Papers

Prediction with expert advice is a fundamental problem in online learning. When the time horizon $T$ is known in advance, the minimax cumulative regret over $n$ experts is asymptotically $\sqrt{\frac{T \ln n}{2}}$. This is achieved by the Multiplicative Weights Update algorithm with a learning rate tuned to $T$, and is known to be tight. If instead the regret bound is required to hold simultaneously at every time $t$, the best known guarantee has been $\sqrt{t \ln n}$—a factor of $\sqrt{2}$ worse—and it has remained unknown whether this factor of $\sqrt{2}$ is necessary. We show that it is not. We give an algorithm, requiring no knowledge of the horizon, whose cumulative regret satisfies $R_t \le \bigl(1 + O(\sqrt{\ln \ln n / \ln n})\bigr)\sqrt{t \ln n / 2}$ simultaneously for every $t \ge 1$.

Text-to-speech systems increasingly process user-generated text (UGT) such as ppl and imo, whose pronunciation must be inferred from the canonical rather than surface form. We introduce UGTPhon, the first grapheme-to-phoneme (G2P) benchmark for UGT in English, Vietnamese, and Korean, together with an inference-grounded taxonomy for fine-grained diagnosis. Existing G2P models and frontier LLMs exhibit a systematic canonical-to-non-canonical performance gap, reaching up to 66.8 PER points. As a benchmark baseline, we propose a simple compositional G2P approach that incorporates canonical-form evidence through exact-match lookup and staged decoding. Across matched ByT5 and Qwen2.5-0.5B backbones, explicit canonical-form modeling consistently reduces non-canonical G2P errors. The 0.5B variant also performs competitively with much larger few-shot frontier LLMs, highlighting the benefit of explicitly modeling canonical-form inference for UGT phonemization.

Let H be a linear group. We show that if there is an invertible matrix x such that all the elements of xH share the same characteristic polynomial then H is virtually solvable. There are plenty of applications that will be presented in future paper. Here, we discuss some applications to the generalized Weigold conjecture and present an alternative straightforward proof of the Formanek–Procesi nonlinearity theorem for Aut(F_n), n>2, over every field. When n>4 our non-linearity proof gives a stronger result than the original Formanek–Procesi theorem.

xlog is a CUDA-native logic programming engine integrating neural perception with deterministic Datalog, probabilistic inference, and epistemic world views through a typed frontend and provider-owned CUDA runtime. Its reasoning modes share device data planes, but their execution boundaries differ: ordinary Datalog and exact inference are host-orchestrated, while certified resident recursive and Monte Carlo sampled cores record zero tracked host-device transfers before a bounded terminal receipt. The probabilistic path supports end-to-end gradients through GPU knowledge compilation from provenance to CNF to Decision-DNNF, exact weighted model counting, and backward gradients. A final smoothed circuit is certified against its source formula before caching or evaluation. Circuit caching yields a 2.74x MNIST-addition training speedup; a worst-case-optimal join subsystem yields a 27.96x geometric-mean gain over xlog's binary-join baseline. MNIST-addition accuracy matches Scallop's (0.9561 versus 0.9468), but no per-epoch speed claim is made because baseline epoch time varies with CPU quota. In five hub-skewed triangle-counting cases, the Souffle-to-fused-xlog execution-time ratio rises from 0.88x at 150k edges, where Souffle is faster, to 5.54x at 1.2M; fused peak device allocations are 85-1,033 MB versus 3,287-44,979 MB for the materializing arm. Exact inference is correctness-equivalent to but slower than ProbLog2. On a public video benchmark, a proximity predicate trained only through symbolic credit replaces hand-set geometry at unchanged held-out accuracy; within Event-Calculus rule search it fails ten-fold cross-validation and does not transfer on a leak-free split. On a maritime corpus, weighted clauses beat crisp selection by 0.065 F1, with the result reproduced by one chronological training pass.

