Geometric Topology
Computations of Floer Lasagna Modules for Traces of Negative L-Space Knots
Colin McCulloch
We show that for all negative $L$-space
knots and framings $n\geq2g(K)$, if a certain cobordism map between cables of $K$ is non-vanishing, then the Floer lasagna module of the
knot trace of $K$ with framing $-n$ is infinite dimensional. Further, for the maps on the hat flavour of link Floer homology induced by band maps, quasi-stabilisations and pair of pants cobordisms we give a description of the map on the $E^{\infty}$-page of Ozsvath and Szabo's spectral sequence for forgetting components.
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Algebraic Geometry
Extending Andreotti's proof of Torelli's theorem to nodal curves
Alex Abreu, Marco Pacini and Nicola Pagani
Let $C$ be a connected nodal curve of genus $g$ over an algebraically closed field $k$ of characteristic zero. Let \[ A(C)=\Big(J(C), {\overline{P^{g-1}_C}}, \Theta(C) \Big) \] be the stable semi-abelic pair (in the sense of Alexeev) associated with its canonical compactified Jacobian $\overline{P^{g-1}_C}$ in degree $g-1$. The canonical triple of $C$ consists of the closure of its canonical image together with two sets of distinguished points encoding the information of the images of the nonseparating nodes and of the branch data of the canonical map. We prove a functorial reconstruction: given connected nodal curves $C$ and $C'$ over $k$, every isomorphism $A(C)\cong A(C')$ of stable semi-abelic pairs canonically induces a projectivity between the corresponding canonical triples of $C$ and $C'$. Passing to isomorphism classes, this recovers the reconstruction statement in the compactified Torelli
theorem of Caporaso-Viviani. Our proof extends Andreotti's Gauss-map strategy. The branch locus of the projection from the normalization of the Gauss graph recovers the nonlinear canonical components and branch data by projective biduality; boundary strata of the compactified Jacobian recover the node-images; and incidence arguments recover the linear components. Along the way, we repair technical gaps in the classical treatments of Andreotti's proof of Torelli's
theorem for smooth curves.
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Quantum Physics
A Case Study on Noise Resilient Operator Selection in Adaptive Variational Quantum Algorithms
Soorya Haravu, Mafalda Ramôa and Bharath Sambasivam
Hardware noise has been shown to significantly impact the accuracy of ADAPT-VQE, a ground state preparation
algorithm. While previous work has studied the impact of noise on its parameter optimization step, its impact on the critical operator selection step remains comparatively unexplored. In this work, we examine the impact of a variety of noise channels on this step, using a linear H$_3$ molecule as a test case. We show that, despite the selection criterion's natural resilience to some noise, both coherent and incoherent noise can prevent convergence for sufficiently high noise rates. We employ
quantum error mitigation techniques–dynamical decoupling, zero noise extrapolation, and Pauli twirling–and show that when combined appropriately, these techniques are capable of restoring a successful convergence profile. Our results highlight how error mitigation can improve the performance of ADAPT-VQE and enable convergence in the presence of hardware noise, offering valuable insights into the implementation of the
algorithm on near-term
quantum hardware.
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Mesoscale and Nanoscale Physics
Visualizing Berry curvature in a Floquet-Chern insulator
Younsik Kim, Rishi Acharya, Hannah E. Aguirre et al. (+3 more)
Circularly polarized light can open a topological gap in a gapless Dirac system, creating a Floquet-Chern
insulator. However, its Berry
curvature has not been directly resolved. Here we use circular-dichroism time- and angle-resolved photoemission spectroscopy (Tr-ARPES) to map the light-induced Berry
curvature of Floquet-Bloch states on the surface of Bi$_2$Se$_3$. By comparing spectra for opposite helicities of the mid-infrared pump, we isolate the induced
geometric response. We observe alternating-sign Berry-
curvature features at Floquet gaps that repeat at intervals set by the pump
photon energy and redistribute with pump field strength in agreement with calculations for a periodically driven Dirac
Hamiltonian. Both the induced Berry-
curvature and the Floquet Dirac gap decay faster than the replica intensity, showing that spectral replicas can persist even after coherent Floquet hybridization weakens. These results establish momentum-resolved Berry-
curvature mapping as a direct probe of light-induced
topology and coherent Floquet band formation.
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All authors Younsik Kim, Rishi Acharya, Hannah E. Aguirre, Lucca Figari, Daniel P. Shoemaker, Fahad Mahmood
Machine Learning
ENCP: Episode-Normalized Conformal Prediction for Vision-and-Language Navigation
Vicky Feliren, A. Taufiq Asyhari and Muhamad Risqi U. Saputra
Uncertainty estimation for
Vision-
Language-
Navigation (VLN) models is a critical task since it can help identify ambiguous and unreliable predictions, enabling
agents to make safer
navigation decisions. As one of the most advanced uncertainty estimation frameworks, conformal prediction (CP) offers a promising approach for uncertainty estimation in VLN. However, given that VLN
agent requires a sequence of steps, standard calibration in conformal prediction fails to provide coverage guarantee it promises over a dependent, variable-length VLN episode. To this end, we propose Episode-Normalized Conformal Prediction (ENCP), which rescales a nonconformity score by the policy's residual confidence and calibrates one maximum score per episode. Under exchangeable calibration and test episodes, this construction covers the ground truth at every step with probability at least $1 - \alpha$, while allowing dependence among steps within an episode. Across four VLN policies and three nonconformity scores on R2R and REVERIE
dataset, ENCP meets all reported empirical step-coverage targets on the seen-to-unseen evaluation. These results demonstrate that ENCP can provide model-agnostic uncertainty estimates, which might be useful for determining when a VLN
agent should defer to a more capable predictor, including human assistance.
