Papers

We study the vacuum structure of maximally supersymmetric Yang–Mills theory in two dimensions. At low energies, the theory decomposes into superselection sectors consisting of orbifold conformal field theories and massive vacua. The sectors are indexed by the cuspidal data appearing in Lusztig's generalized Springer correspondence. This suggests an enhancement of the correspondence to holomorphic factorization algebras.

This work studies how refraction-induced bias on acoustic ranging affects multi-agent collaborative localization in a range of oceanographic conditions and spatial scales. While multi-agent range-aided navigation, which uses range measurements to either fixed infrastructure or other agents, is a promising solution to the challenges of large-scale underwater localization, its accuracy depends strongly on the quality of range measurements. Sound speed variability induces refraction (bending) of acoustic rays, yet, for algorithmic tractability, standard sensor fusion pipelines assume straight-line propagation. This refraction systematically biases range measurements to be longer than the straight-line assumption predicts. However, the effects of this bias on multi-agent collaborative localization on kilometer scales remains unexplored. We present a series of simulated experiments with several agents operating over kilometer scales. The simulation uses HYCOM reanalysis data to recreate realistic oceanographic conditions, ray tracing to generate refraction-informed ranges, and a centralized multi-agent factor graph estimator to quantify the resulting measurement bias on estimated trajectories. Preliminary results indicate that refraction-induced bias can induce significant degradation of estimated trajectories, particularly in regions with sharp sound-speed gradients. We also share the simulation environment to support further studies https://github.com/UMich-RobotExploration/manta-ray.

K-12 robotics and AI education remains difficult to scale, especially in rural regions lacking sustained technical mentorship. Programs like FIRST provide competition pathways and instructional opportunities, but they do not eliminate the need for local programming and robotics expertise. We introduce AI, Robotics, & Community (ARC), a hubs-based framework where colleges train undergraduate mentors and host workshops for nearby K-12 teams. Mature school programs can become secondary hubs that support additional schools, creating a self-reinforcing education loop where mentorship reach propagates geographically and can even grow super-linearly. We first evaluate ARC through a trial deployment at one university. The trial created three rural robotics teams. On five-point Likert surveys, mean increases in K-12 programming knowledge, resource access, and practice opportunities were 2.00, 2.25, and 1.25 points. Likewise, undergraduate confidence teaching technical concepts, adapting explanations, managing groups, and finding mentoring enjoyable and meaningful increased by 1.29, 1.14, 1.00, and 1.14 points. Additionally, we create a spatial Markov model of ARC's growth and simulate it using the state of Indiana as a testbed. Under moderate conditions, we find that ARC reaches 74% of Indiana's 1,925 public K-12 schools and produces 992 robotics programs after 40 years, compared with 161 projected under natural growth alone. Together, these results show ARC can create and support rural robotics programs, train undergraduate AI and robotics mentors, and potentially scale mentorship across a region.

Let $S=k[x_1,\ldots,x_n]$ and let $I=I_\Delta\subsetneq S$ be a nonzero squarefree monomial ideal. Motivated by the classical higher-order Kähler differential modules and by the theory of higher conormal modules, we study not only the higher conormal quotients $I/I^q$, but more generally the shifted quotients $I^r/I^q$, $1\le r<q$, in the same $I$-adic conormal filtration, together with their symbolic analogues $I^{(r)}/I^{(q)}$. We prove that, for every $1\le r<q$ with $q\ge3$, the module $I^r/I^q$ is Cohen–Macaulay if and only if $I$ is a complete intersection. In sharp contrast, $I^{(r)}/I^{(q)}$ is Cohen–Macaulay if and only if $\Delta$ is a matroid, where loops are allowed. Thus, the Cohen–Macaulayness of a single nonexceptional window forces the Cohen–Macaulayness of every window in the corresponding filtration. The unique exceptional pair is $(r,q)=(1,2)$: at this conormal level, we show that the Cohen–Macaulayness of $I/I^2$ forces $I^2=I^{(2)}$, and hence $I/I^{(2)}$ is Cohen–Macaulay.

