Papers

Large language models (LLMs) can generate accurate responses, but these are void of diversity. We attempt to address this for the task of creative short story generation. Drawing on established writing conventions and known LLM limitations, we target variation in genre, tone, style, and named entities. To promote diversity across these dimensions, we introduce DivLM, an LLM post-training framework consisting of two phases. First, we perform continued pre-training on a creative writing corpus and restore instruction-following capabilities using weight residuals. We then apply reinforcement learning with a custom, composite reward function that jointly maximizes diversity across the targeted narrative dimensions while maintaining response quality. Our empirical results on two LLM families show that DivLM increases diversity metrics by more than 9% on average compared to alternative approaches, while preserving instruction following, overall response quality, and similarity to human outputs.

We prove that for any $p>4$ we can find a Schatten class Hankel operator $\Ha_\phi$ defined on the Hardy space of the infinite torus $H^2(\mathbb{T}^\infty)$ that belongs to the Schatten class $S^p$ but does not admit a bounded symbol, extending the previously known range $p>(1-\log\pi /\log 4)^{-1}=5.7388...$.

How can random order change the role of quantum memory in streaming? Later classical input can restore the usefulness of a quantum state consumed by earlier queries. We call this replenishment. We construct an artificial problem based on Hidden Matching, with repeated coordinate data and online matching requests. It admits a one-pass quantum algorithm using polylogarithmic space in uniformly random order, but unconditionally requires polynomial space both classically in random order and quantumly when all updates precede the requests. To prove the quantum lower bound, we strengthen the consumability bounds of Gilboa, Jain, and McClean for Multiple Hidden Matching. Without prior entanglement, any quantum encoding supporting $r$ independent matching requests requires $\Omega(r)$ qubits for $r\le N^{1/2-\delta}$ and every fixed $\delta\in(0,1/2)$, even with simultaneous revelation and arbitrary joint decoding. For sequential requests, the linear bound extends through $r=\Theta(\sqrt N)$. We also adapt Kallaugher's triangle-counting algorithm to uniformly random streams in which every edge is repeated equally often. Rebuilding the quantum sketch and resampling the classical estimator improve its expected-space bound in suitable parameter regimes. Finally, we extend the robust Noisy Gap Cycle framework of Assadi and Sundaresan to quantum streaming. A quantum communication lower bound for Block Hidden XOR yields an $\Omega(n)$ space lower bound in random edge order for large enough cycles, with consequences for several graph problems. Thus random order can enable replenishment of small quantum representations, while substantial space requirements persist for other tasks.

Electroencephalography (EEG) offers millisecond temporal resolution, but inferring underlying neural sources is a severely ill-posed spatial inverse problem. While deep learning has advanced spatial reconstruction, current architectures face a critical dilemma: frame-by-frame models discard vital temporal context, whereas full 4D spatiotemporal networks introduce an architectural trade-off between reconstruction accuracy and inference cost. We propose a novel two-stream framework that explicitly decouples global temporal representation learning from per-time-point spatial refinement. A Transformer-based Temporal Condition Encoder processes the entire EEG sequence via factorized spatiotemporal attention, retaining sensor-resolved features. A fixed inverse then maps these features into source-indexed conditioning for a per-timestep Source-Space Transformer or volumetric convolutional refiner. Extensive evaluations on realistic synthetic data demonstrate that this temporal prior dramatically improves spatial localization, outperforming classical and spatiotemporal baselines, particularly in high-noise and multi-source regimes. Training across diverse leadfields and explicit operator mismatches improves transfer to unseen head geometries and brings template-based reconstruction closer to subject-specific inversion. Furthermore, we apply the model trained only on synthetic EEG data to real-world EEG. A logistic regressor fit on source power differences in eyes-open, eyes-closed conditions successfully decodes age groups.

