ICML 2026 Papers

Prediction-Powered Inference (PPI) is a popular strategy for combining gold-standard and possibly noisy pseudo-labels to perform statistical estimation. Prior work has shown an asymptotic \textit{free lunch} for PPI++, an adaptive form of PPI, showing that the \textit{asymptotic} variance of PPI++ is always less than or equal to the variance obtained from using gold-standard labels alone. Notably, this result holds \textit{regardless of the quality of the pseudo-labels}. In this work, we demystify this result by conducting an exact finite-sample analysis of the estimation error of PPI++ on the mean estimation problem. We give a \textit{no free lunch} result, characterizing the settings (and sample sizes) where PPI++ has provably worse estimation error than using gold-standard labels alone. Specifically, PPI++ will outperform if and only if the correlation between pseudo- and gold-standard is above a certain level that depends on the number of labeled samples ($n$). In some cases our results simplify considerably: For Gaussian data, for instance, the correlation must be at least $1/\sqrt{n - 2}$ in order to see improvement. More broadly, by providing exact non-asymptotic expressions for the variance of PPI++ under sample splitting, we aim to empower practitioners to transparently reason about the benefits of PPI++ in specific applications. In experiments, we illustrate that our theoretical findings hold on real-world datasets.

We present TerraBind, a foundation model for protein-ligand structure and binding affinity prediction that achieves 26$\times$ faster inference than state-of-the-art methods while improving affinity prediction accuracy by up to 20\%. Current deep learning approaches to structure-based drug design rely on expensive all-atom diffusion to generate 3D coordinates, creating inference bottlenecks that render large-scale compound screening computationally intractable. We challenge this paradigm with the hypothesis: full all-atom resolution is unnecessary for accurate small molecule pose and binding affinity prediction. TerraBind tests this hypothesis through a coarse pocket-level representation (protein C$_\beta$ atoms and ligand heavy atoms only) within a multimodal architecture combining pretrained molecular encoders and ESM-2 protein embeddings that learns rich structural representations, which are used in a diffusion-free optimization module for pose generation and a binding affinity likelihood prediction module. On structure prediction benchmarks, TerraBind matches diffusion-based baselines in ligand pose accuracy. For binding affinity, TerraBind outperforms Boltz-2 by 16-20\% in Pearson correlation on both a public benchmark (CASP16) and a diverse private dataset (18 assays). The affinity module also provides well-calibrated uncertainty estimates, addressing a critical gap in compound prioritization for drug discovery. Furthermore, this module enables a continual learning framework and a hedged batch selection strategy that, in simulated drug discovery cycles, achieves 6$\times$ greater affinity improvement over greedy approaches.

Evaluating conditional coverage remains one of the most persistent challenges in assessing the reliability of predictive systems. Although conformal methods can give guarantees on marginal coverage, no method can guarantee to produce sets with correct conditional coverage, leaving practitioners without a clear way to interpret local deviations. To overcome sample-inefficiency and overfitting issues of existing metrics, we cast conditional coverage estimation as a classification problem. Conditional coverage is violated if and only if some classifier can achieve lower risk than the target coverage. Through the choice of a (proper) loss function, the resulting risk difference gives a conservative estimate of natural miscoverage measures such as L1 and L2 distance, and can even separate the effects of over- and under-coverage, as well as handle non-constant target coverages. We call the resulting family of metrics excess risk of the target coverage (ERT). We show experimentally that the use of modern classifiers provides much higher statistical power than simple classifiers underlying established metrics like CovGap. Additionally, we use our metric to benchmark different conformal prediction methods. Finally, we release an open-source package for ERT as well as previous conditional coverage metrics. Together, these contributions provide a new lens for understanding, diagnosing, and improving the conditional reliability of predictive systems.

Why do neural networks generalize well on natural data? Natural data originates from processes subject to specific physical constraints, such as temporal and spatial invariance, that make it easier to learn. We investigate the sufficiency of these properties using 2D cellular automata as a controlled testbed: systems that are perfectly local, symmetric, and deterministic. We find that these conditions alone are \textit{not sufficient} to predict the $k$-step evolution of a cellular automaton. We then examine smoothness (average sensitivity) as an additional criterion and find it predictive but still incomplete. Finally, we introduce a circuit complexity perspective, hypothesizing that natural functions are computable by small circuits. Junta coefficients, measuring the concentration of Fourier weight by interaction degree, provide a tighter predictor of learnability and a correspondence to combinatorial complexity. Across architectures (CNNs, transformers, MLPs), learnable functions are predominantly those with spectral weight concentrated at low degrees and therefore low complexity. These results would be consistent with the hypothesis that natural data is learnable because natural dynamics filters out complex, high-degree interactions.

