NeurIPS 2026 Papers

Diffusion Transformers (DiTs) have established themselves as the preeminent paradigm for high-fidelity generative modeling across various modalities, yet their practical deployment is hindered by the severe computational overhead of iterative sampling. While recent feature-caching methods mitigate this latency through feature reuse or forecasting based on integer-order operators, they remain limited in adapting to the non-stationary and highly curved dynamics of DiT latent trajectories. In this work, we reveal that DiT feature evolution exhibits anomalous diffusion characteristics and a certain degree of spatiotemporal heterogeneity, rendering static, integer-order forecasting operators inadequate and prone to error accumulation. To address this, we propose Fractional Anomalous Dynamics Extrapolation (FADE), a unified framework for training-free diffusion transformers acceleration. FADE models DiT feature evolution via anomalous diffusion and employs a Mittag--Leffler fractional operator to better adapt to high-curvature and non-linear latent trajectories of DiTs. Leveraging the empirical observation that these complex dynamics maintain cross-sample stability, we further construct a Look-Up Table with multiple dimensions through offline profiling. This enables zero-overhead, spatiotemporally adaptive parameter retrieval during online inference. Extensive evaluations across diverse architectures and modalities demonstrate that FADE achieves state-of-the-art acceleration, preserving exceptional generation fidelity under aggressive skip intervals with negligible latency overhead. Our code is anonymously available at https://anonymous.4open.science/status/FADE-8CB5.

Model quantization has advanced tremendously in recent years, producing models that require a fraction of the compute while maintaining baseline accuracy and creating the illusion of lossless compression. Beneath the surface, however, model behavior undergoes severe shifts that simple global accuracy fails to capture. Notably, quantized models experience a high rate of "flips": individual predictions that change from correct to incorrect (bad flips-CI) and vice versa (good flips-IC). Although overall accuracy remains stable, these changes degrade model reliability and introduce unforeseen safety risks. Current literature largely attributes these flips to random rounding noise, a perspective that ignores the specific precision constraints imposed by quantization with or without training. In this paper, we show that flips are driven by quantization's implicit regularization, low-pass filtering, and exacerbated spectral bias. By analyzing these effects via Singular Value Decomposition (SVD), we leverage the model's low-to-high rank internal disagreement to disentangle good flips from bad ones. Building on this insight, we introduce post-hoc approaches to selectively preserve the former while correcting the latter, and we validate the universality of our disentanglement through extensive experiments spanning Post-Training Quantization (PTQ) to Quantization-Aware Training (QAT) and across vision, language, and multi-modal models. With this work, we aim not only to restore the quantized model's hidden reliability degradation but also to elevate it beyond the accuracy ceiling of its full-precision counterpart.

Acceleration for deterministic root-finding problems has been extensively studied in recent years; specifically, the anchor-based, or Halpern-type methods achieve optimal convergence rates with respect to the operator norm. However, acceleration via these methods does not directly carry over to stochastic setting due to accumulation of errors, unless one enforces diminishing variance via increasing batch sizes or variance reduction techniques. In this work, we show that another class of acceleration, namely the *dual-anchor* mechanism, extends to the stochastic setting without such error accumulation, in contrast to anchor-based algorithms. Consequently, we cleanly achieve $\mathcal{O}(\epsilon^{-3})$ complexity with iteration-independent batch size, without any variance reduction or double-loop recursive regularization, for stochastic root-finding (*resp.* fixed-point) problems with cocoercivity (*resp.* square-nonexpansivity) in expectation. For strongly monotone operators, the same algorithm attains a sharper $\widetilde{\mathcal{O}}(\epsilon^{-2})$ complexity, nearly matching the lower bound.

We study the degree-weighted work required to compute $\ell_1$-regularized PageRank using the standard one-gradient-per-iteration accelerated proximal-gradient method (FISTA). For non-accelerated local methods (ISTA), the best known worst-case work scales as $\widetilde{O} ((\alpha\rho)^{-1})$, where $\alpha$ is the teleportation parameter and $\rho$ is the $\ell_1$-regularization parameter. A natural question is whether FISTA can improve the dependence on $\alpha$ from $1/\alpha$ to $1/\sqrt{\alpha}$ while preserving the $1/\rho$ locality scaling. The challenge is that acceleration can break locality by transiently activating nodes that are zero at optimality, thereby increasing the cost of gradient evaluations. We analyze FISTA with respect to a less regularized objective and show that, under a checkable confinement condition, all spurious activations remain inside a boundary set $\mathcal{B}$. This yields a bound consisting of an accelerated $(\rho\sqrt{\alpha})^{-1}\log(\alpha/\varepsilon)$ term plus a boundary overhead $\sqrt{vol(\mathcal{B})}/(\rho\alpha^{3/2})$. We provide graph-structural conditions that imply such confinement. Experiments on synthetic and real graphs show the resulting speedup and slowdown regimes under the degree-weighted work model.

