NeurIPS 2026 Papers

While parameter-efficient fine-tuning methods like low-rank adaptation (LoRA) are standard for large language models, principled estimation of epistemic uncertainty remains challenging. Recent results in the LoRA regime suggest that discrete multi-mode approaches such as deep ensembles offer little benefit over single-mode methods. This contradicts broader observations in deep learning, where ensembling independent optima typically improves generalization, and linking these modes through continuous low-loss valleys further enhances Bayesian model averaging (BMA). Whether such structure exists in the LoRA space and whether it yields functional diversity missed by local or discrete methods has not been studied. We introduce *LoRA-Curve*, a segmented Bézier curve parameterization in the LoRA space, with two variants: a free configuration that jointly optimizes all control points, and an anchored configuration that connects independently fine-tuned LoRA optima. We prove pathwise continuity and Lipschitz regularity of the loss along the curve and empirically show, across reasoning and classification benchmarks with Qwen2.5 7B, that linear interpolation encounters loss barriers, while our anchored multi-segment curves connect independent optima through continuous low-loss valleys. Combined with flat-minima perturbations and a Jensen-Shannon divergence regularizer, *LoRA-Curve* yields measurably higher mutual information of the predictive distribution without sacrificing performance, and links continuous parameter-space traversal to functional diversity.

We study the empirical risk minimization (ERM) of linear Joint Embedding Predictive Architecture (JEPA) and establish its key conditions for optimality. By casting the embedding bottleneck as a rank constraint, we formulate JEPA as a reduced-rank regression problem. This induces a risk decomposition into an irreducible error and an excess-risk bound. Within the irreducible term, we find the rank of the optimal predictor grows with target heterogeneity and saturates at the bottleneck. Within the excess-risk bound, we find spectral conditioning of the whitened end-to-end predictor governs minimization. Together, these conditions prescribe an isotropic regularizer. Under this regularization, we show such JEPA isotropy subsumes canonical JEPA isotropic embedding designs and hence justifies their empirical successes via ERM. Numerical experiments corroborate our theory.

Robot fine-tuning can improve manipulation success while degrading the semantic structure inherited from large vision-language pretraining. This trade-off limits the reuse of vision-language-action (VLA) policies in settings that require compositional instructions, camera changes, and coordination with higher-level agents. We present \textbf{NoTVLA}, a semantics-preserving robot adaptation framework that replaces dense low-level action supervision with a sparse narrative action interface. NoTVLA converts demonstrations into sparse, semantically meaningful waypoints, grounds each decision with a task-relevant visual anchor and depth value, and reconstructs executable motion through a deterministic detokenizer. The resulting interface keeps the autoregressive vision-language backbone close to its pretrained prediction format while delegating high-frequency control to a transparent motion-rendering stage. We evaluate this design through matched and backbone-family comparisons, semantic retention probes, semantic out-of-distribution manipulation tasks, camera and depth perturbations, and deployment-oriented efficiency analysis. The results suggest that robot adaptation should be judged not only by task success, but also by how much task-relevant semantic competence is preserved during fine-tuning.

Rehearsal-free class-incremental learning (CIL) requires a model to learn new classes sequentially without storing previous data, making catastrophic forgetting a central challenge. Adapter-based methods have become a prevalent solution by storing and accumulating task-specific update matrices, yet the effect of the cumulative update magnitude on CIL performance remains underexplored. In this work, we propose Normalized Tensor Adaptation (NoTA), which addresses these two aspects jointly. MPO adapters provide a compact structured space for storing task-specific updates, while global normalization controls the accumulated update that determines the final model. Our empirical analysis reveals a key observation: global normalization consistently improves both matrix-based and MPO-based adapters by stabilizing the cumulative update magnitude across task sequences. We further provide a theoretical analysis showing that global normalization yields a forgetting bound independent of the task sequence length, in contrast to task-wise normalization whose bound can grow with later tasks. Building on the tensor network structure of MPO, we introduce a variant with hierarchical coefficients (H-NoTA), which uses task-level coefficients and inter-core modulation matrices to refine the contributions of historical adapters. Extensive experiments demonstrate that our methods consistently improve rehearsal-free CIL performance while maintaining strong parameter efficiency.

