NeurIPS 2026 Papers

Aligning human-interpretable concepts with the internal representations of modern machine learning systems remains a central challenge for interpretable AI. We introduce a geometric framework to compare supervised human concepts with unsupervised representations derived from foundation models. We formalise concept frustration: a mismatch that arises when an unobserved concept induces relationships between known concepts that cannot be made consistent within an existing ontology. We develop task-aligned similarity measures that detect this phenomenon, and show that frustration is identifiable in task-aligned geometry while conventional Euclidean comparisons fail. Under a linear–Gaussian generative model, we derive a closed-form expression for Bayes-optimal concept-based classifier accuracy, decomposing predictive signal into known and unknown contributions and identifying where frustration impacts performance. Experiments on synthetic data and real language and vision tasks demonstrate that frustration is present in foundation model representations and that incorporating missing concepts reorganises learned representations to better align human and machine reasoning. These results provide a principled framework for diagnosing incomplete concept ontologies and improving alignment in interpretable AI systems.

Hybrid language models that mix attention and recurrent layers have shown promise: theoretically, recurrent layers ameliorate the limitations of pure transformers on state tracking, and empirically, hybrids can outperform pure transformers in loss and downstream evaluations \citep{waleffe2024empirical,merrill2026olmohybrid}. Yet it remains unclear which data or capabilities drive these gains, and to what degree they reflect the theoretical advantages motivating hybrid models. We address this by analyzing the benefits of hybrid models at the token level---which kinds of tokens are better predicted by hybrids than by pure transformers---using the open weights from Olmo 3 \citep{olmo2025olmo3} and Olmo Hybrid \citep{merrill2026olmohybrid}. Hybrids predict tokens better across the board, but we show these gains localize to open-class content words rather than closed-class function words. Across natural language and code, the loss gap shrinks on closing brackets (but not opening brackets), consistent with the hypothesis that attention, not hybrid layers, is largely responsible for processing hierarchical structure. The hybrid advantage also vanishes on repeated $n$-grams. Overall, while attention suffices for tokens involving copying and purely syntactic information, hybrids show an advantage on more semantically conditioned predictions, likely because these are aided by a strong representation of the discourse state. We conclude with discussion and proof-of-concept experiments showing how these findings could refine design principles and pretraining evaluations for hybrid architectures.

Generative ranking models (GRMs) have emerged as a scalable alternative to traditional recommendation pipelines by unifying items and user actions into a single token sequence and formulating recommendation as next-token prediction. Despite their promise, we identify a geometric failure mode: attention interactions with lowcardinality action tokens can induce dimensional collapse in high-rank item representations, as suggested by interaction-collapse theory. To pinpoint the origin of collapse, we view attention mechanism over item–action interleaving sequences as a mixture of directional interaction channels between token types, and find that collapse concentrates in the action-attending-item channel, where low-rank action gating drags the item value stream toward a low-dimensional subspace. To address this, we theoretically show that nonlinearity mitigates collapse, and propose Selective VAlue Nonlinearity (SVAN), a simple yet effective approach that applies nonlinear activation to the value component in the collapsed channel, protecting item representations while preserving the remaining attention geometry. SVAN consistently improves the ranking quality over strong baselines. Further analyses confirm that SVAN alleviates dimensional collapse, yielding up to a 12.58% effective-rank gain, and enhances representation discriminability.

Traditional rendering pipelines rely on complex assets, accurate materials and lighting, and substantial computational resources to produce realistic imagery, yet they still face challenges in scalability and realism for populated dynamic scenes. We present C2R (Coarse-to-Real), a generative rendering framework that synthesizes real-style urban crowd videos from coarse 3D simulations. Our approach uses coarse 3D renderings to explicitly control scene layout, camera motion, and human trajectories, while a learned neural renderer generates realistic appearance, lighting, and fine-scale dynamics guided by text prompts. To overcome the lack of paired training data between coarse simulations and real videos, we adopt a two-stage synthetic-real domain-hedging strategy that first learns a strong generative prior from large-scale real footage, then introduces controllability by using a small amount of paired synthetic coarse-fine data to anchor shared implicit spatio-temporal features across domains. The resulting system supports coarse-to-fine control, generalizes across diverse CG and game inputs, and produces temporally consistent, controllable, and realistic urban scene videos from minimal 3D input.

