Papers

Spatial reasoning benchmarks evaluate vision-language models across diverse tasks, but task-level scores do not reveal which underlying capabilities account for success or failure. Each task requires recovering spatial evidence, representing geometry, and reasoning over it. We disentangle these capabilities by comparing predicted and ground-truth spatial context under a shared schema and coordinate contract. This comparison reveals four recurring sources of error: inaccurate perception, missing information in the spatial context, selection of the wrong measurement, and errors in reference frames or in tracking position and orientation. Guided by this diagnosis, we develop CROSS, a training-free library of typed geometric operators and spatial skills that function over available evidence to support reliable video spatial reasoning. The resulting library supplies verified context to non-coding VLMs or callable skills to a SpatialClaw agent. We evaluate \methodname{} on five benchmarks. \methodname{} raises the average score from 55.9% to 60.2% on ReVSI and improves the SpatialClaw result from 62.8% to 66.3% on DSI-Bench. These gains demonstrate that explicit handling of spatial conventions can repair systematic reasoning failures without additional training.

We improve the error term in the prime geodesic theorem for the modular group. More generally, our result applies to any congruence subgroup of any indefinite quaternion algebra over $\mathbb{Q}$.

An ideal tournament is both efficacious and attractive: it selects the best player as the winner, but only at the end of the tournament in order to maintain suspense as long as possible. We identify and explore the trade-off between these criteria in Swiss-system chess team tournaments via simulations. Organising more rounds is shown to improve efficacy but increase the probability of a stakeless last round. The 2008 reform in the Chess Olympiad ranking is found to be a questionable move, as the previous rule based on board points determines the efficacy-competitiveness frontier, regardless of whether two or three points are awarded for winning a match. Combining board points and match points is better than using match points only. Our results can help optimise the design of the Swiss system, which, besides chess, is also widely used in e-sports.

Building on our classification of shape-Wilf-equivalence classes for triples of patterns of length three, we complete the classification for quadruples and quintuples. The larger pattern sets exhibit structural features that are not captured by the encoding methods used for triples and require additional combinatorial tools. Our main new ingredient is a Dyck-path approach to Ferrers boards containing the staircase board. By introducing distinguished cells and related structural parameters on the associated Dyck paths, we obtain new shape-Wilf-equivalences and, for several classes, explicit formulas for the number of avoiding transversals on a fixed Ferrers board. We further study the corresponding pattern-avoiding perfect matchings through the pattern-preserving bijection of Bloom and Elizalde. Besides deriving recurrence relations, we give bijective interpretations of several matching enumeration sequences in terms of grand Dyck paths, Schröder paths, and Dyck paths. These constructions provide additional combinatorial structure beyond the classification itself. Together with the companion paper on triples, the present work completes the classification of shape-Wilf-equivalence classes for subsets of patterns of length three, apart from the trivial empty and full pattern sets.

AI systems increasingly produce outputs from confidential data, such as a fitness-for-duty assessment from medical records or the predicted properties of a drug candidate from its secret structure. It is important to verify that such outputs are correct without revealing the underlying data. A recent line of work studies verification of AI outputs via interactive proofs and debate for oracle-aided computation, where correctness may depend on an oracle such as human judgment, a physical experiment, or the web. These works focus on verification by a verifier that runs much faster than the computation. However, such efficient verification is impossible for general oracle-aided computation, and these works therefore rely on additional assumptions. We focus instead on privacy: allowing the verifier to run in time polynomial in the computation, we ask whether interactive arguments for oracle-aided computation can be zero knowledge, so that the verifier learns nothing about the confidential data beyond the correctness of the output. We prove that, in general, they cannot. In the random oracle model, there are no zero-knowledge proofs for all oracle-aided computations, even if both the prover and the verifier are allowed to run much longer than the computation itself. The impossibility extends to debate, a canonical model for scalable oversight. On the positive side, we show that if the oracle attaches a cryptographic signature to each of its answers, then every oracle-aided computation can be verified in zero knowledge with an efficient prover and verifier, assuming only collision-resistant hash functions. Beyond privacy, this also gives an alternative approach to scalable oversight that relies neither on an honest opponent, as in debate, nor on the robustness of the computation, as in prior single-prover protocols.

