Papers

We study the unit-demand pricing problem under min-buying behavior, where customers purchase the lowest-priced item that yields non-negative utility. In contrast to the quasi-linear model, we show that uniform pricing becomes substantially more effective under min-buying. First, we study symmetric environments. We show that for min-buying customers with independent and identically distributed valuations, a uniform price across items is optimal. We then extend this optimality result to all valuations drawn from exchangeable and affiliated distributions. However, uniform pricing is not optimal in all symmetric environments: for min-buying customers we construct an exchangeable and non-affiliated valuation distribution for which the gap between uniform pricing and optimal item pricing is logarithmic in the number of items. This gap is tight and matches the worst-case gap in the quasi-linear setting. Next, we consider asymmetric environments in which valuations are independent but not identically distributed. When these valuations are regular and customers are min-buying, we show that a uniform price guarantees approximately 69.86% of the optimal item-pricing revenue and this is tight. Overall, our results highlight that the value of non-uniform pricing substantially diminishes, and often disappears entirely, under more conservative demand models in which customers engage in satisficing behaviors such as min-buying.

Last-mile functional coverage closure for modern chip designs remains costly because a mature UVM environment exposes many controls while direct hits on the remaining bins are sparse. We present a non-intrusive workflow that closes pre-defined bins in an existing, human-authored functional coverage model; it does not synthesize verification objectives from the design specification. The workflow first uses abstract-syntax-tree (AST) parsing and cone-of-influence (COI) tracing to map each residual target to existing testbench knobs. Under a matched 20-simulation budget, Bayesian optimization (BO) is compared with continued constrained-random verification (CRV) and random search over the same AST/COI-reduced space. Formal reachability then removes only targets supported by complete unreachability proofs, after which retained targets are grouped by formal difficulty and processed by group-specific BO under a second matched 20-simulation budget. Cleanup and grouping never add numerator bins; only simulator coverage artifacts do. On OpenTitan AES, first-pass reduced-space BO reaches 241/271 bins; formal cleanup removes two denominator bins; the integrated post-cleanup stage - difficulty grouping, policy routing, and group-specific BO - adds 20 simulator-confirmed hits, yielding 261/271 raw coverage (96.31%) and 261/269 effective coverage (97.03%). On Entropy Source, first-pass reduced-space BO reaches 2117/2277 bins; formal cleanup removes ten denominator bins; the integrated post-cleanup stage - difficulty grouping, policy routing, and group-specific BO - adds 93 simulator-confirmed hits, yielding 2210/2277 raw coverage (97.06%) and 2210/2267 effective coverage (97.49%). These results characterize the integrated diagnosis-and-search workflow; the present evaluation does not isolate the causal contributions of difficulty classification, policy routing, and post-cleanup BO.

Gaps, skips, and mistakes are the normal state of a historical register: rows go missing, tables cross page breaks, columns slip under wrong names, and column sums disagree with the corresponding row entries. Readers read digits correctly but lose the table structure. On seven clean panels of election returns, the best open-source reader reproduces 99.0% of the digits but files only 83.7% of the figures in the correct cells and gets 11 of 30 columns correct. TableVision treats table structure recovery as the problem. On three degraded 1888 pages, Amazon Textract files only 1 of 1494 figures correctly; TableVision correctly files 99.2%, and all 51 columns its exact-total check releases are correct. A dynamic program cuts a volume into blocks by how many columns sum to their last line; witnesses read the cells; the gate classifies each column as exactly reconciling, flagged as faithful to a page whose arithmetic is wrong, or withheld. A theory of the sum check says which errors it cannot see and why its optimal block is about $\theta^{-1/2}$ rows at defect rate $\theta$. On 2201 columns of Wisconsin electoral data, the gate accepts 2042, flags 118, and withholds 41; failure rises with column length $R$ as $1-(1-\theta)^R$ at 1.1 defects per 1000 cells in general elections; official returns confirm 933 of 934 testable accepted sums and all 35 testable flagged totals; and the deployment added 491\,359 gated precinct rows to a 9.3-million-row dataset. One implication is that the design of the verification block is critical.