Although recent training-free acceleration methods have achieved promising speedups for Diffusion Transformers, most rely on historical features, either by directly reusing cached features or by forecasting future features from them. Such a history-to-future design can accumulate errors when the prediction horizon becomes long. To address this issue, we propose FuCa, a Cache-the-Future training-free acceleration framework. Instead of extrapolating future information solely from the past, FuCa caches sparsely computed future features and uses them as online revision signals. FuCa revises the latent-state update and the corresponding velocity, and then recovers skipped timesteps through lightweight interpolation. It requires no extra training or model-specific auxiliary modules, while keeping the number of DiT forward evaluations low. Experiments on FLUX.1-dev, Qwen-Image, Wan2.1-1.3B, and Hunyuan Video show that FuCa achieves up to about 5$\times$ speedup for image generation and more than 4.3$\times$ speedup for video generation, with higher reconstruction quality than existing training-free baselines.

Vector quantization is a fundamental primitive for scalable machine learning systems, enabling memory-efficient storage, fast retrieval, and compressed inference. Recent rotation-based quantizers such as EDEN, RabitQ, and TurboQuant have introduced strong guarantees and empirical performance, but the surrounding comparisons have been difficult to interpret because they rely on different distortion criteria, probability regimes, and implementation assumptions. As our first contribution, we provide a unified theoretical comparison of these methods and show that their relative advantages are criterion-dependent rather than absolute: TurboQuant is favorable for MSE distortion, EDEN is effective for expected inner-product distortion, and RabitQ provides strong high-probability control. This comparison clarifies the design principles behind each advantage and shows that no existing method uniformly dominates across the relevant measures. As our second contribution, we introduce *Block-Sphere Quantization* (**BlockQuant**), a new rotation-based block quantization algorithm designed around the spherical geometry of randomly rotated vectors. Unlike coordinate-wise quantizers, **BlockQuant** quantizes blocks on the sphere, preserving the geometry of rotated embeddings more faithfully. We prove that this block-spherical design improves expected distortion performance, including both reconstruction MSE and expected inner-product distortion. Experiments on real embedding data support these theoretical improvements.

Benchmark recovery is often treated as a deployment certificate for low-bit LLMs, but thresholded controller stacks ship a different object: a frozen score-to-action contract. This paper asks a narrower acceptance question: after quantization, does that interface survive independent threshold retuning against frozen FP16 labels, the strongest cheap repair an operator would plausibly try first? We study one fixed four-action controller, one frozen train/cal/report protocol, and four instruction-tuned checkpoints: Llama-3.1-8B/70B-Instruct and Qwen-2.5-7B/72B-Instruct. In the only score-carrying regime, W4A16, GPTQ + -search stays near FP16 on MMLU yet still leaves 11.9/10.9 percentage-point false tool-trigger rates and 16.1/15.4 aggregate FCR on the two large models. Because BFCL directly labels the tool frontier, that failure already establishes the paper's main acceptance claim even if FAQ and the preservation-only retrieve/stop frontiers are ignored. Aggregate FCR is reported only as interface-wide preservation context because retrieve/stop remain preservation-only. FAQ is included only as a bounded reducibility probe under the same frozen audit target, not as a generic new quantizer or the central novelty claim. FAQ lowers tool FTR and aggregate FCR without obvious MMLU or throughput collapse, but that is secondary non-collapse evidence. The contribution is therefore a single-controller deployment-acceptance counterexample under a frozen permission set: on the retained large-model W4A16 rows, benchmark-close MMLU recovery does not certify preserved tool-trigger behavior. The accompanying contribution is the freeze-and- retune audit protocol that makes that failure measurable.

Mixture-of-Experts (MoE) architectures scale model capacity through sparse expert activation, but their deployment remains memory-bound because all expert weights must reside in memory. Mixed-precision quantization can substantially reduce this footprint by assigning different bit-widths to different experts. Existing approaches, however, typically rely on calibration data to estimate expert importance and determine bit allocation. For frontier MoE LLMs, the original training data, and hence the true training distribution, is proprietary and inaccessible. As a result, calibration sets are inevitably imperfect surrogates, which can misestimate expert utilization and lead to suboptimal bit allocation. Motivated by the substantial cross-expert quality variability observed in modern MoE models, we propose AlphaQ, a calibration-free bit-allocation method for MoE quantization. AlphaQ draws on Heavy-Tailed Self-Regularization (HT-SR) theory and follows a simple principle: experts with more heavy-tailed weight spectra are typically better trained and should receive higher bit-widths, while experts with weaker heavy-tailed structure can be quantized more aggressively. AlphaQ operationalizes this principle by measuring expert-wise spectral heavy-tailedness and solving a budget-constrained optimization problem that minimizes total quantization error under a global bit-budget constraint. Across several MoE models, AlphaQ consistently outperforms calibration-based baselines under matched bit budgets. Notably, on Qwen1.5-MoE, AlphaQ achieves near full-precision accuracy with an average expert precision of only 3.5 bits, while delivering more than 4$\times$ memory compression.

