Papers

Monitoring the chain-of-thought of reasoning artificial intelligence (AI) models remains a key approach to detecting deception and other forms of misbehavior in such models. However, semantic chain-of-thought monitoring depends on reasoning traces being legible and sufficiently faithful to the underlying computations that produced the model's behavior, not to mention accessible. Moreover, there is increasing evidence that chain-of-thought outputs may soon become illegible or unfaithful, if they even remain accessible. Based on cognitive load theory, we investigate a lower-bandwidth signal–the number of reasoning tokens generated–which does not require access to the content of the reasoning trace. Three reasoning-capable large language models answered 210 multiple-choice questions–across analytic, descriptive, and normative reasoning types as well as moral and non-moral domains–under system prompts instructing them to respond truthfully, falsely, or without regard for truth. Across all three models, truth-directed responses elicited fewer reasoning tokens than both lie-directed and truth-indifferent responses. In addition, in one model, untruthful instructions increased the likelihood of reasoning at all. These findings show that explicitly prompted untruthful response policies can produce robust group-level differences in test-time reasoning-token use. While not yet establishing reasoning-token count as a detector of spontaneous deception or general misalignment, our results are a proof of concept that it can serve as a simple, content-independent black-box candidate signal for differentiating untruthful from truthful model behavior when raw reasoning traces are unavailable or unreliable. Future work should test instance-level detection rates, out-of-distribution generalization, learned deceptive policies, hidden objectives, and robustness under adversarial pressure.

Inverse design has emerged as a powerful engineering approach in nanophotonics, leading to devices with unintuitive designs that extend beyond human intuition. However, inverse-designed devices have been limited by costly and time-consuming fabrication iterations, simulation-reality gaps, and the fixed nature of etched devices. Separately, programmable photonics has emerged as an approach to modify the function of photonic devices after fabrication; recent free-form programmable-photonic devices have been scaled to have many degrees of freedom, in principle providing platforms well-suited for programmably realizing inverse design of conventional linear-photonic functions. Here we demonstrate in situ training of a single free-form programmable-photonic device to achieve a variety of functions that each would have been implemented in separate devices in the conventional inverse-design paradigm. Our platform is a thin-film lithium niobate slab waveguide with full programmability over the refractive index of the two-dimensional slab, with a tuning range of up to 1.7e-3 for each of the 10^4 effective pixels. We demonstrate 4 x 4 Gaussian-mode permutations, 4 x 4 Hermite-Gaussian mode demultiplexing, and 8 x 8 Gaussian-mode permutations, with maximum crosstalk of -27dB, -13dB, and -13dB, as well as 4 x 4 matrix-vector multiplication. We further demonstrate engineering of spectral responses, showcasing both wavelength-independent operation throughout the 1500-1600 nm window and wavelength demultiplexing between 1310 nm and 1550 nm, with maximum crosstalk of -8.4dB. Since the device is reconfigured for each function after fabrication, the investment in device fabrication, characterization, and calibration can be amortized across the various photonic functions the device is ultimately used for.

SUSpMV is a Sparse Matrix Vector multiplication (SpMV) accelerator written in the upcoming HDL SUS. By leveraging SUS's unique latency counting and inference mechanism, SUSpMV could be designed with very deep pipelines yet small design complexity overhead. This enables an efficient implementation which employs all 32 HBM channels on the Alveo U280 FPGA at 400MHz for streaming matrix data into 32 Compute Units (CUs). Input and output vectors are stored in DDR memory, which allows zero-overhead chaining of multiplications and increases overall system memory bandwidth by not sharing HBM bandwidth with the CUs. A CU processes the SpMV in tiles of width 1024 and a dynamically chosen height, up to 32768. Each CU is capable of accumulating the multiplications with up to 6 separate matrix entries per cycle, resulting in the combined theoretical peak computational throughput of 153.6 GFLOPs. The matrix storage format is designed to exploit density variation within a given matrix by dynamically switching between one representation optimized for denser regions, and a second optimized for sparser regions, allowing jumps of up to 255 rows between each entry. Evaluation demonstrates a 79% geometric mean improvement over prior work on the same platform. We achieve a peak throughput of 144.9 GFLOPs, or 94% of our theoretical computational throughput, compared to 98 GFLOPs reached by prior work.