We present a theoretical study of distributed quantum sensing using a reconfigurable network of $N$ Mach–Zehnder interferometers to simultaneously estimate weighted linear combinations of relative phase shifts. The proposed scheme relies on injecting a Perelomov coherent state, generated from the SU(1,1) group representation, into one port of a passive quantum circuit while the remaining modes are initialized in the vacuum state, thereby establishing non-trivial quantum correlations among the sensors. Based on multi-parameter quantum estimation theory, our analysis shows that this entangled strategy outperforms the standard shot-noise limit and asymptotically achieves the Heisenberg limit. Furthermore, we highlight the crucial role of the first beam splitter's asymmetry; specifically, the optimal transmission coefficient that maximizes sensitivity corresponds to its maximum imbalance. Compared to a separable approach utilizing the same total average photon number, the entangled strategy yields a more efficient use of quantum resources, guaranteeing an accuracy gain between $1$ and $N$. This demonstrates that the entangled strategy is systematically superior to its separable counterpart. Ultimately, these results illustrate the potential of entangled distributed quantum sensor networks for high-precision measurements and provide clear guidelines for optimizing interferometric architectures in quantum metrology.

The geometrical configuration of the Einstein Telescope (ET) gravitational-wave observatory is one the most important design choices to be made for this future scientific facility. Two baseline configurations are currently being considered, a single triangle or 2 distant L-shaped detectors tilted by about $45^{\circ}$. In this document we present a study of the scientific performance of the ET baseline configurations in both stand-alone mode and in the presence of either an L-shaped Cosmic Explorer detector with 40-km long arms located in the United States or the existing LIGO-Virgo-KAGRA network. We also include in the study an alternative ET configuration, which is currently not being considered and consists of a triangle plus a distant L-shaped detector. We find that in stand-alone mode this alternative configuration performs significantly better than the other two in both the compact binary coalescence and stochastic gravitational wave background scientific cases. The differences in performance between the ET configurations are reduced in the presence of the considered, additional non-ET detectors. We also show that the impact of possible correlated noise in co-located detectors on the stochastic gravitational-wave background performance can be addressed with the addition of extra detectors. Finally, we study the impact on the ET scientific performance of the relative orientation of the future detectors in the network. We find that, while the configurations that include a triangular ET detector are basically insensitive to this orientation, a balanced compromise for the ET configuration consisting of two L-shaped detectors could be represented by a tilt angle between the two detectors of about $30^{\circ}$.

RTL-generation studies increasingly report functional correctness and post-synthesis quality, yet the evaluator itself is rarely treated as an experimental variable. A candidate can appear better when a security rule, protocol obligation, target context, feasibility gate, uncertainty policy, or provenance constraint is omitted. We introduce tool-grounded requirement profiles: machine-readable contracts binding each requirement's meaning to its executable evidence and comparison rule, together with cross-requirement gates, uncertainty handling, and provenance. We audit evaluator stability by freezing candidate pairs and perturbing only their evaluation profile. In a preregistered controlled pilot with six designs, twelve pairs, three requirement families, six evaluator conditions, and 72 decisions, a generic cell-count evaluator reports unsupported improvement for 6/12 pairs (50%; Wilson 95% interval 25.4 to 74.6%; design-cluster bootstrap interval 25 to 75%). The matched evaluator detects all twelve injected regressions, whereas syntax, generic synthesis, context mismatch, and gate ablation each lose the required distinction for 12/12 pairs. In a separately frozen external validation of all 290 public RTLLM v1.1 text-only candidates, 81/215 evaluable comparisons (37.7%; task-cluster 95% interval 24.8 to 51.4%) yield unsupported scalar improvements, including 72 functional-gate reversals. Separately, 26 OpenROAD-flow-scripts runs show why timing context and activity qualification must be part of the contract. The study does not rank generators; it establishes evaluator configuration as a measurable, auditable source of conclusion instability.

