We provide a unifying framework for the design and analysis of multi-calibrated predictors. By placing the multi-calibration problem in the general setting of multi-objective learning---where learning guarantees must hold simultaneously over a set of distributions and loss functions---we exploit connections to game dynamics to achieve state-of-the-art guarantees for a diverse set of multi-calibration learning problems. In addition to shedding light on existing multi-calibration guarantees and greatly simplifying their analysis, our approach also yields improved guarantees, such as error tolerances that scale with the square-root of group size versus the constant tolerances guaranteed by prior works, and improving the complexity of $k$-class multi-calibration by an exponential factor of $k$ versus Gopalan et al.. Beyond multi-calibration, we use these game dynamics to address emerging considerations in the study of group fairness and multi-distribution learning.

Population risk is always of primary interest in machine learning; however, learning algorithms only have access to the empirical risk. Even for applications with nonconvex non-smooth losses (such as modern deep networks), the population risk is generally significantly more well behaved from an optimization point of view than the empirical risk. In particular, sampling can create many spurious local minima. We consider a general framework which aims to optimize a smooth nonconvex function $F$ (population risk) given only access to an approximation $f$ (empirical risk) that is pointwise close to $F$ (i.e., $\norm{F-f}_{\infty} \le \nu$). Our objective is to find the $\epsilon$-approximate local minima of the underlying function $F$ while avoiding the shallow local minima---arising because of the tolerance $\nu$---which exist only in $f$. We propose a simple algorithm based on stochastic gradient descent (SGD) on a smoothed version of $f$ that is guaranteed to achieve our goal as long as $\nu \le O(\epsilon^{1.5}/d)$. We also provide an almost matching lower bound showing that our algorithm achieves optimal error tolerance $\nu$ among all algorithms making a polynomial number of queries of $f$. As a concrete example, we show that our results can be directly used to give sample complexities for learning a ReLU unit.

Generative models for materials, especially inorganic crystals, hold potential to transform the theoretical prediction of novel compounds and structures. Advancement in this field depends on robust benchmarks and minimal, information-rich datasets that enable meaningful model evaluation. This paper critically examines common datasets and reported metrics for a crystal structure prediction task$\unicode{x2014}$generating the most likely structures given the chemical composition of a material. We focus on three key issues: First, materials datasets should contain unique crystal structures; for example, we show that the widely-utilized carbon-24 dataset only contains $\approx$40% unique structures. Second, materials datasets should not be split randomly if polymorphs of many different compositions are numerous, which we find to be the case for the perov-5 and MP-20 datasets. Third, benchmarks can mislead if used uncritically, e.g., reporting a match rate metric without considering the structural variety exhibited by identical building blocks. To address these oft-overlooked issues, we introduce several fixes. We provide revised versions of the carbon-24 dataset: one with duplicates removed, one deduplicated and split by number of atoms $N$, one with enantiomorphs, and two containing only identical structures but with different unit cells. We also propose new splits for datasets with polymorphs, ensuring that polymorphs are grouped within each split subset, setting a more sensible standard for benchmarking model performance. Finally, we present METRe and cRMSE, new model evaluation metrics that can correct existing issues with the match rate metric.

Test-time scaling (TTS) aims to achieve better results by increasing random sampling and evaluating samples based on rules and metrics. However, in text-to-image(T2I) diffusion models, most related works focus on search strategies and reward models, yet the impact of the stochastic characteristic of noise in T2I diffusion models on the method's performance remains unexplored. In this work, we analyze the effects of randomness in T2I diffusion models and explore a new format of randomness for TTS: text embedding perturbation, which couples with existing randomness like SDE-injected noise to enhance generative diversity and quality. We start with a frequency-domain analysis of these formats of randomness and their impact on generation, and find that these two randomness exhibit complementary behavior in the frequency domain: spatial noise favors low-frequency components (early steps), while text embedding perturbation enhances high-frequency details (later steps), thereby compensating for the potential limitations of spatial noise randomness in high-frequency manipulation. Concurrently, text embedding demonstrates varying levels of tolerance to perturbation across different dimensions of the generation process. Specifically, our method consists of two key designs: (1) Introducing step-based text embedding perturbation, combining frequency-guided noise schedules with spatial noise perturbation. (2) Adapting the perturbation intensity selectively based on their frequency-specific contributions to generation and tolerance to perturbation. Our approach can be seamlessly integrated into existing TTS methods and demonstrates significant improvements on multiple benchmarks with almost no additional computation. Code is available at \href{https://github.com/xuhang07/TEP-Diffusion}{https://github.com/xuhang07/TEP-Diffusion}.

Inverse problems in the physical sciences are often ill-conditioned in input space, making progress step-size sensitive. We propose the Deceptron, a lightweight bidirectional module that learns a local inverse of a differentiable forward surrogate. Training combines a supervised fit, forward-reverse consistency, a lightweight spectral penalty, a soft bias tie, and a Jacobian Composition Penalty (JCP) that encourages $J_g(f(x))\,J_f(x)\!\approx\!I$ via JVP/VJP probes. At solve time, D-IPG (Deceptron Inverse-Preconditioned Gradient) takes a descent step in output space, pulls it back through $g$, and projects under the same backtracking and stopping rules as baselines. On Heat-1D initial-condition recovery and a Damped Oscillator inverse problem, D-IPG reaches a fixed normalized tolerance with $\sim$20$\times$ fewer iterations on Heat and $\sim$2-3$\times$ fewer on Oscillator than projected gradient, competitive in iterations and cost with Gauss-Newton. Diagnostics show JCP reduces a measured composition error and tracks iteration gains. We also preview a single-scale 2D instantiation, DeceptronNet (v0), that learns few-step corrections under a strict fairness protocol and exhibits notably fast convergence.

Vision-Language Action (VLA) models unify perception, reasoning, and trajectory generation for autonomous driving, but suffer from significant inference latency due to deep transformer stacks. We present DeeAD, a training-free, action-guided early-exit framework that accelerates VLA planning by evaluating the physical feasibility of intermediate trajectories. Instead of relying on confidence scores, DeeAD terminates inference when predicted trajectories align with lightweight planning priors (e.g., Navigation or Low-precision Planning) within a tolerable deviation (<2m). To improve efficiency, we introduce a multi-hop controller that adaptively skips redundant layers based on the change rate of scores. DeeAD integrates into existing VLA models, such as ORION, without requiring retraining. Experiments on the Bench2Drive benchmark demonstrate up to 28% transformer-layer sparsity and 29% latency reduction, while preserving planning quality and safety.