Mixture-of-experts (MoE) layers increase model capacity without a proportional increase in per-example computation. However, conventional flat routers can yield imbalanced expert utilization and treat experts as an unstructured collection, whose indices carry no topological meaning. We introduce BRANCH-MoE, a routing architecture that places \(E\) experts at the leaves of a binary decision tree of depth \(\log_2 E\). At each internal node the branching probability is centered on the arrival-weighted mean score of the traffic reaching that node. This mean is estimated using an exponential moving average, which promotes utilization of both child subtrees without an auxiliary load-balancing loss. We show that this moving-average estimate admits an explicit noise-lag trade-off. We prove that for linear node maps and log-concave arrival distributions, this mechanism prevents routing-mass collapse. We further establish that, under a frozen router, an expert's execution frequency controls its stochastic-gradient convergence rate, and that confident decisions near the root bound cross-device communication when experts are assigned to devices by tree prefix. We evaluate BRANCH-MoE against Switch softmax, DeepSeek-V3 dynamic-bias, Skywork logit-normalized, and deterministic hash routing on Criteo click-through-rate prediction, Forest Covertype, HIGGS, and YearPredictionMSD, using \(E=16\), top-\(4\) routing, and five random seeds. Our results show that hierarchical routing can preserve task quality and balanced utilization while inducing a topology that supports localized expert co-activation and reduced communication.

We design the first fully polynomial-time randomized approximation scheme ($\mathsf{FPRAS}$) for approximately counting and uniformly sampling common bases of two matroids given by their independence oracles. Moreover, our algorithms generalize far beyond this to Hadamard products of two probability measures on the Boolean cube satisfying a simple nonnegative curvature condition. These algorithmic primitives have myriad applications in statistical physics, polyhedral combinatorics, the theory of quantum many-body systems, and beyond. The central difficulty is that the hard constraints imposed by the two input matroids (or the two input measures, more generally) obstruct traditional approaches based on local Markov chains. Relaxing these constraints can restore rapid mixing, but configurations that satisfy the original hard constraints may become exponentially rare if this is done naïvely. Our main contribution is a novel approach for approximate counting that marries Markov chain Monte Carlo (MCMC) with convex programming to overcome these obstacles: - We relax the intersection by imposing an overlap penalty on the product measure formed by the two input measures. We prove, via an integrated Bochner-type method, that this "soft intersection" satisfies a Poincaré Inequality uniformly over all external fields. - We use samples from the relaxed distribution to solve a dual maximum entropy convex program inspired by the Gurvits capacity. This program reweights the soft intersection measure using external fields to boost the aggregate probability of configurations satisfying the hard intersection constraint, without changing their relative weights. We bound the success probability directly using the uniform Poincaré Inequality and smallness of the gradient norm. AI Disclosure: GPT-5.6 Sol Ultra and GPT-6 Astra Ultra were heavily used to develop the ideas in this paper.

The no-cloning theorem is a cornerstone result in quantum mechanics that forbids copying of general quantum information. More quantitatively, even given $N$ copies of an unknown state, any channel producing an $(N+1)$-copy state incurs a nonzero trace-distance error on some inputs. Turning this around, one can ask about the sample complexity of approximate $N\rightarrow N+1$ cloning: for a desired small error $\epsilon$, what $N$ suffices? For arbitrary pure states on a Hilbert space $H$, the answer is $N\simeq \dim H/\epsilon$ - astronomically large for most $H$ of interest. What if the input is promised to lie in a structured family? We examine a range of families fundamental to many-body physics and quantum information: $n$-mode fermionic Gaussian and Slater states, $n$-mode bosonic Gaussian states, and qudit phase states. For fermions, we construct optimal cloning channels, reducing the complexity from exponential to polynomial in $n$. For bosonic Gaussian states, we construct an explicit cloner that certifies polynomial complexity, without any constraint on the energy of the state; this channel, however, is not optimal in general. The fermionic and bosonic results follow from a single representation-theoretic framework, which generalizes previous work by Werner and by Chiribella and Yang; it also yields the cloners' unitary implementation. Furthermore, we explain why for many families the cloning complexity is linear in the dimension of the family manifold, via a controlled saddle-point evaluation of the frame potential at high $N$. The same calculation accounts for the analogous scaling of tomography complexity. The above framework does not cover phase states; for these we give an independent construction of a channel with optimal cloning fidelity. Our work complements recent results on cloning stabilizer states.