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Quantum Physics
Antidistinguishability of states in General Probabilistic Theories
Satyaki Manna and Anandamay Das Bhowmik
We investigate antidistinguishability of states within the framework of general probabilistic theories (GPTs). We formulate antidistinguishability, strong and equal antidistinguishability as refined notions that imposed additional constraint on the measurement effects. We establish general results relating these notions of antidistinguishability and derive an upper bound on the cardinality of equally antidistinguishable sets in terms of the affine dimension of the state space. We then study antidistinguishability in polygonal theories, obtaining conditions for antidistinguishability of a set of states. In consequence, we show that the set of all pure states in a polygon model is antidistinguishable. Additionally, we identify broad families of strongly and equally antidistinguishable states. Finally, using Random Exclusion Codes, whose success probability is governed by the antidistinguishability of different sets of encoding states, we probe the nonclassicality of polygon theories. We find that certain polygon models can outperform the optimal
quantum value, while their optimal performance converges to the
quantum limit in the large-polygon limit.
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Quantum Physics
Beyond Hardware: Adaptive Algorithmic Control by State-Proxy Equalization
Jianlong Lu, Hongrui Zhang, Thorsten Koch et al. (+1 more)
Recent advances in
quantum computing have been driven primarily by improvements in hardware. Here we show that substantial gains can instead arise from how finite computational resources are allocated throughout a
quantum computation. We introduce Adaptive Algorithmic Control (A2C), a software paradigm founded on a State-Proxy Equalization
theorem, which proves that the optimal allocation for a state-derived proxy-error functional equalizes cumulative computational hardness rather than physical time. The required computational hardness is inferred directly from the evolving
quantum state, avoiding explicit reconstruction of the exponentially large many-body spectrum. Across
quantum optimization problems containing up to 156
qubits, combining exact simulations, large-scale supercomputer computations and IBM
quantum hardware experiments, A2C improves the low-energy sampling probabilities by $22\%$ to over $100,000\%$ under matched
circuit depths and measurement budgets. These results demonstrate that
quantum computational performance depends not only on hardware capabilities, but also on how finite computational resources are organized, establishing adaptive algorithmic control as a complementary software pathway for advancing
quantum computation.
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All authors Jianlong Lu, Hongrui Zhang, Thorsten Koch, Ying Chen
Artificial Intelligence
Verifiable Social Reasoning for LLM Assistants
Amir Taubenfeld, Zorik Gekhman, Avigail Grinstein-Dabush et al. (+6 more)
LLM assistants are widely used for daily social advice, yet evaluating their social
reasoning in such consultation settings remains challenging since (i) it requires setups where the assistant learns about social situations from subjective user narratives, and (ii) social properties, such as others' intentions, typically lack verifiable ground truth. To address these challenges, we introduce Fuse, a multi-
agent simulation framework for studying user-mediated social
reasoning. In Fuse, a target
agent with a hidden motive interacts with other
agents including one representing the user, who then consults the evaluated assistant to infer the target's motive, providing verifiable ground truth by construction. Simulation faithfulness is validated through a human study with 24k annotations. We apply Fuse to 12 LLMs and demonstrate its analytical utility by systematically isolating key factors, showing that (i) user mediation compounds the inherent difficulty of social
reasoning; (ii) LLMs exhibit systematic sensitivity to biased user framing; (iii) models can require more details than humans need to reach a correct prediction; and (iv) longer conversations do not always improve performance despite providing opportunities for clarifying questions. We open-source Fuse and a
dataset with 21k examples.
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All authors Amir Taubenfeld, Zorik Gekhman, Avigail Grinstein-Dabush, Itay Laish, Ariel Goldstein, Marian Croak, Avinatan Hassidim, Yossi Matias, Amir Feder
Statistical Methodology
First-Crossing Reduction and Inference for No-Rescue Effects under Deterministic Rescue
Shu Tamano
Clinical protocols may require rescue medication when a patient's condition crosses a prespecified threshold. The outcome under continued non-rescue is then unobserved after first crossing, preventing point identification without extrapolation assumptions. In this paper, we develop sharp partial identification and inference for this hypothetical estimand while retaining the original no-rescue intervention. We show that bounding this mean reduces exactly to restricting conditional mean effects of withholding rescue at first-crossing histories. Building on this representation, restrictions on prespecified crossing-stratum averages yield three results. (i) A finite convex program gives sharp bounds without modeling post-crossing trajectories, attained by full-data laws that preserve the observed distribution. (ii) Confidence intervals incorporate sampling uncertainty and numerical error to cover the entire sharp set, including strata with no observed crossings. (iii) Under local feasibility conditions, sampling and numerical errors control endpoint accuracy even with zero-probability strata, whereas valid coverage requires no such conditions. Our experiments show that the stratum-average restrictions can yield narrower confidence intervals in larger samples, and that accounting for uncertainty in empty strata maintains valid coverage when rescue is rare.
