidelity performance across a diverse piano repertoire. Central to our approach is a graph-based optimization strategy that guides the robot to generate natural pre-press and key-press fingering strategies that closely resemble human movement patterns. To achieve expressive sound production, the control system is coupled with a physics-inspired acoustic model that modulates keypress velocity to accurately reproduce the dynamic variations specified in musical scores. Quantitative evaluations demonstrate that our expressive control model significantly outperforms baseline methods in both finger morphology similarity and dynamic velocity accuracy. In a perceptual test involving participants from diverse listener groups, performances generated by our system are significantly preferred over baseline robotic performances and are indistinguishable from human performances for non-professional audiences. Furthermore, extensive experiments across multiple musical styles confirm that our method maintains high note-level accuracy while achieving expressive performance. Our approach provides a robust pathway for robotic systems to move beyond mere mechanical accuracy, elevating robotic musicianship to a level of expressive performance comparable to human pianists.

Automatic Music Transcription (AMT) for guitar remains limited by three challenges: existing systems often fail to capture expressive techniques such as slides, bends, and percussive hits; they often assign notes to incorrect string-fret combinations; and they are typically trained on clean recordings, limiting their generalization to noisy real-world audio. To address these challenges, we propose TART, a modular four-stage audio-to-tablature pipeline consisting of (1) an audio-to-MIDI transcription model, (2) an expressive technique classifier, (3) an audio-conditioned T5 encoder-decoder for string-fret assignment, and (4) an automated tablature generator. We evaluate TART in a zero-shot setting on GuitarSet, EGDB, and two augmented benchmarks, Noisy GuitarSet and Noisy EGDB. Averaged across these four benchmarks, TART achieves 81.35% audio-to-MIDI F50 (+6.67 points over the best prior baseline), 71.8% string-fret Tab F1 (+8.5 points over the best prior baseline), and 54.08% end-to-end Tab F1. To our knowledge, TART is the first framework to generate guitar tablature with both fingering and expressive technique annotations directly from guitar audio.

Meta-learning has emerged as an effective paradigm for transferring knowledge across sequential bandit tasks. While substantial progress has been made for stochastic bandits and non-contextual adversarial bandits, meta-learning for adversarial linear contextual bandits (ALCBs) with random action sets remains largely unexplored. To address this problem, we propose Meta-LinEXP3, an online-within-online algorithm that constructs a predictable task-level prior from completed tasks to guide the inner LinEXP3 learner. For known context distributions, we develop a policy-centered estimator that achieves an intrinsic-dimension $\mathcal{O}(\sqrt{n})$ per-task regret bound. For unknown distributions, we introduce a past-only regularized moment estimator with an $\mathcal{O}(n^{2/3})$ leading regret term and explicit finite-sample error. We further establish a direct connection between prior accuracy and transfer regret, showing that increasingly accurate priors yield sublinear transfer-dependent regret across tasks. Experiments demonstrate the effectiveness of Meta-LinEXP3, including its application to structured hyperspectral tensor sampling.

Deep neural networks deployed in the wild must be both efficient and adaptable, requiring model compression and test-time adaptation (TTA). While both are well studied in isolation, their interaction remains poorly understood. We systematically analyze how structured compression affects a model's ability to adapt under distribution shift. Using ResNet-18 and ViT-Base on CIFAR-10-C and ImageNet-C, we evaluate multiple compression methods combined with standard TTA techniques. We introduce a diagnostic framework that examines representational expressivity and adaptation subspace compatibility. Our results reveal a consistent gap: although compressed models retain high accuracy under supervised adaptation, their TTA performance degrades significantly with increasing compression. We show that this stems from reduced representational diversity and structural constraints that limit recoverability. These effects strongly depend on the compression method, highlighting the need to design compression strategies that preserve adaptability.

Graphic designers often blend visual concepts to communicate multiple ideas within a single image, leveraging positive and negative space to create balance, emphasis, and aesthetic appeal. While computational methods have begun to support automatic concept blending, they largely overlook the role of spatial composition in the design. To address this gap, we present an automatic pipeline that explicitly applies positive and negative space throughout the blending process. Our approach first identifies plausible regions for concept integration by combining semantic reasoning from vision-language models with geometric constraints derived from real-world examples. Conditioned on these regions, the system generates blended compositions using a hybrid pixel-vector pipeline: diffusion-based inpainting produces a fast, coarse initialization, which is then refined through vector-based optimization at the point level to ensure structural coherence and balanced semantic expression. A multimodal agent orchestrates this process as a planner and evaluator, enabling iterative improvement and interpretable control. Through an evaluation using both baseline comparisons and a user study, we demonstrate greater expressiveness, creativity, and concept recognizability by effectively leveraging positive and negative space. We further demonstrate the generalizability of our approach across diverse applications, including controllable image and infographic generation.

Protein structure modeling rests on a single computational primitive: the interaction between what a residue is (sequence content) and where it sits (three-dimensional geometry). What is the expressive limit of this layer class? We show that the complete bilinear operator over content-geometry outer products--the sufficient statistic of all second-order interactions--is the expressive ceiling, while the additive message passing of mainstream geometric GNNs is provably blind to content-geometry binding. We then introduce Hyper-Fold, a rank-K separable convolutional backbone approaching this ceiling at message-passing cost: each radius neighborhood is organized into a sequence hyperedge and a contact hyperedge, modulated by an edge-conditioned matrix-valued operator factorized into K learned basis operators with geometry-generated coefficients. Across enzyme function prediction, fold classification, and ligand binding site detection, Hyper-Fold and its hierarchical variant Hyper-Fold-Deep achieve the best results among protein-specific structure encoders; Hyper-Fold-Pocket, an anchored set-prediction head, surpasses UniSite-3D on UniSite-DS and two zero-shot benchmarks with no sequence language model features, 68x fewer parameters, and 4.8x lower latency--suggesting that a sufficiently expressive 3D backbone recovers information that fusion architectures previously borrowed from evolution-scale pretraining.

LLM agents increasingly modify their own prompts, tools, middleware, resources, and execution harnesses at runtime. Such self-evolution can improve capability, but a successful mutation may leave persistent effects that cannot be safely reversed in states different from the one in which it was created. We introduce EvoUndo, a framework for representing, synthesizing, diagnosing, and independently verifying recoverability of model-generated self-modifications across counterfactual states. Across 600 unseen one-shot self-evolution tasks, we identify 197 capability-improving mutations that fail recoverability verification. Under the original recovery representation, conventional repair strategies recover 0/197 of these natural failures. Deterministic oracle analysis recovers 48/197 under the original recovery language L0, while the extended recovery calculus increases empirical oracle recovery to 191/197. A protocol-locked 2x2 grounding-by-expressivity intervention then separates two bottlenecks: exact state-address grounding increases successful recovery from 0/48 to 38/48 (79.2%) when the original language is sufficient, while extending the recovery language enables recovery on 142/143 (99.3%) failures in the oracle-defined S1 stratum. On the primary gpt-oss-120b backbone, adding exact-address diagnostics to the richer language reduces recovery to 133/143 (93.0%); a Qwen3.8-27B replication preserves the grounding and expressivity effects but not this negative interaction, indicating that the latter is model-dependent. These results indicate that reliable agent self-evolution requires co-designing verification, state grounding, witness semantics, and recovery-language expressivity rather than relying on iterative prompting alone.