The growing deployment of Internet of Things (IoT) devices has increased the need for privacy-preserving intrusion detection systems that operate directly on resource-constrained hardware. Federated Learning enables collaborative model training without sharing raw data, but conventional federated models are often too large and unstable for deployment on microcontroller-class devices. TinyML techniques enable compact neural networks but are typically designed for inference-only workloads. This work investigates combining Federated Learning with TinyML-based model compression for intrusion detection in IoT environments. We evaluate compression strategies including knowledge distillation, structured pruning, and quantization within a federated training pipeline. Preliminary results show that training stability plays a critical role in federated TinyML systems. In particular, server-coordinated cosine learning-rate scheduling improves Attack Recall from 46.7% to 93.85% while enabling substantial model compression and efficient edge deployment. These findings provide insights for designing lightweight and privacy preserving intrusion detection systems for IoT devices.

Sequential RecSys are central to modern personalization, exploiting user's historical interaction sequences to drive next-step decisions. Deep learning models, particularly CNN and Transformer-based architectures, have proven highly effective at capturing temporal dependencies in these histories. For transparency and trust, understanding which past interactions drive a given recommendation is increasingly important — both for developers auditing model behavior and for users seeking a rationale. However, the non-linearities that give these models their predictive power also render them black boxes, making it difficult to attribute decisions to specific interactions. While gradient-based, perturbation-based, and attention-based explainability methods exist, a systematic benchmark of their faithfulness for sequential recommendation is missing. We address this gap by introducing a dual-model masking metric in which one model supplies per-timestep attribution scores and a separately trained, masking-robust probe measures the resulting change in predicted probability. Using this metric, we benchmark ten XAI methods across CNN, Transformer, SASRec, and BERT4Rec backbones on KuaiRand and MovieLens, complemented by analyses of temporal attribution patterns, item popularity confounding, and robustness to input corruption. Our key findings are: (1) gradient-based methods, particularly GradientSHAP and Integrated Gradients, yield the most faithful and robust attributions; (2) raw attention weights are unreliable, but gradient-weighted attention restores faithfulness on shorter sequences, with degradation on longer horizons as softmax attention probabilities converge toward uniform importance scores, diminishing the method's ability to identify informative interactions; and (3) temporal attribution patterns in faithful methods reflect genuine task structure rather than recency or popularity bias.

We study identity testing for high-dimensional covariance matrices against dense alternatives of unknown direction, with $p/n \to \gamma$. Along a globally positive quadratic precision path, mixing Gaussian alternatives over a Gaussian Orthogonal Ensemble direction yields a contiguous experiment whose log likelihood reduces to the corrected Frobenius statistic; its upper-tail test attains the limiting weighted-power envelope at every fixed strength. Fixing the prior's Frobenius radius perturbs the mixture by only $O(p^{-1/2})$ in total variation, and exact whitening carries the experiment, the statistic, and its null law to any known null covariance. Separately, under a product-coordinate null, feasibility needs only $4+\eta$ moments, plus identical distributions over time when means are estimated; studentization and an exact degrees-of-freedom correction preserve the local power. A stability inequality turns near-envelope attainment into null agreement with the Frobenius rule, so uniform noninferiority on the typical dense bulk precludes gains at any contiguous alternative. For trace-matched rank-one alternatives, the corrected statistic is the first likelihood direction when $\vartheta_n \to 0$ and $n\vartheta_n \to \infty$; at fixed strength, the log likelihood ratio in the Onatski-Moreira-Hallin fixed-spike benchmark is governed by a richer linear spectral statistic below the Baik-Ben Arous-Peche threshold, while eigenvalue separation permits cost-free largest-eigenvalue enhancement above it. Simulations illustrate the theory.

Sparse communication in decentralized zeroth-order learning requires compatible peer-state coordinates. We characterize this one-hop condition and develop ZO-COSMO, coupling two-query estimation with average-preserving masked consensus using $q$ values per active link. Global supports serve all-neighbor mixing; matching updates require agreement only within each pair. We derive a sharp contraction-per-scalar bound within the matching class and convergence guarantees for the core and sparse-momentum updates. At fixed matching, exact moment identities characterize how shared directions preserve gradient-heterogeneity cancellation and redistribute estimation error and disagreement. Mechanism experiments cover unequal curvatures, noise, and sparse momentum. Further tests span $64$ synthetic agents and eight logical Qwen LoRA workers. At matched payload budgets, Qwen2-7B QNLI gains $3.65$ accuracy points over explicit-index Rand-$k$; edge-local updates gain $3.42$ and $2.53$ points over all-neighbor mixing on eight-worker complete and ring graphs. A matched-first-step ablation gives a $3.92$-point momentum benefit. Seed-aware and same-matching controls distinguish encoding, scheduling, and query correlation.