Low-Rank Adaptation (LoRA) fusion enables the composition of subject and style representations for controllable generation without retraining. However, existing approaches primarily operate through weight-level merging, without explicitly modeling how independently trained LoRAs interact in the shared parameter space. We adopt a geometric perspective on LoRA fusion, interpreting content and style LoRAs as occupying overlapping, non-orthogonal low-rank subspaces, where such overlap can lead to conflicting parameter updates that affect generation quality. This observation motivates us to reformulate LoRA fusion not merely as parameter combination, but as a problem of controlling how updates from overlapping subspaces are combined. Based on this insight, we propose Null Space Projection LoRA (NP-LoRA), a training-free framework that employs projection as a fusion operator to explicitly modulate cross-LoRA interactions. Specifically, NP-LoRA uses principal directions of the style LoRA to define a projection subspace and projects the content LoRA onto the complementary subspace (i.e., the null space of the style LoRA), suppressing interference along dominant style directions while preserving complementary information. To avoid the overly aggressive suppression of hard projection, we further formulate soft projection as a regularized optimization problem that balances content preservation against style-subspace suppression. This objective admits a closed-form solution, yielding a projection operator controlled by a single parameter that continuously interpolates between linear merging and hard projection. Extensive experiments across multiple pretrained LoRA pairs show that NP-LoRA achieves more balanced content-style composition compared to strong baselines, without requiring retraining.

During evolution, biological neurons scale computation by expanding dendritic branches. However, this expansion creates a biophysical dilemma: increased membrane area typically imposes a capacitive load that slows somatic dynamics and narrows temporal bandwidth. Here, we investigate how primate cortical neurons resolve this tradeoff. While primary basal dendrite number is relatively conserved across mouse cortical areas, it increases systematically along the primate cortical hierarchy. Using biophysically constrained multicompartment modeling, we identify a key dimensionless control parameter---the dendritic-to-somato-apical specific membrane resistance ratio, $\rho \equiv R_{m,\mathrm{dend}}/R_{m,\mathrm{sa}}$, that governs the coupling between dendritic morphology and the effective somatic time constant $\tau$. In mouse-like neurons ($\rho>1$), adding basal dendrites progressively increases $\tau$ and promotes reliable low-pass integration. Conversely, human-like neurons operate near a balanced-resistance regime ($\rho \approx 1$), where resistive reweighting counterbalances morphology-driven capacitive loading. This allows $\tau$ to remain nearly invariant despite expanded dendritic topology, shifting the structure-function tradeoff toward faster, more flexible coding with improved high-frequency tracking. Our results reveal a biophysical scaling principle linking evolutionary dendritic architecture to hierarchy-dependent coding, offering potential design rules for preserving temporal bandwidth in dendrite-inspired neuromorphic architectures.

Continual learning (CL) aims to adapt models to new tasks while preserving previously learned knowledge. Recently, Low-Rank Adaptation (LoRA), a representative Parameter-Efficient Fine-Tuning (PEFT) method, has gained increasing attention in CL due to its efficiency and scalability. Several LoRA-based merging methods maintain a single inference model by scaling the newly learned LoRA update with one coefficient and merging it into the previous weights after each task. However, they usually control the whole update with a shared scalar factor, although different update elements may affect previous and current tasks in different ways. To address this issue, we propose Merging Strength Modulation via Joint Loss Estimation (M²LE) It consists of Hessian Information-guided Adaptive Merging (HIM) and Task Simulation Perturbation for Merging (TSP). Instead of searching for a global merge coefficient, HIM directly solves for the target merged update under a joint objective over previous and current tasks. Solving this objective gives an analytic solution that naturally takes the form of element-wise modulation over the current task LoRA update. To improve the stability of the learned update under subsequent merging, we introduce TSP which simulates different tasks interference. Experiments on multiple benchmarks show that M²LE consistently outperforms existing PEFT-based continual learning methods. Our code is provided in the supplementary material.

