Papers

Policy-gradient methods are central to modern reinforcement learning, including LLM post-training. When they struggle, the usual suspects are exploration, credit assignment and action-sampling noise. Classification has none of them. A classifier is a policy whose expected reward, its expected accuracy, is the probability it assigns to the correct label, and because that label is known, the policy gradient is exact and smooth. Yet exact policy gradient loses to cross-entropy, even on expected accuracy. The exact gradient is myopic: it values an update only by what it buys now, but each update also sets where the next one starts, so an update's value depends on how much learning remains. Viewed this way, cross-entropy is patient accuracy, the total error an example would pay if its log-odds rose at unit speed forever, while exact policy gradient is the zero-horizon limit. Truncating this total at the learning that remains yields the horizon loss, a one-line change that moves from cross-entropy toward exact policy gradient as training runs out. In a simple allocation model, it provably escapes the trap that catches each endpoint. On MNIST and on ImageNet with ResNet-50, ResNet-101 and ViT-S/16, the horizon loss improves top-1 accuracy over cross-entropy at a flat learning rate, and the gain grows with label noise.

We develop a Bayesian framework for learning nonlinear operators between infinite-dimensional spaces. Given a map $g_0:\mathcal{X}\to\mathcal{Y}$ between separable Hilbert spaces, we study the recovery of $g_0$ from $n\in\mathbb{N}$ noisy input-output pairs $(\boldsymbol{X},\boldsymbol{Z})=(X_i,Z_i)_{i=1}^n$ with $Z_i= g_0 (X_i ) + E_i$. Here the $X_i\in\mathcal{X}$ are randomly drawn 'design' points in a compact subset of $\mathcal X$, and the $E_i$ are assumed to be i.i.d. draws from a Gaussian white noise process indexed by $\mathcal{Y}$. For any 'operator-valued' prior $\mathbb{P}_G$ supported on the space of continuous operators, we show existence of the posterior $\mathbb P_{G|(\boldsymbol{X},\boldsymbol{Z})}$ as a regular conditional distribution, and provide a characterization of its Radon-Nikodym derivative. For Gaussian priors, we establish algebraic (in the sample size $n$) convergence rates for the posterior mean towards the ground truth; this corresponds to a ridge regularized kernel estimator. Moreover, we show that the posterior mean is minimax optimal (up to logarithmic factors) over hyperrectangles when the smoothness of the prior matches that of the ground truth. To illustrate the applicability of our analysis, we derive explicit learning rates for the Darcy flow solution operator.

Masked diffusion language models (dLMs) offer a promising parallel alternative to autoregressive models for complex reasoning. However, they face a distinct credit-assignment challenge, since a few commitments during denoising sharply reduce the uncertainty over the remaining masked positions and shape much of the response. Most post-training recipes for dLMs do not use this signal to decide which tokens to train on: they typically train on the final text or assign rewards to whole denoising steps, rather than selecting the individual commitments that shape the response. We introduce Pivot-SD, an efficient offline self-distillation framework that supervises only these high-impact commitments (pivots). Pivot-SD selects pivots using an information-gain metric measuring uncertainty reduction over the remaining masked positions. Pivots from successful trajectories are trained with cross-entropy, and pivots from failed trajectories with targeted unlikelihood, leaving the rest of the failed trajectory untouched. Using only 200 questions and four rollouts each, Pivot-SD improves LLaDA-8B-Instruct over full-sequence SFT and budget-matched diffusion RL baselines across math and code benchmarks.

Autoregressive (AR) video models excel at causal generation, but their reliance on next-chunk prediction confines them to a short-sighted, reactive paradigm. This limitation is particularly consequential for reasoning-oriented generation, where achieving a target outcome through valid intermediate states matters more than local visual plausibility. To address this challenge, we propose Learning Prospective Reasoning with Autoregressive Video Models (ProAR), a novel framework that transforms autoregressive video generation into a goal-oriented reasoning process. ProAR introduces two key components: (1) To anchor generation to the long-range outcome, we integrate goal-frame prediction into the autoregressive loop via an asymmetric attention mask, enabling the predicted goal frame to guide the generation of intermediate states without being disrupted by them. (2) To guide short-range transitions, we introduce future representation self-alignment to encourage current hidden states to anticipate upcoming temporal dynamics. By leveraging teacher-forcing in AR training, we extract clean future representations in a single forward pass and align current representations with them using a lightweight, training-only predictor. Together, these two mechanisms seamlessly combine explicit, sparse target supervision with implicit, dense step-wise guidance, promoting coherent, goal-directed reasoning progress with modest computational cost. Experiments show that ProAR's complementary components consistently improve performance across diverse visual reasoning benchmarks. The framework proves highly training-efficient, surpassing fully trained standard AR baselines using only 25% of the training steps. This paradigm also demonstrates promising applicability to embodied reasoning tasks.