We study convex optimization problems over a compact convex set where projections are expensive but a linear minimization oracle (LMO) is available. We propose the *adaptive conditional gradient sliding method* (AdCGS), a projection-free and line-search-free method that retains Nesterov's acceleration with adaptive stepsizes based on local Lipschitz estimates. AdCGS combines an accelerated outer scheme with an LMO-based inner routine. It reuses gradients across multiple LMO calls to reduce gradient evaluations, while controlling the subproblem inexactness via a prescribed accuracy level coupled with adaptive stepsizes. We prove accelerated rates for convex objective functions, matching projection-based methods, without relying on a projection oracle. For locally strongly convex objective functions, we further establish linear convergence without additional geometric assumptions on the constraint set, such as polytopes or strongly convex sets. Experiments on constrained $\ell_p$ regression, logistic regression, and least-squares problems demonstrate that AdCGS improves over projection-free baselines and provides competitive performance when projections are inexpensive.

Modern neural-network optimizers occupy a three-way design space: online adaptivity, architecture-aware geometry, and acceleration. We introduce AcceleGrad#, an accelerated linear-coupling template that couples an adaptive anchor with a norm-induced sharp, mirror, or linear-minimization geometry branch. The scalar-anchor specialization recovers the accelerated $O(1/K^2)$ rate for smooth convex objectives, while the diagonal-AdaGrad clipped-LMO training variant admits local $\mu$-Kurdyka-Lojasiewicz certificates: a generic conservative $O(K^{-1/4})$ rate and, in a SCION cross-entropy regime, a $O(K^{-1/3})$ last-iterate rate to a self-bounded mini-batch noise level. On image classification and language modeling, the training variant improves over Euclidean AcceleGrad and remains competitive with recent non-Euclidean optimizers. Using stochastic gradients directly in spectral oracles also reduces polar-computation time and optimizer overhead in practice.

Current LLM-for-GPU benchmarks largely measure CUDA fluency on isolated operators or short kernel-generation tasks, whereas practical GPU performance engineering often starts from trusted sequential CPU programs and requires correct, end-to-end acceleration. To fill this gap, we introduce \textsc{AccelEval}, a benchmark for whole-program CPU-to-CUDA acceleration. AccelEval contains 42 tasks derived from public repositories and established HPC/application suites across six domains, each equipped with deterministic correctness oracles and three input scales. Beyond pass/fail correctness, AccelEval reports end-to-end speedup over CPU baselines and a novel peak-attainment metric which normalizes each model’s speedup against the best correct solution. Using this framework, we evaluate eight frontier LLMs across multiple input scales, GPU architectures and sample rates. At pass@1 on NVIDIA H200 at medium scale, the strongest model passes 38/42 tasks at 71.2$\times$ geometric-mean speedup over the CPU baseline. On the subset of 11 tasks with human-written CUDA references, the best-of-8 LLM oracle reaches 0.75$\times$ of human CUDA performance. To make CUDA-optimization behavior interpretable and reusable, we decompose correct solutions into 43 CUDA acceleration patterns and show that feeding winner-derived pattern guidance back to models improves paired geometric-mean speedup by 1.78$\times$, compared with 1.18$\times$ for a generic-tips control. Together, these results establish AccelEval as a reproducible diagnostic platform for end-to-end LLM-assisted GPU acceleration. An anonymized open-source release is available at \url{https://anonymous.4open.science/r/AccelEval-2397}.

Block-wise post-training quantization (PTQ) compresses LLMs by minimizing per-block reconstruction error on a small calibration set. We show that the \emph{composition} of this set (200 samples) is a targeted lever at extreme bit widths, acting only on iterative methods. In a controlled study spanning six data-dependent PTQ methods plus a data-free baseline, six models (1.7B--8B) across three families plus 70B verification, three bit widths, and a 10-task evaluation with four-seed replication, we find a sharp \textbf{near-cliff method-class divide}. In each method's pre-cliff regime (where the model retains predictive function), iterative methods (SignRound~V2, OmniQuant, AQLM) gain 0.74--1.93pp on the 10-task average from switching Pile to a fragility-guided dataset (FragCal-DC), while single-pass analytical methods (GPTQ, AWQ) show near-zero response ($|\Delta|{\le}0.30$pp). Both classes are evaluated on functional Pile baselines (0.42--0.61, well above chance); above the cliff, every method becomes data-composition-insensitive. A reconstruction-loss paradox (the method that most reduces its proxy loss gains nothing downstream, while the method that barely moves the proxy gains the most) sharpens the mechanism; fixed-reference held-out evaluation confirms the proxy--downstream disconnect. A wrong-answer contamination ablation retains 87--91\% of the improvement and a data-dependent single-pass control (RTN-opt) shows zero response, isolating the iterative optimization loop. A weight-space probe shows SignRound-V2 preserves higher per-group scale heterogeneity than GPTQ on 9 of 9 (model, width) cells; a scale-flatten knockout shows this heterogeneity is necessary for iterative fidelity. We release FragCal-DC, the discriminative-task instance used here, as a drop-in JSON for the evaluated setting.