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Algebraic Geometry
Equivariant Cohomological Crepant Resolution Conjecture for ADE-orbifolds
Qike Li and Fabio Perroni
Let G be a non-trivial finite subgroup of SL_2(C) and let p : X \to C^2/G be the minimal resolution. We prove the C^*-equivariant Cohomological Crepant Resolution
Conjecture for the ADE orbifold [C^2/G]. More precisely, after specializing the
quantum parameters at suitable roots of unity, we prove that the Bryan-Gholampour transformation induces an isomorphism between the C^*-equivariant
quantum cohomology of X and the C^*-equivariant Chen-Ruan
cohomology of [C^2/G]. Our proof is direct and is based on the McKay correspondence, ADE root systems, and character theory. Following the character-theoretic form of the Bryan-Gholampour change of variables, we use the McKay correspondence to diagonalize the transformation and to reduce the compatibility of the products to a uniform root-system identity. In type A, this reduction admits a discrete
Fourier realization. In type D, the cyclic subgroup of the binary dihedral group leads instead to finite sine transforms, while the exceptional cases E_6,E_7,E_8 are treated by exact
matrix computations over the corresponding cyclotomic fields. As a preliminary result, for a
symplectic complex vector space V and a finite subgroup G of Sp(V), we give an explicit presentation of the C^*-equivariant Chen-Ruan product of [V/G] and identify the resulting
algebra with the Rees
algebra of the center of the group
algebra with respect to the age filtration. In particular, the equivariant Chen-Ruan
algebra interpolates between the center of the group
algebra and its associated graded
algebra, the latter recovering the ordinary Chen-Ruan
cohomology.
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Combinatorics
Twisted Bracelets for Sorting by Transpositions: the Transposition Diameter of $S_{16}$
Luiz A. G. Silva, Luis A. B. Kowada, Noraí R. Rocco et al. (+1 more)
Sorting By Transpositions (SBT) seeks the minimum number of transpositions required to sort a permutation $\pi$ on $n$ symbols into the identity $\iota$. Let $N=n+1$. A cyclic-target pair $(\omega,\beta)$ consists of an even permutation $\omega$ and an $N$-cycle $\beta$ for which $\rho=\omega\beta$ is an $N$-cycle. An SBT instance is the special case $(\bar{\iota}{\bar{\pi}}^{-1},\bar{\pi})$, where $\bar{\pi}$ and $\bar{\iota}$ encode $\pi$ and $\iota$, and $\bar{\iota}{\bar{\pi}}^{-1}\bar{\pi}=\bar{\iota}$. For a prescribed fixed-point-free cycle type, fixed-content words encode $\omega$, with colors distinguishing cycles and ranks recording their orientations relative to $\beta$. A word is realizable exactly when $\rho=\omega\beta$ is an $N$-cycle. Permutations of equal-part colors and shifts of rank origins form auxiliary
symmetries that, together with word rotation and position reflection coupled to rank inversion, define a twisted dihedral action. Its orbits are twisted bracelets, and its realizable orbits correspond bijectively to extended-toric equivalence classes of cyclic-target pairs, where reflection is adjoined to classical toric equivalence. The correspondence yields a Burnside identity, and our method generates one encoding word for each such class. The transposition diameter $TD(n)$ is the largest transposition distance in $S_n$. Combining fixed-point contraction and reductions of the ambient instance space based on cycle structure with exhaustive verification of every remaining twisted bracelet, we prove $TD(16)=9$, closing a twenty-five-year gap. This result also yields $TD(19)=11$ and, for every $n\equiv1\pmod{3}$ with $n\geq16$, $TD(n)\leq\left\lfloor(2n-2)/3\right\rfloor-1$, improving the previous general upper bound by one for these $n$.
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All authors Luiz A. G. Silva, Luis A. B. Kowada, Noraí R. Rocco, Maria E. M. T. Walter
Numerical Analysis
On the Existence of Pressure-Equilibrium-Preserving Numerical Fluxes for Supercritical Fluids
Robin Ben Klein
In this work we propose a new existence
theorem for numerical-flux functions for supercritical fluids that are pressure-
equilibrium-preserving (PEP). In particular, we characterize the existence of consistent numerical-flux functions that satisfy an algebraic PEP property. Our theory links the existence of PEP schemes to
geometric properties of the equation of state describing the thermodynamics of the fluid. When these
geometric properties fail for a pair of states on the same isobar, no PEP schemes of the considered form can exist on a domain containing those states. In our analysis the equation of state itself can be fully general only needing to satisfy some fundamental thermodynamic principles. Recently, PEP compatibility conditions for general equations of state have been derived [1] that rely on the existence of certain thermodynamic derivatives which are not guaranteed to be defined under fundamental thermodynamic principles. The
geometric conditions in our theory do not depend on the existence of these derivatives and recover the recent compatibility conditions in the case that these derivatives are defined. Finally, using numerical experiments we demonstrate for two supercritical fluids that our existence conditions are restrictive and thus that no PEP schemes of the form we consider exist on the domain we specify for these fluids. Using our
geometric perspective, we also shed light on mechanisms by which PEP schemes can develop numerical issues, which we also demonstrate using numerical experiments.