Wildfires pose severe risks to human life, ecosystems, and property. This study presents a machine learning approach for wildfire detection from GOES ABI imagery. A CatBoost model was trained on a large dataset with thousands of ABI images and over 300,000 matching VIIRS fire detections. An evaluation on a separate dataset across five regions showed that the learned CatBoost model outperformed the operational GOES Fire Detection and Characterization (FDC) product. It achieved higher precision, recall, and F1 scores both within and outside the training area. The CatBoost model achieved F1 scores that were 0.16 to 0.38 higher than the GOES FDC in all regions. In addition, out of 51 historical fire events, the CatBoost detected 26 fires before both VIIRS and GOES FDC, compared to only six earlier detections by the GOES FDC. Importantly, the CatBoost model achieved accurate wildfire detection also during nighttime, whereas the GOES FDC obtained very low recall values, around 0.03. This study demonstrates that machine learning models may offer significant improvements over existing geostationary fire products, including higher accuracy, fewer false alarms, and earlier detection.

We study online bipartite matching with unit-inventory reusable resources, where requests arrive in an adversarially fixed order, and each use of a resource makes it unavailable for an independent duration drawn from a resource-dependent distribution. The benchmark knows all requests in advance but cannot observe a duration before choosing the corresponding use. The classical Ranking algorithm of Karp, Vazirani, and Vazirani (STOC 1990) fixes a uniformly random priority order of the resources and matches each arriving request to its highest-priority available neighbor. It achieves the optimal competitive ratio $1-1/e$ for unweighted nonreusable resources, but whether it beats $1/2$ for reusable resources has remained open. We prove that, for unweighted resources with resource-dependent stochastic durations, Ranking achieves a competitive ratio of $(5-2\sqrt3)/3\approx0.511966$. We also give a black-box reduction from unweighted Ranking to resource-weighted matching: any unweighted competitive ratio $\alpha>1/2$ yields a weighted ratio strictly above $1/2$. With independent sampling access to the duration distributions, the reduction gives a weighted ratio of $0.500034$. These results resolve two questions left open by Delong et al. (MOR 2024): whether Ranking beats $1/2$, and whether one can beat $1/2$ under stochastic durations. We analyze Ranking resource by resource, rather than request by request. For deterministic durations, this gives a reduction to random-order greedy for a coverage function. We then extend the analysis to stochastic durations by comparing the residual schedules of Ranking and a greedy algorithm, and apply a finer analysis of the random ranks to obtain the stated $0.511$ bound. For the weighted reduction, we apply Ranking within groups of similar weights and uses weighted greedy to control the loss between groups.

Knill-Laflamme coefficients characterize exact quantum error detection through scalar compressions of error operators to the code space. For prescribed Pauli observables and a fixed code dimension, attainable coefficient vectors form a joint higher-rank numerical range, whose Euclidean norm image is the signature spectrum. We study how operator representation, code dimension, and detection constraints govern this geometry. Our main theorem identifies representation multiplicity as sufficient to lift active expectation data to exact scalar compressions: a lift exists whenever each occupied block has multiplicity at least the code dimension times the rank of the corresponding active state. When multiplicity suffices to realize all active states, the coefficient range is the full active expectation body and is therefore convex and connected, with a closed interval as its signature spectrum. This framework unifies commuting Pauli families, where sufficient common-eigenspace degeneracy yields polytopes, and subsystem stabilizer codes, where protected logical subsystems supply multiplicity spaces for noncommuting gauge observables. Explicit examples show how increasing the code dimension can make a range shrink, collapse, or become empty, while increasing multiplicity can turn a Bloch sphere into a filled ball. In the subsystem setting, parent-Hamiltonian constructions realize exact detecting codes as degenerate ground spaces, selecting distinguished vectors and continuous paths within these ranges. A final three-qubit example shows additional noncommuting detection constraints reduce a tetrahedral range to its barycenter and four vertices, producing a disconnected signature spectrum. The results provide a structural framework for Knill-Laflamme coefficient geometry and motivate sharper criteria for connected coefficient ranges and interval signature spectra under structured error models.