Personalized text generation for authors and literary writing is essential for applications such as adaptive writing assistants, creative support tools, and computational literary analysis. However, existing approaches to author modeling and personalization often represent writing behavior as independent labels, requiring large-scale corpus collection or fine-tuning for each author or stylistic category. Such formulations are costly, difficult to interpret, and poorly suited for generalizing across authors. Inspired by the Big Five model's dimensional view of personality, we propose LiteraryBigFive, a framework that reframes authorial writing characteristics as coordinates within a unified and interpretable space. In this space, we derive each interpretable axis (e.g., Classicism, Emotionality) from activation-space contrasts between author-written and neutral passages, yielding distinct stylistic dimensions that allow texts or authors to be positioned within a five-dimensional system. Beyond localizing different authors, we further introduce an interpretable steering mechanism, which adaptively guides text generation toward target coordinates to perform author-personalized writing. Experimental results show that LiteraryBigFive improves authorial expressiveness while preserving semantic fidelity. The derived author per-axis scores strongly correlate with real-world literary consensus, offering transparent and interpretable explanations of author-specific generation behavior: https://github.com/Znull-1220/LiteraryBigFive.

Multi-layer transformers form the critical component of essentially all large language models (LLMs) in use today. Because of their ubiquity and computational capability, there is a rapidly growing body of work that aims to precisely calibrate the expressive power of transformers as language recognizers by comparing them against standard models of computation studied for decades by the theoretical computer science community. In this endeavor, circuit complexity has by and large emerged as the "correct" branch of computational complexity to analyze the expressive power of transformers; the reason is that parameterizing transformers by the various resources they use, such as attention and precision, leads to direct comparisons with different classes of circuits parameterized by resources such as type of gates, size, and depth. Here, we present an overview of selected results that delineate the expressive power of transformers using concepts and methods from circuit complexity.

Two accounts recur in explanations of the success of rotary position embeddings (RoPE). Expressivity studies associate periodic position information with modular predicates, whereas mechanistic and long-context studies emphasize positional anchors and local offsets. We formalize both accounts for fully uniform, finite-precision soft-attention transformers. We find that, if every rotary component is periodic, RoPE transformers recognize exactly the languages definable in past temporal logic with modular predicates. Conventional RoPE is different: The rotations it computes never repeat. This yields a precision-dependent bounded simulation of fixed-offset look-back operators, rather than an all-length modular characterization. Controlled experiments match this separation: Constructed periodic schedules length-generalize on modular languages, while conventional RoPE behaves more like a bounded locality bias and can impair tasks requiring position-invariant access to distant context. Altogether, our findings shed light on RoPE transformers, bringing theoretical expressivity characterizations closer to models used in practice.

Recent Text-To-Speech (TTS) systems have achieved strong naturalness and zero-shot voice cloning performance, but fine-grained control of expressive speech at the word or phoneme level remains challenging. We propose CtrlSpeech, a controllable, expressive TTS framework with coarse-to-fine control. Built on the DiTAR architecture, CtrlSpeech combines global speaker conditioning with phone-aligned pitch, loudness, and duration signals, enabling localized prosodic control while preserving the target speaker's timbre. This design allows users to adjust expressive attributes at a fine temporal granularity, making speech refinement more flexible and controllable. Experimental results show that CtrlSpeech achieves competitive zero-shot TTS performance and improves controllability over expressive attributes, demonstrating its effectiveness for flexible and practical expressive speech synthesis.

In generative training, a model produces an output and is penalised for its difference from an example. With one output per comparison, a model that produces one common answer can outperform a model retaining a broader repertoire. Explorative Modeling (XM) produces $K$ outputs per comparison and updates on the closest, claiming exploration as a "third pretraining axis" associated with generative expressivity. Here I show the third axis is actually freedom, meaning the weakness of the constraint implied by a model's behaviour. Previous work showed freedom is a property of function rather than form. Parameters, architecture, minimum-description-length (MDL), and data can vary while the behavioural constraint remains unchanged. It was formally proved that weakest models are likeliest to generalise, and freedom selection beat MDL by 110-500% in induction experiments. I prove average XM loss depends on the chance a candidate misses an acceptable region, with exploration raising miss probability to power $K$. For $K>1$, match probability rises with freedom. I then demonstrate empirically that XM optimises for freedom. In a Forward XM experiment, larger $K$ increased or saturated measured freedom, and increased freedom at every tested value under context-dependent targets. I trained XM candidate pools and compared validation selection with a freedom selector that read unlabelled parent contexts. Freedom won in 29 of 30 cases. Generative expressivity is a mode-count proxy for freedom, that discards the extension structure that gives freedom its generalisation significance. XM is a means, freedom an end, and selecting for freedom improved XM under distribution shift.

Recent advances in 4D Gaussian Splatting (4DGS) enable high-fidelity, real-time spatiotemporal rendering, but expose a fundamental trade-off between motion expressiveness and storage efficiency. While anchor-based designs achieve compactness through anchor-level parameter sharing, their rigid uniform parametrization enforces fixed Neural Gaussian counts and feature budgets per anchor. Consequently, insufficient fidelity is addressed by excessive anchor density, rather than lightweight, targeted increases in Neural Gaussian count or feature capacity, resulting in memory waste. To overcome this rigidity, we introduce an adaptive-capacity anchor-based framework that dynamically allocates the representational capacity based on local spatiotemporal demands. Adaptive Anchor Cardinality varies the number of Neural Gaussians per anchor, concentrating primitives in regions of high geometric or motion complexity while suppressing redundancy. In parallel, Adaptive Anchor Feature Masking modulates anchor-level feature channels, assigning rich features to complex regions and lightweight representations to simpler ones. Experiments on MPEG, Panoptic Sports, and N3DV datasets demonstrate substantial storage reduction without degrading visual quality. Notably, on challenging MPEG sequences with complex motion, our method achieves up to 1.5x higher compression than state-of-the-art anchor-based methods while preserving comparable quality.

Action chunking---predicting and executing multiple actions instead of a single action---has proven to be a critical component for learning effective robotic control policies. However, our precise understanding of why action chunking improves performance has remained limited. In this work we seek to close this gap. Through rigorous experimental evaluations in both simulated and real-world settings, we show that existing hypotheses for the success of action chunking---temporal consistency, horizon reduction, and representation learning---fail to explain the success of action chunking. Instead, we find that action chunking benefits from greater non-Markovian expressivity and reduced compounding error compared to Markovian policies, but, in many settings of interest, these effects can be fully captured by delayed policies, which at each step predict a single action based on the observation $k$ steps in the past. We then show that there exists an additional benefit of action chunking that we refer to as implicit ensembling. In particular, by learning a diversity of temporal relationships (that is, $a_t | o_t, a_t | o_{t-1}, \ldots$), action-chunked policies exhibit behavior matching that of a model ensemble, increasing their robustness and generalization ability over policies that only learn a single temporal relationship. Building on these insights, we show that in simulated and real-world robotic control settings, we can match the performance of action chunking without action chunking---by deploying an action chunking policy as an ensemble of policies with randomized delays. Furthermore, we propose a policy class that amplifies the benefits of action chunking by explicitly instantiating an ensemble, and which we show significantly improves over the performance of action chunking in many domains.