We introduce an algebraic framework for constructing a new class of quantum error-correcting codes, bosonic algebraically-restricted constellation (BARC) codes. The code states are finite superpositions of coherent-state constellations constrained by symmetries of solution sets to multivariate complex polynomial systems. The constraints are associated with photon-gain and photon-loss errors, thereby imposing approximate Knill–Laflamme conditions for such errors. For equally-weighted constellation points, we derive upper bounds on the minimum geometric separation between points, indicating how noise-resilient the code is. In the single-mode case, we characterize degree-two polynomial solution sets using an orthogonal group symmetry to obtain explicit ellipsoidal and hexagonal BARC codes. We benchmark representative instances of these families against spherical and cubature codes using the entanglement fidelity with optimal recovery under pure-loss noise.

Deploying a new decision policy creates a cold-start problem for prediction models whose targets depend on the policy's actions: historical observations reflect earlier policies, while real observations under the new policy are not yet available. Simulation offers a way to address this gap by rolling out the target policy across counterfactual scenarios and using the resulting trajectories to learn how the system responds to those controls. The simulation-to-reality (Sim2Real) transfer of this simulator-trained model can then be backtested by evaluating it against real observations from past deployments. Using two real-world inventory-control deployments, we evaluate this process from three angles: simulator fidelity, zero-shot transfer to real behavior, and adaptation as real target-policy observations accumulate. The simulator-trained forecaster achieves lower point-estimate mean absolute percentage error (MAPE) than the same architecture trained on historical real data, reducing MAPE by 1.2-3.1 percentage points in Study 1 and 12.5-18.7 points in Study 2. After deployment, lightweight calibration using early real observations further reduces error by up to 2.5 percentage points. These results provide empirical evidence that simulator-generated counterfactual data can support cold-start forecasting under a new policy, and the resulting model can be further refined as real deployment data become available.

Uncertainty relations impose fundamental constraints on quantum observables, yet optimal bounds are needed to determine their incompatibility through the minimum attainable uncertainty. Here we introduce a covariance-matrix formulation from which infinitely many uncertainty relations follow, encompassing Hermitian observables and non-Hermitian operators and recovering the variance sum as a special case. Within this family, a basis-independent uncertainty for simple and semisimple Lie algebras admits an exact solution: its optimal state-independent bound is an explicit pairing of root system with the highest weight of the representation. The minimum is attained by a highest-weight state, replacing a search over quantum states with a calculation in representation theory. A complementary result establishes that uncertainty is constant within each weight space, yielding a conservation law. The same commutation relations can therefore support distinct uncertainty limits, depending on their realization on the state space. By rendering these limits analytically accessible, the framework turns representation theory into a tool for quantifying quantum incompatibility and may help establish the boundary between attainable and impossible tasks in quantum theory.

We study single-sample prophet inequalities for online combinatorial allocation. Our main contribution is a general reduction from combinatorial to single-item prophet inequalities for valuation classes admitting suitable supporting prices. The reduction uses a free-disposal value to separate buyer-side combinatorial constraints from item-side supply constraints, yielding a modular framework that applies in the stronger Game of Googol model. This framework yields a $\frac{1}{6\sqrt{3}}\approx\frac{1}{10.4}$-competitive single-sample prophet inequality and a $(\beta_{k-1}/4)$-competitive $k$-sample prophet inequality for XOS valuations, where $\beta_k$ is the competitive ratio of a $k$-sample single-item prophet inequality, improving upon the work of [DKL+24]. Both results extend directly to divisible resources with capped-XOS valuations. Along the way, we obtain new results for online free disposal and an optimal single-sample prophet inequality for fractional knapsack in the Game of Googol model.