We investigate how dark matter (DM) admixture modifies the conformal properties and phase structure of dense neutron-star matter within a self-consistent single-fluid framework, with the global DM fraction $F_\chi=N_\chi/N_B$ fixing the local relation $n_\chi=F_\chi n_B$. We derive an exact decomposition of the total trace anomaly, $\Delta_{\rm tot}$, into microscopic contributions. For collider-motivated Higgs-portal benchmarks, explicit Higgs, vector-mediator, and contact-interaction contributions are negligible, while heavy nonrelativistic DM has an intrinsic trace anomaly close to the nonrelativistic limit, $\Delta_\chi\simeq1/3$. Consequently, the DM rest-mass energy fraction dominates the DM-induced modification of $\Delta_{\rm tot}$, producing a smooth upward shift of up to $\sim0.1$ for $F_\chi\sim0.2\%$. In the pressureless, comoving heavy-WIMP regime, we further identify a universal dark-sector scaling governed by the mass-loading parameter $\lambda=F_\chi m_\chi/m_N$: numerical calculations with different $(F_\chi,m_\chi)$ pairs at fixed $\lambda$ exhibit overlapping trace-anomaly, sound-speed, and mass–radius responses for a given baryonic equation of state. In hybrid stars, DM leaves the coexistence pressure and chemical potential essentially unchanged, whereas first-order hadron–quark deconfinement produces sharp discontinuities in the squared sound speed $c_s^2$, $\Delta_{\rm tot}$, and $\Delta_{\rm tot}-\Delta_B$. The combined softening substantially reduces the maximum stellar mass, placing $F_\chi\sim0.2\%$ in tension with the observed $2\,M_\odot$ neutron stars. These results show that the trace anomaly and its density evolution provide a sensitive diagnostic for distinguishing smooth DM-induced modifications of dense matter from genuine first-order deconfinement.

Pyrite-type mineral hauerite MnS$_2$ is a magnetic insulator with localized $S=\frac52$ moments. Below 48 K, it develops a collinear antiferromagnetic order, accompanied by unit-cell doubling and breaking the inversion symmetry. We demonstrate that the latter gives rise to a ferroelectric polarization of up to 360 $\mu$C/m$^2$ rendering MnS$_2$ a type-II multiferroic. Microscopically, the electronic polarization originates from S$_2$ dimers that acquire a dipole moment induced by the frustrated magnetic ordering of neighboring Mn sites. We show that time-reversal symmetry leaves ferroelectric domains intact, and that domain switching necessitates overcoming a high energy barrier set by the magnetic exchange energy scale.

Concept erasure removes copyright-protected, privacy-sensitive, or otherwise undesirable concepts from pretrained text-to-image diffusion models to support content governance and compliance. As erasure requests arrive over time, models must remove new targets without undoing prior erasures. Existing methods do not constrain interference across edits: residual perturbations outside the retain set interact and accumulate, degrading unrelated generations and sometimes collapsing previously erased targets into noise. We propose CEASE (Continual Erasure via Adaptive Subspace Editing), a training-free method that imposes two subspace constraints on a closed-form solver. CEASE adds the token representation of the shared replacement to the solver's invariance matrix and, when interference is detected, projects the current update onto the orthogonal complement of dominant output directions extracted from cumulative past updates. A closed-form decomposition attributes the accumulated interference to repeated activation of the shared replacement and overlap between successive update directions, showing that the two constraints suppress these respective sources. Across continual erasure of celebrities, artistic styles, and instances, CEASE achieves the most consistent erase-preserve trade-off, while existing methods either degrade general generation or insufficiently erase targets.