Music is often used as a medium for communicating emotion, with performers shaping perceived affect through interpretation. This study addresses the challenge of identifying and predicting subtle changes in perceived emotion that are exclusively due to differences in performance. We focus on classical solo piano music, using a set of 6 commercial recordings of Bach's Well-Tempered Clavier Book I, annotated in terms of valence and arousal. By encoding the recordings through performance-specific features only, we isolate performance information from aspects of the composition itself, which tend to dominate the overall perceived emotional category. A preliminary analysis validates that these features vary meaningfully across performers. We then propose a relative regression framework, Delta-VA, to predict deviations in valence-arousal relative to an ``average'' performance, thereby focusing on the changes in emotion brought about by a specific way of playing a piece. In addition to the standard $R^2$ regression score, we introduce geometric evaluation metrics to assess the preservation of pairwise differences between performances. Results indicate high directional consistency with the ground truth, but also a compression in prediction magnitude, indicating that the model tends to underestimate expressive performance effects.

What types of decision problems can a causally masked, finite-precision transformer solve for inputs of arbitrary length? Existing answers often rely on idealized arithmetic, but under finite precision, rounding and evaluation order can change what information attention retains and therefore what the model can compute. We develop an algebraic formalization that derives expressivity directly from the model's implemented dynamics. Its central object is its memory; the finite internal state computed by attention that summarizes the information from the prefix available to all future queries. Each attention head updates its own state independently within a layer, while layers compose hierarchically, providing a uniform route from model assumptions to expressivity bounds. Applying this method to transformers without positional embeddings, we obtain an expressivity hierarchy governed by the attention type under specific numerical semantics. Width-one sliding-window attention supports bounded-suffix memory, while a modified form of soft attention supports irreversible, checklist-like state, and combining the two mechanisms provides an interplay of both. Ordinary left-to-right floating-point soft attention can realize more expressive memory operations than any of the above. Algebraically, the four cases correspond to definite, R-trivial, locally R-trivial, and aperiodic semigroups. Under an explicit free-wiring assumption, all four bounds are tight.

Deep subspace clustering plays a critical role in applications involving multivariate spatiotemporal data, such as sea ice monitoring, disease spread analysis, and tracking neuro-degeneration over time. Despite recent advances, existing methods primarily rely on geometric self-expressiveness, assume static subspace structures, and often fail to capture causal dependencies, local spatial interactions, and long-range temporal dynamics inherent in complex spatiotemporal systems. To address these limitations, we propose a novel Causal Adversarial Subspace Clustering (CASC) framework for discovering evolving latent regimes in high-dimensional spatiotemporal data. CASC integrates a U-Net-inspired deep adversarial clustering architecture with stacked FAConvLSTM layers to preserve spatial and temporal structure while learning robust latent representations. A graph attention transformer-based self-expressive network is introduced to jointly model local spatial relationships, global dependencies, and long-range temporal interactions. Furthermore, we propose two new learning objectives: (1) a Causal Subspace Preservation Loss that aligns self-expression coefficients with latent causal relationships, encouraging clusters to reflect underlying causal processes rather than simple feature similarity, and (2) a Dynamic Temporal Subspace Evolution Loss that captures evolving subspace structures and temporal regime transitions in nonstationary environments. Together, these components transform deep subspace clustering from a correlation-driven paradigm into a causal-temporal regime discovery framework.

Neural hypergraphs are a natural generalization of neural networks, the reference models in modern machine learning. Yet, their deployment has proven demanding: the number of weighted hyperedges required leads to an intractable parameter explosion. However, a novel parametrization that leverages spectral attributes for neural hypergraphs has been recently proposed, that enables to recycle parameters via a weight sharing scheme and consequently yields a significant reduction of the associated computational cost. Preliminary tests carried out on spectral higher-order architectures pointed to meaningful improvements in both performance and interpretability. Building on these results, we advance the benchmarking efforts by evaluating the spectral higher order framework on N-bit parity tasks, a well-established testbed known to be particularly challenging. As we will convincingly argue, Spectral Higher-Order Neural Networks (SHONNs) possess a versatile and highly tunable hypothesis space.

Contrastive learning is increasingly moving toward settings with three or more modalities instead of image-text pairs. Yet, extending models from pairwise to higher-order multimodal alignment can introduce optimization and representation challenges. We identify encoder Jacobian conditioning as a key factor in trimodal contrastive learning: poorly conditioned encoders exhibit collapsing or amplified singular-value spectra, leading to exploding Jacobian condition numbers and degraded multimodal alignment. We introduce geometry-preserving encoders (GPEs) by directly conditioning the Jacobian through regularization and demonstrating that simple modifications like LeakyReLU activations and residual paths recover these geometric benefits. Across a synthetic benchmark and four real-world datasets including missing modalities, improving Jacobian conditioning boosts retrieval and linear probe performance across multiple contrastive objectives, whereas expressive objectives yield little benefit in linear probes. More broadly, our results show that multimodal contrastive learning depends not only on objective expressivity, but also on the geometric and optimization properties of the underlying encoders.

We study the expressivity of shallow polynomial neural networks (PNNs) with monomial activation functions over finite fields. For a given architecture, we define a neuromanifold as the image of the map from all possible network weights into the product of polynomial rings. We quantify the expressivity by the cardinality of the neuromanifold, and derive a natural lower and upper bound. This leads to counting rational points over finite fields, a problem closely linked to the Weil conjectures. Finally, we present an architecture that exhibits a striking difference in the neuromanifolds when considered over a characteristic zero versus a finite-characteristic field, illustrating the critical role of field characteristic in the notion of expressivity.

Humanoid robots have become increasingly popular in applications such as social interaction, education, and service roles, which drives the need for more natural and efficient human-robot interactions. However, currently available humanoid heads often face limitations, including high costs, mechanical complexity, and limited adaptability across diverse environments. To address these challenges, we present an articulated humanoid robot head designed for a receptionist role, integrating a mechanical structure with 21 degrees of freedom (DoF), including mechanisms for the mouth, eyes, eyebrows, and neck, and covered with realistic silicone skin to achieve a human-like appearance and expression. The system integrates a model-based architecture that combines SCRFD, ArcFace, and ByTetrack for face recognition and Llama and Whisper for natural language processing, with hardware support enabling real-time operations and human re-identification. The conversational ability and re-identification capabilities of the humanoid robot head were quantitatively measured, while its emotional expressiveness and human likeness were evaluated through a user study, achieving an average human likeness score of 4.13 out of 5.