Consider the task of identifying an unknown classical codeword delivered to a register of quantum sensor qubits through a sequence of weak phase interactions that each encode one bit. Suppose that each received bit controls an identical $Z$-rotation of angle $\theta$ applied to every sensor qubit; receivers may also use auxiliary qubits within a total qubit budget $Q$, with arbitrary control unitaries and entanglement among all qubits allowed during each reception step. When the total collected signal is weak ($Q\theta \rightarrow 0$), we establish that a sensor coupled to a persistent quantum memory can identify the original codeword more reliably than any receiver with the same $Q$ and $\theta$ but only classical memory between received bits, even when bit flips occur during transmission. In particular, for a family of $[n,k]$ binary simplex codes with even $k$ and $n=2^k-1$, we achieve exact correction of up to $t\leq(k-2)/4$ transmission errors by coupling the sensor register to a persistent quantum memory of the same size, using $Q = \Theta((t+1)\log n)$ and $\theta=\frac{2\pi}{k\sqrt{n+1}}$; for $t=o(\sqrt k)$, every comparable receiver with only classical memory instead has average success probability (over uniformly chosen codewords) tending to zero. Furthermore, under independent bit flips of any fixed probability $p<1/16$, our receiver with persistent quantum memory achieves decoding error tending to zero as $n\to\infty$ using $Q=O(\log n\log\log n)$ total qubits and the same $\theta$. In contrast, every otherwise equivalent receiver with only classical memory has vanishing average success probability under the same stochastic error model.

In this note, we consider tomography of $n$-qubit quantum states $|\psi \rangle$ that are promised to have stabilizer rank $k$ i.e., admit a stabilizer decomposition of $|\psi\rangle = \sum_{i=1}^k c_i |\phi_i\rangle$ where each $|\phi_i\rangle$ is a stabilizer state. We give a tomography protocol for such states up to trace distance $\varepsilon > 0$ running in $\textsf{poly}(n,2^k,1/\varepsilon)$ time and thus can handle $k=O(\log n)$ efficiently. This follows from first showing that the stabilizer extent $\xi(|\psi\rangle)$, which is the minimal $\ell_1$ norm over the coefficients $\{c_i\}$ of any stabilizer decomposition of $|\psi\rangle$, can be bounded as $\xi(|\psi\rangle) \leq 2^{O(k)}$ and improving upon the previous best bound of $k^{O(k)}$. The protocol is then obtained by utilizing a tomography protocol for states with bounded stabilizer extent.

A paradigmatic task in quantum metrology is that of phase estimation. For this task it is commonly believed, under reasonable assumptions about prior information, that a quadratic advantage in sensitivity is the maximum possible advantage offered by the use of quantum resources. In this work, we consider a channel that implements a phase shift by an angle $2\pi k/M$, where $k$ is a uniformly random unknown integer, in addition to a small unknown phase shift of interest. We show that, subject to a constraint on the mean photon number per channel use, there is a super-exponential separation between the quantum Fisher information (QFI) attainable using a squeezed vacuum state and that attainable using coherent states. This advantage holds over any state obtained from a coherent state via phase covariant channels. Specifically, when the mean photon number per channel use is 1, the ratio of their QFI grows as $\Omega[(M/\sqrt{2}e)^M]$. For a mean photon number per channel use of $M/\log(M)$, the squeezed vacuum QFI is $\Omega(M^{3/2}/\sqrt{\log(M)})$, whereas for a coherent state it is at most $\exp[-M\log\log(M)+O(M)]$. We complement this QFI analysis with non-asymptotic estimation results. For a mean photon number per channel use of $M/\log M$, an explicit squeezed-vacuum protocol estimates the phase to accuracy $O(1/M)$ using $O(\sqrt{M\log M})$ channel uses, whereas every coherent state protocol requires at least $\exp[M\log\log M-O(M)]$ channel uses. We consider the effects of noise and show that the ratio of their QFIs can still grow super-exponentially in $M$. Finally, under fixed optical loss and thermal noise, choosing $\bar n=M^2/(\log M)^{3/2}$ allows squeezed vacuum with heterodyne detection to achieve accuracy $O(1/M)$ using sub-polynomially many channel uses, whereas every protocol in the specified classical family requires super-polynomially many.