Vine robots navigate cluttered environments by extending from their tip. Although their ability to operate in such environments has been extensively demonstrated, little work has addressed growth planning, i.e., finding optimal growth paths. Moreover, existing planners do not account for the growth pressure necessary to follow a given path, which can cause the robot to burst when it is too high. In this paper, we address the problem of finding minimum-pressure paths for vine robots growing around polytopic obstacles. We propose an efficient algorithm that is guaranteed to find globally optimal solutions in 2D and approximate solutions in 3D, with an error that vanishes as a discretization parameter approaches zero. First, we derive a growth pressure equation for vine robots of arbitrary shape, which we use to show that there always exists a minimum-pressure path that is piecewise-linear and can bend only at specific points on the obstacles. We then leverage this observation to reduce the growth-planning problem to a shortest-path problem with time-dependent weights, which we efficiently solve using a modified Dijkstra's algorithm. We demonstrate the speed and scalability of our approach through numerical simulations. We also validate our algorithm with hardware experiments and provide an open-source and high-performance implementation in the Python package, VinePlanner: https://github.com/Ahsoka/VinePlanner.

Underwater semantic segmentation is essential for marine ecosystem monitoring, yet remains challenging due to severe visual degradation. Light absorption and scattering often lead to color shifts, low contrast, and blurred boundaries, making shallow detail features unreliable. Existing underwater segmentation methods improve RGB feature aggregation or boundary prediction, but still lack an explicit mechanism to distinguish structure-related details from degradation-induced responses. To address this limitation, we propose GeoCueFormer, a lightweight framework that combines geometry-constrained frequency enhancement with prediction-cued refinement. GeoCueFormer performs stage-specific wavelet enhancement on hierarchical encoder features to complement shallow boundary details while preserving deep structural semantics. A depth-derived spatial gate constrains shallow frequency enhancement toward geometry-consistent regions, and a prediction-cued dual-stage decoder further refines ambiguous high-resolution features. GeoCueFormer obtains 82.23% and 73.04% mIoU on SUIM and DUT, respectively. Under comparable model complexity and standard benchmark settings on SUIM and DUT, it achieves SOTA performance while maintaining a favorable accuracy-complexity trade-off. These results show that distinguishing structural details from degradation-induced interference is more effective for underwater segmentation.

Large language models (LLMs) are increasingly deployed in high-stakes domains such as housing screening. While alignment techniques mitigate explicit racial bias in generated text, they often leave covert attitudinal associations in internal probability distributions untouched. Adapting the matched-guise sociolinguistic paradigm, we examine covert dialect bias in housing-related social judgments across four varieties: Standard American English (SAE), African American Vernacular English (AAVE), Nigerian Standard English (NSE), and Nigerian Pidgin (NP). AAVE reflects the racialized dialect studied in prior covert-bias evaluations, whereas NSE and NP represent Black African, postcolonial varieties absent from this literature. Using 260 meaning-matched sentence quadruples and log-probability scoring over housing-relevant adjectives, we probe ten open-weight LLMs across three contexts varying in social proximity: tenant screening, neighbor acceptance, and roommate selection. Across all ten models, AAVE and NP are consistently associated with more negative adjectives than SAE, with NP penalized most severely. Crucially, each dialect is penalized via distinct stereotype clusters rather than a generic non-standard category. NSE, which carries institutional prestige, displays a context-dependent shift: favored over SAE in formal tenant screening but increasingly penalized as social proximity grows. Our findings reveal that LLMs inherit covert dialect bias along both racial identity and prestige dimensions, echoing documented human housing discrimination and demonstrating its reach across postcolonial English varieties.

We study when the logarithm $\psi$ of a positive finite exponential sum on $\mathbb{R}^d$ satisfies $\det\nabla^2\psi=C\exp(\langle b,\theta\rangle-\lambda\psi)$. This is the Kähler–Einstein equation for metrics induced by exponential maps into projective space and, for natural exponential families, the condition that the Jeffreys prior be a Diaconis–Ylvisaker conjugate prior. First, we classify the bivariate Laurent polynomials with unimodular support satisfying the generalized Einstein condition of Di Scala and Sombra: up to units and monomial changes of coordinates, they are powers of an affine trinomial or products of powers of two independent binomials. Second, we show in every dimension that a smooth compact toric manifold with a projectively induced Kähler–Einstein metric is a product of projective spaces with matched multiples of the Fubini–Study metrics, immersed by a complete Veronese–Segre system up to automorphisms. This proves the compact toric case of the homogeneity conjecture for such metrics and the fixed-point germ and univalent forms of a conjecture of Manno and Salis. Third, without lattice or rationality assumptions, the finite-support exponential families satisfying the equation are, up to affine changes of statistic, exactly the products of multinomial families with a common ratio of categories to trials; this settles the finite-support case of a question of Casalis.

