Papers

Irregular time series, characterized by non-uniform sampling intervals, missing observations, and variable lengths, are ubiquitous in healthcare, mobility, and environmental monitoring, yet effective and interpretable classifiers for this setting are limited. Existing approaches often rely on imputation, which can obscure the temporal structure of the data, or require complex neural architectures that are opaque and difficult to explain. In this work, we extend the Bag-Of-Receptive-Fields (BORF), a fast, deterministic, and interpretable transform for time series, to the irregular setting. Our key contribution is a time-weighted normalization scheme in which each observation is weighted proportionally to its associated time delta, making pattern extraction sensitive to the actual temporal distribution of samples rather than only their index position. This requires deriving an efficient sliding-window recurrence for the time-weighted standard deviation, preserving the linear time complexity of BORF. We benchmark the resulting method against state-of-the-art irregular time series classifiers on datasets from the PYRREGULAR repository, demonstrating competitive classification performance with the added benefit of human-interpretable explanations.

We investigate the phase diagram and critical properties of the two-dimensional classical XY model with interactions decaying as $1/r^{2+\sigma}$. At the marginal case $\sigma=2$, we show that the low-temperature phase is characterized by logarithmic quasi-long-range order (log-QLRO), where spin correlations decay as a power of the logarithm of distance, $C(r)\sim(\ln r)^{-\eta_\ell}$ with $\eta_\ell\propto T$, and that the transition into this phase is a continuous transition beyond both the Ginzburg-Landau-Wilson paradigm and the Berezinskii-Kosterlitz-Thouless mechanism. Our analysis combines a near-exact Gaussian spin-wave theory, an adiabatic renormalization-group analysis, and large-scale Monte Carlo simulations. We find that the $1/r^4$ interaction logarithmically modifies the spin-wave stiffness kernel as $\gamma(k)\simeq\kappa k^2\ln(1/k)$, which suppresses vortex proliferation and gives rise to a nonuniversal correlation-length exponent $\nu\propto1/\sqrt{2\pi\kappa}$. Crucially, our simulations reveal that the short-range algebraic QLRO phase is unstable against a weak long-range perturbation for $\sigma\le2$. These results establish $\sigma=2$ as the crossover boundary between the long-range and short-range universality classes and provide a critical evaluation of recent theoretical proposals.

Fine-grained vision-language alignment in chest radiography enables zero-shot classification, grounding, and segmentation without task-specific annotations. However, this alignment is fundamentally hindered by two intertwined sources of ambiguity: projection-induced visual mismatch and patient-agnostic semantic overlap. First, at the local feature level, frontal and lateral radiographs exhibit distinct appearances for the same clinical finding, rendering a shared patch-text similarity geometry inherently suboptimal. Compounding this visual ambiguity is a semantic mismatch during global contrastive optimization, where instance-level objectives penalize cross-patient pairs as strict negatives even when they share identical positive clinical concepts. To address this dual ambiguity, we propose PLRS-IC, a unified dual-calibration framework for chest X-ray representation learning. At the local alignment stage, Projection-Conditioned Low-Rank Residual Similarity (PLRS) dynamically adapts patch-text matching to projection-specific manifolds using a bounded, parameter-efficient low-rank residual. At the global optimization stage, Information-Content-Calibrated Soft False-Negative Suppression (IC-SFNS) leverages a corpus-derived information-theoretic prior to soften the penalty of semantically overlapping negatives without altering original contrastive assignments. Extensive experiments across nine public zero-shot benchmark settings demonstrate that our framework yields consistent improvements in classification, grounding, and segmentation, validating the necessity of dual-calibration in medical vision-language pre-training.