Bayesian accounts of in-context learning treat context as exogenous evidence, but in multi-turn dialogue this assumption can fail: the assistant changes the user state that generates the next utterance, so the model updates on evidence partly produced by its own policy. We formalize this as Socially Coupled In-Context Learning (SC-ICL). The relevant stability quantity is a \emph{round-trip gain} (the product of belief-to-action, action-to-evidence, and evidence-to-belief derivatives), and in a two-state local reduction the standard spectral condition on the closed-loop matrix factors as a product of a user-side gain and an assistant-side gain. Risk is therefore dyadic: neither a susceptible user nor a responsive assistant becomes unstable without the other side of the loop. We connect this stability boundary to a sigmoidal transition in relational-posterior space, which explains why myopic approval-seeking can become unstable in supportive dialogue. AI--AI experiments instantiate one-step gain assays, free-running conversations, open-loop replay, and prompt-based controllers, and four convergent results support the closed-loop account: high-gain dyads cross an operational collapse criterion while damping and barrier-style controllers sharply reduce it; a trajectory-conditioned spectral estimator separates collapsing from stable runs at the theoretical stability boundary, crossing unity near operational onset; the dyadic pattern recurs across all four pairings of GPT-4o and GPT-5.4-mini as user and assistant simulators; and a persona-only ablation that uses no numeric coupling labels in the prompts reproduces the same dyadic collapse matrix. The results are not clinical evidence; they argue that alignment should evaluate bounded closed-loop inference, not only next-response quality.

Neural networks are often trained with gradient descent (GD) at the edge of stability (EoS), where step sizes exceed classical stability thresholds and standard convergence theory no longer applies. Despite exhibiting non-monotonic loss and oscillatory dynamics, this regime frequently leads to faster convergence and better generalization. Existing theoretical perspectives offer complementary but incomplete insights: one identifies a self-stabilization mechanism that drives GD toward flat regions but does not yield convergence rates; another derives rigorous rates for specific losses but does not explain the underlying stabilization mechanism; and a third unifies these views for overparameterized least squares, but relies on the existence of a minimizer manifold, which is absent in classification settings. In this work, we extend this unified geometric perspective to exponential-tail losses, including logistic and cross-entropy losses, where no finite minimizer exists. We identify a curvature-defined reference subspace that replaces the role of the minimizer manifold, yielding a coupled dynamical system in which orthogonal oscillations are damped by parallel progress along directions of decreasing sharpness. Under regularity conditions, which we verify for logistic and multiclass cross-entropy losses in symmetric data models, we derive explicit bounds for the iterates, not just the loss, covering both the EoS and stable regimes, and revealing a three-phase damping structure in the latter. Our analysis further uncovers a transient implicit bias induced by large step sizes: although GD converges asymptotically to the max-margin direction, large steps can leave persistent orthogonal residuals and, in certain geometries, amplify them.

Routing is foundational in VLSI physical design, directly shaping timing, power, and area. Recent pre-trained Seq2Seq models recast routing as autoregressive generation over DFS-serialized trees, but inherit a text backbone blind to the physical space their tokens describe: DFS decouples sequence position from physical coordinate, breaking spatial reasoning at branching points, in load selection, and along the autoregressive trajectory. We name these failures the \emph{Three Spatial Blindnesses} and propose ChiP-STAR, which augments a T5Gemma backbone with three lightweight modules: a dual-frame rotary encoding coupling sequence order with 3D proximity, a Fourier-factorized attention prior with memory linear in sequence length, and a cumulative coordinate-noise schedule closing the train--inference gap, together adding under $0.5\%$ parameters. We rebuild the AiEDA corpus into the largest geometry-annotated routing dataset to date ($6.4$M nets, $1.8$B tokens, $556$\,GB). ChiP-STAR-Large surpasses iPCL-Large by $5\%$ on Leaf IoU and Connectivity, and commercial ECO signoff yields $3\%$ shorter wirelength and $11\%$ fewer vias. Our code is publicly available at \url{https://anonymous.4open.science/r/iPCL-R-0778/}.

