ICML 2026 Papers

Structure-based drug design (SBDD) can be effectively realized through an iterative refinement via the Design-Make-Test-Analyze (DMTA) cycle, which is a common workflow used by human experts. However, most conventional deep learning-based models as one-shot generators that lack feedback mechanisms, leaving the DMTA loop disconnected. In this work, we propose K-BTS, a Knowledge-Driven Bi-level Thompson Sampling framework that formalizes iterative SBDD as a Dynamic Hierarchical Multi-Armed Bandit problem. K-BTS closes the DMTA loop by decoupling decisions into two levels: an upper-level policy that prioritizes high-potential molecular lineages and a lower-level mechanism that retrieves explicit chemical rules to guide LLM generation. By integrating a dual-level Bayesian update, the framework transforms sparse docking scores into reusable experience. On the CrossDocked2020 benchmark, K-BTS achieves a state-of-the-art Top-1 average docking score. The results from diverse dimensions show that K-BTS ensures search determinism through a smooth, monotonic convergence that synchronizes structural drift with affinity improvement.

We study mechanism design for selling data as a digital good when the value derived from training AI models follows a scaling law. The seller faces a linear cost when producing data, while the buyers benefit from additional data with diminishing returns as data volume increases. This departs from classical auction models by allowing allocations to be continuous quantities of data rather than binary outcomes. We first analyze an offline setting in which all buyer types are realized simultaneously, characterizing profit-optimal mechanisms and showing how virtual-value methods extend to continuous data allocations. We then consider an online setting with sequential arrivals, where production decisions must be made under demand uncertainty. We show that myopic allocation and fixed production plans can be arbitrarily suboptimal, whereas a simple two-stage algorithm that combines upfront production with adaptive expansion achieves a constant-factor approximation to the offline optimum. Finally, we study bilateral data trading under asymmetric information, where both the buyer’s value and the seller’s cost are private. Although the optimal truthful mechanism has a complex structure, we show that simple and implementable mechanisms recover a constant fraction of the first-best gain-from-trade. Overall, our results highlight how scaling laws introduce new algorithmic trade-offs in market design and provide performance guarantees for data markets under uncertainty.

Designing heuristic algorithms for complex optimization problems is a time-consuming and expert-driven process. Recently, Automated Heuristic Design (AHD) using Large Language Models (LLMs) has shown significant promise for automating algorithm development. However, existing works mainly rely on programs to represent heuristics, which are inherently taskspecific and fail to generalize as effectively as established metaheuristics like tabu search or guided local search. To bridge this gap, we introduce Multi-Task Hierarchical Search (MTHS), an LLM-guided evolutionary method that co-designs general-purpose metaheuristics and task-specific programs. MTHS employs a hierarchical representation and adopts a two-level evolution framework to evolve task-agnostic metaheuristics and task-specific program implementations simultaneously across multiple heuristic design tasks. During this evolution, a knowledge transfer mechanism allows learning from elite programs designed for other tasks. We evaluated MTHS on distinct combinatorial optimization problems, where it outperforms both commonly-used heuristics and existing LLM-driven AHD approaches. Our results demonstrate that the hierarchical representations facilitate effective multi-task AHD, and the evolved metaheuristics exhibit strong generalization to related tasks. Code: https://github.com/FeiLiu36/MTHS.

AI-assisted task delegation is increasingly common, yet human effort in such systems is costly and typically unobserved. Recent work by Bastani & Cachon (2025); Sambasivan et al. (2021) shows that accuracy-based payment schemes suffer from incentive collapse: as AI accuracy improves, sustaining positive human effort requires unbounded payments. We study this phenomenon in a budget-constrained principal-agent framework with strategic human agents whose output accuracy depends on unobserved effort. Our first contribution is a general impossibility result showing that incentive collapse is not merely a limitation of simple linear payments, but arises for any payment rule based only on observed task accuracy. To overcome this barrier, we propose a sentinel-auditing payment mechanism that enforces a strictly positive and controllable level of human effort at finite cost, independent of AI accuracy. Building on this incentive-robust foundation, we develop an incentive-aware active statistical inference framework that jointly optimizes (i) the auditing rate and (ii) active sampling and budget allocation across tasks of varying difficulty to minimize the final statistical loss under a single budget. Experiments demonstrate improved cost-error tradeoffs relative to standard active learning and auditing-only baselines.