We develop a gauge-invariant effective field theory for scalar glueball interactions based on the Yang-Mills gluon condensate. Starting from a coherent-state formulation of the Yang-Mills vacuum, we derive an effective Lagrangian for the scalar glueball and its interactions with gluons. The resulting crossing-symmetric amputated four-gluon Green's function is projected onto the color-singlet $J^{PC}=0^{++}$ channel, yielding a normalized scalar glueball form factor that factorizes into universal kinematic structures and an intrinsic glueball function. The formalism predicts a parameter-free effective interaction radius for the ground-state scalar glueball with resonance $f_0(1710)$, $r_{\rm int}=\sqrt{6}/m_\phi=0.28$ fm, which is in excellent agreement with recent lattice Yang-Mills determinations of the mass-radius ($r=0.263(31)$ fm). The predicted momentum dependence of the normalized form factor is consistent with lattice Yang-Mills gravitational form factor data, with the $f_0(1710)$ candidate providing the best overall fit and $r_{\rm int}$. Inclusion of the first excited $0^{++}$ glueball produces modest corrections to the interaction radius ($r_{\rm int}^*=0.240$ fm) while yielding stable and kinematically robust modifications of the form factor. This framework provides a systematic bridge between effective field theory and first-principles lattice Yang-Mills calculations of scalar glueball dynamics.

Many quantum systems are believed to thermalize slowly at low temperatures due to the existence of metastable phases. However, there are cases where further cooling can restore polynomial-time thermalization: we demonstrate that the Davies dynamics of the mean-field interchange model with local dimension $d\geq 3$ and single-site generalized Pauli couplings exhibits this behavior. The dynamical phase diagram is beholden to two distinguished inverse temperatures, $\beta_{\mathrm{min}}(d)$ and $\beta=d$, with the static first-order phase transition lying between them. At low and high temperatures surrounding the interval $(\beta_{\mathrm{min}}(d),d)$, the spectral gap of the Davies generator is bounded below by an inverse polynomial in system size $n$. Meanwhile, in this interval, the gap vanishes exponentially in $n$, indicating metastability. The proof uses Schur-Weyl duality to decompose the Davies generator into a classical Markov generator on Young diagrams, and the restriction to the remaining symmetry sectors whose gap is $\Omega(n^{-1})$. Thus, exponential slowdown arises entirely from the Young diagram chain.

We prove an interior Lipschitz estimate with a sharp height threshold for continuous viscosity solutions of the three-dimensional special Lagrangian equation with subcritical phase $|\Theta|<\pi/2$. If \[ osc_{B_R}u\leq MR^2,\qquad 0\leq M<\sec\Theta, \] then $Lip_{B_{\rho R}}u\leq CR$ for some $\rho>0$ and $C>0$ depending only on $|\Theta|$ and $M$. The threshold is optimal: at $M=\sec\Theta$, there are entire real-analytic solutions whose Lipschitz seminorms are unbounded on every fixed interior ball. The proof uses a two-point maximum principle and algebraic identities specific to dimension three.

Environmental robotic sampling requires considering the dual influence of water currents on robotic motion and particle transport. Existing marine robotics simulators generally model flow, autonomy, and sampling targets separately, limiting joint evaluation of mission cost and sampling performance. H-SPAR integrates spatially and temporally varying velocity fields, Lagrangian particle transport, probabilistic sampling, and ROS 2/Gazebo-based uncrewed surface vehicle (USV) autonomy. In this work, shared precomputed flow fields drive particle advection and current-induced forces during closed-loop vehicle execution. Path-planning experiments show that the existing current-aware planner SVF-RRT* achieves 69.4% lower upstream cost than conventional RRT* at the planning level, but this reduction falls to 41.7% during execution under time-varying currents, reflecting temporal flow variation, vehicle motion constraints, and path deviation omitted during planning. Coverage experiments show that sweep orientation changes the particle-sampling rate by up to 22.2% under the complete H-SPAR configuration. These findings highlight the importance of evaluating planning, vehicle execution, particle transport, and sampling together under consistent hydrodynamic conditions. The project webpage is available at https://sites.google.com/view/h-spar, and the open-source code is available on GitHub at https://github.com/naviiidz/h-spar-sim.