Let $\mathcal{G}(G,A,\alpha)$ be a discrete 2-group, given as the {categorical} extension of an ordinary group $G$ by an abelian group $A$. We define principal $\mathcal{G}$-bundles over a manifold in terms of Čech data over a good open cover. In the case of the manifold $S^2$, we calculate this bicategory explicitly, and identify its 2-skeleton. We compare with the holonomy bicategory $\mathrm{Fun}(*/\!\!/ \pi_{\le 2}(S^2), * /\!\!/ \mathcal{G})$, and provide a concrete equivalence between the two.

LiGa5O8 is an ultrawide-bandgap oxide semiconductor that has recently been experimentally demonstrated to exhibit p-type conductivity; however, the origin of the observed p-type transport remains poorly understood. In this work, we investigate the origin of p-type conductivity by systematically comparing the electrical, compositional, and structural properties of mist chemical vapor deposition (mist-CVD) grown LiGa5O8 thin films exhibiting either p-type conductivity or insulating behavior under different growth conditions. The p-conductive films exhibit room-temperature hole concentrations on the order of 10^18 cm^-3. The emergence of p-type conductivity is found to be strongly correlated with the elemental composition of the films, with X-ray photoelectron spectroscopy (XPS) revealing a reduced Li/Ga ratio in the p-conductive films, indicative of a Li-deficient composition. Raman spectroscopy and X-ray diffraction (XRD) further reveal signatures of e̱ta}-Ga2O3 in the p-conductive films that are absent in the insulating films, demonstrating the formation of a secondary e̱ta}-Ga2O3 phase. Considering the reported type-II band alignment between LiGa5O8 and e̱ta}-Ga2O3, together with theoretically predicted acceptor levels associated Li vacancies (V_Li) in LiGa5O8, the formation of mixed LiGa5O8/e̱ta}-Ga2O3 phases is proposed to facilitate electron transfer from the e̱ta}-Ga2O3 valence band to acceptor states in LiGa5O8, thereby promoting hole accumulation and p-type conductivity.

Multimodal large language models (MLLMs) have made significant progress in visual understanding and generation. However, generating interleaved image–text content remains challenging, as it requires tightly integrated multimodal understanding and generation capabilities. Although existing MLLMs provide promising solutions, most rely on additional training with augmented data, which is computationally expensive and remains limited in preserving visual subjects, temporal consistency, and physical plausibility. In this work, we propose self-correction optimization (SCO), an effective training-free method for consistent interleaved generation. SCO treats the classifier-free guidance update as a reference and performs minimal self-correction under two complementary constraints, including new-event and state-preserving constraints. Specifically, the new-event constraint promotes temporal consistency across image–text sequences, while the state-preserving constraint maintains the coherence of visual subjects throughout subsequent generation steps. Experiments on challenging interleaved multimodal generation benchmarks demonstrate significant improvements in temporal coherence and visual-subject preservation. Furthermore, SCO can be extended to video generation and improves the modeling of physically grounded processes, including robot manipulation and long-horizon handcrafting.

We investigate the computational complexity of analyzing the structural and behavioral properties of deterministic k-pebble automata, which represent a natural framework for studying minimal programmable machines. First, we provide an explicit construction of a three-pebble automaton U capable of simulating any deterministic finite automaton (DFA) on a given input word, establishing a link between pebble automata capabilities, Kolmogorov complexity, and automatic complexity. Next, we restrict our architectural framework to two-pebble programmable machines U(2,N) simulating DFAs with at most N states. We analyze the decision problem ANAL(U(2,5)), which asks whether a five-state program can separate two distinct finite words. By establishing a polynomial-time reduction from the quasi-identity checking problem for finite semigroups, we prove that ANAL(U(2,5)) is NP-complete. Finally, we explore the complexity of separating binary strings under the Exponential Time Hypothesis (ETH), showing how computational hardness implies polynomial lower bounds for the size of the smallest DFAs separating binary strings.