Conformal Prediction (CP) provides a statistical framework for uncertainty quantification that constructs prediction sets with coverage guarantees. While CP yields uncontrolled prediction set sizes, Backward Conformal Prediction (BCP) inverts this paradigm by enforcing a predefined upper bound on set size and estimating the resulting coverage guarantee. However, the looseness induced by Markov's inequality within the BCP framework causes a significant gap between the estimated coverage bound and the empirical coverage. In this work, we introduce ST-BCP, a novel method that introduces a data-dependent transformation of nonconformity scores to narrow the coverage gap. In particular, we develop a computable transformation and prove that it outperforms the baseline identity transformation. Extensive experiments demonstrate the effectiveness of our method, reducing the average coverage gap from 4.20\% to 1.12\% on common benchmarks.

Prediction-powered inference is a recent methodology for the safe use of black-box ML models to impute missing data, strengthening inference of statistical parameters. However, many applications require strong properties besides valid inference, such as privacy, robustness or validity under continuous distribution shifts; deriving prediction-powered methods with such guarantees is generally an arduous process, and has to be done case by case. In this paper, we resolve this issue by connecting prediction-powered inference with conformal prediction: by performing imputation through a calibrated set-predictor, we attain validity while achieving additional guarantees in a natural manner. We instantiate our procedure for the inference of means, Z- and M-estimation, as well as e-values and e-value-based procedures. Furthermore, in the case of e-values, ours is the first general prediction-powered procedure that operates off-line. We demonstrate these advantages by applying our method on private and time-series data. Both tasks are nontrivial within the standard prediction-powered framework but become natural under our method.

Recent work has shown that brain-aligned visual representations can emerge even in randomly initialized, high-dimensional neural networks, suggesting that cortical representations may be discovered rather than fully learned through task optimization. However, how such latent brain-relevant representations are stabilized and refined during development remains unclear. Motivated by this perspective and by neuroscientific evidence of activity-dependent synaptic pruning, we study how brain-aligned representations can emerge and be refined from high-dimensional unsupervised spiking systems. We propose a biologically grounded deep SNN that integrates unsupervised learning with developmental pruning dynamics. Starting from an overcomplete spiking architecture, the model self-organizes through sensory-driven activity while selectively eliminating weak or redundant synapses, progressively yielding compact and informative representations. Without using labels, the resulting network forms hierarchical visual representations that strongly align with neural responses across multiple areas of the mouse and macaque visual cortex, outperforming supervised and unsupervised ANN and SNN baselines. Synaptic pruning further improves alignment and robustness under noisy and few-shot recognition settings. By unifying high-dimensional unsupervised spiking representations with activity-dependent synaptic pruning, this work provides a computational account of developmental refinement in visual cortex and bridges recent findings on emergent brain alignment in random networks with biologically grounded models of representation learning.

Conformal prediction (CP) has become a cornerstone of distribution-free uncertainty quantification, conventionally evaluated by its coverage and interval length. This work critically examines the sufficiency of these standard metrics. We demonstrate that the interval length might be deceptively improved through a counter-intuitive approach termed Prejudicial Trick (PT), while the coverage remains valid. Specifically, for any given test sample, PT probabilistically returns an interval, which is either null or constructed using an adjusted confidence level, thereby preserving marginal coverage. While PT potentially yields a deceptively lower interval length, it introduces practical vulnerabilities: the same input can yield completely different prediction intervals across repeated runs of the algorithm. We formally derive the conditions under which PT achieves these misleading improvements and provide extensive empirical evidence across various regression and classification tasks. Furthermore, we introduce a new metric interval stability which helps detect whether a new CP method implicitly improves the length based on such PT-like techniques. Code is available at https://github.com/benben-cd/PT-Conformal-Prediction

Predicting transcriptional responses to genetic perturbations is a central problem in functional genomics. In practice, perturbation responses are rarely gene-independent but instead manifest as coordinated, program-level transcriptional changes among functionally related genes. However, most existing methods do not explicitly model such coordination, due to gene-wise modeling paradigms and reliance on static biological priors that cannot capture dynamic program reorganization. To address these limitations, we propose scBIG, a module-inductive perturbation prediction framework that explicitly models coordinated gene programs. scBIG induces coherent gene programs from data via Gene-Relation Clustering, captures inter-program interactions through a Gene-Cluster-Aware Encoder, and preserves modular coordination using structure-aware alignment objectives. These structured representations are then modeled using conditional flow matching to enable flexible and generalizable perturbation prediction. Extensive experiments on multiple single-cell perturbation benchmarks show that scBIG consistently outperforms state-of-the-art methods, particularly on unseen and combinatorial perturbation settings, achieving an average improvement of 6.7% over the strongest baselines. The code is available at https://github.com/ttruan2426-dot/scBIG.