Let $N_g$ be the number of Ekedahl-Oort strata intersecting the supersingular locus in the Siegel modular variety. We prove that $N_g\sim 2^{g-1}$ as $g\to\infty$.

Minimum Risk Training (MRT) enables neural machine translation models to directly optimize sequence-level evaluation metrics instead of relying only on token- level maximum-likelihood objectives Shen et al. [2016]. Although introduced a decade ago, recent work shows renewed potential for risk-based optimization in modern language models Yang et al. [2024], Jinnai et al. [2025]. We apply MRT to power outage report generation for the Outage Data Initiative Nationwide (ODIN), transforming heterogeneous reports into standardized XML compliant with CIM IEC 61968-3. Our MRT approach improves Qwen2.5-7B-Instruct overall accuracy from 16.20% to 68.95%, demonstrating the effectiveness of sequence- level optimization for domain-specific structured generation

We establish the quantum channel Stein lemma at every fixed type-I error tolerance in $(0,1)$ and prove an exponential strong converse under arbitrary adaptive strategies. For any finite-dimensional channel pair, the optimal type-II exponent equals the regularized channel relative entropy and is attained by parallel strategies. When this divergence is finite, every strictly larger type-II rate forces the probability of accepting the null hypothesis to decay exponentially, uniformly over strategies and quantum memories. The proof rests on a uniform Stinespring approximation: tensor powers of the null dilation are approximated by tensor powers of the alternative dilation after applying an auxiliary linear map to the environment. The operator-norm error is exponentially small under a squared-norm bound at any rate above the regularized relative entropy. We construct the approximation from a weak testing bound by iterative rate reduction and a fixed-block tensor expansion with an exact residual. It implies right continuity at order one of the regularized sandwiched Rényi channel divergence, which yields the adaptive converse through the channel chain rule. We also obtain a sharp hockey-stick threshold and a subchannel smoothing asymptotic equipartition property for fixed and subexponentially vanishing diamond-norm errors.

Non-speech interference can change a speech representation without causing comparable task loss. We test eight frozen encoders on four tasks, adding non-speech sounds throughout recordings, during speech, or in pauses. Under whole-recording interference, embedding drift tracks task loss across seven sounds, with mean Spearman correlations of 0.81-0.88. Moving the same sound between speech and pauses changes this pattern. At quiet to moderate levels, pause interference produces larger drift, while speech interference usually causes greater loss on intent recognition, speaker verification and speech recognition. Emotion recognition shows a weaker placement effect. Pause interference also changes speech-frame representations beyond the injected region. Even below the estimated recording background, interference can change embeddings as much as repeated speech takes do. Drift helps rank the effects of different sounds, but larger drift does not consistently indicate greater task loss.

Prototype-based neural networks provide inherent interpretability through case-based reasoning, yet suffer from critical limitations: prototypes converge to redundant features, fail to capture diverse semantic parts, and lack quantitative interpretability assessment. We propose Diversity-Aware Prototype Learning (DAPL), which enforces prototype diversity through architectural constraints rather than explicit regularization. Our approach leverages multi-head self-attention with strict one-to-one attention-to-prototype mapping, ensuring each prototype specializes in distinct visual features. We further introduce foreground-aware training to focus prototypes on semantically meaningful regions and develop comprehensive evaluation metrics (Coverage and Diversity) for quantitative interpretability assessment. Experiments on CUB-200-2011 demonstrate substantial improvements: DAPL with foreground-aware training achieves 81.69% accuracy with 0.596 Coverage and 0.427 Diversity, providing the best overall balance across all evaluated prototype-based methods. Code is available at https://github.com/xinmiaolin/DAPL.

