NeurIPS 2026 Papers

Modern data analysis pipelines increasingly rely on large datasets assembled through retrieval, scraping, automated filtering, and post-hoc curation, where the observed sample is often a contaminated mixture rather than the target population. Standard distributional objectives either ignore contamination and converge to the wrong target, or retain only a small trusted subset and discard most of the data. We study supervised and unsupervised distributional learning when a clean reference sample is compared with a pooled sample from $r=(1-\epsilon)q+\epsilon z$, where $q$ is the latent target distribution and $z$ is an unknown contaminant. Motivated by settings with noisy membership scores for all observations and exact labels for a small audited subset, we propose contamination-corrected maximum mean discrepancy (CC–MMD), a design-based estimator that combines proxy scores with audited residual corrections to recover the oracle MMD that would have been computed from the latent clean sample. CC–MMD requires no calibration assumption on the proxy scores and no structural assumptions on the contaminant beyond standard kernel regularity. We prove finite-population design-unbiasedness of the corrected kernel sums, establish asymptotic normality of the audit correction, and show consistency for the target discrepancy $\mathrm{MMD}^2(p,q;k)$. Empirically, CC–MMD tracks the oracle under increasing contamination, improves parameter recovery and prediction in contaminated regression, and enables generative models trained on heavily corrupted mixtures to recover the clean target distribution. These results show that contaminated data need not be discarded or treated as the estimand. With sparse trusted labels and abundant noisy supervision, distributional objectives can be made robust by design.

In learnable logic gate networks, each neuron implements a $k$-input Boolean function. The dominant setting $k{=}2$ was chosen for tractability. We ask: when does wider fan-in help? At fixed parameter budget, each gate costs $2^k$ parameters, so increasing $k$ exponentially reduces width. Combined with the depth--fan-in bound $L \geq \lceil \log_k d \rceil$, this partitions tasks into two regimes: width-dominated (image classification), where more gates beat richer gates, and degree-dominated (parity, arithmetic), where $k{>}2$ is necessary. Our main finding is that representability does not imply learnability: at the regime boundary, the selection mechanism determines training success at identical architecture, and the optimal mechanism inverts between regimes. We formalize this via a Jacobian analysis: the softmax mechanism's positive-semidefinite (PSD) structure gives basin attraction absent from sigmoid. We train multilinear coefficients with exact gradients and Möbius-transform snapping (zero deployment error), and validate on 28 tasks and 5 real-world datasets across multiple selection mechanisms.

Peer review at ML conferences increasingly relies on reviewer scores as the primary decision instrument. As submissions have scaled from thousands to tens of thousands per year, no systematic audit has examined whether this instrument functions uniformly across research areas, or whether acceptance outcomes are in practice shaped by forces that reviewer scores neither capture nor control. This position paper argues that acceptance outcomes are shaped by forces beyond reviewer scores, and that the underlying cause is a measurement design failure, not individual bias. When a fixed numerical scale aggregates quality judgments across communities with structurally non-uniform reviewer pools, absolute scores become incomparable across areas, and area chairs must substitute community priors for score-based decisions. Using ICLR 2021--2026 data covering 50,289 papers across 219 research topics, we show that at any given reviewer score, a paper's acceptance probability varies by up to 8$\times$ depending on its topic. We rule out scoring culture, expert reviewer standards, rational area chair reweighting, and quality dilution as alternative explanations. We call on program committees to adopt inherently calibrated review signals and publish topic-stratified, score-conditional acceptance rates as a first-class fairness metric.