Byte-level byte-pair encoding (BBPE) tokenizers are attractive for multilingual large language models (LLMs) because they cover all Unicode text. In UTF-8-based BBPE, however, many scripts start from a higher fallback cost than English: when no learned merges can be applied, a multibyte character requires multiple byte-derived symbols. We call this worst-case pre-merge cost the encoding floor. A higher floor can increase token counts and per-request cost and shrink usable context. Changing the text encoding can reduce this gap, but a single global encoding can make already-efficient English spans more expensive in mixed-script text. We propose Universal Byte-Level Encoding (UBE), a dual-alphabet tokenizer that keeps 1-2-byte UTF-8 characters on the UTF-8 path while routing 3-4-byte UTF-8 characters through UTF-16. This lowers the encoding floor for 3-byte Basic Multilingual Plane (BMP) characters in scripts with high token premiums (token counts relative to English) without raising it for already-efficient spans in mixed-script text. UBE changes only the byte representation presented to byte-pair encoding (BPE); the merge rule remains standard, and exact decoding is preserved. UBE also composes with alternative boundary policies and morphology-based representations. In a Unicode 17 audit, UBE exactly round-trips all Unicode scalar values and all inputs in the official normalization, grapheme-break, and emoji test suites. Across intrinsic evaluations, UBE lowers dispersion in English-normalized token-count ratios, reducing cross-lingual token-budget disparity. In multilingual language model (LM) experiments, UBE matches BBPE's LM quality. In the main multilingual settings, UBE reduces token counts most for high-premium scripts and slightly lowers English token counts, yielding more usable context under fixed token budgets and faster prompt processing in content-matched benchmarks.

Relativistic jets from AGN are expected to propagate through an inhomogeneous ISM, but the role of small-scale gas inhomogeneities in shaping their early evolution remains uncertain. We investigate this problem using 3D special-relativistic magnetohydrodynamic simulations with PLUTO, following a jet with a Lorentz factor of 10 propagating through a pc-scale medium. We compare a homogeneous ambient medium with two clumpy ambient-medium models, motivated by dense gas in the nuclear ISM, in which clouds occupy volume filling factors of $0.1$ and $1$ per cent. We compute synthetic synchrotron maps and spectra from Lagrangian macro-particles that have been accelerated by diffusive shock acceleration. Jet-cloud interactions deflect the flow, enhance shock formation, and produce a more asymmetric cocoon than in the homogeneous ISM case. Altogether, this results in a substantially stronger mass loading: the entrained mass increases from $0.43$ M$_{\odot}$ in the homogeneous run to $5.3$ and $8.8$ M$_{\odot}$ in the clumpy runs. The clumpy ISM also modifies the turbulence and the material mixing within the jet cocoon. The dynamical differences we find translate into brighter and more irregular synchrotron emission. For the same injected jet, the models with a clumpy medium produce stronger frequency-integrated synchrotron emission than the homogeneous run, with the largest differences in the SED occurring from the sub-mm to the infrared/optical bands. Our results demonstrate that including a small-scale ISM structure provides a more complete description of the early dynamical evolution of young AGN jets and their radiative properties.

We develop a method for proving matrix concentration inequalities by identifying random matrices with associated deterministic operators acting on suitable Fock spaces and controlling norms of these operators and their restrictions to low-order subspaces. Applying this method, we obtain new strengthenings of the non-commutative Khintchine inequality that improve on the state of the art, in particular sharpening recent inequalities due to Bandeira, Boedihardjo, and van Handel (2023) quantifying intrinsic freeness of random matrices. Our proofs of these results are based on relatively simple operator algebra arguments and involve neither Gaussian interpolation nor explicit combinatorics of tracial moments. Further, our techniques apply equally well to several models of non-commutative random variables of interest in the literature, such as operator series constructed from $q$-Gaussian and $\Gamma$-independent systems of operators, treating all of these objects with the same method. We obtain new norm bounds for such operators both in the style of the non-commutative Khintchine inequality and in the style of Lehner's operator norm formula.