Private large language model (LLM) fine-tuning is increasingly important for organizations that need to adapt models using sensitive data, but it often exceeds the memory capacity of commodity datacenter accelerators. Apple Silicon offers a different design point through large unified memory and lower complete-system cost, while recent Apple software support enables distributed execution over RDMA-over-Thunderbolt (TB). This paper studies whether Apple Silicon can serve as a practical platform for private LLM fine-tuning. We characterize RDMA-over-TB communication on Mac Studio nodes, showing that the measured bandwidth is far below nominal TB specifications. Next, we extend Apple's implementation with multi-trunk communication, persistent worker threads, and CPU-side gradient overlap to better exploit multiple direct TB links for LLM fine-tuning workloads. Finally, on a four-node Mac Studio cluster that fine-tunes a Qwen3-9B, our optimizations improve weak-scaling throughput by up to 1.6X over the single-trunk, non-overlapped baseline and reach 936 tokens/s for sequence length 17408. We further compare Apple Silicon with an NVIDIA H100 platform to quantify the trade-off between memory capacity, throughput, and acquisition cost, showing that Apple Silicon can provide a cost-effective solution for private LLM fine-tuning.

Interactive visual interfaces have become an important means of controlling generative image models, enabling users to manipulate generation through prompts, direct manipulation, and a range of interactions. However, existing techniques are typically presented as independent systems, making it difficult to understand how they relate, compare their interaction mechanisms, or identify opportunities for new interface designs. We introduce a design space for interactive visual interfaces for generative image models derived from 51 research systems and practitioner tools. The framework decomposes each system into three complementary components: the user interface (U), the controllable model objects (Z), and the mapping function ($\phi$) that translates user interaction into model operations. This decomposition provides a common representation for analyzing heterogeneous interaction techniques across model families, revealing recurring design patterns and underexplored regions of the design space. We further present an interactive corpus explorer that support comparative analysis, and discuss usage scenarios for both educational settings and HCI/AI practitioners identifying research and design opportunities.

A $\lambda$-translating soliton is a hypersurface in $\mathbb{R}^{n+1}$ satisfying $H=\langle \mathbf{T},\nu\rangle+\lambda$; equivalently, it has constant weighted mean curvature with respect to the log-linear density $e^{\langle T,X\rangle}$, and is an eternal solution of the mean curvature flow with a constant forcing term. In this paper, we first prove that every complete properly immersed $\lambda$-translating soliton with $\lambda>0$ and $\inf_{\Sigma}H>\lambda$ has at least exponential volume growth, in contrast with the linear growth of ordinary translating solitons. We then prove sharp non-existence results for graphic $\lambda$-translating solitons ($\lambda\geqslant 0$) with bounded gradient, and two rigidity theorems.

Mixture-of-experts (MoE) inference on consumer hardware is bounded by weight memory: a 35B-class model is 19.5GB at 4-bit, and sparsity shrinks the compute per token, not the bytes that must be held. Naive offloading to SSD does not help on its own, because layer N+1's experts must be chosen before layer N's output exists, so the reads cannot start early enough to hide behind compute. We present Edge0, a streaming MoE inference engine that closes the gap with a prerouter: a per-layer head predicts the next layer's routing one token ahead, and the prediction is consumed as the routing itself, so the staged expert set equals the routed set and nothing is dropped. An unmerged recovery LoRA, trained on the student path, pays back the quality lost to int4 quantization and routing replacement. On a single 24GB machine, Edge0 serves a 35B MoE at 20tok/s inside 3GiB of peak active memory, within a few points of its fp16 teacher on average across five public benchmarks. An 8B tier runs on the same framework, and the framework, checkpoints, and adapters are open source.