Measurement incompatibility enables quantum advantages in communication and state discrimination. It is also necessary for Bell nonlocality, which is used in device-independent protocols for quantum key distribution and private randomness generation. Classical communication can influence the receiver's outcome and must therefore be accounted for when certifying measurement incompatibility. We introduce union maximal leakage, which quantifies the information needed for a common classical explanation of all observed probabilities and is computed from them by a linear program. If a message of at most $k$ bits precedes the receiver's independent measurement choice, compatible measurements for each message give union maximal leakage at most $k$. This bound holds with any input-independent nonsignalling shared resource. In quantum theory, a violation also implies that the initially shared state is entangled. Conversely, union maximal leakage determines the minimum classical communication needed to reproduce the observations with compatible measurements and arbitrary nonsignalling assistance. For a fixed shared quantum state and receiver measurements, a violation is possible exactly when, for some message value, the receiver's measurements are Bell-nonlocal against two-outcome sender measurements on that state. For binary receiver outcomes, we show that a violation also certifies randomness private from the sender, even when the receiver's measurement depends on the sender's message and the sender retains quantum side information. We quantify this privacy through an explicit conditional entropy bound and establish composably secure randomness extraction in sequential protocols with device memory.

Random circuit sampling experiments, the leading demonstrations of quantum computational advantage, are tested with the linear cross-entropy benchmark (XEB), which scores outcomes by their ideal probabilities. We study what a high XEB score certifies about an untrusted quantum device. In the quantum query model, we show that the honest sampler's ideal score acts as a Tsirelson bound for efficient devices and certified randomness. First, exceeding the ideal score by a constant requires $\Omega(N^{1/3})$ queries for the Haar and Fourier oracle ensembles with $N$ outcomes, and this bound is tight; this proves an earlier conjecture for Haar-random states and extends it to Fourier sampling. Second, for Fourier sampling and for Haar-random states accessed through the canonical state-preparation oracle, the $n$-bit output of a device that makes polynomially many queries and scores within $o(1)$ of the ideal score has $n-O(\log n)$ bits of smooth min-entropy, even against an adversary who is entangled with the device and later learns the oracle; this is nearly optimal. As a corollary, sampling the collision distribution, which is proportional to the square of the ideal distribution, has query complexity $\Theta(N^{1/3})$, and a coherent version of the same algorithm approximately prepares quantum Hadamard products of states with uniform amplitude magnitudes. Both lower bounds rest on progress measures that bound the excess over the ideal score and increase only slightly with each query. For Fourier sampling the measure is the norm of the coherent amplitudes for removing pairs in a purification of the random function, combining the polynomial method with the compressed oracle technique; for Haar-random states it is the square root of the average level in an expansion in Dirichlet orthogonal polynomials, controlled by an exact identity for the effect of one observation.

A spiking neuron is a dynamical system exhibiting a limit cycle (a spike) when subject to sufficiently excitatory input. Famous neuroscience experiments by Bryant and Segundo as well as Mainen and Sejnowski revealed that the spike times of some biological neurons are more reliable when subject to time-varying stimuli compared to constant ones. Provided with an industrial physics-based transient noise SPICE simulation framework compatible with foundry transistor compact models, we have demonstrated similar behaviours for a CMOS analog spiking neuron designed for neuromorphic computing hardware platforms. Under constant excitation current, the neuron operates in oscillatory regime and the empirical periods (interspike intervals) suffer from accumulated phase noise (jitter) during successive cycles, mainly due to the thermal noise of transistors. A time-varying input is reported to be capable of triggering output spikes according to a controlled statetransition mechanism, thereby significantly reducing the spike time jitter in the excitability regime. The physical limitation of the oscillatory or rate-coding regime in terms of reliabilitydissipation tradeoff is further evidenced by a stochastic thermodynamic uncertainty relation, a theorem that applies to general overdamped dissipative stochastic dynamical systems.