Standard Next-Token Prediction (NTP) supervises language models solely through discrete labels in the output logit space. We argue that this sparse, one-hot supervision leaves the latent representation space under-constrained, allowing hidden states to drift into degenerate and anisotropic configurations that limit generalization. To address this issue, we propose Next Implicit Token Prediction (NITP), which augments discrete prediction with dense, continuous supervision directly in the representation space. NITP requires the model to predict the implicit semantic content of the next token, using shallow-layer representations from the same model as stable self-supervised targets. Theoretically, we show that NITP regularizes the optimization landscape by mitigating under-constrained degrees of freedom and enforcing a compact, structured representation geometry. Empirically, across dense and MoE models ranging from 0.5B to 9B parameters, NITP consistently {improves downstream performance with negligible computational overhead}. Notably, on the 9B MoE model, NITP achieves a 5.7\% absolute improvement on MMLU-Pro, along with gains of 6.4\% on C3 and 4.3\% on CommonsenseQA, with $\sim$2\% additional training FLOPs and no additional inference cost. Our implementation is available at https://github.com/aHapBean/NITP.

Conformal prediction converts point predictions into set-valued predictions with coverage guarantees under exchangeability between calibration and deployment data. We study *conformal calibration transfer*, where this requirement fails because labeled calibration is available only in a source space, while prediction sets are needed in a target space linked to the source through *unlabeled paired* observations (e.g., paired modalities or sensor changes). We propose Transported Conformal Calibration (TCC): we transport labeled source calibration into the target space using the paired data, and then correct residual post-transport mismatch using only unlabeled target inputs. We instantiate this correction with two complementary methods: **TCC-KS**, which uses a label-free uncertainty surrogate to detect mismatch and adjust calibration conservatively, and **weighted-TCC**, which reweights transported calibration toward the target domain for improved efficiency when weights are stable. We provide finite-sample target-domain coverage guarantees that adapt to an observable measure of mismatch. Across CIFAR-100-C, Tiny-ImageNet-C, and SEN12MS, we show reliable target-domain coverage transfer without labeled target calibration data, with label-free diagnostics that predict when correction is needed.

Deep attribute graph clustering aims to learn discriminative node representations by leveraging both node attributes and graph topology to partition nodes into distinct clusters. Although substantial progress has been made in attribute-graph clustering in recent years, two key challenges remain: noisy edges in the original adjacency matrix degrade the quality of information propagation, and redundant feature information across different feature views hampers the learning of discriminative representations. To address these issues, we propose a self-supervised attribute graph clustering method based on topological reconstruction and correlation decorrelation. First, we reconstruct the graph topology by computing intersections between k-nearest neighbors and the original adjacency relationships, while simultaneously leveraging global semantic information from K-means clustering to filter out noisy nodes. This reconstructed topology effectively mitigates information redundancy during feature aggregation in Graph Neural Networks. Second, unlike existing augmentation-based contrastive methods, we treat the feature representations from an auto-encoder (AE) and a graph auto-encoder (GAE) as two complementary natural views. We then apply mutual information minimization and a decorrelation constraint to suppress redundant information between views, yielding more discriminative node representations. Extensive experiments on four widely-used graph datasets—ACM, DBLP, CITE, and AMAP—demonstrate that our method consistently outperforms six state-of-the-art baselines.

Diffusion policies have recently emerged as a powerful paradigm for visuomotor control in robotic manipulation due to their ability to model the distribution of action sequences and capture multimodality. However, iterative denoising leads to substantial inference latency, limiting control frequency in real-time closed-loop systems. Existing acceleration methods either reduce sampling steps, bypass diffusion through direct prediction, or reuse past actions, but often struggle to jointly preserve action quality and achieve consistently low latency. In this work, we propose **STEP**, a lightweight spatiotemporal consistency prediction mechanism to construct high-quality warm-start actions that are both distributionally close to the target action and temporally consistent, without compromising the generative capability of the original diffusion policy. Then, we propose a velocity-aware perturbation injection mechanism that adaptively modulates actuation excitation based on temporal action variation to prevent execution stall especially for real-world tasks. We further provide a theoretical analysis showing that the proposed prediction induces a locally contractive mapping, ensuring convergence of action errors during diffusion refinement. Extensive evaluations on nine simulated benchmarks and two real-world tasks show that STEP with 2 steps can achieve an average 21.6\% and 27.5\% higher success rate than BRIDGER and DDIM on the RoboMimic benchmark and real-world tasks, respectively. The code is available at https://github.com/Kimho666/STEP.