Instantaneous Quantum Polynomial Quantum Circuit Born Machines (IQP-QCBMs) have been proposed as quantum generative models that combine a classically tractable training objective—based on the maximum mean discrepancy (MMD)—with a potential quantum advantage motivated by sampling-complexity arguments. While recent works have explored this model across various application domains, fundamental questions remain: does the model suffer from exponentially vanishing loss gradients, known as the barren plateau problem—a pervasive obstacle in quantum machine learning—and how do regimes of trainability relate to regimes of possible quantum advantage? Here, we address both questions analytically. To study trainability, we derive closed-form expressions for the variances of the partial derivatives of the MMD loss function and establish general upper and lower bounds. We explicitly characterize how trainability depends on the generator set and the spectrum of the chosen kernel, identifying regimes in which low-weight kernels avoid exponential gradient suppression under structured topologies. Regarding potential quantum advantage, we reformulate the anti-concentration property in terms of the same generator-set quantities that govern trainability, enabling a unified analysis. We show that sparse IQP architectures can produce classically intractable output distributions while simultaneously remaining trainable, at least at lower-weight frequencies. Our analytical results corroborate the numerical observations of prior work and provides principled guidelines for designing scalable IQP-QCBM architectures.

Generative models excel at synthesizing high-fidelity samples from complex data distributions, but they often violate hard constraints arising from physical laws or task specifications. A common remedy is to project intermediate samples onto the feasible set at each sampling step. However, repeated projection can disrupt the learned sampling dynamics because this feasible set is defined for ''clean'' samples rather than noisy intermediate states. Thus, recent studies first estimate ''clean'' samples and then project them to the feasible set, but this increases algorithmic complexity and accumulates errors across steps. To address these issues, this paper proposes Chance-constrained Flow Matching (CCFM), a training-free method that formulates constraint enforcement during sampling as stochastic optimization while retaining the hard-constraint feasibility guarantee of projection-based methods. By avoiding direct projection of noisy intermediate states onto the clean-sample feasible set, CCFM mitigates the distributional distortion. Unlike approaches that first estimate and project ''clean'' samples, CCFM avoids complex multi-stage procedures. Experiments show that CCFM outperforms current state-of-the-art constrained generative models in modeling complex physical systems governed by partial differential equations, molecular docking problems, and physics-informed motion generation, delivering superior feasibility and fidelity.

Automated systems built on artificial intelligence (AI) are increasingly deployed across high-stakes domains, raising critical concerns about fairness and the perpetuation of demographic disparities that exist in the world. In this context, causal inference provides a principled framework for reasoning about fairness, as it links observed disparities to underlying mechanisms and aligns naturally with human intuition and legal notions of discrimination. Prior work on causal fairness primarily focuses on the standard machine learning setting, where a decision-maker constructs a single predictive mechanism $f_{\widehat Y}$ for an outcome variable $Y$, while inheriting the causal mechanisms of all other covariates from the real world. The generative AI setting, however, is markedly more complex: generative models can sample from arbitrary conditionals over any set of variables, implicitly constructing their own beliefs about all causal mechanisms rather than learning a single predictive function. This fundamental difference requires new developments in causal fairness methodology. We formalize the problem of causal fairness in generative AI and unify it with the standard ML setting under a common theoretical framework. We then derive new causal decomposition results that enable granular quantification of fairness impacts along both (a) different causal pathways and (b) the replacement of real-world mechanisms by the generative model's mechanisms. We establish identification conditions and introduce efficient estimators for causal quantities of interest, and demonstrate the value of our methodology by analyzing race and gender bias in large language models across different datasets.