Neural surrogates for computational fluid dynamics (CFD) have the potential to greatly enhance engineering innovation through accelerating simulation. However, the primary limitation for neural surrogates is the lack of generalization to geometries and applications beyond the training set, which is significant given the diversity of engineering scenarios. Currently, this is addressed by generating a new dataset for a specific application; however, this requires running costly numerical solvers. In this work, we take a step toward addressing this by studying neural surrogates trained across different geometries, boundary conditions, and fidelities. We find that cross-domain pretraining improves zero- and few-shot performance on held-out datasets relative to both training from scratch and transferring from domain-specific experts. In particular, finetuning a pretrained, cross-domain model can achieve 2-3x lower errors at the same sample size and use 8x fewer samples to achieve the same error, compared to training from scratch. This benefit is architecture agnostic and improves with model size and pretraining dataset diversity. Furthermore, we study how and why cross-domain pretraining works in CFD surrogates, and find that simply pooling steady-state datasets is both sufficient and effective. Given the high cost of generating CFD data, leveraging existing datasets through cross-domain pretraining will likely be a valuable strategy as future surrogates expand to tackle new problems and use cases.

The regionally proximal and equicontinuous structure relations are fundamental relations in topological dynamics that capture the equicontinuous behavior in a topological dynamical system and its factors. For minimal actions of abelian groups, these relations are known to be equivalence relations and are known to coincide. In this paper, we generalize these facts to semigroup actions: for minimal actions of commutative semigroups, the regionally proximal and equicontinuous structure relations are equivalence relations and the two coincide. We also develop the machinery of natural extensions for commutative semigroup actions that act by surjections, concluding that the maximal equicontinuous factor of a minimal action of a commutative semigroup is the same as the maximal equicontinuous factor of the group action into which it embeds. We formally verify all of the results in this paper in Lean. The main results are verified in a Palomar submission, and we link to a Github repository containing code for the complete verification.

This paper proposes a novel crowd counting approach, the Gaussian Density Splatting Network (GDSNet). Unlike methods that rely on conventional, grid-based density maps and are sensitive to spatial resolution, GDSNet represents a crowd as a superposition of continuous 2D Gaussian primitives. Our approach is built upon two key contributions. First, a control-point-based fitting mechanism is introduced to structure the prediction of Gaussian parameters. A set of control points is adaptively allocated to define local regions, from which features are pooled to regress each primitive's parameters. Second, we adapt a differentiable Gaussian Splatting framework to the counting task by parameterizing each primitive with geometric parameters and a scalar density mass. This formulation allows the network to be trained end-to-end via spatial matching of differentiably rendered density maps, naturally providing both local density supervision and global count optimization. Extensive evaluations on four standard benchmarks show GDSNet consistently outperforms the state of the art. The code is available at https://github.com/infinite0522/GDSNet-Gaussian-Density-Splatting-Network.

Transformers can execute algorithms on data given in their input. We ask whether they can do the same for causal discovery. We study a standard continuous method that repeatedly updates a candidate causal graph while enforcing acyclicity. We explicitly construct a fixed-weight transformer whose forward pass exactly reproduces one update of this method, so repeated blocks reproduce its optimization trajectory. The transformer carries the current graph and the algorithm's multiplier between updates. We show that retaining the multiplier is essential for exact execution, since different multiplier values can lead to different next updates. We also give conditions under which, within a fixed stage, the number of updates needed to reach a target accuracy can be computed in advance and rounding errors stay bounded as depth grows. Experiments show that the constructed block agrees with a reference update to floating-point precision, while arithmetic replay on synthetic data and seven published benchmark network topologies inherits the reference solver's successes and failures. This separates accurate algorithm execution from accurate causal recovery. In contrast, the ordinary attention models tested under our training budgets do not reliably execute the update or transfer to larger graphs. Whether gradient training can learn an executor in the architecture class of the construction remains open.