Variational Quantum Algorithms (VQAs) are a leading paradigm for near-term quantum computing, yet their training suffers from sensitivity to circuit depth, initialization, and landscape pathologies such as barren plateaus. We study \emph{progressive depth training} (PDT) -- a layerwise curriculum that trains a shallow circuit before appending new layers -- and identify a fundamental obstacle: fixed entangling gates (CNOTs) in hardware-efficient ansätze cause \emph{initialization shock}, an energy spike when new layers are added. We propose \emph{identity-paired progressive depth training} (IP-PDT), which appends forward/inverse block pairs -- each consisting of a standard rotation$+$CNOT block followed by its reverse -- that compose to the identity at initialization. Because the adjacent CNOT rings cancel, the effective circuit retains only \textit{a single entangling layer} surrounded by \textit{overparameterized local rotations}. We prove a simple \textit{Reachable Set Saturation Theorem}: under this construction the variational manifold expands exactly once (when post-entangler rotations are first introduced) and then \emph{saturates}; all subsequent depth increases provide pure overparameterization of single-qubit unitaries. Despite this saturation, progressive addition of rotation parameters can continue to improve optimization outcomes -- a phenomenon we term \emph{trainability beyond expressibility}. We formalize IP-PDT as a continuation method on nested manifolds, prove monotone energy guarantees under an acceptance rule, and connect energy error to ground-state fidelity through spectral-gap inequalities. A detailed resource analysis shows that IP-PDT achieves lower total gate cost than both baselines by eliminating most CNOT gates.

Current voice AI benchmarks typically evaluate isolated capabilities such as speech intelligibility, word error rate, or text-based dialogue quality, but they rarely test whether systems harness the acoustic information that distinguishes spoken language from its textual representation. To this end, we introduce the Real World Voice EQ Bench, a multidimensional benchmark for evaluating voice AI across text-to-speech (TTS), speech-to-speech (STS), speech understanding (SU), and automatic speech recognition (ASR). Our evaluations indicate that performance is highly dimension-specific. For TTS, naturalness, expressiveness, identity stability, and reliability are largely independent evaluation dimensions. For STS, access to audio does not guarantee use of vocal affect, and some agents remain largely transcript-driven. For SU, models perform unevenly across paralinguistic tasks. For ASR, real world accent, emotion, noise, and conversational conditions expose failures that are not captured by established clean-speech benchmarks. Together, these results show that voice AI should be evaluated as a profile of acoustic, expressive, interactional, and robustness capabilities rather than by a single aggregate score.

A theoretical understanding of Transformers is crucial to better understand the capacities and limitations of large language models (LLMs). There is much work analyzing the expressivity of attention-based models. By proposing handcrafted weights or using computational complexity arguments, a large amount of past theoretical works have sought to characterize which tasks are and which are not in the hypothesis class of Transformer models. However, little work investigates the learnability of such solutions. In this work, we make progress towards this goal. Inspired by recent loss landscape analysis work, we propose preliminary sample complexity bounds for learning C-RASP constructions with Transformers.

Diffusion-based policies have recently emerged as powerful policy parameterizations for reinforcement learning, representing state-conditioned action distributions as terminal laws of diffusion processes with parameterized drifts. This terminal-law representation has shown substantial expressive flexibility in practice, enabling diffusion policies to model complex, multimodal, and highly non-Gaussian action distributions; however, it remains unclear what mathematically drives this expressivity and how to fully exploit it when the policy is learned from finite data. In this paper, we identify the drift Lipschitz budget $K$ as a central quantity governing the expressivity and statistical behavior of diffusion policies. We quantify expressivity through approximation: diffusion policies with $K$-Lipschitz drifts can concentrate near optimal deterministic policies and achieve value approximation error of order $1/K$; moreover, we prove a matching lower bound under nondegenerate diffusion noise. This increased expressivity comes with a statistical cost. When the drift is parameterized by neural networks, increasing $K$ improves approximation but increases statistical complexity. Balancing these two terms yields a finite-sample performance gap of order $\tilde{O}(n^{-2/(m+6)})$ for generic neural-network drifts, and a sharper rate $\tilde{O}(n^{-2/(m+4)})$ for one-sided dissipative drift classes, where $n$ is the sample size and $m$ is the dimension of the state space. Numerical experiments provide empirical evidence for the sample-dependent trade-off in $K$, supporting both theoretical regimes. Our framework also suggests a practical implementation principle: choose the diffusion budget $K$ according to the available sample size, and then select a neural-network architecture with the corresponding fixed Lipschitz coefficient.

Motion and emotion are core parts of intelligent, expressive behavior. In this paper, we introduce fog, a function composition framework for implementing and compose motion functions. We demonstrate how fog can be used to express motion and emotion in Heider-Simmel style animations. This code generation framework can help users generate functions for verbs, adverbs, gestures, and emotions to create an open-ended motion vocabulary. It is complemented by an animation editor that helps users refine motion through direct manipulation and dynamically generated UI. We evaluate our approach with a perceptual evaluation, where we test 452 fog-generated animations to see if people can recognize the semantic meaning of the motion. We find that fog's motion functions can be recognized at 68% accuracy, a 2.68x improvement over a chance baseline. In a mixed-methods user study with professionals and novices, we show that fog in interface form can support users with more rapid iteration, exploration, and control.

Modern sequence models are increasingly deployed as agents that interleave token generation with calls to external tools. We give an exact, architecture-level account of when such tool access increases computational expressivity. We model any fixed finite-precision recurrent sequence model, including finite-precision state-space models (SSMs) with $B$ bits of internal state, as a deterministic finite-state controller interacting with an oracle through a finite command/observation interface. Our results form a sharp dichotomy. First, tools that are themselves finite-state add essentially nothing: a product-state simulation internalizes any finite-state bounded-interface oracle with finite memory set $M$ at a cost of only $\log_2 |M| + O(1)$ additional bits, so the augmented system remains finite-state. Second, a single minimal infinite-state tool, namely a tape supporting only local $\mathtt{read}$, $\mathtt{write}$, and $\mathtt{move}$ commands, makes the system Turing complete: for every single-tape Turing machine with state set $Q$ and tape alphabet $Γ$, a controller with $O(\log |Q| + \log |Γ|)$ bits of internal memory simulates it, and we exhibit a concrete exponential separation: $\mathrm{EQ}_n$ requires $2^n$ states without tools but a single constant-size controller with the tape tool. Third, we show that this construction is realized exactly by a natural one-layer finite-precision selective affine SSM controller with binary one-hot hidden states, $\{0,1\}$ transition matrices, and zero biases. Selectivity is essential to the construction. In the supplementary material, we make all constants explicit, prove a logarithmic oracle-assisted universal simulation, where $O(\log B)$ recurrent bits suffice to simulate any $B$-state Turing machine, and prove a matching impossibility result.

