Diagnosing Under-Development of Irreversible Processes in Video Generation

Many physical attributes are \emph{irreversible}: ice melts but does not re-freeze, paper chars but does not un-burn. Do video generators respect this? We show the question is hard to measure, and that what can be measured reliably is \emph{development} rather than reversal. Metrics of local reversal are null-degenerate: a per-clip violation rate scores $0.50$ on pure noise, and a variance-normalized reversal residual sits at its noise ceiling. What survives null-testing is a two-part protocol: progress (a directional attribute correlation) and a stasis rate. Under this protocol, generated video separates cleanly from real footage, and the gap is human-validated. Across seven text-to-video models, real reference footage advances ($ρ{=}{+}0.40$, $35\%$ static) while every generator shows near-zero progress and $92$--$100\%$ stasis; nine annotators rate real footage far above generated ($2.75$ vs.\ $0.99$ on a $0$--$4$ scale). The reliable finding is \emph{under-development}: generators barely advance irreversible attributes rather than reversing them. As a complementary mechanism, we show that post-hoc readout guidance is gameable, whereas enforcing monotonicity by construction in a disentangled attribute latent removes the gameable readout, validated in controlled and semi-synthetic settings.

DiFA: Inference-Time Forward-Process Alignment for Diffusion Models

The prevailing inference framework for diffusion models formulates generation fundamentally as a problem of numerical integration. This perspective casts the model as an exact estimator, neglecting the inherent statistical uncertainty of the denoising process. In this work, we propose Forward-Process Aligned Diffusion prediction (\textbf{DiFA}), a training-free framework that reframes inference-time data prediction refinement as a sequential state estimation problem. Rather than reusing past outputs solely for numerical integration, DiFA treats iterative data predictions along the reverse trajectory as correlated observations to build a forward-aligned temporal consensus. Inspired by Kalman filtering, this consensus aggregates historical predictions according to structural consistency and noise-level compatibility. To counteract the over-smoothing tendency of temporal consensus, we introduce a deviation guidance mechanism to adaptively preserve residual details. Empirically, DiFA yields significant improvements on CIFAR-10 and ImageNet across the evaluated metrics, including FID, IS, and FD-DINOv2, demonstrating that aligning inference with the forward statistical structure substantially improves generative fidelity.

Fixed-Protocol Amortized MPS Tomography with Conformalized Predictive Uncertainty

Quantum state tomography is sample-starved, and the states one prepares live on a narrow, learnable manifold. A $k{=}0$ prior-only control shows that on concentrated families a prior estimate is already near-optimal, so ``high fidelity at few measurements'' can be family memorization rather than tomography; genuine measurement-efficiency needs a model that conditions on the measurements and demonstrably uses them. On a shared matrix-product-state (MPS) core parameterization we study two routes. Approach~A learns a generative prior over MPS cores with measurement-guided posterior inference (gold-standard-validated, but whose few-measurement accuracy the control shows is largely the prior). Approach~B, our main proposal, is a \emph{fixed-protocol amortized} MPS estimator trained once with a gauge-invariant fidelity loss; we deliberately do not rest it on a permutation-invariant set encoder (a plain MLP matches it). The decisive lever is the measurement design: motivated by the fact that local reduced density matrices determine a $χ$-MPS, conditioning on an \emph{informative local} Pauli set rather than random strings turns a modest, memorization-prone estimator into a high-fidelity one ($\approx\!0.95$, up to $+0.59$ over prior-only, decisively passing a shuffled-measurement control). A dropout ensemble, conformally recalibrated, gives $\approx\!90\%$-coverage intervals -- including for observables never measured, where a shot-based interval does not exist. Quality holds as the system grows (fidelity $0.90$ at $n{=}10$, gain \emph{growing} in $n$; $0.88$ at bond dimension $χ{=}4$), the parameterization is polynomial (native contraction to $20$ qubits), and we close the loop on IBM hardware ($5$ states at $0.97$ from hardware-measured Paulis).

Entanglement as a Structural Complexity Axis: A PAC-Bayesian View of Generalization in Quantum Policies and Value Functions

Parameterized quantum circuits (PQCs) are increasingly used as policies and value functions in quantum reinforcement learning, yet it remains unclear when and why quantum policies generalize. We give a PAC-Bayesian account in which generalization is governed not by the raw number of circuit parameters, but by the effective dimension of the Fisher geometry induced by the circuit. This quantity is inflated by entanglement, making entangling connectivity an independent axis of complexity.In controlled experiments that fix the number of trainable rotations and vary only entanglement, we find that circuits with larger Fisher effective dimension exhibit larger train-test gaps, while parameter count is a weak predictor. The resulting bound acts primarily as a ranking certificate: it correctly orders circuits with identical parameter count, which parameter-counting bounds cannot do. We validate this mechanism across supervised classification, quantum contextual bandits, and value-function generalization, where entangled circuits consistently generalize worse than non-entangled circuits of equal parameter count, with gaps shrinking as sample size increases.Our strongest evidence comes from low-variance decision models, including single-observable classifiers, value heads, and one-step policies. In end-to-end multi-step policy learning, entanglement effects remain statistically significant but high return variance leaves the full ordering only partially resolved. Partial-correlation analysis shows that Fisher effective dimension screens off entangling pattern, and controls for training accuracy, readout, and optimizer rule out major optimization confounders. The effect also persists on an IBM Heron quantum processor under real noise. Overall, our results reframe quantum policy design around an entanglement--generalization trade-off rather than expressivity alone.