Multi-pitch estimation in vocal ensembles is challenging because singers occupy overlapping pitch ranges and often sing at closely spaced fundamental frequencies, causing their harmonics to overlap in time-frequency representations. Existing models commonly use harmonic constant-Q transform (HCQT)-based representations to provide frequency-adaptive resolution, at the cost of expensive feature extraction when training mixtures are generated on the fly. We revisit this design and compare HCQT with a linear short-time Fourier transform (STFT), whose frequency bins are directly provided as model inputs. Despite its fixed frequency resolution and the absence of a pitch-aligned input grid, the linear STFT outperforms HCQT while substantially reducing feature-extraction cost. Further analysis shows that a longer analysis window or broader spectral coverage provides no additional improvement, while restricting the input to the predicted pitch range reduces the advantage of the linear STFT. These results suggest that finer frequency resolution does not necessarily improve vocal-ensemble MPE, and that shorter analysis windows can be more effective for time-varying vocal pitches.

The Solovay-Kitaev algorithm states that it is possible to efficiently compile unitaries to accuracy $\epsilon$ in $\text{polylog}(1/\epsilon)$ time using any universal gate set. While Solovay and Kitaev's initial work addressed inverse-closed gate sets, recently Bouland and Giurgicǎ-Tiron showed it is possible to efficiently compile arbitrary gate sets without inverses. However, the exponent of their compilation algorithm is high. For example the inverse-free exponent for a qubit is over $8.62$, while information theoretically it is known that an inverse-free exponent of $3$ is possible in any dimension by a result of Oszmaniec, Sawicki, and Horodecki. This leads to a natural question: can one improve the exponent in Bouland and Giurgicǎ-Tiron's algorithm? And are there any cases where the inverse-free exponent is below 3, thus surpassing existing information-theoretic arguments? To answer this question, we first show that a special case of the inverse-free compiling problem – namely Pauli gates supplemented by an irrational rotation of a qubit - admits a highly efficient compilation algorithm with an exponent at most $\approx 2.138$. Our algorithm fuses ideas from prior algorithms of Kuperberg and Sardharwalla, Cubitt, Harrow and Linden to construct an efficient “Pauli golf” compilation routine. We then extend these ideas to the general inverse-free case for a qubit, where we give a compiling algorithm with exponent at most $2.988$. This result uses a novel form of approximate “aiming” of unitary corrections to improve the compilation efficiency. Our results give two examples of quantum compiling algorithms surpassing information-theoretic arguments, and demonstrate that there are many efficiency gains possible for inverse-free compilation.

Sample-based quantum diagonalization can reduce the classical cost of many-body calculations by restricting diagonalization to configurations identified through quantum sampling, but its efficiency depends on how compactly the target state is represented in the sampled basis. We investigate this dependence for sample-based Krylov quantum diagonalization of the half-filled Fermi-Hubbard ladder using physically motivated one-body orbital rotations. Across position, momentum, bonding/antibonding, and leg-mode representations, the most compressible basis varies systematically with interaction strength and hopping anisotropy, with momentum sampling favored in the weakly interacting regime and geometry- or interaction-adapted representations becoming advantageous as the dominant energy scale changes. Near intermediate interaction and isotropic hopping, however, even the most favorable representation remains poorly compressible. Statevector SKQD calculations further show that basis choice strongly affects sampling efficiency. Hardware calculations on systems containing up to 120 qubits retain qualitative signatures of this basis dependence while revealing increasing particle-number leakage and reconstruction sensitivity with system size. These results show that scalable sample-based diagonalization requires co-design of the sampled representation, quantum circuit, and classical reconstruction procedure.

We investigate the physical requirements to reach the ultimate limits of ground-state metrology – i.e., the estimation of an unknown parameter $\theta$ of an $N$-body Hamiltonian via measurements on its ground state – using many-body probes featuring either short-range or long-range interactions. We characterize the conditions to saturate two fundamental limits of the quantum Fisher information $F_\theta$: the static ground-state bound $F_\theta \lesssim N^2/\Delta^2$, where $\Delta$ is the spectral gap, and the dynamical Heisenberg limit $F_\theta \lesssim N^2 \tau^2$, where $\tau$ is the total protocol duration. To saturate the static limit, we argue that short-range interacting systems require a spectral gap that closes with $N$. At second-order quantum critical points this leads to a universal condition on the critical exponents, $\nu(d+z)=1$, which can be approached arbitrarily closely, as we show for the XXZ chain; cat-like ground states at first-order transitions provide an alternative route to static optimality. In contrast, we find that all-to-all interacting models can achieve optimality even in gapped regimes. Furthermore, reaching the dynamical bound is tightly related to the ground-state preparation time; we demonstrate that its optimal, inverse-gap profile can be obtained via local adiabatic protocols. By analyzing paradigmatic systems – the transverse-field Ising chain, the XXZ chain, a squeezing Hamiltonian, and the two-mode Bose-Hubbard model – we identify specific many-body probes capable of approaching both limits. Overall, our results provide a theoretical basis for the design of (local) many-body ground-state sensors operating at the ultimate limits of quantum precision.