Music and dance are social practices of expression and connection, yet most HCI work in human-AI co-creation centers the solo performer. As generative music matures, we ask not only what AI can compose but what social encounters it can organize around sound. We present Encypher, a collaborative generative music system that translates collective movement qualities into text prompts conditioning real-time music generation for dance cyphers. Through five weeks of co-design with local dancers, a user study with unacquainted participants, a public museum event, and a live performance, we found that users developed shared agency, perceiving the music as a response to the room's energy. While newcomers felt uncertain, the system fostered social presence by prompting them to look to each other for cues. By treating sociality as a design concern rather than a downstream effect, we offer a framework and design implications for AI systems for collaborative, embodied expression.

We introduce a one-parameter family of notions between double ergodicity and metric ergodicity for measure-class preserving (i.e., nonsingular) actions of countable groups on standard probability spaces, providing infinitely many new invariants distinguishing weakly mixing actions. We call these properties (essentially) $k$-chaining, for $k \in \mathbb{N}$. We apply this framework to study boundary actions of free groups of finite rank $r \ge 1$, where the boundary is equipped with a stationary Markov measure. We prove that in this context, weak mixing is equivalent to $(2r-1)$-chaining, as well as to strict irreducibility of the transition matrix of the Markov measure.

Human dishonesty in group settings is highly susceptible to peer influence, particularly when incentivized. Although artificial intelligence (AI) evolves from passive tools into active collaborators, its impact on human moral behavior within groups remains underexplored. We addressed this gap through a two-phase randomized behavioral study (N=280 and N=360). We found AI agents exert substantial social influence comparable in magnitude to that of human peers. Specifically, participants reported more dishonestly when exposed to dishonest rather than honest normative cues. This effect is evident across injunctive, subjective, and descriptive social norms. Interestingly, the only significant adjacent behavioral change occurred when dishonest peer behavior first appeared, whereas further increases from one to four dishonest peers produced weaker and non-monotonic changes. Furthermore, participants rapidly converge on decision-making, showing modest increases in dishonest reporting through repeated exposure. These findings highlight the importance of managing the behaviors and normative signals communicated by AI group members.

The anomalous Hall effect (AHE) reported in epitaxial RuO2/TiO2 has been attributed to a strain-stabilized magnetic state, but strain can be entangled with Ru-Ti intermixing and interfacial charge redistribution, which can produce Ti3+ and potentially localized moments. Here, we disentangle these contributions using Ti-alloyed RuO2 heterostructures in which abundant Ti3+ states are retained while epitaxial strain is independently changed. The strained and relaxed films have nearly identical Ti/Ru compositions and comparable Ti3+ fractions, yet a pronounced nonlinear AHE appears only in the coherently strained film, while the relaxed heterostructure exhibits an almost linear Hall response. Spectroscopic ellipsometry further shows that the AHE-active strained state is accompanied by a reconstruction of the itinerant electronic response, including enhanced metallicity and longer carrier relaxation times. These results show that Ti3+ formation alone is insufficient to generate the anomalous Hall state and identify epitaxial strain, through its modification of the itinerant RuO2 electronic structure, as the dominant control parameter.

Finding the object referred to by language in a partially observed 3D scene is a core capability for embodied agents. Existing approaches either couple object search with online exploration, which can be costly when relevant observations have already been captured, or query pre-built open-vocabulary maps and scene graphs in a static, one-shot fashion. We present Finder, an agentic closed-loop object-finding primitive for embodied grounding. Instead of treating grounding as passive retrieval from a fixed scene representation, Finder maintains a typed loop state that links query-conditioned planning, scoped evidence gathering, candidate verification, and accept/continue/abort control. When evidence is incomplete or ambiguous, the loop can redirect subsequent perception and comparison rather than simply returning the top retrieved object. On open-vocabulary embodied Object Retrieval in Habitat/HM3D and real-world RGB-D scenes, Finder improves the averaged 1m success rate by 15.75 points over strong baselines. The same primitive also transfers to sequential object grounding and embodied object-centric question answering, improving spatial and temporal localization without changing the inner grounding protocol. Project page: https://finder-vln.github.io.

