Debates around algorithmic fairness rarely end. Models considered "fair" by one criterion are soon shown to be unfair by another. We prove that this is unavoidable. Satisfying any finite checklist of fairness criteria never certifies fairness itself, since the model may always violate yet another criterion. We call this the Pok\'emon theorem: you can't catch them all. In fact, trying to catch all criteria recovers the classical impossibility theorems. Since these violations come from differences between the groups' data, a natural remedy would be to make the data fair by learning fair features. Unfortunately, this, too, is impossible: features that scrub out sensitive group information also scrub out all predictive signal. While exact fairness is out of reach, approximate fairness is not. We derive the Pareto frontier between fairness and predictive signal for approximately fair features, and show how to attain it.
\emph{Kullback-Leibler} (KL) regularization is ubiquitous in reinforcement learning algorithms in the form of \emph{reverse} or \emph{forward} KL. Recent studies have demonstrated $\epsilon^{-1}$-type fast rates for decision making under reverse KL regularization, in contrast to the standard $\epsilon^{-2}$-type sample complexity. However, for forward-KL-regularized objectives, existing statistical analyses are either not applicable or result in $\tilde{O}(\epsilon^{-2})$ slow rates. We take the first step towards addressing this problem via a streamlined analysis of forward-KL-regularized offline CBs. We give the first $\tilde{O}(\epsilon^{-1})$ upper bounds in tabular and general function approximation settings, both under notions of \emph{single-policy concentrability}. In particular, our convex-analytical pipeline unifies these settings by exploiting the pessimism principle in a novel way and completely bypasses the proof routines in previous works based on the mean value theorem, which might be of independent interest. Moreover, we provide rate-optimal lower bounds, manifesting the tightness of our upper bounds in terms of statistical rates. Our lower bounds also demonstrate that the forward-KL-regularized sample complexity recovers the unregularized slow rate in the low-regularization regime, similarly to the reverse-KL regularization.
Agents built on large language models (LLMs) rely on reliability techniques such as retry, majority voting, and self-consistency developed in parallel rather than within a common analytical framework. We observe that an LLM sampled at temperature $T$ is a discrete stochastic channel $p(y \mid x)$ in the sense of Shannon's coding theory, and use this identity as the entry point for such a framework. Each of these techniques is a special case of one of six classical reliability operators: diversity combining, hybrid retransmission, iterative generator-critic decoding, rateless sampling, structured redundant verification, and difficulty-adaptive routing. Within the framework we give two closed-form results, a noise-variance threshold above which uniform averaging beats quality-weighted averaging and a contractivity criterion for generator-critic refinement, and turn each into a design rule checkable before committing compute. We further introduce a cost-aware semantic-nearest-neighbor router whose single Lagrangian knob traverses the quality-cost frontier without retraining. Across six local and cloud channel configurations, no fixed model-technique-budget choice dominates. On a 300-item hard split of MMLU, GSM8K, and HumanEval, the router occupies the empirical Pareto frontier: at matched quality its normalized cost is $\approx$56% lower than the best fixed technique, and at matched cost it improves quality by $\approx$7% (26% over single-shot decoding). Judge-free grading of 6,900 outputs confirms that the judge tracks correctness at the item level and that the router's advantage over a fixed policy persists at most cost settings; with internal reasoning enabled, the gain of external refinement shrinks but remains significant for our incremental-redundancy operator. These results argue for consolidating reliability techniques into a single tunable layer informed by channel coding.
This paper investigates the learning theory of Transformer networks for regression tasks on the compact Euclidean domain $[0,1]^d$ and $d$-dimensional compact Riemannian manifolds. We propose a novel constructive approximation framework for Transformers that builds local approximations of the target function and aggregates them into a global approximation via softmax partition of unity (POU). This approach leverages the attention mechanism to achieve spatial localization through affine transformations of the input. The softmax activation plays a crucial role in aggregating local approximations to a global output. From an approximation perspective, we prove that a dense Transformer equipped with only two encoder blocks and standard single-hidden-layer point-wise feed-forward networks can achieve a uniform $\varepsilon$-approximation error for $\alpha$-H\"older continuous functions with $\alpha \in (0,1]$ using $\mathcal{O}(\varepsilon^{-d/\alpha})$ total parameters. Building upon this approximation guarantee, we establish a near minimax-optimal generalization error bound of order $\mathcal{O}\big(n^{-\frac{2\alpha}{2\alpha+d}} \log n\big)$ for the empirical risk minimizer, where $n$ is the training data size. The Transformer architecture studied in this paper uses native softmax attention and sinusoidal positional encodings, with a fixed depth of two encoder blocks. Finally, numerical experiments reveal spatially localized, Gaussian-like attention weights that emerge during training, resembling our Softmax POU weights.