Language model (LM) agents can fail for different reasons, requiring different explanations and interventions. We study how state beliefs, action values, and action preferences interact as LM agents reason and commit to decisions in text-rendered grid worlds. We estimate task-relevant beliefs using report-based and representation-based probes, and action values using inverse reinforcement learning. We find that task-relevant state and value information is often represented more reliably than it is reflected in behaviour. Tracking action preferences throughout reasoning further shows that decisions sharpen around a commitment point and reported belief uncertainty decreases near commitment, although individual belief changes do not consistently explain shifts in action preference. Finally, forced actions follow reasoning prefixes from other decisions when transplanted, whereas the tested reasoning-window activation edits provide limited control over the action. Together, these results suggest that some failures arise not from missing task-relevant information, but from how available information is translated into action. Our measurements distinguish information availability from belief-action consistency without by themselves identifying the cause of each failure. Our code is available at: https://anonymous.4open.science/r/belief-action-gap-F745/

We investigate the growth trajectory of online platforms operating as market makers in two-sided matching markets. Their expansion, often referred to as the “chicken-and-egg dilemma” in the literature, poses an inherent challenge: service providers find value in joining the platform because of the presence of customers, while customers are drawn to the platform by the availability of service providers. Much of the existing literature addresses this expansion challenge through either a static market-clearing lens or aggregate dynamic models, emphasizing how network externalities shape a platform's growth trajectory and equilibrium size. These approaches do not fully capture how gradual growth must be implemented through server-level admission, assignment, and compensation decisions. Embedded in this growth process are intertemporal participation constraints that the platform must satisfy to attract and retain forward-looking servers. To explicitly account for the stochastic dynamics of a platform's gradual growth, we model the system as a Markov process. Potential servers and customers arrive according to Poisson processes, and customer demand is non-decreasing in the number of active servers. Under mild conditions, we characterize the platform's optimal admission, assignment, and compensation policies. The platform admits servers at the maximum feasible rate until it reaches an endogenous target size, which can be smaller than the static market-clearing optimum. In the baseline model, seniority-based compensation acts as an operational substitute for financially subsidized growth: instead of using upfront subsidies to induce early server participation, the platform uses future cash flows to reward early servers for joining when demand is limited and for helping the platform reach later, higher-demand states.

Let $Q \subseteq \mathbb{R}^n$ be a open, convex, and symmetric set and let $f:Q \rightarrow \mathbb{R}$ be a $\vartheta$-self-concordant barrier function, that is also symmetric. We show the associated spectral function $F(X)= \mathcal{O}^2 (f \circ \lambda)(X)$ is a $\mathcal{O}^2\vartheta$-self-concordant function, where $\mathcal{O} = 8\max\{1+3\vartheta, 12\}$, on the domain of all $n \times n$ symmetric matrices $X$, with eigenvalues $\lambda(X) \in Q$. This generalizes the relationship between the standard logarithmic barriers $-\sum_{i=1}^n\log x_i$ and $-\log \det X$ and gives a solution to a conjecture by L.~Tunçel, 1995.

Laurent phenomenon algebras generalise cluster algebras by allowing irreducible exchange polynomials in place of binomials. Lam and Pylyavskyy proved finite type for those arising from graphs and conjectured that the same holds for every Laurent phenomenon algebra admitting a linear seed. We prove this conjecture over an arbitrary unique factorisation domain. Our proof constructs a nonzero element of the upper algebra divisible by every cluster variable. Comparing noninitial cluster variables with the prime factors of this element in the initial Laurent ring bounds the number of cluster variable classes and yields a finite normalised mutation pattern.

Dual-encoder vision-language models systematically fail at negation, scoring ”a cat without a dog” nearly identically to ”a cat with a dog.” We show that this failure is inherent to the single-embedding framework. Under contrastive training, single-embedding methods can at best ignore the negated concept (dilution) but never penalize its presence (rejection). We propose Know-Thy-Not (KTN), a training-free method that introduces an image-side rejection dimension to penalize the negated concept directly in the visual representation. We also introduce COCO-Confusion, the first benchmark requiring genuine rejection to succeed. Across 9 backbones, KTN improves COCO-Confusion mAP by up to +25.6 over vanilla VLMs and +9.6 over the strongest existing method.