We propose AdaDS, a generalizable framework for prompted metric depth estimation, which estimates high-resolution metric depth from images and arbitrarily degraded low-resolution depth prompts. This setting is commonly studied as depth super-resolution, where existing methods typically regress depth values directly and often exhibit artifacts under severe or unknown depth degradation. In contrast, AdaDS exploits the contraction property of Gaussian smoothing: as noise accumulates in the forward diffusion process, the distributional discrepancy between degraded depth prompts and their high-quality counterparts progressively diminishes, eventually approaching an isotropic Gaussian prior. Leveraging this property, AdaDS estimates refinement uncertainty to adaptively select a starting timestep in the reverse diffusion trajectory, and subsequently injects tailored noise to place the intermediate sample in a high-probability region of the target posterior distribution. This strategy enables the generative prior of a pre-trained diffusion model to dominate the estimation process even when upstream prompt refinements are imperfect. Extensive experiments on real-world and synthetic benchmarks demonstrate AdaDS's superior zero-shot generalization and robustness to diverse degradation patterns compared with state-of-the-art methods.

Large-graph spectral learning promises global, trainable propagation beyond local neighborhoods, but explicit spectral layers remain difficult to use in stochastic large-graph training: their bases are commonly obtained by a full-graph spectralization step and their graph-wide contexts are naturally full-batch. Matrix-free polynomial filters avoid eigensolvers and train stochastically, but tie the response to finite propagation bases; explicit spectral-subspace models offer more flexible global responses, but usually pay for full-graph basis construction and context evaluation. We introduce Randomized Adaptive Spectral Estimation (RASE), a matrix-free stochastic training framework for explicit low-rank spectral-context layers. RASE constructs a refreshable randomized block-Krylov/Ritz basis from probe vectors and sparse matrix--vector products, reuses probe-derived summaries as control variates for mini-batch estimates of the spectral context, and keeps the response module replaceable across polynomial, Chebyshev, and transformer-style instantiations. We analyze Krylov/Ritz polynomial-action exactness for the probe-generated subspace and a control-variate variance identity that isolates when the mini-batch context estimator reduces variance. Across 14 node-classification benchmarks, RASE matches its eigenbasis-trained reference within seed noise where the eigensolver is feasible (${\sim}67{\times}$ faster basis on PubMed), and trains the same backbone on the largest graphs where eigensolver preprocessing exceeds a 30-minute budget. The contribution is therefore not a new spectral filter family, but a training route that makes explicit low-rank spectral-context layers matrix-free and mini-batch trainable.

Unit-modulus measurement vectors, due to their phase-only variations, exhibit favorable hardware compatibility and storage efficiency. In this paper, we consider matrix recovery using symmetric unit-modulus rank-one measurements. We identify a fundamental limitation of symmetric unit-modulus measurements---their inability to capture individual diagonal entries, and show that matrix recovery can be achieved using such measurements when the diagonal entries are known or directly measurable. We construct a stacked operator and establish that it satisfies a mixed-norm restricted isometry property ($\mathrm{mRIP}$) for unit-modulus measurements. Leveraging the $\mathrm{mRIP}$ condition, we derive exact and stable recovery results for matrix recovery with unit-modulus measurements in both noiseless and noisy settings. Our work is the first to provide the theoretical foundation for matrix recovery under symmetric rank-one unit-modulus measurements. Numerical experiments further corroborate these theoretical findings.