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Machine Learning
FreqSpaNet: Frequency and Spatial Learning of SFPF for Physical Layer Hardware Integrity Detection
Xiaoxuan Huang, Jinlong Xu, YiZhe Wang et al. (+3 more)
Unauthorized hardware replacement can preserve a wireless device's logical identity while altering its physical implementation, posing a challenge to hardware integrity verification. Spatio-frequency polarization fingerprints (SFPFs) capture device-dependent responses across multiple frequencies and directions, but their frequency and spatial dimensions exhibit different structural dependencies. We propose FreqSpaNet, an SFPF representation learning network for open set hardware anomaly detection. A frequency branch captures local variations among neighboring frequencies, while a geometry-aware spatial branch models directional relationships using angular information. The two representations are combined through adaptive fusion, and complementary pretraining further captures shared information while preserving the distinct characteristics of the frequency and spatial representations. Experiments show that FreqSpaNet achieves a mean AUROC of 96.31%, 9.05 points above the baseline. Results under seven hardware replacement scenarios further verify the effectiveness of FreqSpaNet.
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All authors Xiaoxuan Huang, Jinlong Xu, YiZhe Wang, Meng Zhang, Xian Li, Yuying Bian
Quantum Physics
Query-optimal quantum simulation of Lindblad evolution
Chunhao Wang and Christopher Ye
For the problem of simulating Lindblad
evolution for time $t$ to precision $\epsilon$,
Hamiltonian simulation provides an additive query lower bound, informally, $\Omega(t + \mathrm{polylog}(1/\epsilon))$. However, the best previously known
algorithms for general Lindblad simulation achieve a multiplicative upper bound, informally, $\mathcal{O}(t\,\mathrm{polylog}(1/\epsilon))$, in query complexity. It has remained open whether this multiplicative dependence is necessary. In this paper, we close the gap in query complexity by giving an
algorithm with optimal additive dependence on
evolution time and precision in the block-encoding model. Our approach uses the transducer framework to reduce the query cost of composing first-order approximations to the
evolution channel, together with linear combinations of reuse
circuits of different lengths to suppress catalyst-removal error. We further achieve nearly optimal gate complexity in
evolution time and precision through history compression and an efficient implementation of the query-free part of the transducer using operation reordering and linear combinations of
unitaries, while preserving the optimal query complexity.
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Optics
Hysteresis and trap emission in dc-biased integrated lithium niobate electro-optic modulators
Matthew Yeh, CJ Xin, Donald Witt et al. (+3 more)
The electro-optic effect is crucially important for low power and efficient tuning of integrated photonic
circuits. However, in electro-optic materials such as lithium niobate, dc biasing for an extended duration of time results in the emergence of numerous nonidealities, including hysteresis – a persistent degradation of the magnitude and linearity of the dc electro-optic response. We show that electro-optic hysteresis can be reversed under both zero-bias and reverse-bias conditions, given sufficient time or reverse voltage and consistent with a defect model of the underlying physics. Specifically, we find that drift phenomena at short time scales can be explained by charge trapping dynamics near the contact junction, and thereby devise an active reset protocol that restores the magnitude of the response and partially restores the drift time scales.
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All authors Matthew Yeh, CJ Xin, Donald Witt, David R. Barton, Evelyn L. Hu, Marko Lončar
Artificial Intelligence
LimiX-2: A Contextual Mechanism Network Towards General Structured-Data Intelligence
Xingxuan Zhang, Gang Ren, Hao Yuan et al. (+57 more)
We introduce LimiX-2, a new model in the LimiX family, developed through model and data scaling guided by our previously established scaling laws. LimiX-2 adopts the Contextual Mechanism Networks (CMNs) paradigm and is pretrained with Context-Conditional Masked Modeling (CCMM). CMNs shifts the organizing principle of in-context learning from target-centric prediction to mechanism-oriented joint modeling. Rather than centering the network on the $p(y \mid x, D_{\mathrm{context}})$ objective of conventional tabular PFNs, it is designed around learning $p(x, y \mid D_{\mathrm{context}})$, a context-dependent representation of the joint structure underlying data generation. Pretraining uses synthetic
datasets generated by structural causal models (SCMs) spanning diverse graph structures, functional mechanisms, and observation processes. Evaluations on TabArena, TALENT, and BCCO show that LimiX-2 outperforms current
dataset-specific models and tabular foundation models. Beyond predictive performance, the CMN paradigm also promotes causal awareness in LimiX-2: its feature
attention encodes direct causal relationships, enabling accurate causal skeleton recovery.