With the rising computational and monetary costs of training large language models (LLMs), checkpointing—periodically storing model states for recovery—becomes essential for fault tolerance. Conventional checkpointing entails a severe trade-off between checkpoint frequency (I/O overhead) and computational recovery (recovery time). State-of-the-art approaches mitigate this cost through pipelining checkpoint I/Os, differential checkpointing, or in-memory persistence, yet none leverage the distinct characteristics of LLM training dynamics, where model weight updates are non-uniformly distributed across transformer layers. This observation implies that saving all weights each time might not be efficient. Inspired by this observation, we present LayerCheck, a layer-wise adaptive checkpointing framework that selectively persists layers whose updates exceed a threshold. This design avoids periodic I/O bursts by distributing layer-wise checkpoint writes over time, resulting in smoother and more balanced I/O profiles. Upon recovery, LayerCheck reconstructs a mixed-timestamp composite model state by aggregating the most recently persisted versions of each layer together with their matching optimizer states. Under a bounded per-layer staleness guard, this introduces a controlled perturbation: under standard Adam assumptions it adds a bounded staleness term, and empirically the post-restart loss deviates from the failure-free trajectory by at most 0.54%. Empirical results on multiple open-source LLMs with different datasets further demonstrate that recovered models preserve the original convergence behavior and accuracy while substantially reducing checkpoint overheads. Specifically, LayerCheck achieves up to 22.6x reduction in total checkpoint size and 1.31x reduction in end-to-end training time compared to state-of-the-art systems, significantly lowering the cost of checkpointing.

Let $n\ge 3$ and let $K\subset\mathbb R^n$ be a convex body. For a two-dimensional linear subspace $P\subset\mathbb R^n$, let $K|P$ be the orthogonal projection of $K$ onto $P$. We prove that if for every two-dimensional subspace $P$, the planar convex body $K|P$ has $q$-fold rotational symmetry up to translation, then for $q\ge4$, this forces $K$ to be an Euclidean ball. The case $q=3$ is exceptional: non-spherical examples exist.

We construct infinitely many pairwise non-derived-Morita-equivalent phantom categories $\mathcal{P}_{m}, m\in\mathbb{Z}$ from concrete directed DG quivers with 3 vertices. Moreover, there exists a fixed finite-dimensional DG algebra $C$ such that for each $m\in\mathbb{Z}$, there is a way to reassign cohomological gradings on $C$ (without changing the differential) to obtain a new DG algebra $C_{m}$ with $\mathrm{Perf}(C_{m})\cong \mathcal{P}_{m}$.

For the infinite Fermi-Pasta-Ulam (FPU) system, general solutions can be approximated by counter-propagating waves associated with solutions to the Korteweg-de Vries (KdV) equation as the lattice mesh size goes to zero. We show that, by exploiting the conservation of the FPU Hamiltonian, the continuum limit from the FPU system to the KdV equation with $L^2$-level initial data holds in appropriate norms on an arbitrary time interval, thereby answering an open question posed by Hong, Kwak, and Yang (2021). Moreover, for the local-in-time continuum limit of the FPU system to the KdV equation, we lower the required Sobolev regularity to $H^s$ with $s > - \frac 34$. Our continuum limit results also apply to the case of the Toda lattice in Flaschka's form, thereby lowering the regularity requirement in our previous work (2026). To establish this low-regularity continuum limit, we prove key trilinear estimates that are sharp up to the endpoint by combining linear estimates, the transversality of characteristic curves, and multilinear dispersive smoothing properties of the linear FPU flow.

Zeroth-order (ZO) optimization is an attractive option for memory-efficient LLM fine-tuning, but its fault tolerance remains underexplored. Unlike first-order training, ZO progress can be represented by lightweight seed-and-scalar step logs, yet naive log-only recovery still incurs replay cost that grows with training progress, and shortcut replay does not preserve the executed floating-point trajectory. We present ZOCheck, a fault-tolerant ZO training system that exploits this replayable structure through a CPU shadow process that continuously replays logged updates, materializes consistent recovery images off the GPU critical path, and persists them asynchronously. ZOCheck therefore combines non-blocking checkpointing during training with fast recovery from a near-current state. We also develop a cost model for choosing the snapshot policy under realistic failure rates. Experiments show that ZOCheck reduces checkpoint overhead by up to 219.7x and recovery latency by 1.55x on average compared with asynchronous full-state checkpointing, translating into up to 21.3x lower end-to-end wasted time across the evaluated failure rates, while preserving exact recovery behavior.