The Segment Anything Model (SAM) achieves remarkable performance in visual segmentation. The latest SAM3 extends promptable segmentation to concept-level prediction, broadening the scope of segmentation foundation models. While recent works reveal that SAM and SAM2 are vulnerable to adversarial examples, the robustness of SAM3 under the concept segmentation paradigm remains unexplored. In addition, existing adversarial attacks on SAM-series models exhibit limited cross-prompt transferability. To this end, we propose AdvPCS, a universal cross-prompt adversarial attack for Promptable Concept Segmentation (PCS), including a min-max prompt optimization strategy, a global-local perception deception attack, and a temporal transition deviation attack. Specifically, we first identify the hardest-to-attack prompts via min-max bilevel optimization. In the inner maximization, we enhance diversity over candidate point, box, and text prompts. In the outer minimization, we select prompts with the highest responses based on the confidence scores output by the detector. Given the selected prompts, we apply the perception deception attack to minimize both global and local existence probabilities under joint prompting and employ the temporal memory misalignment attack to maximize inter-frame semantic inconsistency and corrupt memory pointers. Extensive experiments on four benchmark datasets show that a single universal adversarial perturbation (UAP) generated by our method generalizes across frames from different videos and achieves strong attack performance under point, box, and text prompts. In particular, it reduces the average mIoU of various PCS models on the SA-CO dataset to below 5% under text prompts, demonstrating strong attack ability.

Many of the thousands of existing cryptocurrencies suffer from declining adoption, low liquidity and weak security, and merging two of them into a single ecosystem is a natural alternative to abandonment. No rigorous framework exists, however, for determining a fair exchange rate in such a merger. Unlike that of a corporation, the value of a cryptocurrency is driven by network effects, so the exchange rate itself influences the value of the merged asset. We extend the exchange-ratio framework of Mainini, Moretto and Visetti [7] by making the merged value endogenous: the exchange rate determines community migration, migration determines (up to user overlap) the post-merger network state, and an axiomatised valuation function assigns a value to that state. The resulting synergy has no predetermined sign, and the bounds of the bargaining region become self-referential in the exchange rate. We prove that no exchange rate at which the merger destroys value preserves wealth, and that the pre-merger price ratio preserves wealth exactly when the merger does not destroy value at that rate. In that case, under explicit threshold conditions, the price ratio satisfies all five of our fairness conditions – wealth, adoption, security, governance and liquidity preservation – and, under strict versions of these conditions, the admissible set contains a nondegenerate interval around it, the wealth-admissible set one of explicit width. The network-value laws proposed in the literature, from the linear law to Metcalfe's and its generalised power-law forms, share a convexity property that yields the Lipschitz control behind these estimates. Liquidity emerges as the only non-wealth condition that can disconnect the admissible set.

A concept subspace's effect on model behavior does not establish how it relates to the output readout. We introduce a two-sided geometric diagnostic that measures an extracted subspace's overlap with the dominant right-singular directions of the unembedding matrix, evaluated against output-oriented positive controls. Given an extracted basis, the raw diagnostic requires only model weights. Our testbed is the Format-Agnostic Reasoning Subspace (FARS), a ten-dimensional basis extracted from eighteen reasoning concepts expressed in six surface forms. Across nine rank-matched estimators and twenty-six models, four activation-derived concept estimators carry only 0.38–0.80% mean energy in the top-ten readout span. Final-layer PCA carries 3.56%, exceeding FARS in 25 of 26 models. A same-layer next-token control, evaluated using a fitted linear translator for depth matching, carries approximately thirteen times more energy than FARS, with separation in all 25 tested models. Re-extracting FARS on ten disjoint concepts yields 62–100% cross-format retrieval across twenty-four generative models, demonstrating transfer of the extraction procedure rather than a fixed basis. A complementary four-model, three-seed intervention study finds model-dependent source-directed effects that remain well below full-vector replacement. Together, the geometry and intervention controls distinguish concept structure from dominant readout directions while limiting claims of causal sufficiency.

Qiu, Guan, and Yu conjectured that in the even-order Kaleidoscope Yang–Baxter equation every word $\Lambda T^{k_1}\Lambda\cdots T^{k_M}\Lambda$, built from a square-zero matrix $\Lambda$ and integer powers of a shift $T$ of order $N$, vanishes once $M\geq N/2$. We prove this for every even $N\geq4$ and every complex parameter $u$ with $u\neq0$ and $u^N\neq1$, and show that the bound is sharp. For $M=N/2-1$ we determine exactly which words are nonzero; each of them has rank two. After block reduction, the factors associated with the intervening powers of $T$ lower a common flag of length $N/2$ by at least one step. The spectral idempotents of $T$ then give a presentation of the algebra generated by $T$ and $\Lambda$ by paths between levels, in which two paths compose only when the level changes monotonically. This algebra is independent of $u$, has dimension $N^2-N+2$, and is a pullback of two incidence algebras. Its radical is generated by $\Lambda$ and has nilpotency index $N/2+1$, and the algebra has infinite global dimension and infinite representation type. Replacing powers of $T$ by arbitrary functions of $T$ gives exact rank formulas and, for $N\geq6$, rank-one elements in the top radical power. Finally, four conditions on a filtered pair of operators over an arbitrary field recover the threshold and the radical; none of them can be omitted.