The success of autonomous research systems relies on the quality of the scientific hypotheses they generate. Recent studies report that human reviewers often rate LLM-generated ideas as more novel than those from human experts, raising hope that AI can accelerate scientific discovery. Yet it is unclear whether these models can do more than extend existing knowledge. Can LLMs drive genuine innovation by revealing new research directions, or are they limited to repeating and recombining what science already knows? This unresolved question lies at the heart of discussions about AI and the future of science. To address this, we distinguish two types of novelty: distance, which measures how far a hypothesis lies from existing work, and direction, which captures whether the hypothesis pursues new lines of inquiry beyond those already present. These two measures diverge sharply for LLM-generated work. We represent scientific papers in a shared conceptual space using a pretrained scientific-paper embedding model. Within this space, we embed 26.9 million human-authored papers across 1,325 research topics in six natural-science fields and 524,308 LLM-generated hypotheses from eight models. Distance is measured using existing metrics. To quantify direction, we introduce the orthogonal novelty score (ONS). LLMs consistently generate ideas more distant from existing work than human-authored papers, up to 16% further when the LLM is given the papers farthest from the centre of the topic. However, LLM hypotheses have a 15–23% lower median ONS than published papers from the same topic. Thus, LLMs move further from what is already known, but remain within established directions. This pattern persists across changes in various configurations. As a result, LLMs excel at extending the frontier but the creation of new directions is still led by human scientists.

We investigate the early-universe cosmological implications of Unimodular Gravity coupled to Power-Law Nonlinear Electrodynamics in the presence of quantum-corrected horizon thermodynamics derived from the principle of thermodynamic duality. By incorporating both logarithmic and inverse-area corrections to the Bekenstein-Hawking entropy, we derive modified Friedmann equations exhibiting novel $H^4$ and $H^6$ terms that represent genuine quantum gravity effects. We demonstrate that these higher-order corrections become dynamically significant in the high-energy regime of cosmic inflation, naturally modifying the slow-roll dynamics without requiring a fundamental inflaton potential. A comprehensive phase-space analysis reveals that the quantum corrections drive early-time de Sitter-like attractors, providing a robust mechanism for sustained inflationary expansion. Confronting the model with the Swampland program, we show that the correction factor $\mathcal{F}(H)$ modifies the effective slow-roll parameters, enabling the model to satisfy the Swampland de Sitter and Distance conjectures during the inflationary epoch. We calculate the inflationary observables, including the spectral index $n_s$ and the tensor-to-scalar ratio $r$, and demonstrate that the model's predictions are in excellent agreement with the Planck 2018 observational constraints. Our results suggest that thermodynamic duality-induced horizon corrections offer a viable and testable pathway for realizing successful inflation within a well-motivated quantum-gravitational framework.

We show that adding a dimension-six self-interaction to the Abelian-Higgs or Ginzburg Landau model results in a remarkable and rich structure of multi-vortex solutions. Besides the standard type I (attractive) and type II (repulsive) regimes, separated by the Bogomol'nyi-Prasad-Sommerfeld limit (BPS), we identify two new possibilities: type I-II vortices, which attract at short distances and repel at long distances; and type II-I vortices, with the opposite behaviour. Specifically, within the type II-I regime, multi-vortex solutions form chunks of the Abrikosov lattice or clusters. Conversely, in the I-II regime, axially symmetric multi-vortices are stable; nevertheless, depending on the model parameters and topological charge (winding number), they can be either the ground state or not.

Large language models (LLMs) on mobile devices can act as agents that call external software tools to complete complex tasks, but the major challenge of supporting on-device mobile agentic AI with LLMs is the long latency of LLM tool calling on mobile devices. In particular, the decode phase is the main contributor of such long latency, but is hard to speed up on mobile processors as it is bound by memory bandwidth rather than compute power. To address this limitation, in this paper we present SchemaWeaver, a new on-device mobile agentic AI technique that enforces schema-guided parallel decoding in the decode phase of LLM tool calling, to reduce its latency by producing multiple tokens in each decode pass. SchemaWeaver can be generically applied to the LLM inference engine on mobile devices without involving any training efforts or changes on LLMs, and our experiment results on major mobile SoCs and LLM families show that SchemaWeaver can reduce the LLM tool calling latency by up to 3.9 times, compared to the competitive baselines.