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All authors Xingxuan Zhang, Gang Ren, Hao Yuan, Hao Zou, Hongze Tan, Hui Wang, Jianhao Song, Jiansheng Li, Jiayao Zhang, Jinghan Zhang, Kaifang Li, Lang Mo, Li Mao, Mingchao Hao, Nuo Xu, Rui Ding, Ruiji Zhang, Shuyang Li, Siyu Mei, Tianyang Zhang, Weiyang Mu, Yancheng Dong, Yongxian Wei, Yuan Xue, Yuanrui Wang, Yue He, Zijia Yang, Ziyun Li, Dongzhe Li, Fuqiang Wang, Jiandong Liu, Jiawei Chen, Jiaxin Du, Kaijie Cheng, Kehan Li, Lei Sun, Linjun Zhou, Ningbo Dai, Qi Wang, Renzhe Xu, Shaoxing Du, Shumeng Yang, Wang Lu, Wenjing Chu, Xiannan Huang, Xiaoyu Lin, Xing Ai, Xinyan Han, Xuanyue Li, Xuanyue Su, Xukun Zhang, Yan Lu, Yaxin Zhang, Yi Qin, Yifei Huang, Yihan Xu, Yongle Lv, Yuanyuan Jiang, Yushan Han, Peng Cui
Data Structures and Algorithms
Stuffed IBLTs: Optimal Linear Multiset Sketches
Jonas Klausen, Rasmus Pagh and Stefan Walzer
A linear sketch is a randomized linear mapping of a vector $v$ to a lower dimensional sketch vector, designed to preserve relevant information about $v$. We consider sketches of vectors $v \in Z^u$ (for $u \in N$), designed for exact recovery of $v$ from its sketch. Concretely, our Stuffed IBLT is a linear sketch configured with a capacity $n \in N$ and a multiplicity limit $L \in N$ and will recover $v$ with high probability whenever $||v||_0 \leq n$ and $||v||_\infty \leq L$. The sketch can be maintained efficiently under unrestricted updates to $v$, i.e., $v$ is not subject to any constraints in between decoding requests. This makes the sketch useful for streaming
algorithms and for solving the (multi)set reconciliation problem. For any positive constants $c$, $\epsilon$, and for large enough $n$ and $u \geq n^{1+\Omega(1)}$, the space usage of a Stuffed IBLT is within a factor $1+\epsilon$ from the information-theoretic optimum while allowing updates in constant time, and decoding in time $O(n)$ with failure probability $n^{-c}$. This improves the space/time/error probability trade-off over all prior constructions with similar functionality, including the Invertible Bloom Lookup Table (IBLT). The performance of the Stuffed IBLT is essentially the best we could hope for, up to the dependence on $c$ and $\epsilon$. We make the dependence on these parameters explicit, and further show a lower bound demonstrating that the dependence on $c$ is optimal within the class of peeling-based approaches. Our improvement comes from a careful combination of Walzer's spatial coupling technique (SODA '21), the purity heuristic of Houen, Pagh, and Walzer (SOSA '23), and backyarding (Belazzougui, Kucherov, and Walzer, ESA '24; Fleischhacker, Green Larsen, Obremski, and Simkin, ICALP '24), allowing us to eliminate bottlenecks of past approaches.
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High Energy Physics (Phenomenology)
Rotational Brownian Motion and $\mathrm{J/\psi}$ Spin Alignment in Heavy-Ion Collisions
Bhagyarathi Sahoo and Captain R. Singh
The heavy-
quark polarization in ultra-relativistic heavy-ion collisions (HICs) serves as a probe for unfolding the characteristics of deconfined QCD. The present study explores the
spin alignment of $\mathrm{J/\psi}$ in the HICs by employing the rotational Brownian motion of charm
quarks in the presence of a strong
magnetic field. We derive an analytical expression for the polarization of the $c$-$\bar{c}$ pair based on the Fokker-Planck equation under the consideration of
spin-vorticity coupling. These polarized $c$-$\bar{c}$ pairs lead to the formation of the $\mathrm{J}/\psi$ at the hadronization surface via the coalescence and fragmentation mechanisms. Correspondingly, we obtain the $m=0$ diagonal element $\rho_{00}$ of the $\mathrm{J}/\psi$
spin-density
matrix, which quantifies its
spin alignment along the chosen quantization axis. Our study provides a microscopic description of heavy-
quark spin transport and suggests rotational
diffusion as a possible mechanism underlying the observed $\mathrm{J}/\psi$
spin alignment.
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Human-Computer Interaction
Quick-View Takeaways: How Does Title Framing Influences Pattern Identification in Line Charts?
Jasmine Lim, Tapendra Pandey, Arran Zeyu Wang et al. (+1 more)
Visual data communication in digital media is increasingly characterized by short
attention spans and snapshot-based viewing, often employing line charts to convey trends and patterns. Among all visual elements, titles are crucial ones that can shape how viewers interpret visual information and form chart takeaways. In this study, we examine how title characteristics, particularly title word count and intended message, influence people's pattern identification in single-class line charts. Participants viewed 50 line charts collected from online news media and identified the pattern they perceived. Our results demonstrate that both title word count and intended message significantly influence viewers' pattern identification. Our findings highlight the importance of title design in shaping chart takeaways and effective visualization communication.