Root Cause Analysis (RCA) aims to identify the main drivers of anomalies in complex multivariate systems. The task is challenging due to the need for structural causal knowledge for some methods, and the computational cost of inference at test time. This paper introduces PRIM (Prior-fitted Root cause Identification with Meta-learning), a causal meta-learning approach that frames RCA as a Bayesian inference task over a prior of causal models. By marginalising out structural uncertainty, PRIM detects changes in the data-generating mechanism between normal and anomalous periods, infers distributional differences without explicit statistical testing, and implicitly learns causal structure without model fitting at test time. Following the simulation-based meta-learning paradigm of prior-fitted networks (PFNs), PRIM uses a transformer neural process (TNP) that jointly attends over normal and anomalous samples and the structural dependencies of nodes, enabling fast zero-shot inference in systems with up to 100 variables. Across synthetic benchmarks and two realistic benchmark datasets, PetShop and CausRCA, PRIM is competitive with other graph-free methods.
In modern GANs, maintaining an Exponential Moving Average (EMA) of the generator's weights is a standard practice, as such an averaged model consistently outperforms the actively trained generator. However, the EMA generator is used for final deployment only and does not influence the training process. To address this missed opportunity, we introduce Self-Distilled GAN (SD-GAN) that employs the EMA generator as a teacher to guide the active generator (student) via perceptual loss. We prove the local asymptotic stability of SD-GAN in the simplified continuous-time Dirac-GAN setting and show that it dampens the parasitic cycling behavior that plagues conventional GANs. Empirical evaluations across established architectures and datasets demonstrate that SD-GAN improves the final image quality on several metrics (FID and random-FID in particular), stabilizes the optimization trajectory and provides additional learning guidance that is not trivially correlated with the conventional adversarial loss. It also proves effective for fine-tuning pretrained GAN models.
Large language models can generate useful code from natural language, but their outputs come without correctness guarantees. Verifiable code generation offers a path beyond testing by requiring models to produce not only executable code, but also formal specifications and machine-checkable proofs. Progress in this direction, however, is difficult to measure: existing benchmarks are often small, cover only part of the pipeline, lack ground-truth proofs or rigorous specification validation, or target verification settings far from mainstream software development. We present VeriContest, a benchmark of 1,006 competitive-programming problems from LeetCode and Codeforces for verifiable code generation in Rust with Verus. Each problem includes a natural language description, expert-validated formal specifications, judge-accepted Rust code, Verus-checked proofs, and positive and negative test suites. VeriContest is constructed through a three-phase pipeline that scales from manually verified seed problems to semi-automated expansion with human-in-the-loop review. To strengthen benchmark quality, we also use testing to validate postcondition completeness. VeriContest supports both isolated and compositional evaluation of specification, code, and proof generation, and end-to-end verified program synthesis. Evaluating ten state-of-the-art models reveals a sharp gap between ordinary coding and verifiable code generation: the strongest model reaches 97.51% on natural-language-to-code generation, but only 57.16% on specification generation, 13.82% on proof generation, and 6.76% end-to-end. These results identify proof and specification generation as the central bottlenecks for current models and establish VeriContest as a rigorous platform for evaluating and training future systems that generate code with machine-checkable correctness.
Robust optimization (RO) provides a principled framework for decision-making under uncertainty, but its performance critically depends on the choice of the uncertainty set. While large sets ensure reliability, they often lead to overly conservative decisions, whereas small sets risk excluding the true outcome. Recent data-driven approaches, particularly conformal prediction, offer finite-sample validity guarantees but remain largely task-agnostic, ignoring the downstream decision structure. In this paper, we propose a decision-aware conformal framework that learns uncertainty sets tailored to robust optimization objectives. Our approach parameterizes a flexible family of polyhedral sets via data-driven hyperplanes and learns their geometry by directly minimizing the induced robust loss, while preserving statistical validity through conformal calibration. To correct for data-dependent selection, we incorporate a re-calibration step on an independent dataset to restore coverage. The resulting sets capture directional and anisotropic uncertainty aligned with the decision objective while remaining computationally tractable. We provide finite-sample coverage guarantees and bounds on the sub-optimality gap to an oracle decision. This work bridges the gap between statistical validity and decision optimality, providing a principled framework for data-driven robust optimization.