We argue that BF theory with $SO(d+1,1)$ gauge group provides a SymTFT ”skeleton” for building AdS$_{d+1}$/CFT$_d$ pairs via gluing consistency as the bootstrap principle, loosely analogous to how compact Chern-Simons theory is a TQFT skeleton for rational CFTs. This is a non-perturbative $bulk$ framework for quantum gravity. The bootstrap is formulated as presentation independence of physical amplitudes within a universal, defect-closed BF sewing calculus, which includes Wilson lines, codimension-two monodromy defects, and their junctions. The flat BF connection encodes the conformal geometry of the boundary, while Wilson-line path integrals construct candidate quantum-gravity microstates and charge sectors. When the bootstrapped spectrum has a stress tensor, Ward identities naturally connect it to the $B$-field, a relation we call generalized simplicity. In large-$N$, large-gap regimes admitting a gravitational EFT, this motivates the introduction of an effective notion of the $B$-field. In the Einstein limit, this becomes the ”simplicity” relation used in spin-foam models. Conventional spin-foam models try to obtain gravity by constraining BF theory. We suggest instead that BF theory is the Platonic sewing skeleton, from which theories are to be bootstrapped. Despite the topological nature of the skeleton, perturbative local bulk fields can emerge via Wilson-towers of multi-trace primaries, reproducing their one-loop determinants. We note that the BF Fourier kernel is a suggestive higher-dimensional analogue of the modular-$S$ structure. Because the bulk gluing principle in itself does not require a boundary description, the framework is conceptually broader than AdS/CFT. We sketch how de Sitter space may fit into this picture, with a natural role for observers. Our approach elevates gluing consistency to a universal bulk principle underlying theories of quantum gravity.

Dense-retrieval services must switch among embedding-prefix dimensions and index bit rates as latency, quality, and memory budgets change. Tuning a quantizer separately for each rate gives the best quality, but the retrieval tier then holds several code streams and quantizer states at once. We introduce Matryoshka Residual Vector Quantization (MRVQ), a post-hoc residual quantizer for frozen embeddings. Its maximum-rate code can be truncated two ways: dropping residual stages lowers the rate, and dropping embedding coordinates lowers the dimension. One resident artifact therefore serves every (dimension, rate) pair we evaluate. Across FiQA and NFCorpus, four embedding families, and {4, 8, 16}-byte codes, MRVQ is the lowest-RAM design we evaluate. It uses 17.8-22.0x less memory than three separately trained QINCo2 indices, and 1.89-2.02x less than a lean shared-model steelman. The saving is not free: per-rate QINCo2 is 0.026-0.107 nDCG@10 better on FiQA. But MRVQ beats PQ, OPQ, and AdANNS-OPQ at matched code size. We also evaluate a low-build-cost PCA-scalar design that attains quality comparable to RaBitQ and its extension while fitting 420x faster at the median. Finally, we report two negative results: QINCo2 collapses when trained at high rates, and a ranking-bound hypothesis misses its pre-specified acceptance criteria. MRVQ is therefore a low-memory operating point for elastic retrieval, not a universal quality winner.

Federated Learning (FL) is a privacy-oriented learning paradigm that enables collaborative model training while keeping training data local to participating clients. However, it does not guarantee that clients submit policy-compliant contributions or that aggregators process admitted contributions correctly. Existing verifiable FL systems tailor validation rules to specific FL settings, learning workflows, and cryptographic constructions, limiting their applicability across network topologies, participant roles, and aggregation semantics. In this paper, we present PoCoFL, a policy-compliant federated learning framework that separates three aspects: (i) FL type, (ii) policy semantics, and (iii) cryptographic realisation. We provide a formalisation that captures client and aggregation requirements as policy-dependent relations. Clients prove compliance of their contributions using commitments and non-interactive zero-knowledge proofs, while aggregators prove that the recorded set of admitted contributions was processed according to the selected aggregation policy. We demonstrate PoCoFL through four formal instantiations: (i) vanilla, (ii) continual, (iii) personalised, and (iv) threshold-encrypted federated learning. We evaluate the effects of policy enforcement on the learning objectives of vanilla, personalised, and continual FL. We further implement proof-of-concept realisations of all four instantiations, demonstrating the versatility and practical feasibility of PoCoFL. Overall, these results show that PoCoFL can capture complex policy representations while remaining network-topology agnostic.