Low-budget molecular optimization is often framed as Bayesian optimization in a learned latent space, but standard benchmarks typically allow hundreds or thousands of evaluations, whereas a realistic wet-lab round may allow only a few dozen. We revisit this regime using a SELFIES molecular variational autoencoder and GuacaMol objectives at $N=30$ oracle calls. The main finding is not a new surrogate model, but a geometric mismatch in candidate generation. The training latents of the VAE concentrate near a narrow spherical shell, while many high-dimensional optimizers propose candidates from boxes or box-shaped trust regions. Such candidates can leave the decoder's training distribution even when their coordinates look individually plausible. We study a simple geometric constraint, the on-sphere scaffold, that restricts candidate generation to the empirical shell occupied by the VAE training latents. Uniform random search on this shell already outperforms most of the classical box-supported Bayesian optimization baselines. We then introduce two minimal optimizers to probe what remains useful once the support is fixed. GeoWalk performs geodesic local search on the empirical sphere and outperforms every published Bayesian optimization baseline tested. GeoCMA keeps the scaffold but adds covariance learning in a random subspace, becoming preferable when the search representation contains learnable directional or semantic structure, as in LassoBench, NAS-Bench-101 graph-VAE optimization, and GSM8K text-latent prompt optimization. A controlled ablation of three recent Gaussian-process recipes, changing only whether candidates are proposed on the empirical sphere or on the published box-supported domain, shows that the scaffold rather than the surrogate is the load-bearing component. The practical lesson is simple: first match the empirical search support; add a surrogate or covariance learner only when the remaining search space contains directional structure that can be learned from the available budget.

Mamba, a recently proposed linear-time sequence model, has attracted significant attention for its computational efficiency and strong empirical performance. However, a rigorous theoretical understanding of its underlying mechanisms remains limited. In this work, we provide a theoretical analysis of Mamba's in-context learning (ICL) capability by focusing on tasks defined by low-dimensional nonlinear target functions. Specifically, we study in-context learning of a single-index model $y \approx g_*(\langle \boldsymbol{\beta}, \boldsymbol{x} \rangle)$, which depends on only a single relevant direction $\boldsymbol{\beta}$, referred to as *feature*. We prove that Mamba, pretrained by gradient-based methods, can achieve efficient ICL via *test-time feature learning*, extracting the relevant direction directly from context examples. Consequently, we establish a test-time sample complexity that improves upon linear Transformers---analyzed to behave like kernel methods---and is comparable to nonlinear Transformers, which have been shown to surpass the Correlational Statistical Query (CSQ) lower bound and achieve near information-theoretically optimal rate in previous works. Our analysis reveals the crucial role of the *nonlinear gating* mechanism in Mamba for feature extraction, highlighting it as the fundamental driver behind Mamba’s ability to achieve both computational efficiency and high performance.

GANs are appealing because they generate sharp images in a single forward pass. Recent works have stabilized GAN training, but FID may still plateau on diverse datasets like ImageNet-256 because the discriminator's activation magnitudes increase through training. We trace this pathology to the discriminator's incentive to sharpen its decision boundary by rescaling activations rather than by finding better features. Then, building on R3GAN, we treat magnitude preservation as a first-class architectural target across the network: $\ell_2$ weight normalization with centering, magnitude-preserving LReLU and residuals, forced post-update normalization, and feed-forward classifier heads. Across a roadmap of configurations, we perform diagnostic ablations to clarify what does and does not work and why. The resulting models reach FIDs of 2.20 @ 17 M parameters, 1.63 @ 60 M, and 1.52 @ 130 M on class-conditional ImageNet-256. At 1 NFE, this is substantially more efficient than competing diffusion and autoregressive methods, and than prior GAN baselines too (e.g., 10$\times$ more efficient than StyleGAN-XL for similar FID). In sum, our work presents a new SOTA in FID/parameter efficiency derived from simple adversarial training with well-behaved magnitude preserving layers.