We establish an a priori $C^2$-estimate for complex Hessian equations on compact Hermitian manifolds. As an application, we obtain a regularity result for solutions to complex Hessian equation with densities of the right hand side depending on the solution. This generalizes Székelyhidi–Tosatti's result to the setting of complex Hessian equations on Hermitian manifolds.

Beam search repeatedly makes many children, removes duplicates, and keeps the best $B$. We show how many GPUs can perform these steps as one search even when the retained set does not fit on one device. States and candidates stay on the GPUs; the CPU receives only small control and ancestry records. We prove that an abstract distributed pipeline returns the monolithic reduced-key top-$B$ for the same complete candidates, integer scores, Hash128 equivalence, and a fully specified physical-layout tie order, provided that its implementation performs one global reduction per key and race-free routing. A static audit of the historical one-T4 pin leaves cross-buffer uniqueness unresolved and identifies a separate multi-rank scatter risk; neither is a reproduced failure, and other revisions inherit neither defects nor correctness without comparison. On eight H200 GPUs, a Cube4 run completed saturated depth 8 at $B_{\rm eff}=2{,}900{,}361{,}216$ in $931.266$ s: $69{,}608{,}669{,}184$ nominal parent–generator pairs, or a derived $74.746$ million pairs/s. A separate two-T4 Megaminx run yielded a derived $30.274$ million nominal parent–generator pairs/s at $B_{\rm eff}=82{,}837{,}504$. Those tasks and hardware differ, so they do not establish strong scaling. Separately, on one eight-RTX-3060 host, fixed-count eight-GPU speedup was $7.487$ under a common execution profile and $5.605$ under selected stable profiles; weak actual-work throughput gain was $6.113$ and $7.295$. These profile-sensitive ratios use each series' own one-GPU baseline.

The universality index corresponding to a word is the largest integer k such that every word of length k over the given alphabet occurs in it as a subsequence. Relative to languages this notion can be investigated with respect to both existential and universal quantifiers, with the former corresponding to the existence of a word in the language with universality index at least k, while the latter considers the index across all words that the language contains. In this work we study the existential (exists-universality) and universal (forall-universality) subsequence universality (as introduced in [Adamson et al., ISAAC 2023]) for binary languages consisting of all words with a fixed number of letters a, letters b, and subsequences ab. We prove that both exists- and forall-universality admit exact arithmetic characterizations for these languages. Extending the above notions, we end the paper by initiating the analysis of the probability of a fixed word occurring as subsequence of the words in such a language. To this end, we prove that, for every fixed pattern word w and an error tolerance, given as input the subsequence counts describing a language, the ratio of words in the language having the pattern w as a subsequence admits an additive approximation scheme that is polynomial-time in the binary encoding of the input counts.

It is well known that the pumping lemma for regular languages over finite alphabets does not extend to infinite alphabets. Instead, the generalized version of the pumping lemma for infinite alphabets states that the pumped patterns need not be identical, but only equivalent up to a finite-order permutation of the alphabet. This generalized variant of the pumping lemma involves two parameters: the length of the pumped pattern and an upper bound on the order of the permutation. We improve the known permutation-order bounds from factorial to tight bounds governed by Landau's function. We also show that, if the pumping length is sufficiently large, then permutations of order at most two always suffice. Our main structural result concerns the one-register case: every one-register automaton satisfies the classical pumping lemma, with no alphabet permutation. We prove a quadratic upper bound on the pumping length and give a matching quadratic lower bound up to constant factors. The same classical pumping phenomenon is shown for hierarchical register automata. Finally, we prove that, in general, deciding whether a quasi-regular language is pumpable for given constants is undecidable, while the minimal classical pumping length is computable for non-guessing one-register automata.