Kernels encode the inductive bias of a wide range of machine learning models, yet automated kernel design faces a fundamental dilemma. A fixed grammar of base kernels and operators guarantees validity but limits the search to structures expressible by those building blocks. Conversely, unrestricted programs remove this limitation but no longer guarantee validity. In our stress tests, 22-58% of LLM-generated kernels that pass numerical checks on random inputs fail when evaluated at different scales or dimensions. We propose Kernel Autoresearch (Kernaut), which treats kernel design as open-ended model discovery. Coding agents write kernels as programs, while construction contracts ensure that every accepted kernel is valid. A quality-diversity archive retains high-performing kernels with distinct behaviors, and novelty screening steers agents toward functionally new candidates. Our experiments demonstrate that the discovered kernels encode reusable inductive biases that generalize to unseen tasks. On held-out black-box optimization families, a discovered kernel outperforms a meta-learned deep kernel trained on the same episodes. Furthermore, kernels discovered from ten enzyme-kinetic rate laws achieve lower error than tuned ARD and deep kernel baselines on five unseen mechanisms. The discovered kernels are also interpretable programs that human researchers can refine: a human-refined version of one further reduces the held-out predictive error by 5.7% and optimization regret by 7.8%.

Models can be retrained as new data arrive, but deploying every new version risks replacing a good policy with a worse one. We study how to plan policy updates (i.e., meta-policy) before future candidates are trained, balancing the benefits of improvement against the risk of performance regression. Our offline meta-policy maximizes expected cumulative value subject to a budget on the expected number of updates that perform worse than the policies they replace. We estimate the value and risk of possible switches from historical learning trajectories, represent an update schedule as a path in a directed acyclic graph, and select a schedule using dynamic programming. A leading-order analysis identifies the signal-to-noise ratio of policy improvement as a key driver of update frequency, waiting times, and risk allocation: clearer improvements support earlier, more frequent updates, while noisier improvements call for longer waits or greater risk expenditure. Their asymptotic rates also reveal a diminishing marginal cost of achieving greater safety over time. Experiments on synthetic and clinical trial data illustrate the performance–risk tradeoff and compare our method with alternative baselines.

The Cherenkov Telescope Array Observatory (CTAO) marks the next generation of Imaging Atmospheric Cherenkov Telescopes (IACTs), offering a sensitivity improvement of up to a factor of 10 over current instruments. Its first prototype, the Large-Sized Telescope (LST-1), is already in operation at the Roque de los Muchachos Observatory in La Palma, Spain. Deep learning methods have shown significant promise in reconstructing key properties of incident particles, such as energy, arrival direction, and type, using simulated data. Unlike traditional approaches that rely on simplified image shape parameters, deep learning can exploit the full temporal and charge information of the recorded events, providing enhanced performance, particularly at low energies (~20 GeV) accessible by LST-1. This capability is especially valuable for observing distant extragalactic sources like Active Galactic Nuclei, which are key to probing fundamental physics and cosmology. In this work, by producing sensitivity curves, we evaluate the performance of GammaLearn, a deep learning framework tailored for IACT data analysis, by comparing it to the standard analysis used with LST-1 and applying it to real observational data from LST-1.

End-to-end multi-object trackers have narrowed the gap with classical tracking-by-detection on association-difficult benchmarks. Yet they still make spatially implausible errors no classical tracker would, such as assigning one identity to objects on opposite sides of the frame. A model could learn to avoid them, but tracking annotations are scarce, so we encode spatial priors explicitly instead, while keeping inference fully end-to-end with no post-hoc association. We propose three spatial priors, at the data, loss, and representation stages. Spatial ID Switches bias trajectory permutations toward spatially overlapping objects, reducing the mismatch between training and inference confusions. Spatial ID Loss scales each identity's penalty by its box distance, so a distant switch costs more than a nearby one. Spatial Anchor gives each track token its frame position, an explicit spatial cue for attention. We instantiate the three priors in MOTIP2, a tracker adapted from MOTIP and built on the real-time DEIM detection transformer. Trained without extra data, its main model, MOTIP2-L, sets a new state of the art: 73.4 HOTA on DanceTrack, 76.0 on SportsMOT, and 71.1 IDF1 on PersonPath22. MOTIP2 is a family of models spanning the speed-accuracy trade-off: a lighter model, MOTIP2-S, matches the original MOTIP at over 3x the speed, and MOTIP2-X reaches 74.8 HOTA on DanceTrack.