Decision-focused learning (DFL) trains predictors through downstream objectives, but a different loss need not provide an independent parameter-update direction. We characterize this restriction through the predictor Jacobian, using sparse index tracking to distinguish the covariance entries read by the optimizer from the parameter directions available to learning. Rank-one Jacobians make nonzero per-example gradients collinear; a conditional spectral bound describes near-collinearity. A batch-subspace characterization and counterexamples show why these local statements imply neither common minimizers nor collinear batch updates. Experiments examine when geometry translates into decision quality. Across 38 one-parameter equity configurations, DFL gains over MSE remain below 1.8%; a 385-parameter conditional predictor also has pointwise rank one. In validation-tuned shortest-path and knapsack experiments, full-capacity SPO+ reduces mean regret by 11.6% and 10.6%, respectively; only knapsack survives correction across eight comparisons. The capacity contrast persists on fresh datasets across batch orders and training budgets. Holding expressivity fixed, invertible coordinate scaling lowers spectral effective rank and ordinary SGD gains; compensating for the scaling restores the original trajectories. Financial forward-target controls separate forecast accuracy from decision quality; a matched neural comparison finds no aggregate DFL advantage in the tested architecture. These findings distinguish local rank restrictions, coordinate-dependent optimization and predictive accuracy. Predictor geometry helps explain available learning directions, while held-out decision quality remains the test of practical benefit.

We prove that the $(-2,3,7)$ pretzel knot is the only hyperbolic knot of genus at most $5$ with a lens space surgery. Our key technical result asserts that if a genus-$g$ hyperbolic knot $K$ has an elliptic surgery of slope greater than $4g-3$, then the invariant foliations of its monodromy have an orientation that is reversed by the monodromy, and so the opposite of the dilatation must be a root of the Alexander polynomial of $K$. Combined with prior work of Moser, Wu, Bleiler–Litherland, Baker, and Greene, this verifies the Berge conjecture for knots of genus at most $5$.

Modern neural networks scale predictably, yet the mechanisms behind these regularities remain unclear. Neural redundancy is typically characterized by component importance or representational similarity, both indirect proxies. We view redundancy as an input-conditioned, dynamic relation: intermediate computational states are functionally redundant when they induce similar downstream responses. We introduce Conditional Functional Substitutability (CFS) to directly characterize such functional substitution. CFS exposes functional relations and reduction potential missed by conventional importance- and similarity-based measures. Across modalities and Transformer families, CFS reveals systematic functional reorganization with scale. Controlled scaling further shows that performance gains need not track growth in substitutability, while fixed-capacity models with more independent functional structure perform better, providing a functional account of diminishing returns. Predicted CFS further enables dynamic computation with a better performance–computation trade-off than importance-based component selection, suggesting new directions for redundancy-aware computation and more efficient model scaling.

Characterizing entanglement in quantum materials through experimentally accessible observables remains a central challenge. Quantum Fisher information associated with sums of one-site spin operators provides one route by linking entanglement to measurable magnetic response functions. Extending this approach to local composite observables requires new entanglement bounds. Here we establish a rigorous bound for the total nearest-neighbour vector chirality of periodic spin-$1/2$ chains with an even number of sites. The quantum Fisher information per spin cannot exceed $k+1$ for any $k$-producible state, so exceeding this bound certifies entanglement depth of at least $k+1$. Combining infinite density-matrix renormalization group and thermal pure quantum-state calculations, we demonstrate multipartite entanglement encoded in vector-chiral correlations at zero and finite temperatures in an extended $J_1$-$J_2$ XXZ chain. The spin-current coupling between vector chirality and electric polarization offers, in principle, access to this witness through dielectric loss spectroscopy in multiferroic magnets, extending entanglement diagnostics beyond dipolar spin correlations.