We investigate whether continued pretraining on Russian legislative documents improves a Russian ModernBERT encoder on legal text. The adapted model, RuModernBERT-ruLaw, was trained on a corpus reported to contain 304,382 legislative documents and 194,425,905 corpus tokens. Corpus token counts are distinguished from positions produced by the model tokenizer. We compare the original and adapted encoders on a fixed external collection of 1,031 court-decision segments. Both models receive the same hidden positions in each of five masking realizations. At maximum input lengths of 512, 2,048, and 8,192 tokens, mean masked-token cross-entropy decreases by 0.10942, 0.07052, and 0.06604 natural-log units, respectively. The reported 95% intervals summarize sensitivity to masking on this fixed collection; they do not quantify uncertainty across document collections. A second evaluation addresses legal-entity extraction. The original and adapted models achieve entity-level F1 scores of 0.99852 and 0.99820. However, 99.95% of test spans have the same normalized surface form and class in the training split. This evaluation therefore provides limited evidence about transfer to previously unseen forms. The paper explains the masking objective, overlapping windows, averaging rules, and exact entity-boundary scoring using editable diagrams and clearly marked illustrative examples. The comparison supports lower masked-token prediction loss for the studied pair of models and collection. It does not isolate the contribution of distant context or establish practical legal utility.

Motivated by educational applications, we study the problem of computing all corrections that transform a finite automaton into one recognizing a given regular language L. We show that for deterministic finite automata the set of all corrections can be finitely characterized as a regular tree language. The construction is based on a tree encoding of all deterministic finite automata recognizing L, which is extended to correction trees that make individual corrections and their induced edit-operations explicit. Leveraging the closure properties of regular tree languages, we introduce so-called filters for selecting corrections satisfying didactic constraints, enabling the derivation of individualized feedback from student submissions.

We answer, in the principal setting, a question of Matui on the almost finite–purely infinite dichotomy for minimal amenable ample groupoids. We prove that a second-countable Hausdorff minimal principal topologically amenable ample groupoid with Cantor unit space is strongly almost finite if and only if it admits an invariant probability measure; if no such measure exists, then it is purely infinite. We also prove that every bounded-degree uniformly Borel amenable Følner graph is Borel almost finite. The proofs combine the recent three-to-two comparison method of Glasner and Liu with the randomized Følner packing methods of Elek and Timár.

We construct an odd smooth initial density for the unforced incompressible porous media (IPM) equation on $\mathbb T^2$ whose solution develops a finite-time blowup. The components $\partial_{x_2}\rho(t,0)$ and $\partial_{x_1}u_1(t,0)$ tend to $+\infty$ as the maximal smooth existence time is approached, while the density and velocity remain bounded in $L^2$. Starting from a stationary solution, we iterate the angular amplification of localized oscillations with rapidly growing frequencies, adapting the mechanism of Córdoba and Martínez-Zoroa [7] for forced IPM. Each perturbation is constructed from time zero and creates the geometry configuration for the next iteration stage. A one-sided upper bound for the pressure Hessian is applied to control backward preparation and initial perturbations, following an idea from the Euler construction of OpenAI [14].

Bianisotropic metasurfaces provide electromagnetic functionalities that cannot be achieved through electric and magnetic responses alone, enabling asymmetric scattering, directional absorption, and advanced wavefront control. At optical frequencies, however, most demonstrations rely on static nanostructures whose magnetoelectric response is fixed after fabrication. Here, we investigate the opportunities enabled by dynamic reconfiguration of electromagnetic bianisotropy using a thermally tunable silicon–VO$_2$ metasurface operating in the near-infrared. By combining a collective-polarizability framework with numerical simulations and experimental characterization, we show that the insulator-to-metal transition of VO$_2$ modifies not only the electric and magnetic responses of the metasurface, but also its magnetoelectric coupling, providing access to distinct bianisotropic states within a single platform. Temperature-dependent experimental characterization confirms the thermally driven evolution of the absorption asymmetry. Based on this framework, we identify different operational regimes and demonstrate how bianisotropy reconfiguration enables transmissive and reflective directional functionalities, including transmission power-limiting, power-dependent asymmetric reflection, and power-dependent absorptivity/emissivity. These results establish dynamic control of magnetoelectric coupling as a powerful degree of freedom for multifunctional and adaptive photonic metasurfaces for optical and thermal applications.