Reinforcement learning with verifiable rewards (RLVR) has significantly improved the reasoning capabilities of large vision-language models (LVLMs). However, standard on-policy RLVR algorithms face a critical optimization bottleneck in preserving and reinforcing visually grounded reasoning behaviors: valuable visually-grounded reasoning trajectories are discarded after a single update, while uniform token advantage allocation prevents the model from reinforcing critical perception or reasoning steps. To bridge this gap, we propose PIVOT, a dual-level learning framework that anchors policy optimization around informative visual reasoning signals. Specifically, PIVOT introduces a self-calibrated experience replay mechanism, which selectively collects and replays visually-grounded historical experiences as stable reference anchors for policy optimization. Building upon this, we further design a vision-guided advantage allocation mechanism to allocate additional vision-aware advantages to tokens based on their local visual support and impact on downstream reasoning. Extensive experiments across diverse benchmarks demonstrate that PIVOT achieves highly competitive performance in enhancing the multimodal reasoning capabilities of LVLMs.

Parameter-efficient fine-tuning (PEFT) has recently emerged as a pivotal research direction for adapting pre-trained point cloud transformers to diverse downstream tasks. Although existing methods achieve excellent fine-tuning performance with high parameter efficiency, they ignore inference efficiency. To tackle this problem, a novel PEFT method termed position anchor tuning (PAT) is proposed in this paper. As multi-head attention (MHA) and feed-forward network (FFN) are computation-heavy blocks in pre-trained transformers, PAT decreases their computational cost through token aggregation-expansion pairs. Each pair comprises a token aggregation module (TAM) and a token expansion module (TEM). For MHA and FFN blocks, TAMs extract representative tokens from their input tokens based on position anchors in 3D space. These extracted tokens, rather than the original input tokens, are processed by the blocks, thereby reducing the number of tokens involved in computation. Then, TEMs propagate the learned representations back to the original input tokens. Since TAMs are solely responsible for capturing task-specific representations, base-sharing low-rank adaptation (BSLoRA) is further introduced to enable them to learn such representations effectively with only a small number of trainable parameters. Extensive experiments on widely used benchmarks demonstrate that PAT performs comparably to state-of-the-art methods while incurring significantly lower computational overhead and fewer trainable parameters.

Since Taylor's seminal work on the dispersion of soluble matter, the modeling and control of solute dispersion have received considerable attention. This study investigates the solute dispersion in polymer solutions driven by unsteady magnetohydrodynamic-oscillatory electroosmotic flow within a microtube, aiming to reveal the transport mechanisms in complex rheological media through microscale flow. Firstly, based on the Debye-Hückel approximation, analytical solutions for the electric potential and velocity distributions of mixed magnetohydrodynamic-electrohydrodynamic flows are rigorously derived. Subsequently, using Sankarasubramanian & Gill's generalized dispersion model, mathematical models are developed to systematically investigate the temporal evolution of hydrodynamic dispersion. By investigating the synergistic modulation of electrokinetic and magnetic fields, we identify three distinct flow regimes, namely the electric-field-dominant, competitive transition, and magnetic-field-limited regimes, and quantitatively define their boundaries and evolution with oscillatory Reynolds number $Re$ and Deborah number $De$, thus allowing accurate flow regime classification. Moreover, a non-monotonic critical response governing solute dispersion is observed over a wide range of oscillatory Reynolds numbers, which provides a novel control paradigm for microfluidic mixing and separation. Additionally, through a comparative analysis of fractional Maxwell, classical Maxwell, and Newtonian fluids, we show that microscopic structural relaxation plays a crucial role in macroscopic solute transport under multi-field coupling. Our findings help to reveal flow mechanisms for precise mass transport control in electro-magnetically coupled systems, advancing the development of microfluidic devices and biomedical detection technologies.

We prove that the Enots-Wolley sequence, a greedy sequence defined by local divisibility and coprimality conditions, contains every positive integer with at least two distinct prime divisors. This resolves an open conjecture by Shannon and Sloane. The only analytic number-theoretic inputs are the prime number theorem and Mertens' estimate for reciprocal primes.