Model-assisted semi-supervised learning offers a powerful paradigm for enhancing the efficiency of statistical estimation and inference by leveraging black-box predictions on unlabeled data. However, the validity of these methods typically relies on the strict assumption that labeled and unlabeled populations share identical distributional characteristics. Consequently, state-of-the-art approaches, such as prediction-powered inference, become fragile when this assumption is violated. To address the fragility, we propose a robust framework for semi-supervised learning that remains reliable under distributional heterogeneity. By embedding a robust statistical calibrator into the prediction-rectification mechanism, the approach effectively reduces the bias arising from shifted or corrupted unlabeled samples. To maximize data utility, we introduce an adaptive cross-validation procedure to select the optimal calibrator, ensuring a reliable trade-off between statistical efficiency and robustness. Theoretical analysis confirms the consistency of the proposed estimator under mild conditions, while empirical results demonstrate its significant superiority over conventional baselines in heterogeneous environments.

We study principal-agent problems in which a principal commits to an outcome-dependent payment scheme (i.e., a contract) in order to induce an agent to take a costly action leading to a favorable outcome. We consider the online extension of the classical (one-shot) principal-agent problem, in which the principal repeatedly interacts with agents by proposing contracts over multiple rounds. The principal has no information about the agents and, crucially, does not observe their actions. As a result, the principal must learn an optimal contract using only the realized outcomes observed at each round. We focus on the setting with binary-actions and single-dimensional agent types, where the agent's private type represents their cost per unit-of-effort. For adversarial-type sequences, we provide tight $\widetilde\Theta(T^{2/3})$ regret guarantees. Remarkably, this rate is completely independent of the number of outcomes $m$. The upper bound is based on two key components: 1) a reduction to one-dimensional threshold optimization problem and 2) a non-uniform discretization to handle the non-Lipschitz nature of the problem. Moreover, in the case of a single (fixed) hidden type, we show that it is possible to improve the rates and provide a tight $\widetilde\Theta(\sqrt{T})$ regret bound. Our algorithm is based on an explore-then-commit strategy where we first approximately learn the hidden type via a stochastic binary search, and then we commit to a ``robustified'' near-optimal contract.

Maintainable and general software allows developers to build robust applications efficiently, yet achieving these qualities often requires refactoring specialized solutions into reusable components. This challenge becomes particularly relevant as code agents are increasingly used to solve isolated one-off programming problems. We investigate code agents' capacity to refactor code in ways that support consolidation and reusability. We first investigate what makes a good refactoring, finding via simulation results and a human study that proxies of program size, such as Minimum Description Length, better predict preferable refactorings than extant software engineering metrics, such as Maintainability Index. We then present \textsc{Librarian}, a method that combines divide-and-conquer with sample-and-rerank to generate reusable libraries. We compare \textsc{Librarian} to state-of-the-art library generation methods, and study it on real-world Python programs.

Transformers with self-attention modules as their core components have become an integral architecture in modern large language and foundation models. In this paper, we study the evolution of tokens in deep encoder-only transformers at inference time which is described in the large-token limit by a mean-field continuity equation. Leveraging ideas from the convergence analysis of interacting multi-particle systems, with particles corresponding to tokens, we prove that the token distribution rapidly concentrates onto the push-forward of the initial distribution under a projection map induced by the key, query, and value matrices, and remains metastable for moderate times. Specifically, we show that the Wasserstein distance of the two distributions scales like $\sqrt{\log(\beta+1)/\beta}\exp(C t)+\exp(-ct)$ in terms of the temperature parameter $\beta^{-1}\to 0$ and inference time $t\geq 0$. For the proof, we establish Lyapunov-type estimates for the zero-temperature equation, identify its limit as $t\to\infty$, and employ a stability estimate in Wasserstein space together with a quantitative Laplace principle to couple the two equations. Our result implies that for time scales of order $\log\beta$ the token distribution concentrates at the identified limiting distribution. Numerical experiments confirm this and, beyond that, complement our theory by showing that for finite $\beta$ and large $t$ the dynamics enter a different terminal phase, dominated by the spectrum of the value matrix.