We present a cosmology-aware generative model for super-resolution (SR) of cosmological $N$-body simulations in particle phase space. The model jointly generates displacements and velocities, conditioning a generative adversarial network (GAN) based generator and discriminator on evolved low-resolution (LR) fields and five $\Lambda$CDM parameters $(\Omega_m,\Omega_b,h,n_s,\sigma_8)$. We train a single model on 100 matched low-high resolution pairs from the Quijote Latin-hypercube suite at $z = 0$, mapping $512^3$ to $1024^3$ particles in $1\,h^{-1}\,\mathrm{Gpc}$ boxes. On ten cosmologies excluded from SR training, the model reproduces the broad matter distribution and the cosmological variation of clustering and halo abundances. Over $0.1<k<3\,h\,\mathrm{Mpc}^{-1}$, the mean of the per-cosmology maximum absolute power-spectrum errors is $3.6\%$, while FoF halo abundances agree with HR to within $15\%$ in the analyzed mass bins below $10^{14.8}\,h^{-1}M_\odot$. Satellite abundances and occupations retain larger, mass-dependent discrepancies. Corrections measured at one near-fiducial cosmology reduce a shared component of these systematic errors when applied to the other nine test cosmologies. A power spectrum based inference test also shows that calibration reduces the mean shifts in all parameters. These results extend our SR model across cosmologies and provide 6D phase space realizations for subsequent studies of non-linear structure and field-level cosmological inference.

Learning the Hamiltonian of a many-body system from its dynamics is a central task in quantum science, yet the algorithms with the strongest provable guarantees assume some level of quantum control–fast, arbitrary single-qubit gates interleaved with time evolution, and measurements in arbitrary bases–that is beyond the capabilities of near-term analog quantum simulators. Motivated by analog atom- and ion-based platforms, we study Hamiltonian learning under minimal access models. Uniform state preparation and measurements: We first consider the setting where in every experiment, one can rotate each qubit to the same state, perform short-time evolution, and measure every qubit in the same basis. Surprisingly, we show that for generic 2-local Hamiltonians on any interaction graph, all of the parameters can be reconstructed from such experiments. Computational basis state preparation and measurements: We then consider a similarly constrained setting, but where state preparation and measurement are restricted to the computational basis. For nearest-neighbor Hamiltonians with only Pauli $X/Z$ interactions, a class which captures contemporary Rydberg atom platforms, we show that over 1D and 2D rectangular lattices, all of the parameters can be reconstructed from such experiments up to unavoidable gauges. Our protocols introduce new techniques for solving structured polynomial systems over an extensive number of parameters. Taken together, our results suggest that one can learn a great deal from the dynamics of quantum many-body systems even under the most stringent experimental constraints.

Multimodal rumor detectors increasingly rely on retrieved evidence, yet relevant evidence is not necessarily sufficient for verification. Missing provenance, duplicated reports, and unresolved contradictions can produce confident predictions without adequate support. We introduce SAFE-MR, a framework that separates claim veracity from evidence sufficiency. The method decomposes image-text posts into verifiable claims, constructs a relation-aware claim-evidence graph, and aggregates evidence using provenance and contextual compatibility. Separate veracity and sufficiency heads support selective prediction, while evidence interventions encourage stability under irrelevant additions and sensitivity to evidence removal. On NewsCLIPpings, VERITE, and XFacta, SAFE-MR achieves macro-F1 scores of 91.2%, 75.8%, and 85.2%, respectively. Against the matched backbone with evidence, its macro-F1 gains are 2.2, 4.9, and 4.8 percentage points. On the diagnostic selection set, SAFE-MR reduces AURC from 0.105 for maximum-probability rejection to 0.075 and lowers error at 80% coverage from 13.8% to 8.5%. Evidence-perturbation and ablation results support the role of sufficiency learning and intervention training in improving selective verification.