Aligning multimodal generative models with human preferences demands reward signals that respect the compositional, multi-dimensional structure of human judgment. Prevailing RLHF approaches reduce this structure to scalar or pairwise labels, collapsing nuanced preferences into opaque parametric proxies and exposing vulnerabilities to reward hacking. While recent Rubrics-as-Reward (RaR) methods attempt to recover this structure through explicit criteria, generating rubrics that are simultaneously reliable, scalable, and data-efficient remains an open problem. We introduce Auto-Rubric as Reward (ARR), a framework that reframes reward modeling from implicit weight optimization to explicit, criteria-based decomposition. Before any pairwise comparison, ARR externalizes a VLM's internalized preference knowledge as prompt-specific rubrics, translating holistic intent into independently verifiable quality dimensions. This conversion of implicit preference structure into inspectable, interpretable constraints substantially suppresses evaluation biases including positional bias, enabling both zero-shot deployment and few-shot conditioning on minimal supervision. To extend these gains into generative training, we propose Rubric Policy Optimization (RPO), which distills ARR's structured multi-dimensional evaluation into a robust binary reward, replacing opaque scalar regression with rubric-conditioned preference decisions that stabilize policy gradients. On text-to-image generation and image editing benchmarks, ARR-RPO outperforms pairwise reward models and VLM judges, demonstrating that explicitly externalizing implicit preference knowledge into structured rubrics achieves more reliable, data-efficient multimodal alignment, revealing that the bottleneck is the absence of a factorized interface, not a deficit of knowledge.
Susceptibilities are a technique for neural network interpretability that studies the response of posterior expectation values of observables to perturbations of the loss. We generalize this construction to the setting of the regret in deep reinforcement learning and investigate the utility of susceptibilities in a simple gridworld model that nevertheless exhibits non-trivial stagewise development. We argue that susceptibilities reveal internal features of the development of the model in parameter space that one cannot detect purely by studying the development of the learned policy. We validate these results with activation-steering, and discuss the framework's extension to RLHF post-training.
Neural posterior estimation has emerged as a powerful tool for amortized inference, with growing adoption across scientific and applied domains. In many of these applications, the conditioning variable is a set of observations whose elements depend not only on the target but also on unknown factors shared across the set. Optimal inference therefore requires treating the set jointly, which in turn requires training the estimator at the deployment set size -- a regime where memory and compute quickly become prohibitive. We introduce a simple, theoretically grounded strategy that decouples representation learning from posterior modeling. Our method trains a mean-pool Deep Set on sets of size at most two, producing an encoder that generalizes to arbitrary set sizes. The inference head is then finetuned on pre-aggregated embeddings, making training cost essentially independent of the deployment set size N. Across scalar, image, multi-view 3D, molecular, and high-dimensional conditional generation benchmarks with N in the thousands, our approach matches or outperforms standard baselines at a fraction of the compute.
Confidence sequences based on test martingales provide time-uniform uncertainty quantification for the mean of bounded i.i.d. observations without parametric distributional assumptions. Their practical efficiency, however, depends strongly on the choice of martingale updates, and many existing constructions do not exploit prior information about plausible data-generating distributions or mean values. We propose a Bayes-assisted framework that uses a Bayesian working predictive model to adaptively construct confidence sequences. For each candidate mean and time point, the predictive distribution selects, among valid one-step martingale factors, the update maximising predictive expected log-growth; validity is therefore preserved even when the prior or working model is misspecified. We prove that if the predictive distribution is Wasserstein-consistent, the resulting procedure is asymptotically log-optimal, matching the per-sample log-growth of an oracle procedure with access to the true distribution. We instantiate the framework using robust predictives based on Dirichlet-process mixtures and Bayesian exponentially tilted empirical likelihood. Experiments on synthetic data, sequential best-arm identification for LLM evaluation, and prediction-powered inference show that informative priors can substantially reduce confidence-sequence width and sampling effort while retaining anytime-valid coverage.