Ask the Right Comparison:Bias-Aware Bayesian Active Top-$k$ Ranking with LLM Judges

Large language models (LLMs) are increasingly used as cheap, scalable judges that compare candidate outputs pairwise -- to rank responses, select models, or triage papers. Yet LLM judges are both noisy and systematically biased: they favor verbose or well-formatted answers and exhibit position effects, so simply aggregating their votes recovers a ranking of presentation, not of true quality. We study the practical goal of identifying the \topk{} items under a fixed comparison budget, and make two contributions. First, we cast judging as Bayesian inference over latent quality with explicit, judge-specific bias covariates (verbosity, position), regularized by a shrinkage prior so that the data decide which biases a given judge actually exhibits. Second, we introduce a \topk-aware active acquisition rule that chooses the next comparison to maximally reduce uncertainty about \topk{} \emph{membership}, rather than about the full ranking. On a controlled benchmark with known ground-truth quality, judged by sixteen real LLMs spanning open and proprietary families (Llama, Qwen, Phi-4, GPT-4o-mini/5.1/5.5, Gemini, DeepSeek, and Claude Haiku/Sonnet/Opus), naive aggregation plateaus at a wrong \topk{} on biased judges regardless of budget, while our bias-aware model recovers it; \topk-aware acquisition reaches this ceiling with far fewer comparisons than round-robin or a global-uncertainty (D-optimal) rule. Bias is real but heterogeneous and capability-dependent: cheap and mid-tier judges carry a strong verbosity bias that our model corrects (lifting recall from $\sim$$0.5$--$0.6$ to $0.84$--$1.0$), whereas the frontier judges we tested show little bias and already rank accurately, so bias-aware modeling changes little there.

Calibration, Not Compilation: Detecting and Repairing Misspecified Probabilistic Programs Written by Language Models

Language models increasingly write probabilistic programs (in NumPyro, Stan, or Pyro), but a program that compiles, runs, and passes every unit test can still be \emph{statistically} wrong -- a Gaussian likelihood for heavy-tailed data, a Poisson for over-dispersed counts, an invalid prior support, or a pathological parameterization. The right verifier is therefore not a test suite but the Bayesian workflow itself: posterior predictive checks, simulation-based calibration, sampler diagnostics ($\hat R$, divergences, ESS), and held-out predictive density. We study this calibration oracle along three axes. \textbf{Detection:} on a benchmark of $14$ misspecification types across $10$ model families ($200$ instances), it flags the bug with AUC $0.97$ ($88\%$ at $2\%$ FPR \emph{when handed the correct reference program, an upper bound}) -- and a fully \emph{reference-free} version that uses no correct program reaches $62$--$78\%$ (the upper figure from a small automated model search), versus $0\%$ for a unit-test oracle. \textbf{Repair:} used as feedback in an LLM repair loop across fifteen models, calibration significantly outperforms unit-test feedback -- which is itself \emph{significantly worse than no feedback at all}, a passing test inducing false confidence that suppresses repair -- and improves over no feedback on strong-but-unsaturated models (GPT-5.1 $33{\to}92\%$, Claude $75{\to}100\%$; paired McNemar, $n{=}228$). \textbf{Reality:} on programs LLMs write from scratch for neutral briefs, $15$--$47\%$ of runnable ones are statistically misspecified (unit tests catch none), and calibration-guided repair significantly beats LLM-as-judge review, a Bayesian-workflow checklist, and data-summary self-debug. Across all three, the lesson is the same: for probabilistic programs, correctness is calibration, not compilation.

Active Quantum Kernel Acquisition for Gaussian Process Regression

Quantum kernel estimation on near-term hardware is shot-budgeted: every entry of the kernel Gram matrix is a Bernoulli expectation that must be sampled with a finite number of circuit executions. Recent work on quantum kernel classification has shown that allocating shots non-uniformly across kernel entries, weighted by their downstream task sensitivity, can reduce the shot budget required to reach a target accuracy. We extend this idea to Gaussian process (GP) regression, a setting whose downstream quantities (full-spectrum posterior variance, log-determinant, marginal likelihood) couple to kernel error more tightly than the sign-only outputs of classification. We derive three closed-form pair-level sensitivities predictive coupling $|α_iα_j|$, leave-one-out residual, and marginal-likelihood gradient and plug them into a Neyman-style minimum-variance allocation rule. To prevent catastrophic over-concentration when the warm-up sensitivity estimate is itself noisy, we add a high uniform coverage floor justified by a Frobenius lower bound on the missing-entry perturbation. On four UCI benchmarks and two synthetic RBF + Bernoulli controlled studies, the resulting allocator delivers $10$--$21\%$ test-RMSE improvement over uniform allocation across the moderate-budget regime. The gain transfers (i) to genuine ZZ and Pauli-Z quantum kernels on quantum-natural data ($-13$--$15\%$ at low budget, $p<0.05$ paired) and (ii) to four downstream tasks (Bayesian quadrature, heteroscedastic regression, hyperparameter learning, multi-output Cokriging). On UCI features embedded into a ZZ kernel the gain disappears, consistent with the exponential-concentration regime where shot allocation has nothing to exploit.