We spread out geometrically irreducible perverse sheaves. Over an arithmetic base scheme, such sheaves extend from the generic fiber to a relatively perverse, universally locally acyclic sheaf over a dense open of the base scheme. As an application, we prove the arithmetic Kashiwara conjecture by Esnault and Kerz for geometric traits in equicharacteristic and generalize the decomposition theorem for arithmetic complexes to fields finitely generated over a separably closed field. We also recover the Hard Lefschetz theorem for arithmetic perverse sheaves.

We give optimal bounds, up to polylogarithmic factors, for rounding convex bodies to near-isotropic position. A convex body $B(0,r)\subseteq K\subseteq B(0,R)$ in $\R^n$ can be rounded using $\Ot(n^3)$ membership queries; the upper bound extends to logconcave distributions. We prove a matching $\Omegat(n^3)$ lower bound, even when $R/r=n^{O(1)}$. The key lemma states that if $B(0,1)\subseteq K$ and $\Cov(\Unif(K))\preceq\kappa I_n$, with $\kappa\ge1$, then approximate uniform sampling from an initial density bounded by a constant times the uniform density uses $\Ot(n^2\sqrt\kappa)$ expected membership queries. We prove this by simulating reflected kinetic dynamics using the analysis of Eberle and Lörler~\cite{EL26:journal}. Combining this sampler with the ideas of Jia, Laddha, Lee, and Vempala~\cite{JLLV26:journal} for rounding well-rounded bodies yields our $\Ot(n^3)$ query rounding algorithm. We also give a counterexample to an ellipsoid-growth conjecture from previous papers on this topic.

Phase-field models of fracture in fibre-reinforced shells are usually formulated against a single closed-form stored energy, so that the stress, consistent tangent and plane-stress condensation are derived and verified for that expression alone. Here the constitutive law enters instead as a replaceable operator. The Green-Lagrange strain of a geometrically exact Reissner-Mindlin shell is pulled back through the Cholesky factor of the reference metric and resolved on four mutually orthogonal invariants with an exact closure identity, making the separation into fibre, inter-fibre and interaction channels a change of basis rather than a modelling assumption. On a curved midsurface, the metric, Cholesky factor and fibre direction vary through the thickness through the shifter I - zeta b, and the invariants inherit that dependence. The tension-compression split, channel degradation, plane-stress condensation, consistent tangent and finite-element assembly are all expressed in the channel potentials and their derivatives, allowing either closed-form or learned operators. The fibre-transverse interaction energy is stored once and degraded by the product of the fields whose mechanisms it couples. Six conditions define admissible operators; the two linear invariants are proved convex in the deformation gradient, the geometric tangent is shown independent of the material tangent, and the plane-stress condensation is regular wherever the residual stiffness is positive. A three-tier protocol certifies the algebra, solver state and admission of a state as training data. Numerical studies on notched IM7/8552 shells verify the discretisation in thin and curved regimes and show that fibre orientation governs the damage envelope and load capacity, while curvature drives a through-thickness fracture asymmetry that a single midsurface field cannot represent.

Dynamic World (DW) maps land use and land cover globally at 10 m from Sentinel-2 (S2) imagery, but only for cloud-free observations, which limits where and when surface water can be mapped. We use the DW water class as weak supervision for a Sentinel-1 (S1) synthetic aperture radar (SAR) model so that DW-like water maps can be produced for every S1 acquisition. Google's AlphaEarth Foundations (AEF) annual embedding supplies spatial context, while S1 backscatter supplies the acquisition-time observation. On 53 globally distributed scenes with independent annotations of 3 m PlanetScope imagery acquired within 48 h of the S1 overpass, the S1-only model already reaches a pooled water intersection over union (IoU) of 0.77, comparable to 0.75 for the operational OPERA DSWx-S1 product, and adding AEF raises it to 0.85. The fused model improves on the S1-only model on 44 of 53 scenes and exceeds OPERA on 48, and on the independent S1S2-Water benchmark it reaches 0.94, compared with 0.87 for OPERA. Optical land-cover products can thus provide scalable training labels for SAR surface water mapping.