Generative models can produce individually plausible samples while deviating substantially from a reference set in the distribution of key features. For example, a model pretrained on broad drug-like chemical space may generate molecules whose molecular features differ from those of a therapeutic class of interest, such as known antibiotics. Correcting such distributional _miscalibration_ is challenging: direct finetuning on the reference set can overfit and does not control which features are matched. To fill this gap, we introduce kernel Calibrating Generative Models (kCGM). kCGM minimizes a maximum mean discrepancy (MMD) between generated and reference feature distributions using an unbiased score-function estimator, with KL regularization to remain close to the pretrained model. On a reference set of 174 antibiotics, direct finetuning sacrifices chemical validity for feature-distribution matching, whereas kCGM improves target feature matching while increasing validity. We further demonstrate kCGM in protein and DNA generation tasks, showing it can adapt autoregressive, continuous-space diffusion, and discrete diffusion models using only feature-level supervision.

Sparse autoencoders (SAEs) are widely used to decompose language model activations into interpretable features, but recent work finds that many features are not reproducible across random seeds. Intuitively, the more important a feature is, the more reproducible it should be. We test this hypothesis and find a surprising inversion: the 50 most important features by zero-ablation are among the least reproducible across seeds, far below dictionary-wide baselines. We trace this to residual stream anisotropy, a well-studied phenomenon in NLP embeddings that has been documented in transformer representations but not connected to SAE training. In transformer middle layers, a single principal component (PC1) explains 70--99.9\% of activation variance, and its sparse decomposition is non-identifiable: different seeds learn different features that tile the same direction. These features dominate importance rankings, explaining the inversion. We propose an intervention: bypassing PC1 during SAE training, routing it around the SAE and restoring it during inference. Across 9 models from 5 families (124M--70B parameters), this intervention raises top-50 feature recovery to 74--97\%. The recovered features show greater causal consistency under steering ($p < 0.01$ in 8 of 9 models), and shared features produce $4\times$ more accurate logit-lens predictions than orphan features. Our results reconcile recent SAE instability findings with the existence of dense model features: the dominant PC1 direction is real and reproducible, but the individual sparse coordinates used to reconstruct it are not. Once this component is separated, a reproducible core of sparse, semantically coherent SAE features emerges.

Continuous-time generative models compress endpoint-conditioned bridges into Markov velocity fields, but no existing diagnostic measures how much information this compression discards. We introduce the \emph{Markovization gap}---the integrated conditional variance of the bridge velocity given the Markov state---which quantifies this loss before any neural network is trained. To make the gap well-defined across model families, we define \emph{Bridge Graphical Models} (BGMs), separating endpoint coupling, bridge law, Markovian projection, and dynamics representation as independent design choices. This decomposition also formalizes Poisson and electrostatic models as field-line bridge kernels with their own caustic gap. Across synthetic, latent, and pixel-space pilots on CIFAR-10 and Fashion-MNIST, a proxy gap estimated in minutes on CPU consistently ranks coupling/bridge choices in the same direction as training loss and FID measured after hours of GPU training.

Diffusion and flow matching approaches to generative modeling have shown promise in domains where the number of elements in a state is fixed in advance (e.g. images), but require *ad hoc* solutions when, for example, the length of a response from a large language model, the number of atoms in a molecule, or the number of amino acids in a protein chain is not known *a priori*. Here we propose Branching Flows, a generative modeling framework that, like diffusion and flow matching approaches, transports a simple distribution to the data distribution. But in Branching Flows, the elements in the state evolve over a forest of binary trees, branching and dying stochastically with rates that are learned by the model. This allows the model to control, during generation, the number of elements in the sequence. We show that Branching Flows can compose with any flow matching base process on discrete sets, continuous Euclidean spaces, Riemannian manifolds, and "multimodal" product spaces that mix these components, and we demonstrate distribution matching on small molecules and antibody sequences, and that this scales to complicated domains such as protein structures.

Whole-brain 4D fMRI generation is valuable for modeling functional brain dynamics, yet existing fMRI foundation models mainly target representation learning and downstream prediction rather than conditional predictive generation. We introduce BrainWorld, a structural-prior-conditioned generative model for whole-brain 4D fMRI dynamics. BrainWorld uses sMRI as subject-level anatomical context to guide future fMRI generation, integrating structural information into the denoising process rather than treating it as a parallel modality. Evaluated on 22 datasets spanning diverse cohorts and brain states, BrainWorld generates stable 4D fMRI trajectories up to 400 frames, improves downstream performance through generated-example augmentation, and learns transferable multimodal representations that outperform baselines. Together, these results establish BrainWorld as a condition-aware generative framework for long-horizon brain dynamics modeling and multimodal representation learning.