We examine various applications of logic to $\mathrm{AW}^*$-algebras, particularly the monotone completeness conjecture. We develop a model theory for $\mathrm{AW}^*$-algebras equipped with a faithful normalized quasitrace. Using this language, we provide a separable coding which allows us to reduce the finite case of the monotone completeness conjecture to monotone sequential completeness of $\mathrm{II}_1$ $\mathrm{AW}^*$-factors. Combining an explicit recursive axiomatization with the completeness theorem for continuous logic, we show that this case of the conjecture, and Kaplansky's problem whether every $\mathrm{AW}^*$-factor of type $\mathrm{II}_1$ is a von Neumann algebra, are each equivalent in ZFC to a $\Pi^0_2$ sentence of arithmetic, so that their answers are the same in every $\omega$-model of ZFC. We also consider real $\mathrm{AW}^*$-algebras. Here the Baer-$*$-ring notion of an abelian projection must be distinguished from commutativity; following the real-operator-algebra terminology we call the former semi-abelian. Handelman's matrix theorem implies that a real $\mathrm{AW}^*$-algebra with no nonzero central semi-abelian projection has $\mathrm{AW}^*$ complexification. We answer a number of other open problems in real $\mathrm{AW}^*$-algebras.

Recent advances in video world models have enabled plausible interactive environments, yet long-horizon generation places a fundamental demand on visual memory: the previously observed world must remain consistent as the model continues to generate. Existing autoregressive approaches often implicitly rely on the generative model itself to retain such information, leading to spatial memory decay beyond the active context. We introduce World-T3, a camera-controlled video world model with a test-time training memory that consolidates past observations into dedicated model parameters. To robustly update this memory, we propose a recursive least-squares rule that incrementally absorbs novel visual features via online pose-keyed memory updates. Our TTT memory reads out previously observed scene features from the fast-weight state by camera pose, enabling consistent generation with constant storage and per-step computation regardless of rollout length. To facilitate real-time interactive generation with this robust memory, we further distill the autoregressive model into a few-step generator via dual-teacher distribution matching. On a long-horizon revisit benchmark, World-T3 raises revisit PSNR from 13.52 to 18.31 dB and reduces absolute rotation error from 3.344 to 1.075 relative to the strongest baseline on both metrics, while sustaining 20.6 FPS at 1280 x 704 on a single NVIDIA B200 GPU.

Two-dimensional (2D) coronal seismology based on coronagraphic imaging spectroscopy has emerged as a promising method for mapping the coronal magnetic field, but the physical meaning of its inferred quantities under optically thin line-of-sight (LOS) integration remains uncertain. We investigate this problem by synthesizing coronagraphic observables from a global wave-driven magnetohydrodynamic model with a long LOS extent and a structured corona, and by applying the same analysis procedures used for observations. We compare the diagnosed density, wave propagation direction, phase speed, and magnetic-field strength with different LOS-weighted reference quantities from the model. We find that the measured density and the wave propagation direction are both well represented by LOS emissivity-weighted quantities. In contrast, the phase speed is not controlled by emissivity weighting alone: the LOS distribution of wave velocity amplitude also plays an important role. As a result, the inferred magnetic field is better represented by combining the emissivity-weighted density with an amplitude-dependent effective speed. Emissivity weighting nevertheless remains a reasonable approximation, and a useful baseline, over much of the field of view, especially where the LOS does not cross strongly structured plasma-sheet-like regions. These results clarify the physical interpretation of 2D coronal seismology and provide guidance for future coronal magnetic-field tomography and model-constrained applications.

We give a presentation by generators and relations of the group of birational transformations of the plane preserving a differential form with poles along a triple line. This group strictly contains the automorphism group of the affine plane.