Expressive parameterized quantum circuits (PQCs) are often designed under a dilemma: the growth of expressibility and entangling power (EP) that improves Hilbert-space coverage is also expected to randomize an ansatz and activate barren-plateau (BP) conditions. We show that this dilemma is not a one-dimensional tradeoff. The usual picture collapses three inequivalent objects -- parameter-ensemble coverage, fixed-circuit entangling response, and local gradient moments -- into one scalar narrative. For a fixed circuit probed by Haar-product inputs, EP is a global two-copy mean of the output-entanglement distribution, whereas entangling-power deviation (EPD) is a global four-copy fluctuation descriptor. Gradient variance, however, is a local two-copy contraction selected by a parameter light cone and a cost observable. This moment hierarchy yields an analytic separation: equal EP need not imply equal trainability, as witnessed by equal-EP circuits with different EPDs and different gradient variances. These separations turn EP and EPD into a two-dial design rule for PQC ansatzes: EP measures how far the circuit has moved along the coverage dial, while EPD monitors whether input-dependent variability remains. We find that ansatz routes can reach high, Haar-like coverage before EPD and gradient variance collapse, showing that coverage and BP activation are distinct crossover events. The EP/EPD framework thus breaks the apparent one-dimensional expressibility-trainability tradeoff into a practical design rule: search for highly expressive PQCs in the window where coverage is high but BP-like homogenization has not yet erased trainable structure.

We investigate Gaussian process (GP) bandit optimization with quantum kernels, assuming the mean reward function lies in the reproducing kernel Hilbert space (RKHS) induced by the quantum kernel. This setting is motivated by NISQ-era tasks such as quantum control, state preparation and variational quantum algorithms. While quantum kernels can offer a `quantum advantage' via domain-specific inductive biases, naïvely using full, high-dimensional kernels increases model complexity and information gain, leading to higher cumulative regret and poor learnability. To address this, we propose projected quantum kernels and classical kernel approximation techniques that reduce feature dimensionality while preserving key quantum properties. Using these approximate kernels, we develop misspecified GP bandit algorithms and derive regret bounds that characterize the trade-off between approximation error and information gain. The regret bounds provide principled guidance for selecting the optimal model complexity. Empirically, our methods outperform full quantum kernels in sample efficiency, while substantially reducing computational overhead, enabling scalable GP optimization for quantum-native applications.

Spatiotemporal point processes (STPPs) model event data in continuous time and space, with applications in mobility, epidemiology, and public safety. Recent neural STPPs span expressive intensity models, conditional density models, continuous-time latent dynamics, normalizing-flow spatial decoders, and score-based generative mechanisms. Yet comparison remains fragile because implementations differ in preprocessing, coordinate normalization, splits, likelihood conventions, and evaluation protocols. We present SEAHORSE, a unified framework for reproducible STPP experimentation. SEAHORSE formalizes neural STPPs through a common encode-evolve-decode interface and trains, tunes, and evaluates every model family under a single executable benchmark protocol with raw-coordinate likelihood reporting. This enables fair comparisons but, more importantly, controlled diagnostic studies. We pair SEAHORSE with HawkesNest, a synthetic stress-test suite, and show that increasing event-pattern complexity exposes each family's inductive bias, degrading some models sharply and leaving others stable. Code: https://github.com/YahyaAalaila/seahorse.

The stable coloring of the Weisfeiler-Leman (1-WL) test is a cornerstone of Graph Neural Networks because it provides an upper bound to the expressive power of message-passing architectures. Unfortunately, computing it presents two fundamental bottlenecks. First, classic algorithms are inherently sequential and cannot exploit modern massively parallel hardware. Second, these are \emph{global} algorithms, i.e., they require availability in memory of the full graph, severely limiting applicability to real-world instances. We leverage a linear-algebraic interpretation of 1-WL stable coloring and introduce two key contributions: (i)~a randomized refinement algorithm with tight probabilistic guarantees and (ii)~a correctness-preserving batching scheme that decomposes the graph into independently processable subgraphs while provably returning a stable coloring of the original graph. This approach maps directly to GPU-efficient primitives. In numerical experiments, our CUDA implementation delivers speedups up to two orders of magnitude over classical CPU-based partition refinement and, for the first time, successfully computes stable colorings on web-scale graphs with over 30 billion edges, where CPU baselines time out or fail.

As Quantum Machine Learning (QML) transitions toward practical implementation, the field faces a critical architectural bottleneck that challenges the fundamental assumptions of classical statistical learning theory. In classical deep learning, increasing model capacity typically risks overfitting. However, this study advances a counter-intuitive paradigm: unstructured contemporary QML architectures suffer from a profound state of quantum underfitting, driven by the "expressivity-trainability paradox." We demonstrate that the vast Hilbert space capacity of Parameterized Quantum Circuits (PQCs)-traditionally chased as the source of quantum advantage is the direct mathematical cause of Barren Plateaus (BPs), where gradient landscapes become exponentially flat. By synthesizing recent breakthroughs in Dynamical Lie Algebras (DLAs) and Geometric QML, we establish a comprehensive framework linking the algebraic dimension of circuit generators to their optimization dynamics. Furthermore, we empirically validate this framework on a non-linear binary classification task, illuminating a uniquely quantum manifestation of the bias-variance tradeoff: while unstructured architectures achieve near-perfect training accuracy via unscalable parameterization (quantum overfitting), embedding group-theoretic geometric priors acts as a structural regularizer. By restricting the DLA growth to a polynomial regime, our symmetry-preserving approach sacrifices raw memorization capacity to guarantee scalable, gradient-rich training landscapes, offering a robust roadmap for "Trainability-by-Design" in scalable quantum neural networks.

Emotional body motion expressions are an essential element of non-verbal communication. Effectively conveying these expressions through technology is of utmost importance, for example, with virtual reality avatars and in social robotics. Recent advances in generative models have opened new opportunities for advancing research on emotional body motion learning. However, generating accurate emotional expression representations is challenging, given the subtlety of emotional cues, individual variability, and cultural differences. We investigate whether a generative model can implicitly learn emotional body motions directly from culturally grounded motion-capture data, without explicit emotion-motion guidance. Using a dataset of emotional performances by 49 Japanese actors, we trained a Transformer-based generative model to generate expressive motions conditioned on 13 discrete emotion labels. We evaluate the generated motions from two perspectives: (1) an LSTM-based classifier to assess recognizability by machine observers, achieving a recognition accuracy of 22.80%, and (2) a human perception study with Japanese raters to assess alignment with human affective interpretations, yielding a recognition accuracy of 24.91%. Beyond these, we evaluate the utility of generative modeling for three practical tasks: augmenting emotion recognition models, extracting representative emotion-specific motion patterns, and synthesizing smooth transitions between emotion intensities. Our findings highlight the potential of implicit, data-driven generative modeling to enhance affective computing applications and our understanding of emotion expressions.

High-fidelity and expressive controllable human animation is essential for content creation and digital avatar applications. However, existing methods face a dilemma between expressiveness and disentanglement. Mainstream 2D pose-conditioned approaches suffer from "motion-shape entanglement", leading to the leakage of the driving subject's body shape. Conversely, methods relying on 3D priors (e.g., SMPL) achieve geometric disentanglement but struggle to capture facial expressions and complex gestures, resulting in rigid animations. To this end, we propose EMOSH, a novel framework for high-fidelity controllable human video generation. First, an Expressive Human Model (EHM) is introduced as the core control representation. By explicitly disentangling shape and pose parameters, we fundamentally resolve the body shape leakage issue. Alongside this, a robust motion tracker is designed to accurately estimate EHM parameters from video. Second, we propose a Coarse-to-Fine Hybrid Motion Injection strategy, enabling more fine-grained control over expressions and gestures. Furthermore, we introduce a Spatially-Aligned Conditioning mechanism to bridge the domain gap between training and inference, improving identity consistency. Extensive experiments demonstrate that EMOSH outperforms previous methods in both self-driven and cross-driven scenarios, producing high-fidelity videos with vivid expressions while maintaining shape disentanglement.