Latent diffusion models offer an attractive alternative to discrete diffusion for non-autoregressive text generation by operating on continuous text representations and denoising entire sequences in parallel. The major challenge in latent diffusion modeling is constructing a suitable latent space. In this work, we present the Latent Diffusion Language Model (LDLM), in which the latent encoder, diffusion model, and decoder are trained jointly. LDLM builds its latent space by reshaping the representations of a pre-trained language model with a trainable encoder, yielding latents that are easy to both denoise and decode into tokens. We show that naive joint training produces a low-quality diffusion model, and propose a simple training recipe consisting of an MSE decoder loss, diffusion-to-encoder warmup, adaptive timestep sampling, and decoder-input noise. Ablations show that each component substantially impacts generation performance. On OpenWebText and LM1B, LDLM achieves better generation performance than existing discrete and continuous diffusion language models while being $2{\text -}13\times$ faster, indicating that jointly learning the latent space is a key step toward making latent diffusion competitive for text generation.
Vision-Language Latent Diffusion Models (LDMs) (Rombach et al., 2022) provide powerful generative priors for inverse problems. However, existing LDM-based inverse solvers typically require a large number of neural function evaluations (NFEs) and backpropagation through large pretrained components, leading to substantial computational costs and, in some cases, degraded reconstruction quality. We propose a unified Euclidean-Wasserstein-2 gradient-flow framework that jointly performs posterior sampling and prompt optimization in the latent space through a single flow that aligns the prior and posterior with the observed data. Combined with few-step latent text-to-image models, this formulation enables low-NFE inference without backpropagation through autoencoders. Experiments across several canonical imaging inverse problems show that our method achieves state-of-the-art performance with significantly reduced computational cost.
Large language models often improve accuracy on reasoning tasks by sampling multiple chain-of-thought (CoT) traces and aggregating them with majority voting, a test-time technique called self-consistency. When we truncate a CoT partway through and regenerate the remainder, we observe that traces with correct answers reproduce their original answer more often than traces with wrong answers. We use this difference as a reliability signal, prefix consistency, that weights each candidate answer by how often it reappears under regeneration. It requires no access to token log-probabilities or self-rating prompts. Across five reasoning models and four math and science benchmarks, prefix consistency is the best correctness predictor in most settings, and reweighting votes by this signal reaches the plateau accuracy of majority voting with up to $21\times$ fewer tokens (median $4.6\times$). Our code is available at https://github.com/naoto-iwase/prefix-consistency.
Deep neural networks can learn salient features from an in-distribution (ID) training window without identifying the data-generating structure needed for out-of-distribution (OOD) generalization. Understanding this limitation requires examining the identifiability of the data-generating process (DGP). From a single training window, the DGP that yields the correct OOD extrapolation is not identifiable: infinitely many DGPs are observationally equivalent within a fixed tolerance on that window yet diverge arbitrarily beyond it, and no ID criterion alone can reliably distinguish them. A structural commitment---the feature map, label map, and model class $(\varphi, \psi, \mathcal{M})$---specifies the assumed DGP and governs OOD generalization while leaving ID performance essentially unchanged. When architecture, pretraining, data augmentation, input formats, or domain knowledge implicitly supply the correct commitment, the model generalizes beyond the training window. When it cannot infer OOD-relevant structure from ID evidence, it fails to generalize. When the commitment is correct {\em and} identifiable, OOD error vanishes. We demonstrate this mechanism in models trained from scratch and in foundation models across four natural-science settings (chemistry, physics, biology, and histopathology), as well as in a positional-encoding study spanning Transformer, Mamba, and S4D architectures. Finally, a controlled study shows that correct features are necessary but not sufficient for OOD generalization.
Vision Transformers (ViTs) achieve strong performance across vision tasks, yet their deployment with low-precision early exiting remains fragile. Existing quantization methods assume static full-depth execution, making them unstable when exit decisions are perturbed by quantization noise, which can amplify errors along dynamic inference paths. In this paper, we introduce Amortized-Precision Quantization (APQ), a utilization-aware formulation that accounts for layer utilization when modeling quantization error and reveals depth-precision trade-offs. Building on APQ, we propose Mutual Adaptive Quantization with Early Exiting (MAQEE), a bi-level framework that jointly optimizes exit thresholds and bit-widths under explicit risk control to improve inference stability. MAQEE establishes a superior Pareto frontier in the accuracy-efficiency trade-off across classification, detection, and segmentation, with comparisons at predefined task-specific performance targets. On ImageNet, it achieves 79.41% Top-1 accuracy while reducing BOPs by 10.9% relative to utilization-only allocation. Measurements of the deployed models on an RTX 5090 show GPU throughput improvements of $2.26\times$ on ImageNet and $3.06\times$ on CIFAR-100 over full-depth FP32 inference. Source code is available at https://github.com/Rui-Fang/MAQEE.