Accurate forecasting of electricity production is essential for maintaining the operational efficiency and strategic planning of energy utilities. In industrial settings, such forecasts are generated daily to ensure supply-demand balance and optimal management of production assets. However, the increasing complexity of modern power systems and data flows poses significant challenges for ensuring the reliability and consistency of these forecasts. This paper addresses the problem of anomaly detection in short-term production forecasts at EDF, formulated as identifying atypical intra-day patterns that may signal data quality issues or operational irregularities. We introduce TAMIS, a scalable and interpretable system that analyzes daily production time series to automatically detect anomalous days based on deviations from historical patterns learned from past data. Designed for human-in-the-loop workflows, TAMIS surfaces top-ranked anomalies through an automated daily newsletter, enabling efficient expert review and continuous monitoring. An extensive experimental evaluation on real-world industrial data demonstrates that TAMIS achieves the best accuracy-efficiency trade-off compared to baseline methods. To foster further research and reproducibility, we publicly release the anonymized application datasets used in our study.

European option smiles determine the risk-neutral marginal laws of an asset, but not their intertemporal coupling, which is decisive for many applications. The Bass martingale construction selects, among all calibrated martingales, the one closest to Bachelier dynamics; it permits fast calibration at discrete maturities and recovers the Dupire local-volatility (LV) model as the maturity grid is refined. This article develops a modular calibration overlay for existing stochastic and path-dependent volatility models. We sequentially construct a martingale that matches all prescribed marginals exactly while remaining as close as possible, in an adapted Knothe-Rosenblatt sense, to the reference dynamics. As with the Bass LV model, each calibration step is amenable to an efficient Martingale Sinkhorn algorithm. We develop the theoretical foundations, numerical implementation and consider convergence to the SLV model. We also benchmark the method for Heston and Bergomi finite-factor path-dependent volatility dynamics and develop the multi-asset extension.

We show that periodically modulating the self-propulsion of active particles in an asymmetric potential can both enhance rectified transport and reverse its direction, even when the propulsion speed itself never changes sign. Current enhancement results from the nonlinear response of active transport to propulsion strength, whereas current reversal emerges from the interplay between activity-induced spreading and passive relaxation. Our theoretical analysis identifies the regimes governed by these distinct rectification mechanisms and predicts the finite range of driving periods over which current reversal occurs. These results establish cyclic activity as a means of dynamically controlling rectified active transport, with potential applications to the selective sorting of active particles.

Given any tracial von Neumann algebra $\mathcal{A}$, the first author has defined a unitary tensor functor $\Phi:{\rm Rep}(\mathcal{Q}_{\rm aut}(\mathcal{A}))\to {\rm Bimod}(\mathcal{A})$ in his paper [Gos24]. In this paper, we consider $\mathcal{A}$ to be the underlying von Neumann algebra of $C^*(S_3)$ and show that given any DQG $\mathcal{Q}$, which contains $C^*(S_3)$ as a quantum subgroup and has an outer action $\tilde{\Phi}$ (in the sense of Definition 3.4}) on ${\rm Bimod}(\mathcal{A})$, which agrees with $\Phi$ when restricted on ${\rm Rep}(C^*(S_3))$, is monoidally equivalent to the DQG $C^*(S_3)$. Furthermore, given any DQG $\mathcal{Q}$ with an outer action $\Gamma:{\rm Rep}(\mathcal{Q})\to {\rm Bimod}(\mathcal{A})$, such that $ {\rm Out}(\mathcal{A})\subseteq {\rm Im}(\Gamma)$, is either monoidally equivalent to Out$(\mathcal{A})$ or monoidally equivalent to $C^*(S_3)$ itself.