Prosodic emphasis varies across languages, emotions, and speaking styles, yet existing emphasis detection models are largely trained and evaluated on monolingual neutral read speech. We introduce MMEE (Multilingual Multi-Emotion Emphasis), a corpus of 10,000 professionally recorded expressive utterances (14.13 hours) across 7 languages and 34 emotion/style categories, with three-level perceptual labels (10 annotations per sample). We benchmark two state-of-the-art architectures under monolingual, cross-lingual, multilingual, cross-emotion, cross-dataset, and data-scale settings. Monolingual models show limited zero-shot transfer, degrading across typologically distant languages, while multilingual training substantially improves robustness. Models transfer robustly between high- and low-arousal emotions; bidirectional transfer between synthetic and perceptual benchmarks suggests shared prosodic structure; and performance stays robust even at smaller training scales.

Billions of scientific papers lead to the need to identify essential parts from the massive text. Scientific research is an activity from putting forward problems to using methods. To learn the main idea from scientific papers, we focus on extracting problem and method sentences. Annotating sentences within scientific papers is labor-intensive, resulting in small-scale datasets that limit the amount of information models can learn. This limited information leads models to rely heavily on specific forms, which in turn reduces their generalization capabilities. This paper addresses the problems caused by small-scale datasets from three perspectives: increasing dataset scale, reducing dependence on specific forms, and enriching the information within sentences. To implement the first two ideas, we introduce the concept of formulaic expression (FE) desensitization and propose FE desensitization-based data augmenters to generate synthetic data and reduce models' reliance on FEs. For the third idea, we propose a context-enhanced transformer that utilizes context to measure the importance of words in target sentences and to reduce noise in the context. Furthermore, this paper conducts experiments using large language model (LLM) based in-context learning (ICL) methods. Quantitative and qualitative experiments demonstrate that our proposed models achieve a higher macro F1 score compared to the baseline models on two scientific paper datasets, with improvements of 3.71% and 2.67%, respectively. The LLM based ICL methods are found to be not suitable for the task of problem and method extraction.

Speech-to-speech translation (S2ST) should preserve not only lexical meaning, but also expressive attributes: emotion, scenario style (e.g., news reporting vs. dramatic dialogue), and nonverbal vocalizations (NVs). Moreover, collecting cross-lingual target speech that is both translation-faithful and expressively aligned with the source is difficult at scale, making reference-based evaluation impractical. We introduce STEB (Speech-to-Speech Translation Expressiveness Benchmark), a 32.6-hour Chinese--English benchmark that evaluates both standard dimensions (translation fidelity, speaker similarity, duration alignment) and expressiveness dimensions (emotion, scenario style, NV preservation). For expressiveness evaluation, STEB uses a caption-then-summarize framework that converts speech into structured expressive attributes and compares source and hypothesis attributes with an LLM judge. Human validation shows statistically significant correlations with listener judgments across all expressive dimensions. We evaluate six S2ST systems covering cascaded systems, end-to-end models, and speech large language models. Many systems, especially cascaded ones, achieve strong translation fidelity, but they still struggle with emotion preservation (best: 3.82/5) and NV preservation (best: 2.31/5). These results reveal a gap between semantic transfer and expressive transfer, identifying expressiveness preservation as an open challenge for S2ST. Audio samples are available at https://cmots.github.io/steb.github.io/.

Objectives: To develop a codebook for self-stigma across cognitive, affective, and behavioral domains, and to estimate the prevalence, co-occurrence, and temporal patterns of these indicators in Reddit posts by people who use drugs. Methods: We developed a ten-indicator codebook through consensus-based abductive coding spanning cognitive (self-labeling, pessimism/self-defeatism, deservingness/worthlessness), affective (shame, guilt/self-blame, despair/hopelessness), and behavioral (concealment, anticipated rejection, desire to quit, ambivalence) domains; two coders reached substantial agreement (Cohen's k = 0.72). We then scaled classification with a large language model validated against expert coding (k = 0.73, F1 = 0.80), analyzing 72,115 thread-initiating posts from 1,660 English-language users (2006-2025). Results: 3,838 posts (5.3%) from 1,228 users (74.0%) contained self-stigma; all ten indicators discriminated self-stigma posts (RR 3.6 to 86.2), led by self-labeling (56.0%) and despair/hopelessness (48.5%). Self-stigma was integrated: core and behavioral indicators were strongly associated at the user level (OR = 4.65, 95% CI 3.12-6.94, p < 0.001), and 87.0% of posts with behavioral indicators also contained a core indicator. Contrary to progressive models, behavioral indicators emerged earlier than core ones (desire to quit at median position 0.08 vs. shame at 0.38). Nine of ten indicators were stable across posting trajectories; only pessimism increased (OR = 1.62, 95% CI 1.25-2.10). Conclusion: Among people who use drugs online, self-stigma is an integrated phenomenon in which behavioral indicators rarely appear without internalized ones and often precede them. Most expressions remain stable over time, but pessimism about change deepens, marking a target for early digital intervention and showing that progressive stage models do not map directly onto textual disclosure.

This paper studies the expressive power of ASPIC$^+$ argumentation frameworks with uncertain preference profiles by comparing them with several abstract formalisms with uncertain defeats. Most of our results are negative (and some of them are theoretically unexpected). We also conjecture a positive, non-trivial threshold for the expressivity of uncertain preferences, and prove some essential preliminary steps toward the confirmation of this conjecture.

In recent years, weight quantization that encodes the learnable parameters of large language models in an $n$-bit format has garnered significant attention due to its potential for model compression and inference acceleration. Many practical techniques have been developed; however, the theoretical understanding of many aspects, especially the approximation and degradation of expressive power as the number of quantization bits decreases, remains unclear. In this paper, we provide a theoretical investigation into the expressive capability of large language models relative to the number of quantization bits. We argue that 1.58-bit is the limiting precision for weight quantization by establishing the universal approximation and expressive collapse properties of weight-quantized models with respect to the number of quantization bits. Additionally, we confirm that weight quantization leads to expressive degradation, in which the expressive capacity of weight-quantized models degrades polynomially as the number of quantization bits decreases. These theoretical findings provide a solid foundation for advancing weight quantization in the context of scaling laws and shed insights for future research in model compression and inference acceleration.