Designing proteins with desired functions or properties represents a core goal in synthetic biology, therapeutic development, and drug discovery. Recent advances in protein language models (PLMs) have enabled the generation of highly designable protein sequences, while preference alignment provides a promising way to steer designs toward desired functions and properties. Nevertheless, they often trigger catastrophic forgetting of pretrained knowledge, degrading basic designability and failing to balance multiple competing objectives. To address these issues, we draw inspiration from On-Policy Distillation (OPD), an advanced post-training method renowned for mitigating catastrophic forgetting through its mode-seeking nature. In this work, we propose ProteinOPD, a multi-objective preference alignment framework that can effectively balance multiple preference objectives while maintaining the inherent designability of PLMs. ProteinOPD adapts a pretrained PLM into preference-specific teachers and distills their knowledge into a shared student via token-level OPD on the student’s own trajectories. During this process, the student is aligned to a unique normalized geometric consensus of weighted teachers while ensuring bounded optimization under conflicts. This bridges the gap for OPD in multi-objective/teacher alignment. Extensive experiments show that ProteinOPD achieves substantial gains on target preference objectives without compromising the designability, with a 8× training speedup over RL-based alignment competitors.

Bilateral trade models the task of intermediating between two strategic agents, a seller and a buyer, who wish to trade a good. We study this problem from the perspective of a profit-maximizing broker within an online learning framework, where the agents' valuations are generated by a smooth adversary. We devise a learning algorithm that guarantees a $\tilde{O}(\sqrt{T})$ regret bound, which is tight in the time horizon $T$ up to poly-logarithmic factors. This matches the minimax rate for the stochastic i.i.d. case, and is also well separated from the adversarial setting, where sublinear-regret is unattainable. By extending the strong regret guarantees from the i.i.d. case to the smooth adversary, we significantly broaden the scope of settings where such fast rate is achievable, while closing an important gap in the regret landscape of this fundamental economic problem. To overcome the challenges posed by this adversary, we leverage a continuity property of smooth instances and combines this with a hierarchical net-construction of the broker's action space, which is analyzed via algorithmic chaining. We showcase the applicability of these techniques by deriving a similarly tight $\tilde{O}(\sqrt{T})$ regret bound for a related mechanism design model: the joint ads problem.

Structure-based drug design increasingly employs LLM agents to iteratively refine ligands against a target pocket, yet a viable ligand must satisfy two often-conflicting objectives---binding affinity and druggability---which single optimization steps rarely improve together. To quantify this difficulty, we introduce two diagnostic metrics: the first measures how often a single edit improves both objectives, and the second measures how often a gain on one objective comes with a loss on the other. Applying these diagnostics to current LLM-agent pipelines exposes a consistent failure mode: the agent performs molecular editing without knowing how the pocket-ligand complex responds to local modifications, thus rarely achieving joint improvement. Inspired by medicinal chemists, who probe the pocket-ligand complex with controlled analog edits before choosing an optimization direction, we propose PROBE, an optimization framework built around edit--response probing. PROBE first decomposes the ligand into editable sites and builds a pocket-specific site map that flags where joint gains are plausible, where the two objectives are likely in tension, and where liability substructures should be changed; it then performs controlled probe edits whose responses are distilled into an EditManual. Guided by the site map and EditManual, PROBE runs an iterative multi-agent loop in which an affinity agent, a druggability agent, and a co-optimization agent jointly produce edits. On the CrossDocked2020 benchmark, PROBE achieves state-of-the-art performance and substantially mitigates the failure modes exposed by our diagnostics metrics.

We show that an "old dog," the classical discrete Laplace (aka. geometric) mechanism, can "perform new tricks": * It can be post-processed to yield a simple, unbiased estimator of any subexponential function $f$ of the original data, giving a simple, discrete, multivariate version of the recent unbiasing result for the Laplace mechanism by Calmon et al. (FORC '25). * It can be post-processed to output the same distribution as the Laplace mechanism or the Staircase mechanism with identical privacy parameters. Thus, the discrete Laplace mechanism is a versatile mechanism that should be preferred over the Laplace and Staircase mechanisms whenever the data is discrete (or can be made discrete while controlling $\ell_1$-sensitivity). We show bounds on the variance of our estimator, compared to the mean square error of the biased estimator that simply evaluates the $f$ on the output of the mechanism. Though our unbiased estimator has exponential running time for worst-case functions, we show that it can often be computed in linear or polynomial time for concrete, structured functions. We showcase the properties of our methods empirically with several use cases including profile and entropy estimation, as well as distributed/federated data analysis applications in which unbiasedness is key to accuracy.