Token mixing layers play a key role in how language models can learn and generate long-range dependencies. Their efficiency relies on the necessary trade-off between decoding speed and the memory requirements, along with the cache size. Considering causal generation, this paper explores new trade-offs thanks to a unified framework which separates two crucial features: (i) the direct influence of inputs on outputs in one generation step; (ii) the recurrent propagation of information through past outputs. This framework encompasses major architectures such as attention and state-space models, but also generalizes the recurrence equations by allowing each state to depend on multiple past states rather than only the immediate predecessor. By introducing structure, we design new recurrence patterns that provably achieve the desired complexity, while providing theoretical insights on their expressivity -- trading runtime for expressivity in a principled way. Empirical validation is performed on synthetic tasks, along with language modeling. Together, these results provide a unified toolkit for the understanding and design of efficient and expressive token mixers across model families.

Existing evaluations of conformal prediction, such as prediction efficiency and test-conditional coverage, are defined in expectation over the calibration data. In practice, when only one calibration set of limited size is available, prediction sets often exhibit high variability in size, especially for methods with localization. We formalize this concern as set stability, defined as the variance of the conditional expectation of the set size given the calibration data. To improve stability without requiring additional target-task labels, we propose Stable Conformal Prediction (StCP), a transfer learning approach that utilizes labeled source-task data and unlabeled target data. Theoretically, we characterize the marginal coverage and stability of StCP; empirically, it delivers more stable prediction sets than standard conformal prediction methods, especially for those with localization, when calibration data are limited.

Performative prediction captures the phenomenon where deploying a predictive model shifts the underlying data distribution. While simple retraining dynamics are known to converge linearly when the performative effects are weak ($\rho < 1$), the complexity in the regime $\rho > 1$ was hitherto open. In this paper, we establish a sharp phase transition: computing an $\epsilon$-performatively stable point is PPAD-complete---and thus polynomial-time equivalent to Nash equilibria in general-sum games---even when $\rho = 1 + O(\epsilon)$. This intractability persists even in the ostensibly simple setting with a quadratic loss function and linear distribution shifts. One of our key technical contributions is to extend this PPAD-hardness result to general convex domains, which is of broader interest in the complexity of variational inequalities. Finally, we address the special case of strategic classification, showing that computing a strategic local optimum is PLS-hard.

Meta-learning methods perform well on new within-distribution tasks but often fail when adapting to out-of-distribution target tasks, where transfer from source tasks can induce negative transfer. We propose a causally-aware Bayesian meta-learning method, by conditioning task-specific priors on precomputed latent causal task embeddings, enabling transfer based on mechanistic similarity rather than spurious correlations. Our approach explicitly considers realistic deployment settings where access to target-task data is limited, and adaptation relies on noisy (expert-provided) pairwise judgments of causal similarity between source and target tasks. We provide a theoretical analysis showing that conditioning on causal embeddings controls prior mismatch and mitigates negative transfer under task shift. Empirically, we demonstrate reductions in negative transfer and improved out-of-distribution adaptation in controlled simulations and a real-world clinical prediction setting for cross-disease transfer, where causal embeddings align with underlying clinical mechanisms; we include the judgments from a medical expert in the clinical prediction task and obtain improved performance in predictions of unseen diseases.

Standard conformal prediction (CP) procedures are typically formulated in terms of p-values, but reliance on p-values alone limits flexibility, for example, when combining dependent evidence across models or data splits. Recent work has explored e-value formulations for conformal inference, yet a direct connection between p- and e-value formulations in CP has been missing, especially regarding their statistical efficiency. We first identify limitations of classical p-to-e calibrators in the CP setting, showing that they are not set-preserving and can lead to overly conservative prediction sets. To address this, we propose a novel P2E calibrator that converts conformal p-values into e-values without altering the prediction set induced by the original conformal p-value. We establish both theoretically and empirically that our calibrator can yield significant efficiency gains over existing p-to-e calibrators. This e-value formulation enables principled use of recent advances in e-value merging and randomization, where we demonstrate its impact in two applications: cross-conformal prediction (CCP), whose variants typically provide only approximate $1-2\alpha$ coverage, and conformal aggregation (CA). In both cases, our e-value-based methods satisfy the desired $1-\alpha$ coverage guarantee while improving efficiency over standard baselines. More broadly, our approach expands the flexibility of CP and opens new directions for efficient, distribution-free uncertainty quantification.

We study a learner who sequentially makes and broadcasts predictions of some underlying adversarially varying state. Many downstream decision makers with different goals and different long-term constraints consume these decisions to choose actions. In this setting we give the first algorithm that obtains simultaneous *dynamic regret* guarantees for all of the decision makers --- where regret for each agent is measured against a potentially changing sequence of actions across rounds of interaction, while also ensuring vanishing constraint violation for each agent. We can promise these dynamic regret bounds not just marginally, but simultaneously on many different intersecting subsequences, which lets decision makers compete with strategies that adapt with both long-term drift and short-term variation. Our results do not require the decision makers to maintain any state, but just to react myopically to our predictions.