Large language model (LLM) routers are increasingly deployed to optimize quality, latency, and cost through dynamic model selection and request rewriting. However, a compromised router can cause ineligible selection on the control plane, unendorsed rewriting or unfaithful relay on the data plane, undermining LLM routing integrity. We present VeriRouter, a verifiable LLM routing framework. Under an endorsed public context binding a private semantic index and rewrite banks, VeriRouter combines ZK proofs with a provider-issued serving certificate to establish integrity across both planes while keeping the router's private routing assets hidden from clients. For model selection, we design an efficient ZK proof for semantic search. For rewriting, local checks enforce message preservation and additions from committed banks. On real-world workloads, VeriRouter's model-selection and rewrite proofs average 21.92~s and 4.24~s, yielding 1,307$\times$ and 101$\times$ speedups over the fastest completing baselines. Relative to serving without verification, VeriRouter adds only 4.08 s under per-turn selection and 0.11 s under session-pinned selection.

Given a set $P$ of $n$ point sites in the plane, the $k$ nearest neighbors problem is to build a data structure that, for a query point $v$ and a query integer $k$, reports the $k$ nearest point sites of $v$ in $P$ efficiently. For the Euclidean metric, after four decades of efforts, an optimal data structure has been developed with $O(n)$ space, $O(\log n+k)$ query time and $O(n\log n)$ preprocessing time [Mat92b, Cha00, AC09, CT16]. In contrast, for a family of distance functions, the state-of-the-art data structure [AES99, KMR+20, Liu22] attains $O(n\log\log n)$ space, $O(\log n+k)$ query time and expected $O(n\log n)$ preprocessing time. An open question is the existence of an optimal data structure with $O(n)$ space and $O(\log n + k)$ query time for distance functions more general than the Euclidean metric. Such an optimal data structure also remains unknown for non-point sites in the Euclidean metric, even for disk sites or, more generally, additively weighted Euclidean distances. We develop an optimal $k$-nearest-neighbors data structure for additively weighted Euclidean distances with $O(n)$ space, $O(\log n + k)$ query time and expected $O(n\log n)$ preprocessing time. Since this data structure can be adjusted to disk sites, it serves as an initial result toward optimality for non-point sites. We also adapt our data structure to point sites under a family of convex metrics, including commonly used $L_p$ metrics and uniform orientation metrics. The data structure can be further extended to distance functions that satisfy certain axioms. Thus, we demonstrate the existence of optimal $k$-nearest-neighbors data structures for distance functions more general than point sites in the Euclidean metric. Our main technical advance is to generalize Matoušek's shallow partition theorem for hyperplanes [Mat92b] to these settings, while achieving a logarithmic crossing number.

Training large language models is constrained by both wall-clock time and memory footprint, and recent matrix-aware optimizers sharpen this tradeoff: Muon can improve optimization but its dense polar update remains expensive. We propose Monarch-Muon, a structured matrix-aware optimizer for weights parameterized by Monarch factors. The resulting structure reduces weights, gradients, and optimizer state, and exposes small independent update subproblems in place of a single dense orthogonalization; we formalize this through a blockwise trust-region interpretation. In quality runs, Monarch-Muon improves over Monarch-AdamW at fixed structure: 3.06 vs. 3.09 in the dense 257M model and 2.68 vs. 2.77 in the 1B MoE model; the two-block MoE variant also matches dense AdamW while using 15% fewer active and 25.4% fewer total parameters. In 6.89B-parameter systems measurements, Monarch-Muon reduces peak memory from 68.9 to 52.9 GB, Muon optimizer state from 14.60 to 6.77 GB, and the Muon optimizer step from 1288 to 304 ms.

Continuum gyrokinetic codes use structured, field-aligned grids on nested flux surfaces; particle-in-cell codes support unstructured meshes and open field lines but carry a statistical noise floor. We present a continuum drift-kinetic solver that occupies neither position: a semi-Lagrangian discontinuous Galerkin discretization on unstructured triangular poloidal planes extruded toroidally, whose parallel advance is a map along the exact field line in the flux-coordinate independent manner, so the mesh is never aligned with the field, with adiabatic electrons and a long-wavelength polarization field solve. Every operator is verified against an independently computed reference, from Landau damping to the geodesic-acoustic root and a linear ion-temperature-gradient eigenvalue problem, every measured rate within 4% except the geodesic-acoustic damping, within 12%. A linear toroidal ion-temperature-gradient demonstration on a canonical-Maxwellian equilibrium recovers a radially coherent mode whose growth rate, 0.065 c_s/a, is stationary in time. The collisionless zonal-flow residual is the one measurement still moving: it rises with poloidal refinement from 0.72 to 0.87 of the model's own orbit-quadrature prediction for the measured observable and has not converged. The solver is fully device resident, and every result is reproduced between CPU and GPU builds and across MPI process counts. The code, the data behind every table and an artifact description are in a public repository.