Long-context decoding in large language models (LLMs) is increasingly bottlenecked by the memory and computation required to attend over an ever-growing Key-Value (KV) cache at each autoregressive step. Although token-level sparse attention reduces this burden by restricting computation to a small subset of relevant past tokens, its practical gains are often offset by repeatedly recomputing layer-wise sparse indices as the context grows. A common remedy is to share sparse indices across layers by computing them only at designated anchor layers, but such static reuse ignores the layer-wise evolution of attention patterns, causing the reused indices to progressively deviate from the layer-specific optima and incur substantial attention loss. By revisiting cross-layer sparsity from the perspective of attention dynamics, we find that inter-layer salient token shift is highly localized: although the exact top-$\kappa$ indices differ across layers, the core high-attention tokens remain stable, with changes concentrated near the expanded boundary of previously selected regions. Motivated by this, we propose Prism Attention, a proposal-refined sparse attention framework. It replaces rigid cross-layer index reuse with a coarse-to-fine strategy, preserving layer-wise adaptability while retaining the efficiency benefits of cross-layer sharing. Extensive experiments show that Prism Attention achieves state-of-the-art performance among mainstream sparse attention methods on both reasoning and long-context benchmarks, while achieving $2.6\times\sim7.5\times$ kernel speedup over FlashAttention at 128K context length.

Score-based diffusion models achieve state-of-the-art performance for inverse problems, but their practical deployment is hindered by long inference times and cumbersome hyperparameter tuning. While pretrained diffusion models can be reused across tasks without retraining, inference-time hyperparameters such as the noise schedule and posterior sampling weights typically require ad-hoc adjustment for each problem setup. We propose principled reparameterizations that induce invariances, allowing the same hyperparameters to be reused across multiple problems without re-tuning. In addition, building on the RED-diff framework, which reformulates posterior sampling as an optimization problem, we further develop the OptDiff pipeline. OptDiff provides a simplified tuning framework that facilitates the integration of convex optimization tools to accelerate inference. Experiments on image reconstruction, deblurring, and super-resolution show substantial speedups and improved image quality.

Autoregressive transformers with no positional embeddings (NoPE) can recover absolute position. A common explanation is that causal attention creates a position-dependent variance signal, but this account is incomplete because LayerNorm removes per-token scale, so a viable mechanism must encode position in *direction*, not magnitude. We describe the most compact mechanism with two-layer NoPE transformers that accurately extract position. In Layer1, prefix averaging creates a shared beginning of sequence (BOS)-direction component. In Layer2, the attention's output-value matrix maps the \bos{} and \nbos{} contributions into two distinct directions, and a position-dependent \bos{} attention weight acts as a mixing coefficient that interpolates between them. The resulting directional trajectory is linearly decodable for position. Interestingly, we show two transformer variants that converge to the same theoretical mechanism and instantiate it when trained to predict position.

We introduce Pion, a spectrum-preserving optimizer for large language model (LLM) training based on orthogonal equivalence transformation. Unlike additive optimizers such as Adam and Muon, Pion updates each weight matrix through left and right orthogonal transformations, preserving its singular values throughout training. This yields an optimization mechanism that modulates the geometry of weight matrices while keeping their spectral norm fixed. We derive the Pion update rule, systematically examine its design choices, and analyze its convergence behavior along with several key properties. Empirical results show that Pion offers a stable and competitive alternative to standard optimizers for both LLM pretraining and finetuning.