Universal approximation is a necessary qualitative property of learning architectures to benefit from scaling laws. While it is generically verified on a variety of neural architectures and random feature models, it typically involves infinite width limits. In this work, we focus on deep self-attention models and consider instead the `dual' regime, where approximation power is enabled entirely by depth, and featuring strong parameter sharing across layers, motivated by recent models such as the Looped Transformers. More specifically, we ask whether one can find a predefined finite set of parameters, each defining an attention block, such that the resulting finite set of transformations can map any collection of $N$ sequences of $n$ tokens to any other collection of $N$ sequences of $n$ tokens. Crucially, these transformations are fixed independently of the input and output collections: only the order in which the blocks are applied, their signs, and their durations depend on the particular interpolation task. Our main result establishes it for residual softmax attention using only two frozen single-head blocks with Gaussian-initialized projection matrices. The result holds at both continuous and finite depth. We also characterize the restrictions imposed by causal masking and establish corresponding universal interpolation guarantees.

Decision-focused learning for linear optimization is complicated by the discontinuity of the optimizer, where small cost errors may leave the decision unchanged or move it to a different vertex. We show that this non-smooth pointwise behavior becomes locally quadratic after averaging over the data distribution, and we derive the curvature in closed form, specifically, a matrix-valued measure supported on the walls of the normal fan. This measure depends only on the feasible set, with the data distribution entering only as a weight. We then offer a tractable approximation for this curvature, computable with just one projection to the feasible set. We prove that the approximation weakly converges to the true population curvature. We offer one application of our findings, a decision-aware scenario generation method for expected-cost linear optimization. Our experiments test the quadratic and weak convergence laws and show a 30.8% regret improvement over uniform allocation on battery arbitrage.

We address the problem of testing whether an unknown $n$-qudit state $\rho$ is $a$-close to a product state or $b$-far away from any product state, as measured in terms of state overlap. We provide a time-efficient algorithm to solve this problem that requires an $n$-independent number of copies of the unknown state. Our random coloring argument shows that for any unknown state there always exists a partition of $[n]$ into $q$ parts such that the square of the overlap with the closest product state with respect to this partition is only an additive factor $O(1/q)$ larger. This reduces the problem to tolerant testing of $q$ parties, with potentially growing local dimensions. Combining this insight with blockwise spectral projection arguments we can show that the natural $k$-copy generalization of Harrow & Montanaro's product state test provides an efficient tolerant tester. We use the same random coloring and blockwise spectral projection techniques to obtain a substantially improved algorithm for closest product state learning. In particular we give an algorithm that takes in $\widetilde{O}\big((nd)^2\big)\, 2^{\widetilde{O}(1/\varepsilon^8)}$ copies of the unknown state and produces an $\varepsilon$-approximately optimal product state. The key technical components of this learner are a qudit variant of the Bakshi et al. high-fidelity product state learning algorithm and a sampling technique based on Werner's optimal cloning channel.

Whether spin noise of a neutron star is stationary is, in two-component models, a question of whether stellar angular momentum is conserved internally or exchanged externally through independent stochastic torques on the crust and superfluid. The question is posed in the two components' angular velocities, but radio pulsar timing observes only the crust, through its rotational phase after a deterministic timing model is fitted. We develop a Gaussian process method for testing spin noise stationarity directly with such phase data. Starting from the exact analytical phase means and covariances of a singular, nonstationary and a minimal, stationary two-component model, we show that the crust phase covariances are semiseparable and construct a likelihood that scales linearly with the number of observations, with the timing model marginalized analytically. We analyze simulated phase data from both models using full-state and crust-only observations, and after differentiation into local spin frequencies. Integration, timing model removal and differentiation neither create nor destroy the distinction between stationary and nonstationary spin noise, but determine how much survives in a finite, noisy data set. With both components observed, the models are distinguished decisively and the generating parameters are recovered. With the crust alone, both models describe the observed phase equally well over much of parameter space, and the Bayes factors are of order unity and prior-limited. The minimal model nonetheless ties the hidden superfluid phase to the observed crust phase through a single factor set by the superfluid inertia fraction, so an independent estimate of this fraction, as from glitches, turns it into a falsifiable prediction that a continuous gravitational wave observation of the interior could test.

