NeurIPS 2026 Papers

Model merging integrates task-specific fine-tuned models into a single multi-task model, but often suffers from parameter interference caused by conflicting task-vector updates. Existing methods typically mitigate conflicts by pruning task vectors based on weight magnitude or random heuristics, treating Transformers as unstructured ``bags of parameters'' and overlooking their inherent modularity. In this paper, we propose \textbf{C}ontribution-\textbf{A}ware \textbf{S}tructured \textbf{S}parsity (CASS), a unified framework that reduces parameter interference by identifying and preserving task-specific components. At the core of CASS is a contribution-aware structured mask that identifies task-relevant attention heads and FFN neurons. We instantiate this mask in two settings: CASS-Merging, the primary post-hoc setting where masks serve as a plug-and-play denoising filter for existing merging operators, and CASS-Tuning, an extension for scenarios with fine-tuning access where masks constrain gradients to reduce structural overlap between task vectors. Our analysis shows that task-relevant components are sparse and partially disjoint, supporting structured component-level filtering as an effective way to reduce merging interference. Extensive experiments across vision (ViT, 20 tasks) and language (RoBERTa, 8 tasks; Qwen2.5, 4 tasks) benchmarks demonstrate that CASS improves a range of representative merging baselines.

The Hessian of the energy with respect to the nuclear positions is indispensable in atomistic modelling. However, constructing this matrix requires $O(N)$ Hessian vector products, traditionally limiting high-accuracy Hessians to small systems. Machine learning interatomic potentials (MLIPs) have accelerated atomistic modelling by providing highly accurate energies and forces at $O(N)$ cost, yet the resulting $O(N^2)$ cost of Hessians remains a practical bottleneck for large systems. Based on the insight that we can derive the sparsity pattern for an MLIP's Hessians in closed form, we show in this paper how to use techniques from sparse automatic differentiation to reduce the cost of a local MLIP's Hessians to a system-size-independent number of Hessian-vector products, yielding overall $O(N)$ total cost without any approximations. We benchmark our approach on a variety of systems ranging from alkane chains to water clusters to A$\beta$40 conformers. Depending on the MLIP configuration, we achieve the linear scaling regime already on relatively small systems, resulting in large runtime reductions between $2\times-15\times$ for these systems. This opens up the possibility of scaling high-accuracy MLIP Hessians to very large systems, such as proteins that were previously inaccessible.

Deep-learning-based 3D MRI reconstruction is limited in practice by the GPU memory and compute cost of full-volume training. A common workaround is to train at lower resolution and run inference at higher resolution, but standard neural networks are resolution-specific and degrade substantially when evaluated outside the training setting. We instead use resolution-agnostic neural operators (NOs) and propose KIR-NO (k-space-to-Image Reconstruction Neural Operator), a coarse-to-fine, discretization-agnostic framework for accelerated 3D MRI reconstruction. KIR-NO is trained with full backpropagation on memory-feasible low-resolution volumes and applied zero-shot to higher-resolution volumes at inference, without fine-tuning. Its core building block is a 3D local neural operator based on discrete-continuous convolutions: convolutional filters are parameterized in a continuous basis (we propose and empirically compare two 3D bases, piecewise-linear and Morlet-wavelet) and sampled at arbitrary voxel resolutions while preserving the local inductive bias of convolution. KIR-NO integrates these learned operators with physics-based consistency: a k-space neural-operator head first refines the undersampled Fourier measurements, and image-space neural-operator cascades then refine the reconstruction through interleaved data-consistency updates. Across 3D knee (SKM-TEA) and brain (BraTS 2021) MRI benchmarks, KIR-NO consistently outperforms classical and CNN baselines: it improves over a state-of-the-art 3D CNN by 4.13 dB PSNR at half resolution under 4× acceleration on SKM-TEA, with gains persisting at 8× and 16×, and exceeds the same baseline by 13.63 dB under zero-shot full-resolution transfer on BraTS. Together, these results show that KIR-NO enables scalable, memory-efficient, and resolution-flexible 3D MRI reconstruction across anatomies.