Automated design of multi-agent interactions with desirable equilibrium outcomes is inherently difficult due to the computational hardness, non-uniqueness, and instability of the resulting equilibria. In this work, we propose the use of game-agnostic _differentiable equilibrium blocks_ (DEBs) as modules in a novel, differentiable framework to address a wide variety of incentive design problems from economics and computer science. We call this framework _deep incentive design_ (DID). To validate our approach, we examine three diverse, challenging incentive design tasks: contract design, machine scheduling, and inverse equilibrium problems. For each task, we train a single neural network using a unified pipeline and DEB. This architecture solves the _full distribution_ of problem instances, parameterized by a context, handling _all_ games across a wide range of scales (from two to sixteen actions per player).

Temporal causal representation learning methods assume that causal mechanisms switch instantaneously between discrete domains, yet real-world systems often exhibit continuous mechanism transitions. For example, a vehicle's dynamics evolve gradually through a turning maneuver, and human gait shifts smoothly from walking to running. We formalize this setting by modeling transitional mechanisms as convex combinations of finitely many atomic mechanisms, governed by time-varying mixing coefficients. Our theoretical contributions establish that both the latent causal variables and the continuous mixing trajectory are jointly identifiable. We further propose TRACE, a Mixture-of-Experts framework where each expert learns one atomic mechanism during training, enabling test-time recovery of mechanism trajectories, including intermediate mechanism states never observed during training. Experiments on synthetic and real-world data demonstrate that TRACE recovers mixing trajectories with up to 0.99 correlation, substantially outperforming discrete-switching baselines.

Guidance methods, such as classifier-free guidance (CFG) and auto-guidance (AG), have advanced noise-to-data generation in diffusion models. Recently, bridge models have introduced a data-to-data generative process that can exploit an instructive clean prior. In this work, inspired by previous methods creating quality difference between denoising results as guidance, we propose a training-free bridge guidance method, termed Prior Guidance (PG). Specifically, we introduce a weak prior, which is unseen during bridge pre-training, hindering prior exploitation and thereby degrading denoising result. Then, we contrast it with the seen prior to highlight and enhance prior exploitation via a scaling factor. Moreover, we analyze the underlying mechanism of prior exploitation in the bridge process and design frequency-modulated prior guidance (FMPG), which tailors the guidance scale to low- and high-frequency bands coherent with bridge generative dynamics. To address prior exploitation in image in-painting, we develop a cascaded framework, CFG-FMPG, which first generates a noisy hidden representation via CFG and then exploits it as a generative prior with FMPG, fulfilling their complementary strengths without compromising inference efficiency. Experiments demonstrate that our PG methods consistently improve pre-trained bridge models across diverse image translation tasks.

Efficient long-context understanding is increasingly vital for large language model (LLM) applications such as multi-turn dialogue and program analysis. However, the core self-attention scales quadratically with sequence length, creating a fundamental computational bottleneck. Existing sparse attention methods alleviate this issue but face trade-offs: training-based methods are costly and cannot be directly applied as acceleration plugins for other models, while inference-time methods often compromise efficiency or cross-modal generality. To address these limitations, we present UniSparse, a unified mechanism that introduces the notion of composite tokens—compact representations that aggregate multi-granularity contextual information. Building on this abstraction, UniSparse dynamically constructs sparse attention through multi-granularity compression and block-level selection, enabling efficient and hardware-friendly execution on GPU. Across multiple modalities and tasks ranging from synthetic benchmarks to real-world applications, UniSparse consistently surpasses state-of-the-art sparse attention methods (e.g., MInference, XAttention, FlexPrefill) in both accuracy and efficiency, achieving $\ge$ 99\% of full-attention accuracy and up to 2.61$\times$ faster attention computation than FlashAttention.

We design efficient approximation algorithms for maximizing the expectation of the supremum of families of Gaussian random variables. In particular, let $OPT:=\max_{\sigma_1,\cdots,\sigma_n}\mathbb{E}\sum_{j=1}^{m}\max_{i\in S_j} X_i$, where $X_i$ are Gaussian, $S_j\subset[n]$ and $\sum_i\sigma_i^2=1$, then our theoretical results include: - We characterize the optimal variance allocation -- it concentrates on a small subset of variables as $|S_j|$ increases, - A polynomial time approximation scheme (PTAS) for computing OPT when $m=1$, and - An $O(\log n)$ approximation algorithm for computing OPT for general $m>1$.