State Space Models (SSMs) offer an efficient alternative to Transformers for sequence modeling, yet conditioning pre-trained SSMs for iterative generation typically operates outside the recurrent operator, through input injection or activation modulation. While such mechanisms expose the model to conditioning information, they leave the underlying temporal dynamics fixed. We introduce MaRK (Markov-adapted Recurrent Kernels), a dynamic operator-conditioning framework that maps context vectors directly into bounded modulations of a frozen SSM's recurrence ($A$), read-in ($B$), read-out ($C$), skip ($D$), and discretization ($\Delta$) parameters. Viewed through the lens of Linear Parameter-Varying systems, MaRK induces a context-indexed family of Markov parameter sequences, allowing each diffusion timestep to reshape the model's input-output memory kernel. We instantiate MaRK on a frozen 111M-parameter Hydra SSM backbone and study three adapter geometries: Hypernet, Chebyshev polynomial, and Discrete Cosine Transform kernels. Since these adapters modify the Markov parameter sequence through low-rank auxiliary maps on the frozen backbone, parameter-efficient fine-tuning arises as a structural consequence of the adaptation mechanism itself, requiring only 7.5--13M trainable auxiliary parameters to transition from a bidirectional objective to an iterative diffusion regime. The bounded recurrence parameterization further yields an analytic Affine Quadratic Stability certificate for the modulated recurrence. Through synthetic LPV recovery experiments and Markov-operator diagnostics, we show that MaRK recovers coordinate-invariant temporal operators under matched assumptions and produces distinct, stable timestep-conditioned memory profiles. Empirically, the Chebyshev variant yields the strongest performance, achieving an average validation loss of 2.63, followed by the DCT (2.66) and Hypernet (3.60) geometries. Together, these results provide initial evidence that dynamic operator modulation is a principled operator-level conditioning mechanism for adapting SSMs beyond input-stream injection and adaptive normalization.

Reinforcement learning with verifiable rewards (RLVR) enhances the reasoning capabilities of large language models (LLMs), but at the expense of significant computational overhead due to compute-intensive rollout processes and frequent policy updates. Online prompt selection, a widely adopted strategy for improving training efficiency, maintains per-prompt Bayesian posteriors to predict prompt difficulty and prioritize informative prompts before committing rollout budget. However, these methods assess prompt informativeness without accounting for how reliably learning signal is extracted from sampled responses. In GRPO-based RL algorithms, the realized advantage of a response depends not only on its own outcome, but also on the randomly sampled outcomes of its peers through group normalization. Our experimental and theoretical analysis show that the resulting uncertainty in group composition induces composition noise, a non-vanishing variance component that creates an irreducible lower bound on gradient estimation error. Consequently, the standard group-relative advantage fails to faithfully characterize response-level utility, degrading gradient estimation and thereby impairing downstream prompt selection. To address this issue, we propose a unified Marginalized Posterior-Predictive framework, MaPP, for data-efficient RLVR, which first denoises response-level advantage estimation and then improves prompt selection using a shared Beta posterior. Specifically, for each response, MaPP replaces the standard group-relative advantage with a composition-invariant intrinsic advantage via closed-form Beta-Binomial marginalization. This yields a closed-form posterior-predictive advantage estimator whose error provably diminishes as the posterior concentrates. Then, building on the same posterior, MaPP derives an uncertainty-aware prompt selection score that more faithfully characterizes prompt informativeness, improving data efficiency without additional rollout cost. Experiments across mathematics, planning, and visual geometry on five model backbones show that MaPP consistently outperforms GRPO and strong selection baselines, achieving up to +2.45 average accuracy improvement over the strongest baseline under the same rollout budget, a new state-of-the-art.