Vision-language-action~(VLA) models have emerged as a promising paradigm for autonomous driving. However, existing VLA models still suffer from a fundamental mismatch: driving actions require precise 3D geometric cues, while visual-language understanding and reasoning are largely conducted in a 2D semantic space. In this paper, we propose GeoCoTDrive, an explicit geometric chain-of-thought framework that grounds geometry in a planning-oriented manner. GeoCoTDrive follows a think with 2D first, drive with dedicated 3D priors paradigm. It first grounds 2D regions corresponding to decision-critical cues, and then retrieves localized 3D priors by sampling features from a geometric foundation model within the grounded regions. These localized geometric features are interleaved into the autoregressive context to support the trajectory generation. To supervise this process, we introduce planning-relevant grounding, a new region-level grounding task that focuses on local spatial cues directly affecting ego planning decisions, and construct the PlanningGrounding dataset to endow VLAs with planning-oriented grounding capability. Experiments across multiple end-to-end autonomous driving benchmarks show that GeoCoTDrive consistently improves safety-critical planning performance, demonstrating the effectiveness of the explicit geometric chain-of-thought process for VLA-based planning.

Rényi entropy estimation has been comprehensively investigated by Acharya, Orlitsky, Suresh and Tyagi (SODA 2015; IEEE Trans. Inf. Theory 2017) and consequent works, whereas only the sample complexity of Rényi entropy estimation of integer order has been settled. In this paper, we settle the sample complexity of Rényi entropy estimation of noninteger order, thereby completing the complexity picture of Rényi entropy estimation. Specifically, we show that for any noninteger $\alpha > 0$, it is sufficient and necessary to use \[ \Theta\!\left(\frac{d^{\max\{1/\alpha,1\}}}{\varepsilon^{1/\alpha}\log(d)} + \frac{d^{|1-1/\alpha|}}{\varepsilon^2}\right) \] samples to estimate the Rényi entropy of order $\alpha$ of an unknown discrete distribution over an alphabet of size $d$ to within additive error $\varepsilon$. For the upper bound, we reduce the bias using a refined polynomial approximation estimator for large probabilities. For the lower bound, we employ a different hard instance equipped with a new moment matching construction. The constructive moment matching has constant bounded high-order moments, while attaining a fixed ratio between the $\alpha$-th moments, which is of independent interest.

Recent advances in multimodal foundation models have made them capable generalist physical agents for a range of manipulation tasks. However, successful operation in an unfamiliar environment may require an agent to seek task-relevant information through interaction when it is absent from the observations: it may need to determine where a relevant object is, inspect an unobserved property, or discover the effect of an unfamiliar tool. We thus introduce RoboQuest, a benchmark for goal-directed embodied exploration, where agents must actively acquire task-relevant information through physical interaction, use the resulting evidence to adapt subsequent actions, and autonomously decide when to commit to task completion. RoboQuest comprises ten mobile manipulation tasks centered on three forms of uncertainty: search, manipulation-based inspection, and interactive testing. We evaluate five frontier multimodal agents through a common visuomotor interface, as well as a $\pi_{0.5}$ policy fine-tuned on the full-episode demonstrations we release. The best agent succeeds in only 23% of the episodes, and the fine-tuned policy almost never succeeds. Isolated tests of the execution skills the tasks are built from, with the hidden information supplied, show that the agents can carry out most of the required actions, and our failure analysis attributes only a minority of the failures to execution. Our failure analysis further finds that the agents often stop exploring too early as they make decisions before observing the required evidence for task completion. We also find that agents rarely prevent or repair the disturbances caused by their exploration. Moreover, learning by trial and error remains difficult for most models.

