ICLR 2026 Papers

Massive training datasets are fueling the astounding progress in molecular machine learning. Since these datasets are typically generated with computational chemistry codes which do not randomize pose, the resulting geometries are usually not randomly oriented. While cheminformaticians are well aware of this fact, it can be a real pitfall for machine learners entering the burgeoning field of molecular machine learning. We demonstrate that molecular poses in the popular datasets QM9, QMugs and OMol25 are indeed biased. While the fact can easily be overseen by visual inspection alone, we show that a simple classifier can separate original data samples from randomly rotated ones with high accuracy. Second, we validate empirically that neural networks can and do exploit the orientedness in these datasets by successfully training a model on chemical property regression using the molecular orientation as _sole_ input. Third, we present visualizations of all molecular orientations and confirm that chemically similar molecules tend to have similar canonical poses. In summary, we recall and document orientational bias in the prevalent datasets that machine learners should be aware of.

Molecular understanding is central to advancing areas such as scientific and drug discovery, yet Large Language Models (LLMs) struggle to understand molecular graphs effectively. Existing graph–LLM bridges often adapt the Q-Former-style connector with fixed-length static tokens, which is originally designed for vision tasks. These designs overlook stereochemistry and substructural context and typically require costly LLM-backbone fine-tuning, limiting efficiency and generalization. We introduce **EDT-Former**, an **E**ntropy-guided **D**ynamic **T**oken Trans**former** that generates tokens aligned with informative molecular patches, thereby preserving both local and global structural features for molecular graph understanding. Beyond prior approaches, EDT-Former enables alignment between frozen graph encoders and LLMs without tuning the LLM backbone (excluding the embedding layer), resulting in computationally efficient finetuning, and achieves state-of-the-art results on MoleculeQA, Mol-Instructions, and property prediction benchmarks (TDC, MoleculeNet), underscoring its effectiveness for scalable and generalizable multimodal molecular understanding.

Discrete diffusion models have recently shown great promise for modeling complex discrete data, with masked diffusion models (MDMs) offering a compelling trade-off between quality and generation speed. MDMs denoise by progressively unmasking multiple dimensions from an all-masked input, but their performance can degrade when using few denoising steps due to limited modeling of inter-dimensional dependencies. In this paper, we propose Variational Autoencoding Discrete Diffusion (VADD), a novel framework that enhances discrete diffusion with latent variable modeling to implicitly capture correlations among dimensions. By introducing an auxiliary recognition model, VADD enables stable training via variational lower bounds maximization and amortized inference over the training set. Our approach retains the efficiency of traditional MDMs while significantly improving sample quality, especially when the number of denoising steps is small. Empirical results on 2D toy data, pixel-level image generation, and text generation demonstrate that VADD consistently outperforms MDM baselines.

Long-context models (LCMs) have demonstrated great potential in processing long sequences, facilitating many real-world applications. The success of LCMs can be attributed to their ability to locate implicit critical information within the context for further prediction. However, recent research reveals that LCMs are often susceptible to contextual noise, i.e., irrelevant tokens, that can mislead model attention. In this paper, we conduct a fine-grained analysis of the context noise and propose an effective metric, the Integrated Gradient (IG) score, to detect and quantify the noise information within the context. Our findings reveal that even simple mitigation of detected context noise can substantially boost the model's attention on critical tokens and benefit subsequent predictions. Building on this insight, we propose Context Denoising Training (CDT), a straightforward yet effective training strategy that improves attention on critical tokens while reinforcing their influence on model predictions. Extensive experiments across four tasks, under both context window scaling and long-context alignment settings, demonstrate the superiority of CDT. Notably, when trained with CDT, an open-source 8B model can achieve performance (50.92) comparable to GPT-4o (51.00).

We introduce *TopoFormer*, a lightweight and scalable framework for graph representation learning that encodes topological structure into attention-friendly sequences. At the core of our method is *Topo-Scan*, a novel module that decomposes a graph into a short, ordered sequence of topological tokens by slicing over node or edge filtrations. These sequences capture multi-scale structural patterns, from local motifs to global organization, and are processed by a Transformer to produce expressive graph-level embeddings. Unlike traditional persistent homology pipelines, *Topo-Scan* is parallelizable, avoids costly diagram computations, and integrates seamlessly with standard deep learning architectures. We provide theoretical guarantees on the stability of our topological encodings and demonstrate state-of-the-art performance across graph classification and molecular property prediction benchmarks. Our results show that *TopoFormer* matches or exceeds strong GNN and topology-based baselines while offering predictable and efficient compute. This work opens a new path for parallelizable and unifying approaches to graph representation learning that integrate topological inductive biases into attention frameworks.