Many machine learning tasks are invariant under transformations such as translations and rotations. The $G$-bispectrum is a complete invariant that determines a signal up to a group action, but its computation is costly and existing implementations each cover a single group. We present bispectrum, an open-source, fully unit-tested PyTorch library providing efficient, differentiable selective $G$-bispectra for seven group actions. Selectivity reduces the number of coefficients from $O(|G|^2)$ to $O(|G|)$ for finite groups, from $O(m^{5/2})$ to $O(m)$ for planar rotations on the disk with $m$ harmonics, and from $\Theta(L^3)$ to $\Theta(L^2)$ for spherical 3D rotations using our augmented selective spherical bispectrum at band limit $L$. The library is invariant up to floating-point error and computes selective $G$-bispectra in sub-millisecond time on GPU. We evaluate them as pooling layers on PatchCamelyon and OrganMNIST3D against five baselines. Across 46 comparisons, bispectral pooling remains competitive, matching all baselines on PCam and improving on max pooling by 5.0 percentage points on OrganMNIST3D. On Spherical MNIST, our method with an MLP head reaches 95.8% on rotated test digits, matching a spherical CNN at $4\times$ lower latency and coming within 0.3 percentage points of a tensor-product network at $364\times$ lower latency. Selective $G$-bispectra provide fast, competitive invariant layers for finite and continuous groups.
Sequential recommendation has increasingly shifted toward generative recommenders that combine sequential patterns with semantic item information. Yet these methods are often evaluated on a small set of widely used benchmarks, raising a key question: do these benchmarks actually require the advanced modeling capabilities that modern generative recommenders claim to provide? We conduct a benchmark audit with an intentionally simple graph heuristic. Starting from only the last one or two interacted items, it retrieves candidates from a few-hop item-transition graph and ranks them by item-feature similarity. Despite using no sequence encoder, generative objective, or training, this heuristic matches or outperforms many modern baselines, with relative NDCG@10 improvements of 38.10% and 44.18% over the best competing baseline on Amazon Review Sports and CDs. We show that this behavior reflects shortcut solvability rather than an artifact of one heuristic. We identify three shortcut structures that can make next-item prediction easier than expected: low-branching local transitions, feature-smooth transitions, and limited dependence on long user histories. These shortcuts need not appear together; even one or two strong signals can make simple local retrieval highly competitive, while weakening them makes the benefits of more sophisticated models clearer. Across 14 datasets, model rankings vary substantially with dataset properties, yet the heuristic remains competitive on 10 of them. Our findings suggest that strong performance on standard benchmarks does not always demonstrate advanced sequential, semantic, or generative modeling ability. We call for more careful dataset selection and dataset-level diagnostic analysis when using benchmarks to support claims about new recommendation models.
Joint audio-video generation models are rapidly approaching professional production quality, raising a central question: do they understand audio-visual physics, or merely generate plausible sounds and frames that violate real-world consistency? We introduce AV-Phys Bench, a benchmark for evaluating physical commonsense in joint audio-video generation. AV-Phys Bench tests models across three scene categories: Steady State, Event Transition, and Environment Transition. It covers physics-grounded subcategories drawn from real-world scenes, plus Anti-AV-Physics prompts that deliberately request physically inconsistent audio-video behavior. Each generation is evaluated along five dimensions: visual semantic adherence, audio semantic adherence, visual physical commonsense, audio physical commonsense, and cross-modal physical commonsense. Across three proprietary and four open-source models, we find that Seedance 2.0 performs best overall, but all models remain far from robust physical understanding. Performance drops sharply on event-driven and environment-driven transitions, and even strong proprietary systems collapse on Anti-AV-Physics prompts. We further introduce AV-Phys Agent, a ReAct-style evaluator that combines a multimodal language model with deterministic acoustic measurement tools, producing rankings that closely align with human ratings. Our results identify cross-modal physical consistency and transition-driven scene dynamics as key open challenges for joint audio-video generation.