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All authors Jasmine Lim, Tapendra Pandey, Arran Zeyu Wang, Ghulam Jilani Quadri
Robotics
Dissecting Motion-Prior Regularization for Data-Scarce Robotic Insertion
Ning Hu, Shuai Li and Jindong Tan
This study asks whether training-time motion-prior regularization can improve insertion success when a
diffusion policy is learned from only 15 demonstrations. Minimum jerk discourages abrupt changes in predicted translational acceleration; speed-
curvature regularization instead couples movement speed to path geometry. These are candidate mechanisms for task completion, not safety guarantees. We compare the priors individually and jointly, neither prior, and generic smoothness, with 80 real-
robot trials per setting pooled over four recorded condition classes. Joint and minimum-jerk-only settings each achieved 70/80 successes (87.5%), versus 69/80 (86.3%) for speed-
curvature only, 66/80 (82.5%) for neither prior, and 67/80 (83.8%) for generic smoothness. Success rates and Wilson 95% confidence intervals are visualized for direct comparison. Joint regularization exceeded neither by 5.0 percentage points but provided no observed gain over minimum jerk alone. The results motivate minimum jerk as the simpler candidate for replication, without establishing synergy, biomechanical specificity, improved safety, or distribution-shift robustness.
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Optimization and Control
Bridging the Gap Between Homogeneous and Heterogeneous Asynchronous Optimization Is Surprisingly Difficult
Alexander Tyurin
Modern large-scale machine learning tasks often require multiple workers, devices, CPUs, or GPUs to compute
stochastic gradients in parallel and asynchronously to train model weights. Theoretical results typically distinguish between two settings: (i) the homogeneous setting, where all workers have access to the same data distribution, and (ii) the heterogeneous setting, where each worker operates on different data distributions. Known optimal time complexities in these settings reveal a significant gap, with far more pessimistic guarantees in the heterogeneous case. In this work, we investigate whether these pessimistic optimal time complexities can be overcome under different assumptions. Surprisingly, we show that improvement is provably impossible under widely used first- and second-order similarity assumptions for any randomized
algorithm. We then turn to the interpolation regime and demonstrate that the weak interpolation assumption alone is also insufficient. Finally, we introduce a minimal combination of irreducible assumptions, strong interpolation and the local Polyak-Lojasiewicz condition, to derive a new time complexity bound that matches the dependence on worker computation times in the best-known result in the homogeneous setting, without requiring identical data distributions.
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Quantum Physics
Predictive Structure Behind Rare Outcomes in Random Quantum Circuits
Myeongsu Kim, Travis Humble and Sabre Kais
Local random
quantum circuits can occasionally produce unusually large output probabilities. However, the final output distribution containing such a peak does not by itself reveal how the peak formed during
circuit evolution. We investigate whether states formed during
circuit evolution carry structural signatures that predict subsequent peak formation. In numerical experiments,
circuits selected for large terminal peaks exhibit stronger pairwise correlations and probability redistribution, together with lower bipartite
entanglement and output
entropy, than controls generated by the same random-
circuit model. Their intermediate states retain higher fresh-peak event probability when the remaining gates are independently regenerated. Within an unconditioned ensemble, a fixed structural score computed from the initial
circuit segment predicts new-peak probability. Averaged equally across n=8-16, a replay with equal numbers of remaining-
circuit evaluations shows that score-based allocation yields 1.80 times as many peaks as uniform allocation and about 18% more than a fixed baseline based on probability concentration and redistribution. Randomizing relative phases while preserving computational-basis probabilities strongly attenuates the selected-state advantage, demonstrating a functional contribution from relative-phase organization. Controlled gate-selection tests further show that the identified structure can guide
circuit construction to promote peak formation. Together, these results connect rare output events to intermediate-state structure with predictive and constructive value under finite-depth local dynamics.
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Combinatorics
Kemeny's constant via matrix compression and eigenvalue interlacing
A. Abiad, Á. Carmona, A. M. Encinas et al. (+3 more)
Kemeny's constant quantifies the expected time for a random walk to reach a randomly chosen vertex, capturing global properties of a Markov chain. We develop a
matrix-analytic framework for bounding Kemeny's constant of a finite connected weighted graph using degree-weighted compressions of the normalized adjacency
matrix, pinching inequalities, and
eigenvalue interlacing. Our main partition
theorem gives lower bounds in terms of the compressed spectrum, with complete equality characterizations, and converts structural graph information into spectrally computable estimates. For instance, when applied to proper color partitions, the proposed method yields a sharp lower bound on Kemeny's constant in terms of the chromatic number \[ K(G)\ge n-2+\frac{1}{\chi(G)}, \] which extends a bipartite bound of Ciardo, Dahl, and Kirkland (2022) to arbitrary chromatic number, and which is incomparable with the normalized Hoffman bound by Chung (1997). For unweighted graphs, we also characterize all equality cases of this bound. We further illustrate the power of the proposed
matrix framework by deriving spectral bounds for NP-hard graph problems involving normalized cuts and conductance. Our results include an asymptotically sharp conductance bound, two-sided interlacing bounds from principal submatrices and quotient
matrices, and estimates for the change in Kemeny's constant under connectivity-preserving deletion of multiple edges.