We derive the classical logarithmic soft graviton theorem for the scattering of massive particles in four-dimensional asymptotically flat spacetime using a position-space analysis of the Weyl tensor. Starting from the Iyer-Damour multipole solution in harmonic gauge, we obtain an infinite tower of antipodal matching relations across spatial infinity for all five Newman-Penrose Weyl scalars, at linear order in $G$ and for the leading matter-induced logarithms at order $G^2$. We connect the relation relevant to the logarithmic soft theorem to the radiative-gauge formulation of Boschetti-Campiglia and Compère-Robert. We then compute the required asymptotic fields directly from scattering data, including matter contributions and nonlinear effects responsible for graviton drag. Combining these results with the Newman-Penrose evolution equations yields position-space proofs of the classical leading and logarithmic soft graviton theorems, independently confirming the frequency-space derivation of the latter originally performed by Laddha and Sen.

We study functional inequalities along Wasserstein geodesics. If $\mu$ 0 and $\mu$ 1 are respectively $\kappa$ 0 -and $\kappa$ 1 -strongly log-concave probability measures on R n , we prove that their quadratic Wasserstein geodesic satisfies for all probability measures $\nu$ on R n . The coefficient is sharp. By linearization, this recovers the Poincaré estimate of Han and Zhu [15]. On the real line, we prove convexity of the square roots of the optimal T 1 and T 2 constants along monotone interpolation between arbitrary probability measures. The argument applies to more general transport entropy inequalities. We also establish convexity of the rescaled L p Poincaré constants for every finite p $\ge$ 1, including the square root of the Poincaré constant and the inverse Cheeger constant. Finally, we construct a planar Wasserstein geodesic whose endpoints satisfy T 2 and all finite-p L p -Poincaré inequalities, whereas every interior interpolant fails these inequalities.

In atmospheric neutrino analyses, the usable zenith-angle range is generally restricted to upward-going events to suppress the cosmic-ray muon background. Motivated by the exceptionally low underground muon background at the China Jinping Underground Laboratory (CJPL), we investigate whether extending the zenith-angle acceptance can improve the sensitivity of atmospheric neutrino oscillation measurements. An existing 1725 m$^{3}$ liquid-nitrogen volume is adopted as the basis of a simplified detector model, in which the accepted zenith-angle range is extended from $\cos\theta_{\mu}\in[-1,0]$ to $\cos\theta_{\mu}\in[-1,0.3]$, and the projected oscillation sensitivity is evaluated for a 10-year exposure. The atmospheric neutrino flux is estimated by interpolating standard flux predictions as a function of geomagnetic latitude. Neutrino interactions in the surrounding rock and the liquid-nitrogen volume are simulated for neutrino energies of $E\ge0.1$ GeV, followed by secondary-particle transport and geometry-based event selection. For the benchmark oscillation parameters $\Delta$m$^{2}_{32}$ = $2.4\times10^{-3}\ \mathrm{eV}^{2}$ and $\sin^{2}\theta_{23}=0.5$, the neutrino-induced muon flux from the surrounding rock is estimated to be $(3.65 \pm 1.00)\times10^{-13}$ cm$^{-2}$ s$^{-1}$ sr$^{-1}$, corresponding to a muon yield of $(0.13 \pm 0.034)$ day$^{-1}$ in the 1725 m$^{3}$ liquid-nitrogen volume. Three-flavor neutrino oscillations are incorporated into a Poisson-likelihood $\chi^{2}$ analysis to evaluate the sensitivity to the oscillation parameters. Extending the usable zenith-angle range leads to a clear improvement in the projected oscillation sensitivity at the 90% confidence level over a 10-year exposure.

Federated learning (FL) is a promising paradigm of machine learning, which preserves user privacy by enabling learning without sharing raw data with a cloud server. Straggling clients have been a problem for FL as they introduce delays in aggregating the local models and hence, the convergence of the global model. Therefore, it is important to have a mechanism that ensures fast convergence of the global model as well as good FL participation rate. Another issue for the convergence of a model in FL is the non-independent and identically distributed (non-iid) data across the clients. Prior approaches based on probabilistic client selection do not work well under non-iid data especially when the number of clients is small. We show scenarios where such approaches fail and propose a joint client-training data selection algorithm for fast convergence of FL models. Our experiments on CIFAR-100 dataset show that convergence of the FL model can be significantly improved over prior works that can consider non-iid data and heterogeneous computation and higher model accuracy.