Dynamic Sparse Training (DST) is an effective paradigm for sparse to sparse training of neural network connectivity under a fixed parameter budget. Recent advances in network-science for AI introduced epitopological learning methods, such as Cannistraci-Hebb Training (CHT), demonstrating that network automata applied to the mere network topology enables gradient-free predictions of the sparse connectivity evolution that can trigger significant increase in task performance. However, these methods were currently developed for standard MLP-like fully-connected architectures and need significant rethinking to be extended to convolutional neural networks (CNNs) due to element-wise weight sharing and spatially repeated interactions. In this work, we bridge this gap by introducing epitopological learning DST for CNNs through channel-wise network modeling to address the prohibitive complexity of element-wise modeling, which treats each kernel-channel as a single network node. Results show orders-of-magnitude improvements in time complexity of link-regrowth when applied at channel-level with respect to element-level. We also enhance the channel-wise formulation with lightweight contextual modulation to improve expressivity. Extensive experiments on CIFAR-10, CIFAR-100, and Tiny-ImageNet with ResNet and VGG architectures demonstrate that our method achieves performance comparable to dense training using only 30% of the parameters, which significantly reduces computational cost. Furthermore, our approach improves robustness under noisy inputs. These results highlight the effectiveness of topology-aware sparse training and the benefit of decoupling graph construction from sparse update rules in convolutional networks.

Deep neural networks continue to grow in parameter count, driving up training and inference cost on GPUs. Sparse neural networks and Dynamic Sparse Training (DST) promise to reduce these costs, but most implementations rely on binary masks over dense tensors and recover little of the theoretical compute, memory, or energy savings. We propose SNACK, a truly sparse GPU layer that stores and computes only non-zero connections. SNACK exposes a simple PyTorch API for restructuring connections and backpropagating gradients entirely in the sparse paradigm, and uses a custom COO-format SpMM CUDA kernel with a batch-to-Streaming-Multiprocessor mapping tuned for the small-batch, high-sparsity regime typical of large-model training and single-stream inference. At the kernel level, SNACK is up to $7\times$ faster than the masked dense baseline (Dense+Mask) and competitive with cuSPARSE, Sputnik, and FlashSparse at 95\% sparsity. At 90\% sparsity, a single SNACK layer accelerates training by $8\times$ and $3.7\times$, and inference by $4\times$ and $2\times$, over Dense+Mask and fully dense layers, respectively, while using 25\% less memory than dense and substantially less energy. End-to-end, SNACK reduces GPT-2 peak training memory by up to 40\% and graph-style inference latency by $4.8\times$ over Dense+Mask at 99\% sparsity.

Attribute-efficient PAC learning of sparse halfspaces has been a fundamental problem in machine learning theory. In recent years, machine learning algorithms are faced with prevalent data corruptions or even malicious attacks. It is of central interest to design computationally-efficient algorithms that are robust to malicious corruptions. In this paper, we consider that there exists a constant amount of malicious noise in the data and show that it is possible to learn an underlying $s$-sparse halfspace $w^* \in \mathbb{R}^d$ with $O(s^2\log^5 d)$ samples. Specifically, we follow a recent line of works and assume that the underlying distribution satisfies a certain concentration condition and a margin condition at the same time. As a complementary result, we provide an information-theoretic sample lower bound under such conditions. Strong evidence shows that our sample complexity is nearly optimal. To show the robustness of our algorithm, we provide a new gradient analysis that carefully handles the sparsity admitted constraints in hinge loss minimization program, which could be of independent interest.

We introduce a model for neural scaling laws under sparse activations. In the model, test loss is often dominated by rare coordinates that are never observed in the training input. This mechanism induces a novel bottleneck absent from dense models. We derive the asymptotic population loss in both the underparameterized and overparameterized regimes, and show that the loss exhibits a double-descent peak near the interpolation threshold---where the number of parameters is just sufficient to fit the training data---resulting in a loss curve governed by two distinct scaling exponents---one for the overparameterized regime and one for the underparameterized regime---with a gap determined by the degree of sparsity. Additionally, we derive a compute-optimal frontier that favors increasing dataset size over model capacity under fixed compute budgets. We also analyze gradient-descent dynamics and identify a scaling law for the probability that fixed-step gradient descent becomes unstable. We further show that the sparsity-induced effect persists under nonlinear activations. Experiments validating the theory can be found at https://anonymous.4open.science/r/sparse-scaling-neurips2026-3CDB/SparseScaling1.ipynb.

State-of-the-art neural network sparsification relies on alternating dense and sparse training phases. While computationally expensive, dense phases are critical for performance. Our empirical analysis reveals the mechanics behind this gain: upon reintroduction, previously masked parameters receive disproportionately large gradients that drive essential mask rewiring and parameter sign-flipping. Building on these insights, we optimize the performance-to-FLOPs Pareto frontier through three innovations: (1) zero-initializing masked parameters during dense phases to promote relevant sign flips, (2) truncating dense phases based on early mask convergence, and (3) replacing the dense phase entirely with a sparse rewiring phase that updates only the active mask and a small, high-gradient fraction of out-of-mask weights. Evaluated on CIFAR100 and ImageNet, our variant ARC (Alternating Rewiring Compression) matches baseline AC/DC performance at a fraction of the computational cost, establishing a superior performance-to-FLOPs frontier also compared to standard sparse-to-sparse algorithms.