Trajectory smoothness has been proposed as a cheap, training-free signal for curating imitation-learning demonstrations, most recently by rinse, which introduces Spectral Arc Length (SAL) and a contact-aware Trajectory-Envelope Distance (TED). We test whether these published metrics survive episode-length controls on real robomimic data. On can/mh, SAL separates better from worse operators with AUROC 0.952, but episode length alone achieves 0.957, and inside a duration-matched band SAL falls to 0.628 while raw mean jerk, the baseline rinse argues against, rises to 0.896. The confound replicates on square/mh. On can/mg, where every episode is exactly 150 steps, SAL is at chance (0.454) and TED is inverted (0.376) against task success, while jerk reaches 0.706. Training GMM behavior-cloning policies on each metric's curated subset (10 seeds), curating by TED costs roughly a third of downstream success relative to random selection of the same size (0.240 vs. 0.360, p=0.0001, surviving Bonferroni correction), while SAL and jerk are indistinguishable from not curating. Under a diffusion policy TED still ranks worst, though its deficit is not resolvable at five seeds, and jerk becomes significantly better than both baselines, so the curation decision does not transfer unchanged across the two policy configurations we tested. Inspecting trajectories shows why TED inverts: successful manipulation requires sustained high-deviation motion through contact, while failure is low-amplitude hovering that a smoothed envelope follows closely.

Clinical decision-making is a sequential process of information collection, clinical inference, and forecasting under partial observability, often without a uniquely correct treatment decision. Large language models (LLMs) have demonstrated strong medical question-answering capabilities but extending these advances to clinical reasoning remains challenging because many clinical tasks are only partially verifiable. Recent clinical reinforcement learning (RL) work has therefore largely focused on diagnostic endpoints, where correctness can be more directly verified. Oncology treatment decision making is a particularly challenging instance of this problem that extends beyond medical question-answering in which multiple decision trajectories can be clinically defensible for the same partially observed patient state. We formulate oncology treatment planning as an interactive RL problem under partial observability and construct patient-specific, process-aware rewards from decision processes observed in real world clinical records. The agent must learn to sequentially acquire information from a structured patient representation before committing to a first-line treatment recommendation, and is evaluated on information gathering, treatment selection, and reasoning alignment. Using GRPO and GDPO to optimize Llama-3.1-8B-Instruct within this environment, RL substantially improves the base policy beyond frontier model capabilities. The GDPO-trained policy increases Mean@3 scalar clinical reward by $79.60\%$ over base Llama and exceeds GPT-5.2 by $18.82\%$ under the same interactive environment, while reducing query count during training. Overall, our results show that patient-specific, partially verifiable rewards can provide an effective learning signal for interactive clinical RL when both the patient state and the underlying clinical decision process are only partially observed.

Dynamic Sparse Training (DST) periodically prunes and regrows connections, inducing a discrete dynamical mechanism over network topologies. At extreme sparsity ($\ge 99\%$), this dynamic tends to destroy input-output information pathways, and performance with standard magnitude/random updates degrades sharply. We formalize forward, backward, and functional reachability on layered sparse graphs, derive closed-form expectations for reachable neurons and edges, and show that Monte Carlo realizations match the theory. Guided by this reachability-based structure, we bias pruning toward non-functional edges and regrowth toward functionally consistent candidates. We introduce this reachability-driven modification of topology evolution as Reachability-guided in DST, referred to as guided DST. On CIFAR-10/100 and Tiny ImageNet, guided DST recovers large accuracy gaps versus unguided DST (up to $+14.4$ points at $99.9\%$ sparsity on CIFAR-100), and on MLP-Mixer guided DST remains trainable at $99.99\%$ sparsity while unguided random regrowth degrades sharply. These results cast extreme-sparse training as a connectivity-preserving dynamical process. Our implementation is publicly available at https://github.com/mzjaworski/ea_dst.