Marine ecosystems are impacted by various threats such as oil spills, algal blooms, and sediment floods, which disrupt habitats, wildlife, and human activities. Advances in satellite imagery and Artificial Intelligence (AI) have enhanced our capabilities for early detection and mitigation of such hazards. In this paper, we propose a marine event detection pipeline for Earth observation satellites equipped with multi- or hyperspectral sensors. Our approach includes a self-supervised neural network encoder that compresses satellite images into a reduced latent space, enabling efficient onboard processing. A machine learning anomaly detection model identifies deviations from normal sea patterns to detect environmental anomalies. We compare its performance against traditional algorithms such as Isolation Forest, One-Class Support Vector Machine and Local Outlier Factors. Our lightweight, resource-efficient pipeline is optimized for deployment on satellites with limited computational resources, ranging from embedded CPUs to AI hardware accelerators. By prioritizing the transmission of critical information, our solution enhances system responsiveness and optimizes satellite communication bandwidth. Demonstrated through current integration across multiple missions, including European Space Agency's (ESA) Phisat-2 mission and Microsoft/Thales Alenia Space IMAGIN-e mission, our pipeline aims to improve marine environmental monitoring by providing timely alerts and efficient data reduction.

Whether some problems require quantum proofs has been a central question in quantum complexity (Aharonov and Naveh, 2002; Aaronson and Kuperberg, CCC 2007). Recently, breakthrough work of Bostanci, Haferkamp, Nirkhe, and Zhandry (STOC 2026), followed by a simpler separation due to Bostanci, Huang, and Vaikuntanathan (FOCS 2026), established a classical oracle separation between $\mathsf{QMA}$ and $\mathsf{QCMA}$. However, while they are not in $\mathsf{QCMA}$, the problems used in both separations still lie in $\mathsf{AM}$: they admit a two-message public-coin proof system with a classical verifier. In this work, we ask whether some problems truly require quantum proofs. More formally, we consider the complexity class $\mathsf{QCIP}$, introduced by Buhrman, Le Gall, and Weggemans (2024), where an efficient quantum verifier interacts with an unbounded prover over a classical channel for an arbitrary polynomial number of rounds. We construct a classical oracle $\mathcal{O}$ such that $\mathsf{QMA}^{\mathcal{O}}\not\subseteq\mathsf{QCIP}^{\mathcal{O}}$, thus showing that some languages indeed require quantum proofs, with no classical replacements. Since $\mathsf{QCMA}=\mathsf{QCIP}[1]$, this strengthens the earlier $\mathsf{QMA}$–$\mathsf{QCMA}$ separations, which now follow as a special case of our result. As a technical contribution, we extend to the complexity theory setting the techniques developed by Cakan, Goyal, and Shmueli (CRYPTO 2026) in the context of cryptography for analyzing classically interacting quantum machines. We believe this may be of independent interest.

Many machine learning methods aim to approximate the lower-dimensional manifold on which the data lives. A desirable feature of such methods is that they should capture the epistemic uncertainty of this learned manifold. One model that achieves this is the Gaussian Process Latent Variable Model, in which a Gaussian Process (GP) mapping from the latent space provides an estimate of the uncertainty of the manifold. However, the effectiveness of this uncertainty estimation is limited by the mean-field variational approximation between the GP inducing points and the latent variables. In this work, we apply Amortized Structured Stochastic Variational Inference to allow the variational posterior for the latent space to be conditionally dependent on the value of the inducing points. We demonstrate that this more flexible variational posterior improves several metrics relating to the reconstruction of points on the data manifold.

Stationarity rewards memory, but after a change the same history can mislead. We ask when forgetting should be permitted. E-process-authorized Thompson sampling (e-ATS) gives each arm full-history and discounted Beta states. An anytime-valid e-process first authorizes the discounted state, then a reversible relevance score controls its influence. Before authorization, e-ATS exactly follows optimistic Thompson sampling (OTS). Under a Beta-Bernoulli prior-predictive stationary model, e-ATS's probability of ever departing from OTS is at most the chosen $\alpha_E$, without fitted thresholds. Relative to e-ATS, removing authorization increased mean normalized dynamic pseudo-regret by $38.4\%$ on the registered suite but reduced it by $7.5\%$ on the literature-derived replay suite. Therefore, evidence controls when adaptation begins, not whether it always helps.