Sequence modeling is currently dominated by causal transformer architectures that use softmax self-attention. Although widely adopted, transformers require scaling memory and compute linearly during inference. A recent stream of work linearized the softmax operation, resulting in powerful recurrent neural network (RNN) models with constant memory and compute costs such as DeltaNet, Mamba or xLSTM. These models can be unified by noting that their recurrent layer dynamics can all be derived from an in-context regression objective, approximately optimized through an online learning rule. Here, we join this line of work and introduce a numerically stable, chunkwise parallelizable version of the recently proposed Mesa layer (von Oswald et al., 2024), and study it in language modeling at the billion-parameter scale. This layer again stems from an in-context loss, but which is now minimized to optimality at every time point using a fast conjugate gradient solver. Through an extensive suite of experiments, we show that optimal test-time training enables reaching lower language modeling perplexity and higher downstream benchmark performance than previous RNNs, especially on tasks requiring long context understanding. This performance gain comes at the cost of additional flops spent during inference time. Our results are therefore intriguingly related to recent trends of increasing test-time compute to improve performance -- here by spending compute to solve sequential optimization problems within the neural network itself.

Personalizing large language models (LLMs) is increasingly important as they are progressively integrated into real-world applications to support users’ daily lives. However, existing approaches often fail to distinguish which components of response predictions by model and ground-truth response in training data truly reflect user preferences, resulting in shallow personalization alignment. In this paper, we introduce NextQuill, a novel LLM personalization alignment framework grounded in causal preference modeling. We approach personalization from a causal perspective, recognizing that model-predicted responses (model side) and user-written ground-truth responses (data side) are both outcomes shape by user history (characteristics) and other context factors. To better capture user preferences, we define causal preference effects as the causal effect of the user history/characteristics on outcomes from the model/data side. Building on this foundation, NextQuill introduces two complementary alignment strategies: (1) aligning model-side causal preference effects (on predictions) with those of ground-truth data, rather than indiscriminately aligning all predictions, and (2) emphasizing learning the preference-driven ground-truth tokens, identified via data-side causal preference effects, rather than treating all tokens equally. As such, NextQuill shifts the alignment process toward learning from causal preference effects, facilitating more effective and personalized LLM adaptation. Experiments on multiple personalization benchmarks demonstrate that NextQuill substantially improves personalization quality. Code is available at \url{https://anonymous.4open.science/r/NextQuill-1E4E}.

Scaling laws for language model training traditionally characterize how performance scales with model size and dataset volume. Prior work has explored architecture variants and data treatments such as dataset filtering and noise injection in language model pretraining; however, these studies have not formalized data quality within a principled scaling law. We introduce a dimensionless data-quality parameter Q, and propose a quality-aware scaling law extending the Chinchilla framework to predict loss as a joint function of model size, data volume, and data quality. The law is motivated by an effective-sample-size and information-theoretic view of noisy or redundant corpora, and it admits two practical estimators for Q: (i) a corruption rate proxy and (ii) a deficiency measure. Through synthetic experiments in neural machine translation and autoregressive modeling--where we systematically control data quality via multiple levels of noise injection--we show that loss scales predictably with data quality and that higher-quality data can substantially reduce model size and hence compute requirements. Our results demonstrate a sublinear decay of effective data with quality and robustness to moderate data corruption; out-of-sample evaluations further validate the predictive form of the law. Unlike prior empirical analyses, our work establishes an explicit, generalizable law for data quality, offering concrete guidance for balancing data curation effort and model scale in large-scale pretraining.

Modeling long spatiotemporal sequences requires capturing both complex spatial correlations and temporal dependencies. Convolutional State Space Models (ConvSSMs) have been proposed to incorporate spatial modeling in State Space Models (SSMs) using the convolution of tensor-valued states and kernels. Yet, existing implementations remain limited to $1\times 1$ state kernels for computational feasibility, which limits the modeling capacity of ConvSSMs. We introduce a novel spatiotemporal model, ConvT3 (ConvSSM using Tridiagonal Toeplitz Tensors), designed to equivalently realize ConvSSMs with extended $3\times 3$ state kernels. ConvT3 structures a state kernel for its corresponding tensor to be composed as a structured SSM matrix on hidden state dimensions and a constrained tridiagonal Toeplitz tensor on spatial dimensions. We show that the structured tensor can be diagonalized, which enables efficient parallel training while leveraging $3\times 3$ state convolutions. We demonstrate that ConvT3 effectively embeds rich spatial and temporal information into the dynamics of tensor-valued states, achieving state-of-the-art performance on most metrics in long-range video generation and physical system modeling.