Respecting a-priori known symmetries of underlying data is a key principle in designing efficient neural architectures. Convolutional neural networks are a canonical example, encoding translation equivariance. Extending this inductive bias to richer symmetry groups such as $\mathrm{SE}(2)$ in the most effective way possible is an ongoing architectural and computational challenge. Building on classical invariant theory, we derive invariant feature maps that are provably optimal: minimal and information-preserving with respect to the symmetry group. Our construction is designed to integrate seamlessly into standard architectures, requiring no modification to nonlinearities or normalization layers. As a concrete implementation, we introduce a plug-and-play module for convolutional neural networks that enforces $\mathrm{SE}(2)$ invariance, capturing both translations and rotations within standard architectures. The resulting models are both efficient and expressive. Experiments show competitive or improved accuracy compared to state-of-the-art equivariant methods at significantly lower computational cost. Finally, we provide a theoretical and empirical analysis of the relationship between equivariance and invariance, offering insight into their roles in controlling robustness and flexibility.

The question of the link between the nucleon properties and the equation of state of ultra-dense matter, both being composed of quarks and gluons, is investigated by adopting a soliton model to describe internal nucleon properties and a direct mapping between nucleon and quark matter to obtain the equation of state of ultra-dense matter. We compare $\pi+\omega$ and $\pi+\omega+\rho$ soliton models and analyze the presence of a pressure singularity at the nucleon center due to the $\rho$ field. This singularity impacts the equation of state in ultra-dense matter. Only the pressure derived from the canonical energy-momentum tensor has a singularity, while the Belinfante pseudo-gauge transformation of the energy-momentum tensor generates an internal pressure without a singularity. We then investigate predictions for the equation of state of ultra-dense matter based on different prescriptions for the nucleon pressure. It is shown that none of the prescriptions agree with the thermodynamical pressure defined in uniform matter. The mismatch between any equation of state and the thermodynamical one questions the simplicity of the direct mapping between finite-size nucleon properties and uniform matter as well as the role of the nucleon surface in the internal energy density and the pressure.

Symmetry-aware robot policy learning requires coupled observation-action transformations. For pixel observations, even simple physical symmetries can induce complex, viewpoint-dependent image transformations that are difficult to specify by hand. Existing symmetry-aware methods often rely on representations with predefined transformations, requiring preprocessing tailored to the sensing setup and task. We introduce MIRROR, a framework that learns how a known symmetry group operates jointly on observations and actions in partially observable Markov decision processes (POMDPs) from offline interaction data. MIRROR couples these transformations through adversarial tuple matching over one-step transition tuples, while explicit group-consistency regularization penalizes violations of the group-operation axioms. On four Robosuite tabletop manipulation tasks, MIRROR achieves the lowest aggregate error on three of four symmetry-quality metrics, including a 61% reduction in compatibility error (which measures consistency under transformation composition) relative to an adapted LaLiGAN baseline. Using the learned transformations in frame-averaged behavior cloning (BC) yields higher mean success rates than vanilla BC on all four tasks, increasing average success from 80.48% to 85.12%, with per-task gains up to 9.66 percentage points. We also repeat symmetry discovery and policy training in simulation with heightmap and segmentation-mask observations, then deploy the resulting policy zero-shot on a real Kinova GEN3 arm. Project page: https://pomdp-mirror.github.io.

We develop a Fisher-information framework for optimizing single-photon detector gating in periodic experiments, in contrast to previous more empirical or heuristic gating choices. After each photon detection, such a detector is insensitive for a dead time, so that an early background detection can obscure a later signal. Gating preserves availability for informative photons by selectively deactivating the detector. In our high-pile-up simulation of distance-attenuated lidar, our practical data-independent gating design reduces the worst-case asymptotic range variance by more than half relative to the free-running acquisition (which does not use any gating). More generally, we characterize achievable detector-active frequencies as a convex polytope and construct an adaptive rule that asymptotically attains an optimal "oracle" design without prior knowledge of the physical parameters. We also derive practical criteria that quantify the potential gains of gating and/or photon attenuation over unattenuated free-running acquisition.