Miniaturizing magnonic circuits and increasing their processing speed require spin waves with progressively shorter wavelengths. However, conventional directional couplers rely on the dynamic dipolar interaction between spatially separated waveguides, which rapidly weakens in the exchange-dominated regime. As a result, their coupling length increases as the spin-wave wavelength decreases, limiting further device miniaturization. Here, we introduce an exchange-mediated directional coupler by replacing the nonmagnetic gap between two waveguides with a magnetically modified YIG spacer. The spacer provides a continuous exchange pathway and preserves the splitting between the symmetric and antisymmetric modes at large wavenumbers. We develop an analytical model to describe this mechanism and verify it using micromagnetic simulations. Based on this concept, we design a straight coupler without curved access waveguides, with a footprint of only 400 nm * 30 nm. For a spin-wave wavelength of approximately 100 nm, the device transfers approximately 98% of the normalized output power to the target waveguide. Its performance remains nearly unchanged even when the damping of the spacer is strongly increased. These results overcome the short-wavelength limitation of dipolar couplers and provide a route toward highly integrated magnonic circuits for information processing.

Randomised copies of a connectome are the usual baseline for asking whether measured wiring matters, and the answer depends on what the randomisation preserves. We evolved embodied foraging agents whose brains are a compressed adult Drosophila connectome (FlyWire v783; 512 cell-type groups and 1,000 Kenyon cells) alongside agents built on randomised wiring, in pre-registered experiments with ten seeds, four ecologies and 600 generations. Two standard randomisations, a column shuffle and degree-preserving edge swaps, route 10.6 to 10.7 % of olfactory output directly onto descending motor groups, against 0.012 % in the connectome. On the registered primary endpoint, fitness averaged over the run, no difference was detected; at the last common-garden probe the connectome was behind both controls (-0.22 and -0.20 fitness units on seed means). Against controls that keep every sensory-output and motor-input edge and rewire only the interior, the seed-mean difference lay within a +/-0.10 equivalence bound (+0.002 and -0.074, unchanged under a calibration that also matches activity spread), although per ecology the interior column shuffle was ahead by 0.26 in one of four ecologies at ten seeds, a lead that ten further pre-registered seeds did not replicate. Rewiring the connectome so that it acquires the shortcut raised its fitness by 0.44 (10 of 10 seeds) and its dependence on olfaction from 0.15 to 0.99; graded doses raised both in step; at comparable swap counts the full dose was ahead of an interior-only sham by 0.53 (10 of 10 seeds); and a sham that rewired the same boundary edges without creating shortcuts matched the connectome (+0.007) while the full dose was ahead of it by 0.60. What a null preserves at the sensory-motor boundary can decide an evolutionary connectome comparison, and sensory-to-motor path statistics belong next to the degree statistics a null is said to preserve.

Standard language model RL algorithms credit every token of a long rollout with the same advantage determined by the terminal reward. Actor-critic methods can provide finer-grained credit assignment, but learned critics are generally considered too inaccurate to trust when training LLMs with RL. In recent works, even when a critic is present, it is used only for baseline estimation, so every trajectory must be rolled out to its terminal reward. We introduce Actor-Critic with Action Chunking (AC2) that removes the need to roll every trajectory to completion. AC2 instead assigns credit to action chunks: short continuations of prefixes of past trajectories. A learned critic scores the state reached at the end of each action chunk, allowing the policy to update without observing a terminal reward. We make critic-based credit assignment reliable through three design choices. First, we introduce local readiness which uses critic-based updates on a problem only when the critic is sufficiently accurate on that particular problem. Second, when available, we provide the critic with a reference solution from a previous successful rollout. Third, we assign credit over action chunks of 10k tokens rather than individual tokens, giving the critic a more meaningful portion of the trajectory to evaluate. We train Qwen3-4B on FineProofs-RL using AC2 and evaluate on IMO-ProofBench. AC2 exceeds GRPO's peak validation score of 18.5% using 2.5x fewer decoding FLOPs. This gain comes from two sources, (1) AC2 requires 25% fewer training steps to reach this score, and (2) each step generates fewer tokens because the policy does not need to continue every trajectory to completion. Conceptually, we demonstrate that we can remove the need to roll out every trajectory to completion, opening up a large previously unexplored design space for LLM RL algorithms.