Artificial Neural Networks (ANNs) are powerful tools for complex decision-making tasks. While existing activation mechanisms often promote sparsity through thresholding, they lack explicit awareness of feature channel relevance, causing networks to continuously suffer from interference by noisy channels. Such irrelevant activation signals can propagate through the network and adversely affect the final decision. Inspired by observations that channel relevance can be reflected in both intrinsic activity levels and extrinsic decision weights, and that there is strong consensus between these two aspects, we propose AIEC (Activation with Intrinsic-Extrinsic Consensus), a novel activation mechanism that has the ability to identify and suppress irrelevant feature channels during training. With a basic threshold activation, AIEC integrates an intrinsic Activation-Counting Unit that tracks channel activation statistics, an extrinsic Decision-Making Unit that learns channel decision weights, and a Consensus Gatekeeping Unit that suppresses irrelevant channels based on the agreement between intrinsic and extrinsic channel relevance assessments. Extensive experiments demonstrate that AIEC can effectively suppress irrelevant channels and encourage sparser representations. Furthermore, AIEC is compatible with a wide range of mainstream ANN architectures and achieves superior performance compared to existing activation mechanisms across multiple tasks and domains. Code is available at https://github.com/horrible-dong/AIEC.

Online advertising platforms rely on machine learning models to predict click-through rates (pCTR) and conversion rates (pCVR) for auction mechanisms. We introduce a novel framework to study the interaction between recommender system model quality, auction format, and autobidder behavior. We formalize when model improvements---defined via a refinement relation inspired by filtrations in probability theory---lead to improvements in platform-level Evaluation Criteria Metrics (ECM) such as revenue, welfare, or liquid welfare. Our main contributions are: (1) a formal definition of model improvement based on cluster refinement, and (2) a systematic characterization of ECM monotonicity across different combinations of bidder types (tCPA, max-CPA), auction formats (first-price, second-price, VCG), and budget constraints. We show that first-price auctions with uniform bidding guarantee revenue monotonicity for tCPA bidders without budgets (via Jensen's inequality), while second-price auctions and budget constraints can break this property. We provide full numerical constructions for the non-monotonicity results. Our findings have practical implications for advertising platforms seeking to align model improvements with business outcomes.

Shapley values are a principled attribution measure widely used in interpretable machine learning, but their exact computation scales exponentially with the number of players, motivating a wide range of approximation methods based on value function evaluations of sampled coalitions. This raises the question of whether approximation accuracy can be improved by *adaptively* selecting coalitions for evaluation based on previous evaluations. This is particularly relevant in settings where the value function is *costly* and the number of evaluations is severely limited, such as retraining-based feature importance, data valuation, and hyperparameter importance. For this purpose, we propose $\texttt{ShaplEIG}$, a Bayesian experimental design approach that approximates the expensive value function using a Gaussian process surrogate and adaptively selects coalitions based on their expected information gain about the Shapley values. By the linearity of the Shapley values in the value function, we show that the expected information gain is available in *closed form*. Furthermore, we propose an *efficient* computation scheme that reduces the complexity from exponential to polynomial in the number of players via elementary symmetric polynomials. In extensive experiments across diverse costly applications, our method consistently improves sample efficiency in the low-budget regime over state-of-the-art baselines.

We show that Chain-of-Thought (CoT) expands the expressiveness of Transformer in-context learning (ICL). Specifically, we show CoT enable efficient simulation of In-Context Gradient Descent (ICGD) for $N$-layer neural network. Different from CoT, a Transformer with fixed depth and hidden dimension has fixed ICL capacity in one forward pass. Simulating larger models or more optimization steps in-context requires deeper or wider Transformers. CoT removes this limitation by providing an expandable workspace via the sequence trajectory. This enables arbitrary-step and arbitrary-capacity ICGD within a constant-depth Transformer. Second, we provide a provable efficient guarantee unique to CoT through dynamical masking. The attention mechanism only process the relevant tokens for the current update step. This eliminates the redundant ``process everything'' cost of single-pass deep models. Specifically, we prove this CoT mechanism improves the computational cost of the prior best in-context result [Wu et al., ICML 2025] by $O(N)$. Numerical validations support our theory.

We consider problems of parameter estimation where design variables can be actively optimized to maximize information gain. To this end, we introduce JADAI, a framework that jointly amortizes Bayesian adaptive design and inference by training a policy, a history network, and an inference network end-to-end. The networks minimize a generic loss that aggregates incremental reductions in posterior error along experimental sequences without density evaluations. Inference networks are instantiated with diffusion models that can approximate high-dimensional and multimodal posteriors at every experimental step. JADAI achieves superior or competitive performance across adaptive design benchmarks.

We study experimental designs that balance nonlinear functions of covariates, extending classical methods that primarily target linear balance. Building on the Gram-Schmidt Walk (GSW) framework of Harshaw et al (2024) for linear covariate balancing, we introduce a design that directly controls imbalance in nonlinear structure, including polynomial and more general smooth function classes. Like GSW, the proposed design retains sufficient robustness against model misspecification. Our implementation operates directly on a Gram matrix, avoiding the expensive step of explicitly constructing the nonlinear covariate expansions. We further accelerate the nonlinear design via a low-rank approximation of the Gram matrix, achieving runtimes comparable to the GSW of Harshaw et al (2024) while preserving nonlinear covariate balance and robustness.