In robotics, scene representation plays a pivotal role in understanding and interacting with the environment. The advent of Neural Radiance Fields (NeRF) and its variants, as a novel representation, has opened a new frontier of research. In applications such as semantic mapping and simulation, roboticists aim to build scenes using multiple NeRF models, each representing an object. While extensive datasets of 3D mesh models already exist, there is an urgent need to develop tools to convert these assets to NeRF models for rapid algorithm development and testing. This paper presents a new pipeline for converting existing mesh models to NeRF representations by artificially generating a ground truth point-based radiance field through sampling mesh geometry and texture. This approach alleviates the need for camera-based sampling or rendering multi-view images of the original mesh to train the NeRF model. Extensive benchmarking demonstrates that our method yields comparable rendering quality to the baselines. Additionally, the application of this representation is shown by constructing unified NeRF scenes and performing collision simulations with extracted geometry.

Modern large-scale systems rely on distributed protocols to maximize efficiency while preserving the correctness guarantees of single-process execution. However, designing such protocols is non-trivial: adding resources to a system inherently increases its complexity, which in turn introduces faults that must be addressed during design. One such fault class, arising in systems that use distributed shared memory (e.g., replicated databases), is consistency violating fault (cvf), a fault in which a process accessing shared memory reads stale data previously written by another process. Cvfs are inherent to systems that prioritize availability over strict consistency. Prior work has shown that self-stabilizing programs remain correct under high availability, provided such faults stay within a tolerable bound. Characterizing the behavior of self-stabilizing programs in the presence of cvfs can therefore help system designers build systems that are both correct and efficient. In this paper, we study self-stabilizing programs under cvfs to understand when and where such faults occur, enabling runtime measures that improve computational efficiency. Since exhaustive state-space exploration does not scale, it suffers from state-space explosion; our study investigates two complementary approaches: a conflict-based state-space exploration technique for monotonically stabilizing $({\Delta} + 1)$-Graph Coloring programs, and a machine-learning-based approach for a Maximal Independent Set program. We propose a conflicting-edges-based state-space exploration algorithm alongside a rigorously validated ML model, evaluated on an out-of-distribution dataset through structural consistency checks against known graph invariants.

Embedding tables are among the largest components of modern language models. Most compression methods fix a coding geometry such as coordinate blocks, low-rank subspaces, or unrestricted codebooks, and optimize within it. We instead ask whether the coding geometry can itself be discovered. We introduce OrBIT, a structure-guided embedding compression framework that learns reusable local geometry from orbit dynamics and uses it to constrain a small set of shared codewords. The global reconstruction residual then decides where the fixed coding budget is spent, while redundant overlapping charts let local errors compensate one another after gluing. Our theory shows how tight-chart geometry controls distortion, how the global residual directs sequential allocation, and how data-geometry-guided refinement improves the codec. The resulting orbit machinery is compiled away, leaving a compact decoder in which the learned structure governs what is stored, where capacity is allocated, and how local information is assembled globally. Across four LLM embedding tables, OrBIT achieves $37.9\times$ compression on GPT-2 and over $23\times$ on each 7B table relative to 16-bit storage, while delivering competitive rate-distortion performance against established quantization and low-rank baselines.

Tactile feedback provides embodied agents with physical information beyond visual observations, enabling more reliable interaction with the real world. However, despite the rapid progress of vision-tactile-language-action (VTLA) policies, there remains a lack of unified benchmarks for evaluating tactile-enabled robot manipulation across simulation and the real world. To address this gap, we introduce OpenViTac, a visuo-tactile manipulation benchmark for evaluating robot policies across simulation and the real world. OpenViTac organizes contact-rich manipulation into four tactile-relevant capability dimensions and provides paired simulation-real-world settings for consistent evaluation of VLA, WAM, and VTLA policies. Building upon this benchmark, we investigate how different tactile representations and integration strategies affect the performance of pretrained VLA models. Correspondingly, we introduce OpenVTLA, a tactile augmentation framework that combines the best-performing representation and integration strategy. Furthermore, we leverage the paired benchmark setting to study sim-real co-training and analyze factors affecting cross-domain policy learning. Together, OpenViTac provides a unified platform for evaluating and advancing visuo-tactile robot manipulation.