Recent years have witnessed meteoric progress in *reasoning models*: neural networks that generate intermediate *reasoning traces* (RTs) before producing a final output. Despite the rapid advancement, our understanding of how RTs support reasoning, and where this paradigm fails, remain incomplete. To promote greater clarity, we introduce PITA: a novel large-scale dataset of over 23 million statements in propositional logic and their corresponding proofs. As a benchmark for robust reasoning, we focus on length generalization: if a model is trained to determine truth or falsity on statements with proofs up to fixed length, how well does it generalize to statements requiring longer proofs? We propose notions of (1) *task depth* and (2) *task breadth*, which measure respectively (1) the number of proof steps required to solve a proposition and (2) the number of unique propositions within a task family. We vary these quantities across subsets of PITA, and find that RT models generalize well on relatively *broad* and *shallow* subsets, while deteriorating on relatively *narrow* and *deep* subsets compared to non-RT baselines. As a controlled point of comparison, we study a separate, tractable transitive inference task that exhibits qualitatively similar behavior. Our accompanying theory explains the scalings observed in this simpler setting, suggesting one mechanism by which breadth can favor RT models while depth can expose long-context weaknesses. Our findings suggest salient benefits and limitations of proof-like reasoning traces in controlled length-generalization settings.

One key application of autoencoders is to learn how to compress token sequences. Since the difficulty of compression depends on factors such as sequence length, vocabulary size, structural regularity, and input noise, it would be valuable to understand how these factors affect the performance of different architectures. Surprisingly, however, there is no benchmark for comparing autoencoder architectures that allows control over these aspects of difficulty. We introduce the Bottleneck Benchmark (BB), an open experiment framework in which encoder and decoder communicate only through a fixed-size latent and that allows to configure the previously mentioned difficulty aspects for any customizable data generator. As a case study, we evaluate BiLSTM, Transformer, and Bidirectional SSM encoders on copy, sort, and set tasks, finding that performance differences arise from inductive biases under noise and length rather than raw capacity.

Access to modern generative systems is often restricted to querying an API (the ``black-box" setting) and many properties of the system are unknown to the user at inference time. While recent work has shown that low-dimensional representations of models based on the relationship between their embedded responses to a set of queries are useful for inferring model-level properties, the quality of these representations is highly sensitive to the query set. We introduce the discriminative factorization to distinguish between high- and low-quality query sets in the context of black-box model-level classification. Under this framework, the probability of chance-level classification decays exponentially in the query budget. On three auditing tasks, estimated factorization parameters predict the empirical performance decay rate. We conclude by showing that query sets selected using the estimated discriminative field reproduce the empirical ordering of oracle query sets.

We present BitDance, a scalable autoregressive (AR) image generator that predicts binary visual tokens instead of codebook indices. With high-entropy binary latents, BitDance lets each token represent up to $\mathbf{2^{256}}$ states, yielding a compact yet highly expressive discrete representation. Sampling from such a huge token space is difficult with standard classification. To resolve this, BitDance uses a binary diffusion head: instead of predicting an index with softmax, it employs continuous-space diffusion to generate the binary tokens. Furthermore, we propose next-patch diffusion, a new decoding method that predicts multiple tokens in parallel with high accuracy, greatly speeding up inference. On ImageNet 256$\times$256, BitDance achieves an FID of **1.24**, the best among AR models. With next-patch diffusion, BitDance beats state-of-the-art parallel AR models that use 1.4B parameters, while using **5.4$\times$** fewer parameters (260M) and achieving **8.7$\times$** speedup. For text-to-image generation and image editing, BitDance trains on large-scale multimodal tokens and generates high-resolution, photorealistic images efficiently, showing strong performance and favorable scaling. When generating 1024$\times$1024 images, BitDance achieves a speedup of over **30$\times$** compared to prior AR models. We release code and models to facilitate further research on AR foundation models.