In this paper, we obtain two complete lattices that are sober with respect to the Scott topology, whereas the Scott space of their product is not a sober space. Thus, we answer a question posed by Miao, Xi, Jia, Li and Zhao in [8].

In interactive scenarios, an autonomous driving system is required to generate ego actions under the influence of other agents' behaviors. Existing World Action Models (WAMs) typically model other agents as components of the world model rather than as decision-makers that fundamentally shape the action of the ego agent, which impairs their performance in dense interaction scenarios. We introduce Reciprocal World Action Models (ReWAM), a game-theoretic world action modeling framework that captures the reciprocal influence between the ego agent and other agents by representing them as conditional responders whose actions are mutually influenced. We instantiate this framework with a Level-$k$ response hierarchy, where role-specific ego and other action DiTs exchange compact strategy tokens through cross-agent attention while remaining grounded in a shared representation of the future driving world. To learn the response policy of the ego agent from demonstrations, we formulate expert actions as samples from the best response distribution and jointly optimize the entire hierarchy using conditional flow matching. Our framework is evaluated on the NAVSIM dataset and achieves state-of-the-art performance compared to baselines. The improvement is particularly significant in interactive scenarios, validating that modeling reciprocal responses provides a more effective foundation for interaction-aware world action generation.

In this paper, we study nonlinear Schrödinger equations arising in the study of Markovian open quantum systems. These equations are derived from the normalization of linear stochastic Schrödinger equations. First, we prove the global well-posedness of the linear equation in the energy space, which is less regular than the usual space for this equation. Then, we show the indistinguishability of solutions to the nonlinear SPDE under a relaxation of the usual monotonicity assumption. Finally, by proving the pathwise uniqueness and normalizing the solutions to the linear equation, we are able to prove the well-posedness of solutions to the required class of nonlinear stochastic equations.

Causal interventions such as activation patching and distributed alignment search (DAS) are the main tool for making mechanistic claims about neural networks. Recent work showed that these interventions routinely push representations off the model's natural distribution, and that such divergence is sometimes harmless and sometimes pernicious: it can recruit pathways the model never uses on natural inputs, so that an intervention produces the expected answer through the wrong mechanism. No method currently tells the two cases apart. We make this question testable by planting hidden pathways inside pretrained language models; the pathways are silent on every benchmark prompt by construction, so which interventions depend on them is known exactly. Across 72 configurations and 100,800 interventions on GPT-2 small, we find three things. (i) Nearest-neighbour and local-PCA distances at the intervention site, as used in prior work, score below chance (AUROC 0.35-0.47) at picking out interventions that give the right answer through a planted pathway. (ii) Hidden-Pathway Contribution (HPC), a label-free test that clamps downstream units to the regime of natural runs with the same output and measures how much of the decision disappears, flags pathway-dominated interventions with AUROC >= 0.99 when the pathway shows up as unit-level out-of-regime activity, but fails when every unit stays within its natural range, which we identify as the open problem. (iii) Optimised interventions actively seek hidden pathways: on a gender task, DAS routes 90-95% of its successes through planted pathways for three of four families, and a downstream on-manifold penalty cuts this share to under 5% at a cost of 6-11 points of success rate. In unmodified GPT-2, successful interventions show almost no unit-level out-of-regime reliance.

Persistent homology can be differentiated and incorporated into learning pipelines, but no analogous framework exists for zigzag persistence, which is needed when the underlying topological structure evolves non-monotonically over time. We develop such a framework for sequences of simplicial complexes obtained by thresholding time-dependent filtering values on a fixed complex. By assigning persistence diagram endpoints the real-valued times at which linearly interpolated filtering values cross the threshold, we transfer the continuity of the filtering values to the diagram points. This yields smooth local lifts of the resulting persistence-diagram-valued map, from which we derive differentials almost everywhere under mild regularity conditions on the parametrization of the filtering values. We prove local Lipschitz continuity outside an explicit measure-zero exclusion set; standard stochastic subgradient convergence guarantees therefore do not apply directly. We argue that, even without such guarantees, this exclusion set is small enough in practice to allow effective optimization. We test this empirically in two experiments: sensor network coverage optimization and dynamic graph classification.