Let Gamma be a convex-cocompact group of isometries of a CAT(-1) space X and let Y to X/Gamma be a Galois cover with a word-hyperbolic group of deck transformations. We show that, for almost every geodesic xi with respect to the Bowen-Margulis-Sullivan measure on the lift of X/Gamma, there exist m,sigma > 0 and a standard Brownian motion B(s) such that, for any lambda > 1/4, d(p(g(s,xi)), o) = ms + sigma B(s) + o(s^lambda), where g(s,xi) denotes the geodesic flow acting on the geodesics of Y and p the canonical projection to Y. The result is a consequence of an almost sure invariance principle for random walks on hyperbolic groups with dependent increments. Its proof makes use of a new Ruelle operator theorem for skew products and Martin boundary techniques for random walks with dependent increments.

This study empirically evaluates whether cost-efficient Large Language Models (LLMs) can be trusted to generate enterprise code to a written specification. Three models (Gemini Flash 3, GPT-5.4 mini and Claude Haiku 4.5) were asked to solve 992 algorithmic problems as Java Spring Boot service methods conforming to a mandated signature and data-transfer-object specification, crossing four model and agentic coding tool combinations with two prompt variants to yield eight configurations, with iteration forbidden and hardcoded answers explicitly prohibited. Eight problem statements were withheld to probe how models respond to missing input. The 7,593 resulting methods were classified by an eight-class outcome taxonomy describing what each does about producing an answer, then deployed and executed, giving 7,936 measured requests joined to that classification. Structural conformance approached ceiling, yet 38.4% of methods do not compute the value they returned and only 12.9% of returned answers were correct. Conditioning on outcome class shows that response reliability and correctness are inversely related, whereas genuinely computing methods answered least often and were correct 19.3%. Limitations include single generation runs per configuration, partial harness coverage, single-pass timing, syntactic classification, and probable corpus contamination.

Fresh-market blueberries require selective, gentle picking, which is labor-intensive and expensive. Over-the-row machine harvesters are fast but non-selective, bruising mixed-ripeness fruit and limiting yield to the processing market. Selective robotic harvesters typically target individual fruits rather than fruit clusters, which limits harvesting efficiency for small, densely clustered blueberries. This paper presents CLASP, a Cluster-Level Autonomous Selective Picking robot with a Soft Active Rolling-Band Gripper (SARB-Gripper). Two compliant bands envelop the cluster and roll against the fruit, drawing mature berries off in sequence, while closed-loop regulation of the pulling force keeps the applied load below the immature detachment threshold. A global-to-local perception pipeline pairs an eye-to-hand camera for global cluster detection and target selection with an eye-in-hand camera for local localization and cluster orientation estimation. Field measurements confirm a clear detachment-force separation between mature and immature fruit, and the SARB-Gripper reproduces a commanded pulling force to within \SI{3.7}{\percent}, enabling selective harvesting at the cluster level. In end-to-end field trials, CLASP autonomously grasped 23 of 25 presented clusters (\SI{92}{\percent}). With the component cost of approximately \$3326 per unit, CLASP offers a scalable approach to selective cluster-level harvesting for fresh-market blueberries.

How do elephant trunks generate complex postures without relying solely on fine segmental activation? We propose that part of this complexity arises from a low-dimensional geometric shortcut: dual-helicity coupling between opposite-handed oblique muscles. In a simplified soft-robotic prototype, varying only two geometric parameters generates a broad library of elephant-like postures, suggesting a dual-layer control architecture with implications for continuum robot design and biological hypotheses.

Model explainability is essential for understanding and trusting machine learning models. Existing explainable AI methods often explain predictions through feature importance, counterfactual explanations, or rules. However, a region-level characterization of when and only when a prediction behavior arises remains less explored. This paper proposes Causal Sufficient and Necessary Regional Explanations (SNRE), a framework that learns an input region $A$ and output region $B$ such that membership in $A$ is both sufficient and necessary for the model output to fall in $B$. Motivated by the classical Probability of Necessity and Sufficiency (PNS), we formulate a region-level PNS measure through stochastic interventions and derive a differentiable finite-sample estimator for optimization. SNRE parameterizes the input-output region pair with explicit and interpretable algebraic region families, together with a learnable feature mask, balancing expressiveness and interpretability. Experiments demonstrate that SNRE learns region pairs with strong sufficiency-necessity performance, robust explanation behavior, and practical utility for model analysis.