Boosting converts weak hypotheses with a small edge over random guessing into highly accurate predictors, but the expressive power of the resulting classifier can depend strongly on the structure of the base class. We study this phenomenon through the $\gamma$-VC dimension introduced by Alon et al. (STOC 2021). Our first result shows that this parameter characterizes the sample complexity for weak-to-strong learning up to a constant factor scaling in $\gamma$. We then sharpen the general relationship between the classic VC dimension and the $\gamma$-VC dimension. Finally, we also give improved upper and lower bounds on the $\gamma$-VC dimension for the fundamental concept classes of decision stumps and axis-parallel rectangles in $\mathbb{R}^d$.

Predictive mapping can support robotic exploration and navigation by estimating unseen geometric layouts from partial occupancy observations. However, occupancy-only representations may fail to distinguish semantically different structures with similar geometry. This is particularly relevant for indoor doors, which may appear as occupied cells like walls but indicate possible connected rooms or corridors beyond the observed region. This work investigates whether semantic door cues improve predictive geometric occupancy mapping around such ambiguous regions. We modify a subset of the CogniPlan dataset by inserting door-induced ambiguities into partial occupancy maps while keeping the ground-truth layouts unchanged. We compare a geometry-only control model with a semantic-cued model trained on the same modified dataset, where the semantic-cued model receives an additional door channel. Evaluation uses L1 error, F1 score, and Intersection over Union (IoU) over both the full map and a 10-pixel door-region mask. Full-map performance remains broadly similar between models, but localized door-region results show a clear qualitative improvement: L1 decreases from 0.004342 to 0.000025, while F1 and IoU improve from 0.031311 and 0.015905 to 1.000000 and 1.000000, respectively. These results suggest that semantic cues can improve predictive occupancy completion in regions where geometric observations alone are ambiguous.

Looped Transformers improve parameter efficiency by repeatedly applying shared Transformer blocks over multiple recurrent loops, increasing computational depth without increasing the parameter count. However, KV cache memory still scales with the number of loops, becoming a key memory bottleneck that limits batch size and inference throughput. KV cache quantization can alleviate this bottleneck, but existing methods often suffer substantial accuracy degradation at aggressive low-precision regimes. We observe that looped Transformers offer a unique opportunity: KV states across loops are highly similar. Based on this observation, we propose ResidualQuant, which uses the final-loop KV states as a reference and represents the remaining loops with low-precision residuals. Our method further combines least-square scaling and rotations applied to the residuals, as well as loop-wise mixed precision, to enable accurate quantization down to INT2 while retaining efficient reconstruction. Across multiple looped Transformer models and mathematical reasoning and code generation benchmarks, ResidualQuant consistently improves the accuracy-memory tradeoff over state-of-the-art rotation-based KV quantization. In particular, our method retains accuracy close to BF16 under mixed-precision settings while reducing theoretical KV storage by 80.7%, achieving up to 13.0% higher accuracy than the rotation-based baseline at the same memory budget. On an RTX 5090, the reduced KV memory traffic improves fixed-batch decode throughput by up to 2.73x, while the smaller memory footprint enables up to 2x larger batches, improving peak throughput by up to 4.15x.

How large of a minimum degree does an $n$-vertex graph need before we are sure that it contains a perfect matching? Dirac's theorem states that a graph on an even number of vertices in which each vertex has degree at least $n/2$ has this property. In this short expository note, intended to be used in the classroom, we discuss how this statement generalizes to hypergraphs. In particular, we highlight an elegant connection between fractional perfect matchings in hypergraphs and a probabilistic inequality about nonnegative random variables, which was conjectured by Feige. We also present a very short self-contained proof of Feige's conjecture.