We study the low-energy interaction of negative kaons with deuterons using chiral $\bar{K}N$ interaction models (OR and BCN) as input. The three-body $K^-d$ amplitude is constructed within the Fixed-Center Approximation to the Faddeev equations, where the unitary constraints missing in the conventional approach are formally implemented with the incorporation of coherent multiple-scattering processes. The unitary procedure is extended to coupled channels including charge-exchange processes, as well as isospin-breaking effects through the use of physical particle masses. This provides a consistent description of the low-energy $K^-d$ amplitude and allows for the determination of the scattering length and the effective range. The resulting framework is then used to assess the compatibility of the BCN $\bar{K}N$ interaction model with the recent SIDDHARTA-2 measurements of kaonic hydrogen and kaonic deuterium through a bootstrap analysis. The procedure leads to a readjustment of the BCN parameterization which produces visible effects in several isospin-sensitive $\bar{K}N$ scattering observables, hence highlighting the additional information provided by the new kaonic-atom measurements to better constrain the poorly known isovector component of the ${\bar K}N$ interaction.

In this paper, we extend the paradigm of the Geometrical Trinity of Gravity to the Carrollian geometry to construct a comprehensive framework of dynamically equivalent theories for Magnetic Carrollian gravity. Utilizing the inherent ambiguities and freedoms of affine connections on degenerate metrics, we systematically relax the metric-compatibility and zero-torsion constraints of the rigid magnetic sector. By imposing global flatness on these modified connections, we prove that the curvature of a Magnetic Carrollian universe can be dynamically traded for isolated kinetic energy densities of torsion and non-metricity. Unlike the Lorentzian Trinity which maps gravity to alternative gravitational frameworks, the Carrollian equivalences can also map spacetime geometry to non-gravitational theories. Specifically, we demonstrate that intrinsic torsion recovers Electric Carrollian gravity as the Teleparallel equivalent of Magnetic Carroll gravity; purely spatial torsion reproduces kinetic terms stracturally similar to the magnetic Hamiltonian of scalar-charge Fracton gauge theory; and temporal torsion sectors map independently to $U(1)$ Maxwell electric fields and Carroll-Weyl conformal dilaton theories. Finally, by formulating a Symmetric Teleparallel Carroll connection with minimal non-metricity, we show that the Magnetic Carrollian Lagrangian is dynamically equivalent to an ultralocal, isotropic Electric Carrollian gravity upon exploiting the present freedoms in connection. These results establish a geometric dictionary translating Carrollian gravitational dynamics into the language of tensor gauge theories, electromagnetism, and dilaton theory.

Throughput in DSP and machine learning workloads is often limited by two temporal structures, i.e., loop-carried recurrences and long-latency, multi-cycle compute nodes. On spatio-temporal coarse-grained reconfigurable arrays (CGRAs), both bottlenecks can be addressed by overlapping iterations across the multi-context modulo configurations. Yet, existing CGRA mappers schedule a fixed dataflow graph (DFG) that treats recurrence-aware scheduling and operator-level pipelining separately, limiting inter-iteration overlap and inflating routing pressure. To tackle this, we present CONFERM, a recurrence-aware temporal mapper that uses the dominant temporal con-straint to guide the DFG representation and expose opportunities for loop-carried pipelining. CONFERM identifies and prioritizes bottleneck regions during scheduling. The regular loop-carried offsets across interleaved iterations allow the emitted control sequence to repeat at a shorter cadence than the original initiation interval, thus delivering higher throughput with lower CGRA configuration overhead. Across ten benchmark kernels, CONFERM improves throughput by 2.18x over state-of-the-art mappers. Its uniform iteration offsets shorten the emitted initiation interval by 46%. CONFERM's mapper pass also converges faster by 5.07x on average with the same heuristic mapper backend.