We show two unconditional quantum space advantages in the random-order streaming model. First, we show the Yamakawa-Zhandry Code Intersection problem admits exponential quantum advantage in the streaming model when its inputs are streamed in random order. This means quantum computers exhibit exponential space advantage even when simply receiving $(x,f(x))$ pairs for a uniformly random function $f$ in a uniformly random order. Notably, our classical space lower bound does not follow from a communication lower bound. Instead, we utilize density-restoring partitions from communication complexity directly with potential-function analysis in the style used to prove memory-sample tradeoffs for learning. The resulting argument is distinct from both lines of work. Second, we use our framework to show quantum space advantage for the Optimal Polynomial Intersection (OPI) problem in certain regimes via a streaming version of the Decoded Quantum Interferometry algorithm. In particular, we show that for degree $d$ and $n$ evaluation points, attaining $1/2 + \Omega(\sqrt{d/n})$ fraction of satisfied OPI constraints via streaming requires $\Omega(n)$ classical bits of memory but only $O(d\log n)$ qubits. This yields provable quantum advantage in a "low-rate" regime when the number of evaluation points is much larger than the degree, with a space advantage that can be as large as exponential in certain parameter settings.

In our previous paper on the matter, we proved that real quantum theory (RQT) cannot be experimentally falsified without the experiment falsifying quantum theory (QT) as well. Our result is in direct contradiction to the central claim of an article by Renou et al., published in Nature [600, 625–629 (2021)], reporting a bilocal network experiment that could falsify real quantum theory without falsifying quantum theory. The purpose of this note is to address several seemingly natural attempts to recover the experimental conclusion of Renou et al. We first explain how these results, although based on nonlocality experiments, are far from a Bell-like level of proof. Then we explain why the proposed experiment requires an experimentally untestable premise about independent preparations necessarily being represented as product states. Finally, we discuss some concerns that lie outside the scope of both results.

Contactless radar sensing offers a promising approach to continuous vital-sign monitoring. However, indoor multipath can distort direction estimates and generate ghost responses. This paper presents a reconfigurable intelligent surface (RIS)-assisted monopulse radar whose RIS phase configuration is controlled by a soft actor-critic agent to improve angular localization. The proposed framework combines simultaneous sum and difference beams with a programmable reflected path, enabling a single radar node to adapt the propagation environment without relying on multiple synchronized sensors. A compact multipath model formulates RIS control as a continuous-action reinforcement-learning problem whose reward penalizes bearing errors and misleading multipath reinforcement. Numerical results compare the proposed method with conventional monopulse processing without an RIS, a frequency-modulated continuous-wave range-angle fast Fourier transform baseline, random RIS phase configurations, and deterministic RIS controllers. The evaluation considers different target separations, signal-to-noise ratio levels, and multipath conditions.

Success conditioning is a strategy for improving decision-making policies in stochastic environments; it updates a policy by increasing the probability of taking actions that yield successful outcomes. Success conditioning is common to many reinforcement learning applications, yet its limiting behavior and convergence rates are not well understood. In this work, we demonstrate that success conditioning converges to an optimal policy on a broad class of Markov decision processes (MDPs). We also derive convergence rates in some common settings. For discounted MDPs, we prove convergence within $\mathcal{O}(1/\varepsilon^p)$ iterations to an $\varepsilon$-optimal policy, where the exponent $p$ depends on problem data. For single-period MDPs, such a policy is obtained within $\mathcal{O}(\log(1/\varepsilon))$ iterations.

Masked discrete diffusion models offer a promising alternative to autoregressive generation, but iterative sampling can be costly, and intractable sequence likelihoods complicate reward fine-tuning. We introduce IDRF, a framework for reward fine-tuning of few-step masked discrete diffusion generators. Starting from a standard reverse-KL-regularized objective, IDRF replaces the intractable sequence-level KL penalty with inverse-distillation regularization. With an optimal auxiliary denoiser, we prove that the population inverse-distillation loss upper-bounds the sequence-level KL divergence to the reference distribution. IDRF optimizes a trajectory-based surrogate of this loss without reference-model rollouts, so the student keeps its own few-step sampler. We view few-step generation as a finite-horizon Markov decision process and optimize reward with a clipped policy-gradient objective over the student's trajectories. Across DNA, image, and text generation, IDRF achieves high reward with up to $32\times$ fewer denoising steps than the reference while mitigating reward hacking and preserving sample quality.