Continual learning requires models to adapt to new domains and new classes while retaining prior knowledge. Many existing methods rely on continued optimization, using regularization, replay, or parameter expansion to prevent new updates from overwriting previously learned knowledge. Instead, we propose replacing continual training with continual inference: a PFN-based model that is meta-trained, and then frozen, adapting to new classes only by extending an in-context evidence set. Our model, Latent Concept PFN, performs in-context Bayesian inference over a latent concept space that captures semantic structure shared across domains and classes. As each new domain or class arrives, exemplars are added to the memory; adaptation reflects updated posterior beliefs over latent concepts rather than gradient updates. No parameters are changed, reducing forgetting. The same method handles both domain and class incremental continual learning without task identity. Concept annotations are only used during meta-training, acting as a soft anchor on the latent space rather than a fixed bottleneck. Unlike fixed-vocabulary concept methods, the model also handles noisy, ambiguous, or incomplete annotations by combining concept labels with raw input evidence to discover distinctions beyond the predefined concept set. Experiments on class and domain incremental learning datasets demonstrate competitive continual learning performance while learning interpretable latent concepts.

Document-level text simplification involves transformations that go beyond sentence-internal edits, addressing discourse coherence, anaphora resolution, and cross-paragraph consistency. Despite advances in sentence-level simplification for high-resource languages, document-level simplification in morphologically rich, low-resource languages such as Estonian remains largely unexplored. This study presents a comprehensive evaluation of five state-of-the-art multilingual large language models (LLMs) for document-level simplification in Estonian. Three prompting strategies are examined: single-pass generation, pipeline-based modular agents, and guideline-augmented pipelines. The evaluation framework integrates automatic metrics assessing readability, semantic preservation, and discourse coherence, alongside a structured manual annotation protocol. The findings indicate that Gemini-2.0 and LLaMA-3.3 produce outputs with near-native fluency and strong meaning preservation, whereas other models display notable grammatical and semantic limitations. This work contributes novel document-level coherence metrics, evidence-based prompting strategies, and publicly available resources for reproducibility.

In this paper, we introduce the crystallization $C(SO_0(2n+1)/SO_0(2n-1))$ of the $C^*$-algebra $C(SO_q(2n+1)/SO_q(2n-1))$. We show that every irreducible representation of $C(SO_0(2n+1)/SO_0(2n-1))$ arises as the limit, as $q \to 0^+$, of a family of irreducible representations of $C(SO_q(2n+1)/SO_q(2n-1))$. As a consequence, we prove that $C(SO_0(2n+1)/SO_0(2n-1))$ is the universal $C^*$-algebra generated by a finite set of generators and relations. We then construct a chain of unital essential short exact sequences of $C^*$-algebras, enabling us to compute the $K$-groups of $C(SO_0(2n+1)/SO_0(2n-1))$ and determine explicit generators for them. Using the theory of homogeneous $C^*$-extensions, we prove that $C(SO_0(2n+1)/SO_0(2n-1))$ is isomorphic to $C(SO_q(2n+1)/SO_q(2n-1))$ for every $q \in (0,1)$.

Pseudospin-1 Dirac systems exhibit unique physics distinct from conventional Dirac cones, such as flat-band crossings and non-Abelian characteristics, yet their topological transport properties have remained largely untapped in passive, time-reversal-invariant settings. Here we uncover an in-plane polarity of the Berry-curvature texture in a pseudospin-1 Dirac Hamiltonian, a previously unexplored geometric degree of freedom encoded in the sign-resolved distribution of Berry curvature despite zero net Berry flux, and reveal a new mechanics where Berry curvature induce pseudospin Hall behaviors in a system. We show that the oriented coupling between this momentum-space polarity and a real-space mass gradient governs a geometric selection rule that dictates the emergence of gapless pseudospin Hall modes. By engineering the intracell couplings of a four-site planar lattice, we independently program the Berry-curvature polarity and the spatial mass gradient without altering the host lattice symmetry. Acoustic experiments directly confirm this directional selection rule: reversing the mass gradient closes or reopens the dispersive gap, while pseudospin-selective source excitation launches counterpropagating pseudospin branches along arbitrary prescribed axes. Our work establishes quantum geometric polarity as a versatile tool for reconfigurable wave routing, sensing, and high-capacity quantum applications.