Dissipativity is a fundamental system-theoretic property closely related to stability, passivity, and input–output stability, and is particularly important in robotics, where learned dynamics models are often embedded within feedback control loops. However, most existing approaches for learning dissipative dynamics are based on continuous-time formulations, which require ODE solvers during training or inference and can therefore be computationally expensive. Moreover, because practical implementations are inherently discrete-time, direct discretization of a continuous-time passive system does not necessarily preserve passivity, motivating the need for explicit discrete-time guarantees. This study proposes a method for learning incrementally dissipative dynamics from input–output time-series data using a deep multilayer perceptron formulated directly in discrete time. Through a constrained parameterization and a dedicated training procedure, the proposed model guarantees incremental dissipativity by construction rather than through regularization. Lyapunov-based analysis establishes the corresponding dissipativity and stability guarantees, while simulations on robotic dynamical systems demonstrate competitive prediction accuracy, computational efficiency, and consistent preservation of incremental dissipativity compared with baseline methods.

Compositionality, the ability to represent complex acoustic scenes as combinations of simpler sound sources, is central to auditory perception and classical additive signal models. Still, it remains unclear whether modern pre-trained audio representations internalize additive structure without compositional supervision. Existing evaluation frameworks of audio compositional reasoning largely focus on cross-modal audio-text alignment, leaving open whether audio representations themselves exhibit additive compositional structure independent of text grounding, analogous to vector arithmetic in word representations. To investigate this, we adopt a two-step diagnostic for frozen audio representations. First, we quantify linear alignment between representations and sound source labels using canonical correlation analysis. Second, we test additive compositional generalization via leave-one-combination-out reconstruction, grouping clips by exact source-label set, averaging their representations, and predicting held-out means from per-source contributions fitted only on training combinations. With larger combination holdouts, CLAP outperforms the permuted and label-overlap baselines on FSD50K, while the speech models do not outperform the label-overlap baseline. We examine representations generated by Wav2Vec2, HuBERT, and CLAP on FSD50K and CHiME-Home datasets. All three models show consistently higher linear correlation and more accurate leave-one-combination-out reconstructions than the permuted baselines. However, only CLAP shows large cosine similarity gains, which could be associated with its training on many kinds of audio and text. Finally, we note that all three models exhibit reconstruction residuals, revealing limits of additive compositionality such as nonlinear or non-compositional audio structure.

Physical AI has gained increasing attention for its role in developing AI systems that better understand, predict, and control real-world dynamics. Achieving this requires AI models that not only achieve high prediction accuracy but also preserve fundamental physical properties of dynamical systems. In this paper, we propose a deep discrete-time dissipative recurrent neural network (DissipNet) that explicitly enforces dissipativity, a key property related to stability and energy dissipation, through structural weight constraints and a dedicated training algorithm. By construction, the proposed network is capable of learning dissipative dynamics while preserving their inherent stability, which is formally analyzed using Lyapunov theory. In contrast to Physics-Informed Neural Networks (PINNs), which incorporate governing equations into the training loss but do not guarantee preservation of internal analytical properties such as dissipativity or passivity, our approach provides explicit guarantees on stability at the model level. We demonstrate the effectiveness of the proposed method through several modeling applications, and compare its performance with a naive recurrent neural network (RNN) and a PINN-based model.

Kinetic models of protein aggregation describe populations by size, not by spatial organization or morphology. We extend Lumry-Eyring nucleated polymerization to a model in which the monomer is a density field and each aggregate is a region bounded by a level set. Growth is a flux condition on the available sites of a surface. Condensation is a reaction between the bonding sites of two surfaces in contact, at a rate set by the bond rate and the contact geometry. The availability of those sites is a field on the interface, and its equilibrium value follows from Wertheim's perturbation theory. The collision efficiency and the Fuchs stability ratio are therefore computed, not fitted. In a well-mixed limit the model's spatial averages satisfy the rate equations term by term; the monomer fraction agrees to eight parts in ten thousand, a difference that arises from equating aggregate size with volume. The condensation kernel's exponent is $0.5806\pm0.0013$ against the $0.600\pm0.010$ fitted to a monoclonal antibody. The computed stability ratio reproduces thirteen of fourteen published conditions at twelve $k_BT$, but only with the bond rate at the top of its range. In a many-body box, aggregates merge at $2.2$ to $3.8$ times the two-body rate.