Test-time adaptation updates a deployed model using only unlabeled target data, but standard entropy-based methods often rely on deterministic confidence and can reinforce overconfident errors under distribution shift. We propose MIRA, Mutual Information guided calibration for Reliable Test-Time Adaptation, a source-free online adaptation method that uses lightweight last-layer Gaussian perturbations to probe prediction reliability. For each target batch, MIRA reuses a single feature extraction pass and samples perturbed classifiers around the source classifier, forming an efficient local stochastic ensemble. Rather than fitting a Bayesian posterior, MIRA treats the perturbation scale as a local probing radius and selects a batch-specific scale using mutual information and prediction agreement. The resulting perturbation-sensitivity signal identifies predictions that are confident and locally stable under classifier perturbations, while suppressing brittle predictions with high stochastic disagreement. MIRA then performs adaptation with an MI-confidence weighted entropy loss, which down-weights perturbation-sensitive or low-confidence samples before they drive entropy minimization. This weighted loss reduces the influence of brittle predictions that can otherwise cause harmful adaptation under distribution shift. The method requires no source data, retraining, model ensembles, or offline posterior fitting, and can be applied as a plug-and-play modification to entropy-minimization TTA. Experiments on distribution-shift benchmarks show improvements in accuracy, calibration, and negative log-likelihood, suggesting that mutual-information-guided perturbation probing and weighted adaptation yield more robust online TTA than deterministic confidence.

Fine-tuning Vision Language Models (VLMs) with parameter-efficient methods like Low-Rank Adaptation (LoRA) is crucial for task adaptation. However, imbalanced training dynamics across modalities often lead to suboptimal accuracy due to negative interference, a challenge typically addressed with inefficient heuristic methods such as manually tuning separate learning rates. To overcome this, we introduce **MARS** (**M**ultimodal **A**daptive **R**ank **S**earch), an approach to discover optimal rank pairs that balance training dynamics while maximizing performance. Our key innovation, a proposed framework of dual scaling laws, enables this search:~one law models module-specific convergence time to prune the search space to candidates with aligned dynamics, while the other predicts final task performance to select the optimal pair from the pruned set. By re-purposing the LoRA rank as a controller for modality-specific convergence speed, MARS outperforms baseline methods and provides a robust, automated strategy for optimizing VLM fine-tuning.

Long-to-Short (L2S) model merging seeks to combine the strong reasoning capability of long chain-of-thought models with the concise style of base models, but existing methods that rely on linear interpolation and first-order activation statistics fail to capture how the loss landscape responds to parameter displacement, leading to degraded accuracy on hard tasks. We propose Low-Rank Hierarchical Merging (LHM), a training-free framework that replaces heuristic statistics with lightweight second-order curvature information. LHM consists of three components: (1) a low-rank Hessian approximation that efficiently estimates per-layer Hessian traces via Hutchinson's estimator on random inputs, eliminating the need for task- specific data; (2) a Layer Second-Order Sensitivity (LSOS) index that combines Hessian trace with task-vector norm to quantify per-layer fusion difficulty; and (3) a Dual-Constraint Coefficient Mapping (DCCM) that converts LSOS scores into layer-adaptive merge coefficients while jointly satisfying a fusion-error bound and a global length-reduction target. Experiments across six mathematical benchmarks on 1.5B and 7B models show that LHM outperforms state-of-the-art methods such as ACM-TIES and ORCA, achieving over 4\% accuracy gain and up to 93.1\% reduction in output length relative to the long-CoT model.

Scaling critic capacity is a promising direction for enhancing off-policy reinforcement learning (RL). However, larger critics are prone to overfitting and unstable in replay-buffer-based bootstrap training. This paper leverages Low-Rank Adaptation (LoRA) as a structural-sparsity regularizer for off-policy critics. Our approach freezes randomly initialized base matrices and solely optimizes low-rank adapters, thereby constraining critic updates to a low-dimensional subspace. Built on top of SimbaV2, we further develop a LoRA formulation, compatible with SimbaV2, that preserves its hyperspherical normalization geometry under frozen-backbone training. We evaluate our method with SAC and FastTD3 on DeepMind Control locomotion and IsaacLab robotics benchmarks. LoRA consistently achieves lower critic loss during training and stronger policy performance. Extensive experiments demonstrate that adaptive low-rank updates provide a simple, scalable, and effective structural regularization for critic learning in off-policy RL.