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All authors A. Abiad, Á. Carmona, A. M. Encinas, E. Ghorbani, M.J. Jiménez, Á. Samperio
Optics
Stitch-Free, Diamond-Scribed Silicon Nitride Photonic Integrated Circuits for the Visible Band
Kishor Kumar Mandal, Lekshmi Eswaramoorthy, Parul Sharma et al. (+5 more)
Silicon nitride photonic integrated
circuits for the visible band are conventionally built with a buried
oxide overcladding and singulated with wafer-scale tooling, constraints that preclude evanescent access to the guided mode for externally integrated emitters. We report a PECVD grown $Si_3N_4$ platform designed around an air-clad waveguide whose evanescent field remains accessible along the full device length. Two process elements make this geometry practical at chip scale. Fixed-beam moving-stage electron-beam lithography writes 500 nm single-mode waveguides as one continuous exposure across the 5 mm chip, removing write-field stitching which, given the $\sigma^{2}/d^{4}$ scaling of sidewall scattering in this high-confinement geometry at 635 nm, would otherwise dominate the loss budget. Chip singulation is performed by pen-type diamond scribing along lithographically patterned markers registered to in-plane direction, cleaving the Si(100) substrate to yield end-facets within $2^\circ$ of normal at $80 \%$ yield. Structural characterization by scanning electron microscopy confirms stitch-free waveguide geometry and undamaged, near-vertical scribed facets; light is coupled end-fire into fabricated devices and guided to a microring with evanescent bus-to-ring coupling confirmed by scattering imaging, and a sidewall-roughness-dependent scattering-loss model indicates that loss remains low in the roughness regime consistent with the observed facet and sidewall quality. Building on the intrinsic emitter-resonator coupling demonstrated in, this platform extends monolithic $Si_3N_4$ photonics toward scalable visible-to-near-infrared
quantum and classical
circuits.
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All authors Kishor Kumar Mandal, Lekshmi Eswaramoorthy, Parul Sharma, Anuj Kumar Singh, Brijesh Kumar, Tanmay Gupta, Venu Gopal Achanta, Anshuman Kumar
Computer Vision
Det-LIME: Detector-Aware, Multi-Instance Local Interpretable Model-Agnostic Explanations for Automated Marine Mammal Detection
Jiayi Zhou, David W. Johnston and Brinnae Bent
Despite the rapid uptake of black-box object detectors in marine mammal research and monitoring, explainability techniques are rarely integrated into conservation workflows. Furthermore, most classification-oriented explainability tools are ill-suited to detection tasks involving imagery of social organisms or those with colonial life histories, as they ignore multiple detections within a scene and produce single-instance outputs that blur evidence across individuals. These methods also generate low-resolution, often biologically irrelevant visuals, limiting their utility for debugging, targeted data augmentation, and refined data collection. We proposed Det-LIME, a detector-aware, multi-instance adaptation of Local Interpretable Model-Agnostic Explanations (LIME) that produced instance-specific, box-aligned explanations by combining per-detection weighting, a proximity kernel that emphasizes regions near each box, and Intersection-over-Union-based matching to track the same instance across perturbations. We evaluated Det-LIME on aerial drone imagery for harbor seal detection, with an additional seabird case study to assess generality, and compared it with vanilla LIME, Stabilized LIME, Deterministic LIME, and gradient-based attribution methods. Using the Attribution Ratio and Max Saliency Hit Rate metrics, we showed that Det-LIME consistently improved multi-instance attribution. In practice, these higher-resolution, instance-aware explanations provide insight into model outputs and support post-processing, debugging, and actionable improvements in modeling and data collection or augmentation.
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Number Theory
Hypothetical connection of the theta functions of Dirichlet characters with the real cyclotomic fields
Yuri Matiyasevich
We consider a possible approach to the Lindelöf hypothesis for Dirichlet $L$-functions. It is based on a special form of the functional equation for the corresponding theta functions. To estimate $L_\chi(0.5+it)$ we need to solve certain systems of linear equations. The entries to the corresponding
matrices are formed by the summands to the series for theta functions and their derivatives. Numerical data suggest that the inverse
matrices have a deep structure and allow us to state a number of
conjectures. In particular, it seems that for a character modulo $q$ certain entries to the inverse
matrices tend to finite limits when the sizes of the
matrices run over arithmetical progressions with step $2q$. Moreover, these limits belong to the real cyclotomic field $\mathbb{Q}(\cos(\pi/q))$ (up to a scaling factor of $\sqrt{q}$).
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Disordered Systems and Neural Networks
Bias-Induced Crossover in Absolute Capacity of Dense Associative Memory
Yuto Sakurai, Takeaki Shimokawa, Kazunori Iwata et al. (+1 more)
The absolute capacity of dense associative
memory has mainly been analyzed for unbiased patterns. Here we examine the effect of bias in centered binary patterns under the Krotov-Hopfield single-site criterion $P_{\mathrm{error}}=1/N$, where $P_{\mathrm{error}}$ is the probability that a single-site flip lowers the energy of a stored pattern and $N$ is the number of
neurons. Each pattern component takes $1-q$ with probability $q$ and $-q$ otherwise, where $0<q\le1/2$. For
polynomial interactions of order $n$, a signal-to-noise analysis gives an absolute capacity of order $N^{n-1}/\ln N$ at $q=1/2$. For fixed $q<1/2$, however, the capacity is $O(N^{n/2})$ for even $n\ge4$ and $O(N^{(n+1)/2})$ for odd $n\ge5$. For $n=3$, both the unbiased and fixed-bias capacities remain $O(N^2/\ln N)$. For $n\ge4$, these different asymptotic forms imply a nonuniform large-$N$ limit near $q=1/2$. Asymptotic matching predicts a bias-induced crossover in the region $1-2q=O(\ln N/N^{\lfloor n/2\rfloor-1})$. The crossover originates from a bias-dependent crosstalk mean that reduces the stability of sites carrying the more frequent value $-q$. Computer simulations are compared with the finite-size conditioned-Gaussian predictions. An activity-dependent control potential that cancels the conditional crosstalk mean restores the $N^{n-1}/\ln N$ capacity for fixed $0<q<1/2$ within the conditioned-Gaussian approximation.