Generative artificial intelligence (GenAI) is increasingly described in higher education as a tool, collaborator, evaluator, proxy, and infrastructure. These labels are not neutral: they shape who is seen as acting, knowing, and, crucially, being answerable when someone uses AI. This study examines how scholars distribute such responsibility across 366 English-language titles and abstracts published between November 2022 and 14 August 2026. A corpus-assisted discourse analysis combined frequency counts, five-word collocations, actor-predicate associations, obligation-clause coding, and heuristic analysis of passives, nominalisations, and reporting metonymies. The final corpus contained 91,405 tokens, drawn from 8,734 unique records screened after deduplication. AI was the most frequently named actor, appearing 2,050 times and entering 447 predicate associations, most involving action. Students, by contrast, were more often associated with knowing, judging, and verifying, yet no sentence ever made AI explicitly responsible. Responsibility fell largely on educators, institutions, and policy, or disappeared through passive and nominalised constructions. Even frequent phrases such as "responsible AI" and "responsible use" rarely identify who is accountable for what. The findings reveal a persistent gap between giving AI functional agency and assigning normative accountability.

Personalized recommendation depends critically on how user representations are constructed from historical behavior. Two paradigms have emerged for constructing semantic user profiles in content-based recommendation. First, aggregate methods derive user representations as numerical aggregates of semantic item embeddings. Second, LLM-based methods generate natural-language summaries of user preferences and encode them through a text encoder. Each paradigm can be combined with temporal disentanglement of recent versus historical behavior. LLM-based profile generation is significantly more expensive than aggregate approaches, raising the question of when this additional cost is justified. We present a systematic comparison of four semantic user-profiling strategies, factorially crossed across representation type and temporal handling, evaluated on a real-world production dataset. The comparison reveals how these strategies differ across user behavior types, across both accuracy and beyond-accuracy dimensions of recommendation quality, and across the temporal-window setting that governs the disentanglement.

We develop a general framework for model specification testing in stationary functional time series. The approach is based on an autoregressive approximation that represents a broad class of stationary functional processes through coefficient kernels whose dimension and autoregressive order may increase with the sample size. Different model assumptions induce different structural restrictions on these kernels, and our tests are constructed by measuring deviations from the corresponding restrictions. We illustrate this principle for three problems: testing a prescribed order of a functional autoregressive model, testing a functional autoregressive moving-average specification, and testing separability of autoregressive coefficient kernels. The resulting statistics are based on weighted $\mathcal{L}^2$-distances, and the critical values are obtained by a multiplier bootstrap. We establish a quantitative bootstrap approximation that is uniform over a class of weight functions and prove asymptotic validity and consistency of the proposed tests. The methodology allows for data-adaptive weighting and is illustrated by simulations and a data example.

Learning an interacting many-body Hamiltonian at the Heisenberg limit generally requires control that preserves local information for evolution times of order $1/\varepsilon$ to attain $\varepsilon$ precision. To achieve this, existing protocols often rely on trusted many-qubit operations or increasingly rapid control pulses, creating a precision barrier when gates involve unknown multi-qubit interaction or have finite duration. We show that neither resource is necessary for geometrically local Hamiltonians. Our protocol applies only static single-qubit fields, whose strength is independent of system size and grows polylogarithmically with $1/\varepsilon$. These fields generate emergent prethermal symmetries that suppress thermalization for the entire learning experiment while retaining informative symmetry-preserving dynamics. On a $d$-dimensional lattice of $n$ qubits, this enables learning every coefficient to accuracy $\varepsilon$, with failure probability at most $\delta$, using total evolution time $\mathcal{O}(\log^d(1/\varepsilon)\log^2(n/\delta)/\varepsilon).$ Thus, our learning protocol attains the information-theoretically optimal \(1/\varepsilon\) dependence up to polylogarithmic factors using product-state preparation, single-qubit measurements, and non-adaptive experiments. More broadly, our results establish emergent prethermal symmetries as a resource for quantum learning, opening a route to Heisenberg-limited characterization of many-body systems where fast or trusted many-qubit control is unavailable.