Neural network loss landscapes have many symmetries, which are preserved by gradient flow but broken by finite-stepsize stochastic gradient descent (SGD). A canonical example of such a symmetry is scale in homogeneous networks: one can scale up the parameters in one layer and down in the next without changing the network output. Previous work has documented cases in which SGD breaks this symmetry in favor of balancing gradient noise or minimizing fluctuations. Here, we show that the solution geometry of undercomplete linear autoencoders instead selects a preferred sign for scale drift: on the PCA solution manifold, SGD favors large decoder weights. This directed scale drift occurs on a slow timescale, and its dynamics admit an analytically-tractable effective description. However, it cannot continue indefinitely: increasing scale eventually drives the dynamics towards a finite-stepsize stability boundary. The resulting solutions are sharper than a balanced baseline in the sense of the maximum eigenvalue of the loss Hessian, but different sharpness measures can move in opposing directions. Thus, undercomplete autoencoders give a concrete illustration of how loss geometry can convert residual gradient noise into directed motion along a manifold of functionally-equivalent solutions.

Large language models (LLMs) are increasingly used to support legal practice, education, and research, yet their reliability in national legal systems outside the United States remains largely undocumented. We introduce an expert-validated benchmark for evaluating LLM reliability on the Colombian legal system. The benchmark comprises 1,042 items spanning ten areas of law and three question formats (closed multiple-choice, semi-open, and open-ended IRAC), built through a human-in-the-loop pipeline with multi-stage expert review. We evaluate 15 contemporary proprietary and open-weight models with format-appropriate metrics. Accuracy on closed questions ranges widely, from 0.905 (Gemini 3.1 Pro) to 0.577, but on free-text legal answers factual correctness never exceeds 0.45 (on a 0-1 scale) for any model. We find a dissociation between answer relevancy and correctness (Spearman rho = -0.46): models reliably sound responsive while frequently being wrong, a pattern of particular concern for non-expert users. Closed-question accuracy and free-text correctness are strongly rank-correlated (rho = 0.94), so cheap multiple-choice screening predicts model ranking but overstates absolute reliability. An independent rubric-based LLM judge and blind human expert scoring both reproduce the free-text ranking (rho >= 0.88). The judge further reveals that only about half of the norms models cite are correct; the rest are wrong or non-existent. Reliability varies systematically by legal area and follows an inverted-U across question complexity. Our results indicate that current LLMs require expert supervision for Colombian legal tasks, and that grounding answers in authoritative sources is a promising path to higher reliability. We release the benchmark construction pipeline to support reproducible evaluation.

We study the sample complexity of finding a point with expected hypergradient norm at most $\epsilon>0$ in nonconvex–strongly-convex stochastic bilevel optimization using fresh, globally unbiased first-order samples with bounded variance. For lower-variable smoothness order $p\ge1$, F$^2$SA-$p$ achieves $\widetilde O(p\epsilon^{-4-2/p})$ (Chen et al., 2026), but necessity of the exponent $4+2/p$ was open. We prove matching upper and lower bounds $\Theta_p(\epsilon^{-4-2/p})$ under fixed nondegenerate regularity budgets, with constants allowed to depend on $p$. The lower bound holds for unrestricted randomized algorithms under a fixed sample budget, allows dimension to grow with accuracy, and preserves global unbiasedness and all prescribed lower-variable smoothness bounds, even with a scalar lower variable and exact upper gradients. We further characterize the minimax fixed-budget complexity under $L_j=M\Lambda^j(j!)^\beta$ for $j\ge3$: $Q_{p,\beta}^*(\epsilon)=\Theta\left(\epsilon^{-4}\left[\inf_{1\le r\le p,,r\in\mathbb N} r^\beta\epsilon^{-1/r}\right]^2\right)$, for $p\in\mathbb N\cup{\infty}$, with constants independent of $p$. At infinite order, this gives $\Theta(\epsilon^{-4})$ for $\beta=0$ and $\Theta(\epsilon^{-4}\log^2(1/\epsilon))$ for $\beta=1$. A gradient-difference method with weighted independent batches attains these bounds uniformly in order. Thus quantitative smoothness yields precise gains, whereas qualitative analyticity alone still permits $\Theta(\epsilon^{-6})$ complexity.