Several propagation-based and analyser-based X-ray phase-contrast imaging experiments with over 100 m between the imaged objects and the detector were carried out at the Imaging and Medical beamline (IMBL) of the Australian Synchrotron. These experiments were aimed at characterization of possible phase-contrast imaging setups at IMBL. Effects of the beam divergence, polychromaticity and X-ray source size on the contrast and spatial resolution of images were evaluated quantitatively in different imaging scenarios. The results of this work will be used for improving the existing and developing new imaging capabilities at the beamline. Applications to X-ray phase-contrast tomography of biomedical samples, particularly for medical breast cancer imaging, are briefly discussed.

We characterize when compressed vector representations admit exact linear or affine readouts of a finite lexicon's truth conditions: one fixed map per predicate, sending each entity vector to the corresponding truth vector. A necessary and sufficient row-space condition determines existence; the augmented truth matrix has rank r, giving minimum dimension r in the linear case, and r-1 in the affine. Exact readouts return values in a shared truth basis on which Boolean connectives act unchanged; separability alone requires an intervening threshold. For binary relations, exact bilinear readout of identity or strict total order requires linearly independent entity vectors. Experiments with GloVe and word2vec distinguish exact affine recovery, linear separability, and held-out prediction: most predicates are strictly separable, but none admits an exact affine readout from the pretrained embeddings. Supervised transductive training attains exact affine recovery to numerical precision at every tested dimension meeting the bound. At the embeddings' original dimension, geometries constrained to exact linear recovery retain 98-99 percent of the pretrained variance on the feature norms, and 80-83 percent on the WordNet lexicon.

We study the problem of scheduling jobs on a serial-batch machine with the aim of minimising the total weighted late work. In a serial-batch setting, jobs within a batch are processed sequentially, and none are removed from the machine until the last job in the batch completes its processing. The processing time of a batch is the sum of the processing times of the jobs within it, and the completion time for each job in the batch is equal to the makespan of the jobs in the batch. When a new batch begins, a constant setup time is required for the machine. We show that minimising the total weighted late work in this environment is $NP$-hard even if all jobs have a common due date and unit weight. For the general problem, we present a pseudo-polynomial time dynamic programming algorithm. Additionally, we explore two special cases, i.e., one with a common due date and another with an agreeable condition among due dates, processing times and weights. For both special cases, we develop specialised pseudo-polynomial time dynamic programming algorithms. The proposed approaches are equipped with specialised acceleration techniques to enhance their computational performance. The extended experiments demonstrate that the dynamic programming algorithms outperform Gurobi in time efficiency.

Recovering latent interaction structures from multi-agent dynamics is important for understanding and predicting interacting systems. Trajectory-based structural inference has achieved promising performance, but conventional formulations assume that the trajectories of all modeled agents are available. In practice, agents may become unobserved at deployment because of limited sensing, occlusion, or communication failure. Existing studies have considered unseen-node estimation, structural inference under partial observations, and missing-value imputation, yet the joint recovery of hidden-agent trajectories and their interactions remains underexplored. We formulate this problem as structural inference under hidden agents. Its key difficulty is a circular dependency: recovering interactions involving a hidden agent requires an estimate of its trajectory, while trajectory reconstruction can itself benefit from structural information. To address this challenge, we propose Structural Inference under Hidden Agents (SIHA), which combines structure-agnostic initialization with structure-guided iterative refinement. SIHA reconstructs hidden trajectories from visible observations, infers interactions using Neural Relational Inference, and feeds the estimated structure back into hidden-state reconstruction through multi-strength structural attention and iterative state–structure updates. Experiments on three benchmark dynamical systems demonstrate consistent improvements in visible-to-visible structural inference, while also showing benefits in hidden-state reconstruction and future prediction. Motion-capture experiments with simulated whole-limb occlusion further demonstrate its effectiveness in realistic hidden-agent settings.