Let $A$ and $B$ be strongly Morita equivalent $C^*$-algebras, implemented by a nonzero imprimitivity bimodule $X={}_AX_B$ with its canonical operator-space structure. Denote by $Z_X$ their common multiplier centre, canonically identified through $X$. The coefficient action gives a complete contraction $\Theta_X:A\otimes_{Z_X,h}B\to\operatorname{CB}(X)$, where $A\otimes_{Z_X,h}B$ is the central Haagerup tensor product obtained by balancing over $Z_X$ and $\operatorname{CB}(X)$ is the space of completely bounded maps on $X$. We show that $\Theta_X$ is injective exactly when every Glimm ideal of $A$ is $2$-primal, and isometric, equivalently completely isometric, exactly when every such ideal is primal. For each positive integer $\ell$, norm preservation for sums of at most $\ell$ elementary tensors is equivalent to $(\ell^2+1)$-primality of every Glimm ideal. These conditions may equivalently be imposed on $B$. This extends the corresponding theorems of Somerset and Archbold–Somerset–Timoney to imprimitivity bimodules. We also show that, after matrix stabilization, the optimal constants bounding the central Haagerup norm by the completely bounded norm coincide for $X$, $A$ and $B$, at every finite tensor length and on the completed products, and agree with the corresponding constants after compact stabilization.

Cyclic coordinate descent is widely used to train support vector machines, but global linear convergence alone gives limited guidance about the rate on a particular instance. We study exact cyclic coordinate minimization for box-constrained convex quadratics and develop global contraction bounds that capture both coordinate order and boundary geometry. Our convergence certificate combines two ingredients: interactions between successive coordinate updates, encoded by the triangular part of the normalized Hessian, and objective growth, captured by a matrix lower bound on the optimality gap. It remains valid for cases with singular Hessians, nonunique minimizers, and updates clipped at the boundary. An error-bound specialization of our analysis strictly sharpens the Wang-Lin factor when both use the same error-bound constant. In the positive-definite case, the analysis shows that the worst-case contraction of one Gauss-Seidel sweep remains a global upper bound under box constraints, with equality for an interior optimizer. We also demonstrate the limitations of Hessian-only bounds by constructing a two-coordinate family with a fixed singular normalized Hessian, whose worst-case contraction approaches one as its boundary margin vanishes. The theory is complemented by practical procedures for bounding the worst-case contraction on individual instances and numerical evaluation on several classical SVM datasets.

How search strategies evolve in finite, depletable landscapes remains a question in foraging theory. We study this problem with an evolutionary simulation in which agents forage on a two-dimensional toroidal lattice containing non-renewable resources distributed uniformly or as Lévy dust. Each agent carries a heritable genome encoding step lengths, velocities, and turning angles, and selection acts on a fitness function combining energetic gain, movement cost, and coverage efficiency. By allowing movement traits to evolve without imposing a prescribed power-law step-length distribution, we test whether evolved trajectories are better described by intermittent-search or Lévy-walk dynamics. Our results indicate that evolved search is more consistent with intermittent dynamics than with strict scale-free Lévy motion in the finite depletion-driven landscapes considered here. We characterize the dynamics by fitting second- and fourth-order displacement moments to intermittent-search and Lévy-walk models. While a Lévy-like random walk fits the evolutionary trajectories well (mean adjusted $R^2$ > 0.9 in most tested conditions), intermittent search achieves a closer fit (mean adjusted $R^2$ > 0.99) for all tested resource distributions. This preference holds across the tested grid sizes and resource densities. Five independent evolutionary runs per environment on a 503 x 503 grid at nominal resource density $\rho$ = 0.15 reproduce this preference for the uniform environment and five Lévy-dust environments. Evolution rapidly reshapes the movement genome toward short displacements while retaining a sparse tail of longer relocations, consistent with local exploitation punctuated by occasional transfer. The framework provides a controlled setting for studying how search rules emerge under resource limitation and may inform resource-constrained exploration in autonomous systems.