Recent studies have revealed two intriguing phenomena in large language models: attention sinks and massive activations. However, the co-emergence and co-existence of these two phenomena remain poorly understood. In this work, we revisit the prevailing view that massive activations are the primary mechanism responsible for concentrating attention on sink tokens, and provide a more nuanced interpretation of their relationship. Through both theoretical analysis and empirical evidence, we demonstrate that massive activations and attention sinks jointly act to prevent excessive token mixing in self-attention. Specifically, attention sinks suppress mixing among non-sink tokens, whereas massive activations suppress mixing between sink tokens and non-sink tokens. Furthermore, our theory provides a principled explanation of how KV-biases, gating mechanisms, and normalization layers can remove massive activations while largely preserving attention sinks. We further conduct intervention analyses and find that removing the value vector of the sink token can recover attention sinks even when massive activations are entirely suppressed. Overall, this work provides a mechanistic perspective on how massive activations and attention sinks interact under normalization and self-attention layers, offering new insights into their functional roles in Transformer models.

Self-attention in Transformers relies on globally normalized softmax weights, causing all tokens to compete for influence at every layer. When composed across depth, this interaction pattern induces strong synchronization dynamics that favor convergence toward a dominant mode, a behavior associated with representation collapse and attention sink phenomena. We introduce $\textbf{Krause Attention}$, a principled attention mechanism inspired by bounded-confidence consensus dynamics. Krause Attention replaces similarity-based global aggregation with distance-based, localized, and selectively sparse interactions, promoting structured local synchronization instead of global mixing. We relate this behavior to recent theory modeling Transformer dynamics as interacting particle systems, and show how bounded-confidence interactions naturally moderate attention concentration and alleviate attention sinks. Restricting interactions to local neighborhoods also reduces runtime complexity from quadratic to linear in sequence length. Empirically, we validate Krause Attention across diverse settings, including vision (ViT on CIFAR/ImageNet), autoregressive image generation (MNIST/CIFAR-10), large language models (Llama/Qwen), and language models trained from scratch at multiple scales (100M/200M). Across these domains, Krause Attention achieves consistent performance gains while improving computational efficiency, highlighting bounded-confidence dynamics as a scalable and effective inductive bias for attention. Project page is available at https://jingkun-liu.github.io/krause-sync-transformers/.

Influential benchmarks incentivize competing model builders to strategically allocate post-training resources towards improvements on the leaderboard, a phenomenon dubbed \emph{benchmaxxing} or \emph{training on the test task}. In this work, we initiate a principled study of the incentive structure that benchmarks induce. We model benchmarking as a Stackelberg game between a benchmark designer who chooses an evaluation protocol and multiple model providers who compete simultaneously in a subgame given by the designer’s choice. Each competitor has a model of unknown latent quality and can inflate its observed score by allocating resources to benchmark-specific improvements. First, we prove that current benchmarks induce games for which no Nash equilibrium between model developers exists. This result suggests one explanation for why current practice leads to misaligned incentives, prompting model providers to strategize in opaque ways. However, we prove that under mild conditions, a recently proposed evaluation protocol, called tune-before-test, induces a benchmark with a unique Nash equilibrium that ranks models by latent quality. This positive result demonstrates that benchmarks need not set bad incentives, even if current evaluations do.

The *de novo* generation of high-affinity epitopes tailored to specific major histocompatibility complex (MHC) proteins is a pivotal challenge in computational immunotherapy. However, current methods struggle to effectively integrate the MHC context into the generation process, and often fail to guarantee high binding affinity due to the neglect of discriminative signals from non-binders. To bridge these gaps, we present **EpiCoCo**, a probabilistic framework for **Epi**tope generation via MHC-context **Co**-modeling and **Co**ntrastive affinity learning. EpiCoCo treats the pMHC complex as a dynamic, co-adaptive system by operating on the joint E(3) graph. In addition, we introduce Contrastive Affinity Guidance (CAG), an inference mechanism that leverages the gradient difference between learned high- and low-affinity distributions. CAG actively drives the generation trajectory towards high-affinity manifolds while utilizing repulsive signals to filter out candidates with poor binding potential. Extensive evaluations demonstrate that EpiCoCo achieves a mean binding free energy of -45.20 REU, a 23% improvement over the state-of-the-art, while maintaining high structural plausibility. The results validate that context co-modeling and negative-informed guidance are essential for generating valid, high-potency immunotherapeutics.