Simulation and experimental measurements provide complementary data for learning spatiotemporal physical systems, but standard simulation-to-experiment fine-tuning optimizes only the experimental objective after transfer and can degrade simulation performance. We formulate simulation–experiment prediction as a multi-objective learning problem with domain-specific simulation and experimental risks. On four fluid systems from RealPDEBench and two model capacities, we compare Simulation only, Experiment only, Sim$\rightarrow$Exp, and Joint training, evaluating every final model on both held-out domains. Sim$\rightarrow$Exp tends to specialize more strongly to experimental data at the cost of simulation-domain forgetting. Joint training consistently achieves the best balanced performance over a broad range of simulation–experiment evaluation weightings, while substantially improving simulation retention over Sim$\rightarrow$Exp. Joint also better preserves simulation-only fields absent from experimental measurements. Project page: https://mahindrautela.github.io/morph.

Reinforcement learning (RL) for video generation usually assigns one scalar reward to an entire sampled video. Yet a video is not uniformly flawed: some visual tokens may already satisfy the prompt, whereas others require correction. A scalar reward cannot localize errors, causing optimization to perturb satisfactory tokens while under-targeting the tokens that actually need to change. We introduce Token-Level Video Reinforcement Learning, TVRL, a framework that derives token-level credit from the reward being optimized. Our key insight is that the answer likelihood of a frozen vision-language model provides both signals: its outputs contribute to the video-level reward, while magnitudes of its video-input gradients reveal which generated video tokens most affect that score. We instantiate TVRL in Group Relative Policy Optimization by averaging prompt-derived question rewards into one group-relative advantage and using detached, question-conditioned token-credit maps to reweight dense denoising-transition log-probabilities inside the clipped policy ratio. On VBench-2.0, TVRL achieves an Overall score of 57.69, outperforming the base model by 3.60 points. TVRL also improves matched GRPO baselines across three SDE samplers (SAGE, Flow, and Dance) by 2.68–3.15 points and across four reward models (VideoAlign, VideoScore2, UnifiedReward2, and Qwen3.5-9B) by 1.33–3.15 points.

We present Informed Belief Localization Trees* (Informed BLT*), a sampling-based belief space planning (BSP) algorithm that scales to large outdoor digital twins with point-cloud observations. We adapt RRT* and Informed RRT* to belief space using the $2$-Wasserstein ($W_2$) metric. Assuming isotropic Gaussian beliefs, sampled belief states can be connected efficiently while accounting for available information and probabilistic collision constraints. This enables steering and rewiring without repeatedly propagating observations, and allows previously computed measurement information to be reused. We present a framework to generate semantically labelled digital twins for planning in real-world environments with point-cloud-based localization. Experiments in simulated environments and digital twins show faster initial solution discovery in most maps with competitive cost convergence.

Personalized social media commonly relies on explicit follow graphs to shape what content users encounter; yet how much attention crosses ties they have not formed remains largely undocumented at scale. We study this question on Bluesky, a large decentralized microblogging platform whose default feed relies on a simple, reverse-chronological content recommender. We analyze 173 million user-author interactions (likes, reposts, replies, and quotes) collected from a near-complete platform dump between February and September 2023. We decompose each interaction by attention-path length (already followed, relayed by a followed account, reachable within two follow-hops, or beyond) and find that 74.5% of interactions reach the user through an account they already follow. Measured by distance in the follow graph rather than by route, 80.6% of interaction lands within two follow hops, far beyond the 22.4% an expected-degree null predicts. We then characterize how exploration varies across users and over tenure. A broad-reaching minority generates three quarters of all exploratory activity, while aggregate declines in exploration with tenure mask three distinct individual trajectories. Finally, attention reaching beyond two hops converts into new follow ties at less than one third the rate of two-hop-local exploratory attention. Together, these results depict a platform where out-of-network exploration is substantial in volume but strongly constrained by network proximity and unlikely to translate into new social ties.

We prove everywhere regularity for Lipschitz solutions to the prescribed vertical mean curvature system in the plane, where the codimension is arbitrary and the mean curvature is in $L^r, \, r > 2$. This strengthens and extends our previous result on the Lawson-Osserman conjecture, https://arxiv.org/abs/2308.04997.