Estimating the causal effects of medical treatments is difficult when clinically important outcomes are costly to measure or require long follow-up. Short-term or inexpensive surrogate outcomes offer a potential alternative, but surrogate biomarkers may be unavailable or difficult to identify. Advances in artificial intelligence (AI) have enabled increasingly accurate prediction of clinical outcomes from inexpensive, high-dimensional measurements, which creates an opportunity to use AI predictions themselves as surrogates. To this end, we develop a framework for estimating treatment effects from paired measurements obtained before and after treatment for each treated individual. A pretrained AI model is applied to the before and after measurements, and our estimator compares the resulting outcome predictions. We characterize the technical assumptions under which this within-person contrast identifies the average treatment effect on the treated, even when clinical outcomes are never observed for treated individuals. When these assumptions cannot be justified, we use prediction-powered inference to correct bias using a small number of observed clinical outcomes and obtain valid inference. Synthetic and real-world cardio-oncology experiments demonstrate the validity and accuracy of the approach.

We study the challenging problem of distribution-free sequential changepoint detection for independent observations with unknown and completely unrestricted pre- and post-change laws. For over two decades, the primary existing solution for this problem has employed Vovk's conformal test martingales and associated e-detectors, which control the probability of false alarm (PFA) and the average run length (ARL) respectively. The majority of these works focus on validity, with statistical efficiency usually left for simulations. We develop a comprehensive theory of how conformal p-values behave under non-exchangeable data with a changepoint at an unknown time $T$. We use this to analyze the post-change growth and resulting detection delays and find that the standard existing methods are provably suboptimal for PFA and ARL control, and can lead to delays that are $\Omega(T)$ and $\Omega(\sqrt{\text{ARL}})$ respectively. We construct new conformal e-processes and e-detectors with learned scores and a fixed, distribution-independent betting dictionary. For any distribution pair with positive finite KL divergence, our methods asymptotically achieve $\log T/\mathrm{KL}$ delay for PFA control and $\log\mathrm{ARL}/\mathrm{KL}$ delay (with a sharp leading constant of 1), which are both proven to be minimax optimal in a suitable double-array framework. Simulations illustrate the large empirical benefits of our new approach.

We study the fluctuation spectrum and renormalized one-loop quantum mass of the Christ–Lee kink over the full positive range of its deformation parameter. The fluctuation equation is reduced exactly to general-Heun form, yielding parity-resolved continuum solutions and implicit quantization conditions for the discrete spectrum. At the first nontrivial continuum crossing, the odd Heun solution truncates to a polynomial, giving the exact threshold \(\epsilon_1=\sqrt{\sqrt{3}-1}\). For small deformation, the kink separates into two widely spaced \(\phi^6\)-like interfaces and the fluctuation operator develops a long central cavity. This geometry explains the logarithmic growth of the bound-state count, the asymptotically geometric hierarchy of continuum-threshold crossings, and the emergence of a soft relative-translation mode. In the opposite limit, the spectrum approaches the \(\phi^4\) Pöschl–Teller problem, while its even threshold resonance becomes a shallow bound state at finite deformation. The one-loop correction is evaluated in a fixed vacuum-normal-ordering prescription using a common-regulator spectral trace and independently through an imaginary-frequency functional determinant. The two calculations agree throughout representative finite deformations and reproduce the exact \(\phi^4\) limit. In the small-deformation regime, the extended central region produces a logarithmically enhanced negative quantum correction. These results provide a unified analytic and numerical description of how the spectral reorganization of the Christ–Lee kink controls its semiclassical quantum mass.

Full tomography of a generic many-qubit quantum state requires exponentially many copies, while suitable structural constraints can make reconstruction sample-efficient. Existing approaches exploit, for example, limited entanglement structure, low magic, or constrained state-preparation circuits. Here we consider a class of mixed states that can simultaneously exhibit extensive entanglement and extensive magic. Specifically, we introduce Clifford-encoded block-product (CEBP) states, obtained by applying an unknown global Clifford unitary to a tensor product of arbitrary mixed states supported on unknown blocks of bounded size. We show that, for a fixed block size, CEBP states can be reconstructed using polynomially many copies by exploiting Clifford-preserved Pauli correlations to recover the latent structure and reduce the remaining problem to local tomography. Our result demonstrates that sample-efficient tomography can arise from bounded complexity in a latent frame even when the physical state is highly entangled, highly magical, and mixed, and suggests complexity modulo structured transformations as a broader organizing principle for quantum-state learnability.