Standard attention stores keys/values losslessly but reads them via a per-head convex average, blocking channel-wise selection. We propose the Free Energy Mixer (FEM): a free-energy (log-sum-exp) read that applies a value-driven, per-channel log-linear tilt to a fast prior (e.g., from queries/keys in standard attention) over indices. Unlike methods that attempt to improve and enrich the $(q,k)$ scoring distribution, FEM treats it as a prior and yields a value-aware posterior read at unchanged complexity, smoothly moving from averaging to per-channel selection as the learnable inverse temperature increases, while still preserving parallelism and the original asymptotic complexity ($O(T^2)$ for softmax; $O(T)$ for linearizable variants). We instantiate a two-level gated FEM that is plug-and-play with standard and linear attention, linear RNNs and SSMs. It consistently outperforms strong baselines on NLP, vision, and time-series at matched parameter budgets.

Masked generative models (MGMs) can generate tokens in parallel and in any order, unlike autoregressive models (ARMs), which decode one token at a time, left-to-right. However, MGMs process the full-length sequence at every sampling step, including \mask tokens that carry no information. In contrast, ARMs process only the previously generated tokens. We introduce ``Partition Generative Models'' (PGMs), which replace masking with partitioning. Tokens are split into two groups that cannot attend to each other, and the model learns to predict each group conditioned on the other, eliminating mask tokens entirely. Because the groups do not interact, PGMs can process only the clean tokens during sampling, like ARMs, while retaining parallel, any-order generation, like MGMs. On OpenWebText, PGMs achieve $5-5.5\times$ higher throughput than MDLM while producing samples with lower Generative Perplexity. On ImageNet, PGMs reach comparable FID to MaskGIT with a $7.5\times$ throughput improvement. With twice as many steps, the FID improves to 4.56 while remaining $3.9\times$ faster than MGMs. Finally, PGMs remain compatible with existing MGM samplers and distillation methods.

Mixture models excel at decomposing complex, multi-modal distributions into simpler probabilistic components, but provide no insight into the conditions under which these components arise. We introduce explainable mixture models (EMM), a framework that pairs each mixture component with a human-interpretable rule over descriptive features. This enables mixtures that are not only statistically expressive but also transparently grounded in the underlying data. We formally examine the conditions under which an EMM exactly captures a target distribution and propose a scalable, differentiable learning procedure for discovering sets of rules. Experiments on synthetic and real-world datasets demonstrate that our method discovers interesting sub-populations in both univariate and multivariate settings, offering interpretable insights into the structure of complex distributions.

Molecular conformer generation is a fundamental task for drug discovery and material design. Although deep generative models have progressed in this area, existing methods often overlook the hierarchical structural organization inherent to molecules, leading to poor-quality generated conformers. To address this challenge, we demonstrate that capturing the spatial arrangement of key substructures, such as scaffolds, is essential, as they serve as anchors that define the overall molecular distribution. In this paper, we propose a hierarchical multi-scale molecular conformer generation framework (MSGEN), designed to enhance key substructure awareness by leveraging spatially informed guidance. Our framework initiates the generation process from coarse-grained key substructures, progressively refining the conformer by utilizing these coarser-scale structures as conditional guidance for subsequent finer-scale stages. To bridge scale discrepancies between stages, we introduce a molecular upsampling technique that aligns the structural scales, ensuring smooth propagation of geometric guidance. Extensive experiments on standard benchmarks demonstrate that our framework integrates seamlessly with a wide range of existing molecular generative models and consistently generates more stable and chemically plausible molecular conformers.

Mathematical modeling is the process of understanding and predicting complex real-world phenomena. Traditionally, it is a time-intensive effort reliant on deep human expertise and iterative refinement. Automating this intricate process, therefore, offers the potential to significantly accelerate discovery and broaden the application of mathematical modeling across diverse domains. Such automation, however, must address inherent challenges, including fundamental modeling uncertainty, balancing multiple conflicting objectives, and incorporating subjective qualities into assessing model utility. We approach this by conceptualizing mathematical modeling as a sequential decision-making problem under uncertainty. In response, we introduce $\texttt{MATHMO}$, a novel adaptive search method designed to automatically navigate the complex decisions in selecting mathematical frameworks, specifying model formulations, and defining algorithmic procedures. Specifically, $\texttt{MATHMO}$ employs a principled bi-level search strategy---combining high-level exploration across diverse frameworks and local intra-framework model refinements---leveraging Large Language Models for exploration, surrogate evaluations, and incorporating subjective preferences into the automated process. We demonstrate $\texttt{MATHMO}$'s efficacy on diverse real-world tasks, where it successfully discovers Pareto-efficient frontiers of models that balance varied objectives, including subjective criteria.

Incorporating robustness in generative modeling has enticed many researchers of the field. To this end, we introduce a new class of multivariate power-law distributions---the symmetric Pareto (symPareto) distribution---which can be viewed as an $\ell_1$-norm-based counterpart of the multivariate $t$ distribution. The symPareto distribution possesses many attractive information-geometric properties with respect to the $\gamma$-power divergence that naturally populates power-law families. Leveraging on the joint minimization view of variational inference, we propose the ParetoVAE, a probabilistic autoencoder that minimizes the $\gamma$-power divergence between two statistical manifolds. ParetoVAE employs the symPareto distribution for both prior and encoder, with flexible decoder options including Student's $t$ and symPareto distributions. Empirical evidences demonstrate ParetoVAE's effectiveness across multiple domains through varying the types of the decoder. The $t$ decoder achieves superior performance in sparse, heavy-tailed data reconstruction and word frequency analysis; the symPareto decoder enables robust high-dimensional denoising.