Background music that matches the mood of a text has been shown to make readers feel more immersed and improve their reading experience, motivating recommender systems that pair books with mood-matched music. In this direction, we present Sentiment Aware Generative Adversarial Network for Cross Domain Recommendation (SAGA-CDR), a two-phase cross-domain recommendation framework that personalizes music suggestions and emotionally aligns them with the book being read. In the first phase, transformer-based sentiment embeddings are constructed from user reviews and mapped across domains via a Conditional Generative Adversarial Network, whose mask-conditioned generator handles missing sentiment components and injects stochasticity for richer preference transfer. A compact rating neural network then fuses sentiment-specific interaction scores with a collaborative filtering prior to predict music ratings. In the second phase, large language models classify each book into a valence-arousal emotional quadrant, and candidate tracks are filtered to match that quadrant. Experiments on both the English Amazon and Chinese Douban datasets show that SAGA-CDR achieves the best rating prediction accuracy on Amazon (RMSE 0.98) and the lowest RMSE on Douban (0.91), with ranking performance competitive with the strongest sentiment-aware baseline, even in cross-lingual settings.

We consider the following data compression problem. Given a string $x \in \{0,1\}^m$ of Hamming weight at most $n$, compress it into a shorter string $y \in \{0,1\}^s$ so that any bit $x_i$ of $x$ can be retrieved without any error using at most $t$ quantum queries to the standard oracle encoding of $y$. If queries are allowed to be adaptive we show how optimal compression up to a logarithmic factor can be achieved. If the queries are required to be made non-adaptively, we show schemes whose space is optimal in its dependence on $m$ except for a logarithmic factor, and is at most quadratically worse when compared to the optimum in its dependence on $n$.

A recurring design principle in modern optimizers is to decouple update magnitude from the raw gradient norm, yet its consequences for learning-curve and resource scaling remain unclear. We isolate this mechanism by studying normalized SGD in a random-feature model with power-law teacher and data covariance. Fixed-norm updates induce an effective learning rate that grows as gradients shrink. We derive a dynamical mean-field theory (DMFT) describing the joint dependence of the loss on training time, model width and batch size. Normalization initially accelerates SGD, mapping the power-law exponent $r_{\rm SGD}<1$ to $2r_{\rm SGD}/(1-r_{\rm SGD})$, with exponential convergence at $r_{\rm SGD}=1$ and formal finite-time convergence for $r_{\rm SGD}>1$. At finite step size, however, the same feedback ultimately breaks the acceleration and leads to marginal stability. The late-time theory yields width-limited, edge-of-stochastic-stability (EoSS), and deterministic edge-of-stability (EoS) regimes. These phases determine when larger batches or wider models reduce serial training time at comparable compute. We quantify in which of these phases increased batch size or width can compensate the excess compute use per step by fewer optimization steps to target loss. Linearized ResNet experiments on CIFAR-5M support the predicted acceleration, breakdown, and resource-scaling trends. Together, these results connect normalization-induced acceleration, EoS effects, and width–batch allocation within a solvable theory.

A major open problem in quantum complexity is the question of unitary synthesis—namely, is it possible to efficiently implement any unitary, given the ability to evaluate any classical function in superposition? Inspired by a recent work by Brakerski and Yuen (CRYPTO 2026), we propose an “average-case” unitary synthesis problem, which asks whether it is possible to efficiently implement a Haar random unitary given access to a random Boolean function. We then demonstrate a superpolynomial query lower bound, establishing that unitary synthesis in this model is impossible. Along with our main result, we settle in the negative a question Brakerski and Yuen pose, of whether scalable pseudorandom unitaries (PRUs) can be implemented in the ROM-PRU model. In particular, we show that in the ROM-PRU model, no $\Omega(N^{1+\gamma})$ unitary design on $n$ qubits, where $N=2^n$, can be efficiently achieved for any $\gamma > 0$. On the other hand, we construct an $O(N)$-design in $\text{poly}(n)$ queries in the same model, surpassing the previously best known results which constructed $O(\sqrt{N})$-designs.