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All authors Yuto Sakurai, Takeaki Shimokawa, Kazunori Iwata, Kazushi Mimura
Materials Science
Designing Homogeneous Ti-Nb-Fe-Sn $\beta$ Titanium Alloys by PBF-LB: A Pre-Alloyed Powder Blend Strategy
João Felipe Queiroz Rodrigues, Kristína Bartha, Mariano Casas-Luna et al. (+10 more)
Metastable $\beta$ titanium
alloys are attractive for biomedical and structural applications owing to their low elastic modulus, high specific strength, and excellent corrosion resistance.
Laser powder bed fusion (PBF-LB) enables complex-shape production and controlled compositional variation through powder blending. However, processing elemental Ti-Nb blends often results in chemical heterogeneity from incomplete dissolution of Nb-rich particles and non-
equilibrium phase formation. To address this, low-modulus Ti-Nb-Fe-Sn
alloys were produced by PBF-LB using Ti-42Nb, Ti-20Nb-15Fe, and Ti-20Nb-20Sn master-
alloy powders blended with commercially pure Ti. Ti-23Nb-3Fe-4Sn, Ti-26Nb-2Fe-4Sn, Ti-29Nb-1Fe-4Sn, and Ti-32Nb-4Sn were fabricated using an uncommonly large 70 $\mu$m layer thickness with layer remelting, followed by heat treatment at 1000 $\deg$C for 2 h and water quenching. After heat treatment, all
alloys exhibited low porosity, homogeneous chemical distribution, and single $\beta$-phase microstructures with predominantly equiaxed grains and weak crystallographic texture. Thermodynamic calculations indicated that solidification descriptors alone could not explain the non-monotonic grain-size
evolution, which was attributed to inherited solidification structure, transient TiFe-like phase formation, Nb/Sn partitioning, and/or solute-drag-controlled $\beta$-grain growth. Hardness and yield strength decreased with decreasing Fe and increasing Nb contents, from 268 to 224 HV and 691 to 468 MPa, respectively. Young's modulus, determined by resonant ultrasound spectroscopy, ranged 63-81 GPa. These results demonstrate that pre-alloyed master-
alloy blends combined with remelting and heat treatment provide an effective route for producing chemically homogeneous Ti-Nb-Fe-Sn $\beta$
alloys while revealing how small compositional changes govern grain-growth behavior and mechanical response.
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All authors João Felipe Queiroz Rodrigues, Kristína Bartha, Mariano Casas-Luna, Gilberto Vicente Prandi, Márcio Sangali, Kateřina Ficková, Jiří Kozlík, Michaela Šlapáková, Martin Koller, Adam Strnad, Josef Stráský, Miloš Janeček, Rubens Caram
Artificial Intelligence
JustFit: Just-in-Time State Management for Local LLM Serving
Yuhua Chen
Local
agents need
memory for model execution and working history. We present JustFit, an MLX runtime that coordinates their overlapping allocations: KVExec executes and checkpoints four-bit KV with bounded workspace, PhaseSwap loads phase-dependent components, and StateTrans preserves history across execution modes. With Qwen3.8-27B MXFP4 on a 24 GiB M4 Pro MacBook, JustFit reaches 327,680 retained positions across two requests, 10.67 times the evaluated baseline's 30,720-position single-request record. One request completes the full 262,144-position native window at median 5.986
tokens/s. Each shape completes 16,384 outputs per request in three fresh processes: B1 uses one cold build and two prefix extensions; B2 uses three ordered prefix extensions (Section 4). Image encoding can proceed while preserving a live 196,608-input text request. A controlled, repetitive 32K+6K workload reaches median 18.284
tokens/s at 15,626 MiB; a separate AIME 2026 evaluation scores 29/30. Coordinating execution and state lifetimes makes longer histories feasible on personal hardware.
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Machine Learning
Iterative Calibration and Learning: Mitigating Teacher Bias in LLM Distillation without Target-Domain Reward Feedback
Haichen Hu, Yuheng Zhang and David Simchi-Levi
Large
language model (LLM)
distillation can propagate teacher bias under
covariate shift when target reward feedback is unavailable. We propose Iterative Calibration and Learning (IterCaL), which alternates source-reward teacher calibration through
token-level branching with student learning on target
prompts. We prove
polynomial convergence in expected average KL to the oracle student, the reference-regularized target-reward maximizer within a potentially misspecified student class; a quantified source-to-target calibration discrepancy gives an explicit additive true-return term. Our separation shows that regularized direct teacher matching retains positive oracle-KL error at its population optimum for every shared reference penalty, even when the teacher is stronger than every student. On the same instance, IterCaL converges to the oracle using source rewards alone.
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