Visual Autoregressive (VAR) models enhance generation speed but face a critical efficiency bottleneck in later stages. In this paper, we present a novel optimization framework for VAR models that fundamentally differs from prior approaches such as FastVAR and SkipVAR. Instead of relying on heuristic skipping strategies, our method leverages attention entropy to characterize the semantic projections across different dimensions of the model architecture. This enables precise identification of parameter dynamics under varying token granularity levels, semantic scopes, and generation scales. Building on this analysis, we further uncover sparsity patterns along three critical dimensions—token, layer, and scale—and propose a set of fine-grained optimization strategies tailored to these patterns. Extensive evaluation demonstrates that our approach achieves aggressive acceleration of the generation process while significantly preserving semantic fidelity and fine details, outperforming traditional methods in both efficiency and quality. Experiments on Infinity-2B and Infinity-8B models demonstrate that ToProVAR achieves nearly 3.5× average acceleration with minimal quality loss, effectively mitigating the issues found in prior work. Our code will be made publicly available.

As large language models expand beyond natural language to domains such as mathematics, multimodal understanding, and embodied agents, tokens increasingly reflect metric relationships rather than purely linguistic meaning. We introduce DIST2Loss, a distance-aware framework designed to train autoregressive discrete models by leveraging predefined distance relationships among output tokens. At its core, DIST2Loss transforms continuous exponential family distributions derived from inherent distance metrics into discrete, categorical optimization targets compatible with the models’ architectures. This approach enables the models to learn and preserve meaningful distance relationships during token generation while maintaining compatibility with existing architectures. Empirical evaluations show consistent performance gains in diverse multimodal applications, including visual grounding, robotic manipulation, generative reward modeling, and image generation using vector-quantized features. These improvements are most notable in low-data regimes, demonstrating DIST2Loss’s strength under resource constraints.

Masked diffusion models (MDMs) have achieved notable progress in modeling discrete data, while their potential in molecular generation remains underexplored. In this work, we explore their potential and introduce the surprising result that naively applying standards MDMs to molecules leads to severe performance degradation. We trace this critical issue to a *state-clashing*-where the forward diffusion trajectories of distinct molecules collapse into a common state, resulting in a mixture of reconstruction targets that cannot be learned with a typical reverse diffusion with unimodal predictions. To mitigate this, we propose **M**asked **E**lement-wise **L**earnable **D**iffusion (**MELD**) that orchestrates per-element corruption trajectories to avoid collisions between different molecular graphs. This is realized through a parameterized noise scheduling network that learns distinct corruption rates for individual graph elements, *i.e.*, atoms and bonds. Across extensive experiments, **MELD** is the first diffusion-based molecular generator to achieve 100% chemical validity in unconditional generation on QM9 and ZINC250K datasets, while markedly improving distributional and property alignment over standard MDMs.

Reward models (RMs) are fundamental to aligning Large Language Models (LLMs) via human feedback, yet they often suffer from reward hacking. They tend to latch on to superficial or spurious attributes, such as response length or formatting, mistaking these cues learned from correlations in training data for the true causal drivers of quality (e.g., factuality, relevance). This occurs because standard training objectives struggle to disentangle these factors, leading to brittle RMs and misaligned policies. We introduce CROME (Causally Robust Reward Modeling), a novel framework inspired by an explicit causal model designed to mitigate reward hacking. CROME queries an oracle LLM for rubrics that are (or the oracle deems to be) causally relevant to answering a specific prompt. Then, it employs the following synthetic targeted augmentations during training: (1) Causal Augmentations, which are pairs that differ along specific causal attributes (subset of the Oracle identified rubrics), to enforce sensitivity along each causal attribute individually, and (2) Neutral Augmentations, which are tie-label pairs varying primarily in spurious attributes, to enforce invariance along spurious attributes. Notably, our neutral augmentations are produced without any knowledge of unknown spurious factors, via question swapping and response interventions only along causal rubrics. We show that the CROME augmentation strategy using rubrics from popular LLM APIs significantly outperforms standard baselines on RewardBench, improving average accuracy by up to 5.3% and achieving gains of up to 7.1% and 12.4% in reasoning and safety. The robustness of CROME is further testified by significant gains in DPO-aligned policies and Best-of-N alignment across various benchmarks, including AlpacaEval 2.0, RewardBench, safety-focused WildGuardTest, and the reasoning-specific GSM8k.