Piecewise-affine neural networks (e.g., with ReLU or LeakyReLU activations) implement continuous piecewise-affine maps, and the number of affine regions provides a natural proxy for expressive capacity. However, the gap between theoretical region capacity and the affine regions realized after training remains insufficiently understood. We study this gap from two complementary perspectives. First, we give a rigorous, architecture-dependent theorem for affine line-segment probes: for multilayer perceptrons with piecewise-affine activations, the number of affine pieces realized along an affine line-segment probe is upper bounded by an explicit product of layer-wise width terms (and activation breakpoint factors). This yields a neuron-threshold lower bound for representing target functions with prescribed one-dimensional piece complexity, formalizing the minimal region budget required for complex signals. Second, we exactly enumerate affine regions realized within bounded 2D and higher-dimensional domains under controlled task complexity. Under fixed architectures and training protocols, increasing input--label complexity yields trained solutions with markedly fewer realized regions in the evaluation domain, even though worst-case architectural capacity is unchanged; we call this reduced region usage expressivity saturation. Moreover, in the most challenging regimes, 2D visualizations show that region-usage collapse often coincides with degraded decision boundaries. Finally, we visualize the training dynamics of affine-region partitions and decision boundaries, revealing a consistent refinement process during optimization.

Verification of multi-agent systems requires the ability to check meticulous topological properties when it comes to agents that can move through space in continuous time. This demands a logic with sufficient expressiveness to capture these dynamics. MuTGL logic has interesting properties for expressing entangled space-time properties. However, this logic lacks the expressivity needed to analyse reachability within specific distance bounds, or to track the length or the cost of communication chains: these are fundamental for decentralized monitoring, or graph-theoretic analysis of distributed protocols, where algorithmic complexities often relates with the system's communication graph diameter. We then introduce an extension of muTGL, including a new operator called the space horizon. This addition allows us to bound the distance of communication chains, hence enhancing the logic's expressiveness. We show that this operator allows to encode modalities from other logics, such as reachability or escaping which were not available in vanilla muTGL, while allowing a deeper entanglement of spatial and temporal properties. We provide a centralized offline monitoring algorithm for this logic and illustrate it on several examples on simulations of Consensus-Based Bundle Algorithms, distributed protocols for task allocation.

Precise 3D spatial orchestration in text-to-video generation remains a significant challenge, particularly for multi-object scenes where semantic layout and temporal dynamics are often entangled. While existing depth-conditioned models achieve good structural fidelity, they necessitate dense, frame-accurate guidance that is labor-intensive to author for dynamic events involving deformable objects. We present LooseControlVideo, a framework that enables intuitive and expressive control by using sparse, oriented 3D boxes as a "blocking" proxy. This allows users to author high-level layout and trajectory while leveraging a video generative model to generate realistic occlusions, dynamics and interactions. We achieve this by fine-tuning a Wan 2.2 backbone on a video dataset annotated with DNOCS, a novel encoding for 3D size, orientation and depth-ordered occlusions. Furthermore, our method allows for localized refinement, such as adjusting a jump trajectory or adding an interaction, with minimal disruption to the global scene context. Extensive evaluations on the nuScenes, HO-3D, and BEHAVE benchmarks demonstrate that LooseControlVideo significantly outperforms existing 2D-box and flow-based baselines. Our findings indicate a 1.2x to 3x improvement in Trajectory Error; 2x improvement in Rigid Motion Consistency; and a 1.5x to 2x increase in Occlusion Accuracy over current state-of-the-art layout-conditioned models, demonstrating that oriented 3D primitives provide good geometric prior for complex, multi-agent video authoring.

Bridges between graph neural networks (GNNs) and logical formalisms have been established by fixing architectural choices, such as the types of aggregation, combination, and activation functions. These choices define restricted classes of GNNs for which tight correspondences with logical formalisms can be obtained, by showing that logical formulae can be translated into equivalent GNNs and, conversely, that GNNs can be translated into equivalent formulae. In this paper we take a semantic perspective by establishing the logical expressiveness of classes of GNN classifiers that are preserved under structural properties: embeddings (extensions), injective homomorphisms, and homomorphisms. We show that, for each such property, there exists a fragment of graded modal logic characterising the class of GNNs. In particular, preservation under embeddings, injective homomorphisms, and homomorphisms corresponds to existential graded modal logic, its existential-positive fragment, and existential-positive modal logic, respectively. These results characterise the expressiveness of broad classes of GNNs independently of specific architectural choices, but we also show that each of these classes admits a GNN architecture of the same expressiveness. Technically, our approach uses a new well-quasi-order result for trees of bounded height, yielding finite representations of unravelling-invariant classes.

Deep neural networks are widely believed to derive their expressive power from their ability to form \textbf{hierarchical representations}, capturing progressively more abstract and compositional features across layers. In language modeling, \textbf{transformers} have emerged as the dominant architecture, with early layers capturing local syntactic patterns and later layers encoding more complex clause-level dependencies. While this intuition has shaped model design, there remains a lack of rigorous theoretical work demonstrating \textbf{how} deep transformers represent such hierarchical structures. In this work, we analyze the expressiveness of deep transformer models through the formal lens of bounded-depth, non-recursive context-free grammars. For this class of grammars, we explicitly construct transformers with positional attention whose depth grows linearly with grammar depth, while the neuron count scales with the number of derivation-tree shapes and quadratically with the number of production rules. Our theoretical results support the linear representation hypothesis by demonstrating that these architectures possess the structural capacity to encode abstract grammatical states into low-dimensional, linearly separable subspaces within the residual stream.

Positional encodings (PEs) enhance the power of graph neural networks (GNNs), both theoretically and empirically. Two of the most popular families of PEs - spectral (e.g., Laplacian eigenspaces, effective resistance) and walk-based (polynomials of the adjacency matrix) - are theoretically equivalent in expressive power, with expressivity between the 1-WL and 3-WL tests. However, this equivalence assumes the GNN uses the "complete" version of these PEs, which requires $O(n^3)$ time and space complexity. Instead, practitioners commonly use truncated variants of these encodings, such as the first $k$ eigenspaces or powers of the adjacency matrix. However, the theoretical properties of these truncated PEs are unknown. In this work, we initiate the study of these truncated PEs. Theoretically, we show that, under truncation, several families of PEs are fundamentally different in expressive power. As a corollary, we show that truncated spectral PEs are no longer stronger than the 1-WL test. We also study a family of spectral PEs, the $k$-harmonic distances, to highlight the differences in expressive power of even closely related truncated PEs. Finally, we experimentally show that a mix of truncated PEs is preferable to any single family on real-world datasets.

Text-to-image diffusion models have achieved impressive results in synthesizing high-quality images from natural language prompts. However, commonly used prompting strategies remain relatively generic, limiting the model's ability to accurately express emotional intent and nuanced affective attributes. This work proposes EPIG, a method that enhances emotional expressiveness at the prompt level prior to image generation. Grounded in psychologically informed emotion representations (valence-arousal) and leveraging structured, role-aware prompt enrichment, EPIG enriches emotion-related components of prompts without modifying or retraining the image generation backbone. The resulting emotion-aware prompts guide the generative process toward more emotionally coherent visual outputs, with particular effectiveness in controlling arousal. EPIG is lightweight, training-free, and well suited for resource-constrained and personalized image generation scenarios. Experimental results on a benchmark of 10 diverse prompts show that EPIG reduces mean arousal error compared to strong baselines, including naive insertion and LLM-based prompt expansion, with reductions of 14% and 12%, respectively. These improvements are statistically significant. EPIG also preserves valence alignment and semantic consistency, as measured by CLIPScore and supported by ablation studies. The effect is more pronounced on prompts containing explicit subjects such as humans, children, or animals, where the reduction reaches 17%, highlighting the subject-sensitive behavior of the proposed method.