What Do Flow-Based Inverse Solvers Approximate? A Posterior-Transport View

A growing family of training-free solvers -- FlowDPS, FLOWER, PnP-Flow and their diffusion ancestors (DPS, DAPS) -- repurpose a pretrained flow-matching prior to solve imaging inverse problems by adding a measurement-guidance term to the deterministic probability-flow ODE. Despite strong empirical results, what these per-step corrections actually approximate -- and how far the resulting samples are from the true posterior $p(x\mid y)$ -- has not been characterized. We give a posterior-transport account of flow-based inverse problem solving. Our starting point is a simple but consequential fact: for a \emph{deterministic} flow prior, Bayesian conditioning is realized entirely by a \emph{reweighting of the source distribution}, not by a drift correction; pushing the reweighted source through the \emph{unmodified} velocity field yields exact posterior samples. From this we show that trajectory-guidance solvers can be read as the minimum-kinetic-energy \emph{correction} field needed to morph the unconditional source into the posterior, and that FlowDPS / FLOWER / PnP-Flow correspond to distinct zeroth-order / Gaussian / proximal approximations of this single object; we bound the resulting posterior bias in Wasserstein distance. A controlled $2$D study with a closed-form posterior confirms the theory decisively: source reweighting matches the true posterior to the Monte-Carlo floor on every metric, whereas trajectory guidance incurs $200$--$800\times$ larger error and collapses posterior modes, \emph{regardless of guidance strength}. Guided by the analysis we propose a cheap, principled velocity-correction solver that is competitive across two in-domain priors (AFHQ, CelebA) and two out-of-distribution settings while, unlike point-estimate source-space optimizers, producing diverse posterior samples with uncertainty that correlates with reconstruction error.

Intrinsic Flow Matching on Quantum Pure-State Manifolds with Phase-Aligned Transport

Quantum pure-state ensembles live on complex projective space, making flat Euclidean generative modeling geometrically mismatched. We introduce Intrinsic Flow Matching (IFM), a deterministic transport framework on $\mathbb{CP}^{d-1}$ that learns tangent velocity fields using Pancharatnam phase-aligned conditional paths. IFM replaces local score teachers and reverse-time stochastic sampling with manifold probability flow, while horizontal parameterization removes redundant ambient directions. We show that the IFM objective recovers the induced marginal transport field, represents deterministic projective ensemble flows, and yields endpoint and stability guarantees. Empirically, IFM often improves over ambient Euclidean flow matching across higher-qubit, multimodal, spin-coherent, physics-inspired, and amplitude-encoded MNIST image-vector benchmarks, with strongest gains on high-dimensional and coherence-sensitive tasks but not uniformly across every metric.

Effective Dimension Governs Generalization in Quantum Kernel Vision Models

Recent quantum vision models-quantum vision transformers and quantum convolutional networks-report two striking but unexplained empirical phenomena: (i) ansatze with more, or more uniformly distributed, entanglement generalize better, and (ii) injecting quantum noise can improve test accuracy rather than degrade it. These observations are currently treated as curiosities, discovered by grid search and explained, if at all, by hand. We show that both are manifestations of a single, measurable quantity: the \emph{effective dimension} $d_{\rm eff}$ of the (noise-shaped) quantum feature kernel. Working primarily with quantum-kernel vision models-a quantum feature map read out by a kernel classifier-we give a spectral account in which entanglement structure and quantum noise are two knobs that move $d_{\rm eff}$; in an overfitting regime, contracting $d_{\rm eff}$ acts as ridge-like regularization. We analyze the mechanism: an \emph{exact} decomposition of the depolarized kernel $K_p=(1-p)^2K+\tfrac{p(2-p)}{D}\mathbf{1}\mathbf{1}^\top$ with $d_{\rm eff}(K_p)\to1$, a contraction result (and its boundary) for amplitude damping, a kernel-machine capacity bound, and a capacity/alignment risk decomposition; the monotone contraction operative in our entangled experiments is verified empirically, not proven in general. Along the one-parameter depolarizing family the collapse is instead exact by construction; we use it only to confirm the kernel decomposition to machine precision and at up to $12$ qubits, not as evidence for $d_{\rm eff}$. Amplitude damping contracts $d_{\rm eff}$ and lifts test accuracy by up to $+13\%$ along an inverted-U sweet spot; the effect's sign flips between the over- and under-fitting regimes; noise injection matches an explicit spectral-filtering frontier. Our results organize two reported anecdotes into a single measurable principle for designing quantum-vision models.