We present an in-depth evaluation of LLMs' ability to negotiate, a central business task requiring strategic reasoning, theory of mind, and economic value creation. To do so, we introduce **PieArena**, a large-scale negotiation benchmark grounded in multi-agent interactions over realistic scenarios adapted from MBA negotiation courses at an elite business school. We evaluate language agents across three pairing regimes: mirror-play, cross-play, and human–LM play. We develop a ranking model for continuous negotiation payoffs that yields order-invariant, uncertainty-quantified leaderboards while correcting for systematic experimental asymmetries. We further study the effects of joint-intentionality agentic scaffolding and find asymmetric gains, with large improvements for mid- and lower-tier LMs and diminishing returns for frontier LMs. As calibration anchors, we collect human–human and human–LM negotiation data from trained business school students, finding that a representative frontier language agent (GPT-5) matches or exceeds this human baseline in our evaluation settings. Beyond deal outcomes, PieArena provides a multi-dimensional behavioral profile that reveals cross-model heterogeneity in instruction compliance, computation accuracy, as well as judge-assessed deception and reputation, illustrating the value of evaluation beyond outcome-only leaderboards.

The evolution of colour vision is captivating, as it reveals the adaptive strategies of extinct species while simulta- neously inspiring innovations in modern imaging technol- ogy. In this study, we present a simplified model of vi- sual transduction in the retina, introducing a novel opsin layer. We quantify evolutionary pressures by measuring ma- chine vision recognition accuracy on colour images shaped by specific opsins. Building on this, we develop an evolu- tionary conservation optimisation algorithm to reconstruct the spectral sensitivity of opsins, enabling mutation-driven adaptations to to more effectively spot fruits or predators. This model condenses millions of years of evolution within seconds on GPU, providing an experimental framework to test long-standing hypotheses in evolutionary biology , such as vision of early mammals, primate trichromacy from gene duplication, retention of colour blindness, blue-shift of fish rod and multiple rod opsins with bioluminescence. More- over, the model enables speculative explorations of hypo- thetical species, such as organisms with eyes adapted to the conditions on Mars. Our findings suggest a minimalist yet effective approach to task-specific camera filter design, op- timising the spectral response function to meet application- driven demands. The code will be made publicly available upon acceptance.

Motivated by the success of large language models (LLMs) with broad generalizability and robustness to noisy or unreliable pre-training data, we seek to bring similar capabilities to PDE solvers. In addition, inspired by the posterior predictive mean-based inference mechanism of the in-context learning in prior-data fitted networks (PFNs), we propose PDE-PFN, a prior-data fitted neural solver that approximates the posterior predictive mean of PDE solutions via in-context learning. PDE-PFN builds on a PFN architecture with self- and cross-attention mechanisms of Transformer and is pre-trained on noisy approximate solutions generated by physics-informed neural networks, serving as diverse but not necessarily exact priors. Through experiments on a range of two-dimensional PDEs, we demonstrate that PDE-PFN achieves empirical generalization across heterogeneous equations, robustness under noisy priors, and zero-gradient-update in-context inference capability. Our approach not only outperforms task-specific baselines but also provides a flexible and robust framework for advancing SciML.

I show that ordinary least squares (OLS) predictions can be rewritten as a restricted attention module, akin to those at the heart of transformer architectures. This connection emerges by reframing OLS as a similarity-based prediction rule operating in a learned embedding space. From this perspective, least squares does not estimate coefficients per se, but instead selects an embedding that minimizes squared prediction error by matching training and test vectors through inner products — mapping naturally onto the query-key-value structure of attention. I then extend the framework to dimensionality reduction, nonlinearity, and connections to time series econometrics. Monte Carlo simulations and real-data experiments on UCI/OpenML benchmarks show that a direct implementation of nonlinear Attention Regression performs competitively against standard machine learning baselines. In the other direction, within a transformer architecture for tabular data, an attention block can be replaced by an explicit regression on polynomial-expanded features, matching or exceeding the standard transformer's predictive accuracy at a fraction of its parameter count.