Expressive performance rendering (EPR) aims to generate realistic performances constrained on sequences of notes. However, flow matching audio editing models manipulate only synchronized music samples of the same duration, limiting their understanding of expressive timing. We introduce PianoKontext, a flow matching rendering model for classical piano music that generates variable-length performances in the latent space of a pretrained Music2Latent model. We synthesize MIDI scores into deadpan audio and employ Dynamic Time Warping (DTW) in the latent space to construct paired data for training. The aligned embeddings are concatenated in DiT blocks, allowing for a simple and effective learning of the dependencies between the score and performances. Audio samples are available at our demo page: https://realfolkcode.github.io/pianokontext_demo/.

A central principle in quantum machine learning is that an ansatz should be expressive enough to represent the quantum data of interest. Yet, the expressibility is statistically meaningful only insofar as it can be learned from finitely many copies of an unknown quantum state. In this work, we develop an information-theoretic Occam theory for quantum data generated by finite-size quantum circuits. For the class $S_{n,G}$ of $n$-qubit pure states preparable with at most $G$ two-qubit gates, a metric-entropy argument gives the realizable sample law $\widetildeΘ(G/ε^2)$ in the circuit-limited regime. For an arbitrary source $\hatρ$, we introduce the best $G$-gate approximation error $d_G(\hatρ)$ and the approximate circuit complexity $C_η(\hatρ)$. We prove an agnostic quantum Occam theorem: with $M$ copies, one can learn up to the best $G$-gate approximation error plus a statistical penalty $\widetilde{O}(\sqrt{G/M})$. We then remove the need to know $G$ in advance through an adaptive model-selection theorem whose oracle inequality selects the circuit complexity justified by the data. Matching lower bounds yield a sample-supported expressibility law: at trace-distance accuracy $ε$, $M$ samples can support only $G_{\rm supported} \simeq Mε^2$ gates, up to logarithmic factors and tomography saturation at $2^n$. Thus, the circuit complexity becomes an adaptive statistical resource rather than a static promise. Our framework turns bounded circuit complexity into a model-selection principle for quantum machine learning.

We introduce a new tool, Express, for converting a non-causal attention approximation into a causal approximation with matching approximation guarantees. When combined with the state-of-the-art Thinformer approximation, Express improves upon the best known causal attention guarantees, delivering $\log^{3/2}(n)/s$ approximation error with only $O(s)$ memory and $O(s^2 \log^2(n))$ compression overhead for a sequence of length $n$. We pair these developments with an efficient I/O-aware Triton implementation, demonstrate substantial speedups over FlashAttention 2, and use Express to overcome four resource bottlenecks in the language modeling pipeline: long-context prefill, KV cache compression, long-form memory-constrained decoding, and long-form compute-constrained decoding.

Safety judges are increasingly deployed to evaluate model outputs against evolving criteria, yet recent meta-evaluation work shows they remain brittle under prompt and rubric variation, with false negative-rate swings of up to 0.24 reported for stylistic perturbations alone. We argue that safety judgment is fundamentally a rubric-following problem: a robust judge must apply the given evaluation criteria consistently across rubric formulations rather than memorize one specific template. We propose a training strategy that combines (i) instance-conditioned dynamic rubrics generated from prompt-response-label triples to expose the judge to the variability of evaluation criteria, and (ii) a reliable-to-expressive curriculum that begins with clean fixed-rubric supervision and progressively introduces noisier dynamic-rubric data. We evaluate on a single human-labeled set under three contrasting rubric prompts (HarmBench-style, ShieldGemma-style, and a domain-specific rubric). Our 12B curriculum judge achieves 94.12-94.88% accuracy across the three rubrics with a cross-rubric range of only 0.76, outperforming general-purpose LLMs, dedicated safety classifiers, and reasoning-oriented judges up to 30B in both peak accuracy and stability. An ablation shows that naively mixing dynamic rubrics into SFT increases cross rubric variance (1.44 -> 3.60); only the curriculum schedule recovers and improves on the fixed rubric baseline (variance 0.76).

Physical reservoir computing harnesses nonlinear mechanical dynamics but, by convention, freezes the substrate and trains only a linear readout, presuming the substrate is not usefully trainable. We revisit that premise for networks of nonlinear oscillators whose mass, damping, and stiffness are learned end-to-end through a symplectic integrator. Our central result is a trilemma: memory horizon, gradient stability, and dynamical expressivity cannot be simultaneously maximized, because all three are governed by the damping. The backward gradient decays at a rate set by the damping, capping how far back credit can propagate, while forward sensitivities grow exponentially in the largest Lyapunov exponent, so usable gradients require damping above a stability floor. Since the Lyapunov exponent falls as damping rises while the memory ceiling falls as the horizon grows, stable training is confined to a band that contracts with horizon and closes at a critical point. We test every step on a twenty-oscillator network. A damping sweep finds the largest Lyapunov exponent monotone and crossing zero at a well-defined stability floor, confirming the theorem's key assumption. A compute-matched comparison of learned versus frozen substrate on delayed recall across nine horizons shows the learned substrate dominating at short horizons and the advantage closing and reversing near a horizon of eleven steps, the predicted signature of band closure; trained models settle near the stability floor, seeking the edge of chaos unprompted. The analytic ceiling overestimates the empirical crossover roughly fivefold, a gap between detectable and learnable gradient that we report rather than tune away. The contribution is a confirmed account of when training a physical substrate beats freezing it.

Quantum combinatorial optimization offers theoretical advantages for complex financial modeling, but physical implementation on Noisy Intermediate Scale Quantum (NISQ) devices is severely constrained by hardware topology. This study presents a hardware benchmarking analysis between a Hardware Efficient Variational Quantum Neural Network (HE-VQNN) and the Warm Start Quantum Approximate Optimization Algorithm (WS-QAOA) for a hybrid Mean Variance and Conditional Value at Risk (CVaR) portfolio objective. By implementing a novel classical quantum hybrid proxy matrix to bypass the CVaR auxiliary qubit bottleneck, we map up to 16 assets from the NIFTY 50 index onto an IBM heavy hex processor. We systematically quantify algorithmic resilience to the "SWAP tax" incurred during routing. Empirical results reveal a critical operational trade-off: WS-QAOA provides exact theoretical mapping but suffers catastrophic hardware decoherence due to exponential nonlocal gate overhead. Conversely, HE-VQNN preserves hardware coherence but lacks the mathematical expressibility to capture dense tail risk asset correlations. This study exposes the limitations of dense financial optimization on current architectures forces an nonviable choice between algorithmic inexpressibility and hardware decoherence. This is indicative of a deeper limitation as to what can and cannot be done with NISQ computers lacking in all-to-all connectivity.