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NeurIPS 2026

On the Origin of Algorithmic Progress in AI: Evidence from Language Model Pre-Training

Hans Gundlach, Alex Fogelson, Jayson Lynch, Ana Trisovic, Jonathan S Rosenfeld, Anmol Rattan Singh Sandhu, Neil Thompson

Algorithms have been estimated to increase AI pretraining FLOP efficiency by a factor of $22,000$ between 2012 and 2023 (Ho et al., 2024) . Running ablation experiments on key innovations from this time period, we are able to account for less than $10\times$ of these gains at small compute scales. Surveying the broader literature, we estimate that additional innovations not included in our ablations also account for less than $10\times$, yielding less than $100\times$ efficiency gains total in low-compute regimes. This leads us to conduct scaling experiments, which reveal that much of this efficiency gap can be explained by algorithms with scale-dependent efficiency improvements. In particular, we conduct scaling experiments between LSTMs and Transformers, finding exponent differences in their compute-optimal scaling law while finding little scaling difference for many other innovations. These experiments demonstrate that -- contrary to standard assumptions -- an algorithm's efficiency gains are tied to compute scale. Using experimental extrapolation and literature estimates, we account for $3,360\times$ efficiency gains over the same time period, with scale-dependent innovations accounting for close to 90\% of log-efficiency gains by 2023. Our results indicate that algorithmic progress for small models has been far slower than previously assumed, and that measures of algorithmic efficiency are strongly reference-dependent.

NeurIPS 2026

On the Optimal Sample Complexity of Offline Multi-Armed Bandits with KL Regularization

Kaixuan Ji, Qiwei Di, Heyang Zhao, Qingyue Zhao, Quanquan Gu

Kullback-Leibler (KL) regularization is widely used in offline decision-making and offers several benefits, motivating recent work on the sample complexity of offline learning with respect to \emph{KL-regularized performance metrics}. Nevertheless, the exact sample complexity of KL-regularized offline learning remains largely from fully characterized. In this paper, we study this question in the setting of multi-armed bandits (MABs). We provide a sharp analysis of KL-PCB~(Zhao et al., 2026), showing that it achieves a sample complexity of $\tilde{O}(\eta SAC^{\pi^\*}/\epsilon)$ under large regularization $\eta = \tilde{O}(\epsilon^{-1})$, and a sample complexity of $\tilde{\Omega}(SAC^{\pi^\*}/\epsilon^2)$ under small regularization $\eta = \tilde{\Omega}(\epsilon^{-1})$, where $\eta$ is the regularization parameter, $S$ is the number of contexts, $A$ is the number of arms, $C^{\pi^\*}$ is the policy coverage coefficient at the optimal policy $\pi^*$, $\epsilon$ is the desired sub-optimality, and $\tilde{O}$ and $\tilde{\Omega}$ hide all poly-logarithmic factors. We further provide a pair of sharper sample complexity lower bounds, which matches the upper bounds over the entire range of regularization strengths. Overall, our results provide a nearly complete characterization of offline multi-armed bandits with KL regularization.

NeurIPS 2026

On the Nonlinearity of Learning Rate Scaling for LLM Training

Zaiwen Yang, Huaqing Zhang, Jing Xu, Jingzhao Zhang

Learning-rate transfer is critical for reducing the cost of training large language models: instead of sweeping learning rates at target scale, practitioners extrapolate from smaller runs. Existing approaches often assume that the optimal learning rate follows a log-linear scaling law in data scale and model size. We carefully examine and evaluate this scaling law. In our empirical study of GPT-2--style models from 22M to 407M parameters trained on 5B to 100B tokens, the optimal learning rate develops upward curvature at larger scales, leading to inaccurate extrapolation. We find that this curvature largely disappears when learning rates are replaced by effective learning rate (the step size in normalized weight space), and when data $D$ extrapolation is used instead of model size $N$ extrapolation. Next, we explain nonlinearity in scaling: weight-norm converges to equilibrium slower when optimal learning is small, requiring a larger step size to reduce the transient phase. Experiments with AdamH, which directly controls the effective learning rate, further support this explanation.

NeurIPS 2026

On the Nature of Attention Sink that Shapes Decoding Strategy in Omni-LLMs

Suho Yoo, Youngjoon Jang, Joon Son Chung

The goal of this paper is to strengthen the reasoning of Omnimodal Large Language Models (Omni-LLMs) at inference time, without additional training. These models jointly process video, audio, and text, and given the large number of tokens they consume, how attention is routed across them is central to their behaviour. We focus specifically on attention sinks, tokens that absorb a disproportionate share of attention mass regardless of their semantic content, to understand how this routing unfolds. To this end, we conduct a systematic analysis of sink behaviour in Omni-LLMs. Our analysis yields two key findings: (i) high sink attention does not solely indicate head redundancy, suggesting that sink value representations play additional functional roles; (ii) the sink value vector acts as a shared bias added to every token's output, serving as a global signal that organises the representation as a whole. Building on this, we propose OutRo, which correspondingly aligns non-sink token representations with the sink in feature space, and relaxes the causal mask for sink tokens at an early layer to sharpen this bias before the rest of decoding proceeds. This design enhances the reasoning process without requiring additional forward passes or access to attention maps. Based on extensive experiments, OutRo consistently improves performance on seven video QA benchmarks and demonstrates strong generalisation, while incurring only a 1.1\x decoding overhead.

NeurIPS 2026

On the Meta-Design of Allocation Problems

Unai Fischer Abaigar, Emily Aiken, Christoph Kern, Juan C Perdomo

There is an extensive literature that studies how to find optimal policies in resource allocation problems, taking the underlying design parameters that define the allocation, such as what data is collected, how many people can be served, and quality of service as fixed constraints. Yet, from a planner's perspective, these design parameters are themselves optimization variables that are just as important in determining overall welfare as selecting the optimal targeting rule for a given set of constraints. This realization motivates a rich set of meta-design questions exploring how planners should make principled decisions about investments in prediction, capacity constraints, and treatment quality, all of which lie upstream of classical policy optimization. Building on initial theoretical work in this space, our paper has three main contributions. First, we formally define the broad meta-design space of resource allocation problems. Second, we develop empirical tools that enable practitioners to reliably navigate it. Third, we demonstrate the framework in two real-world case studies on German employment services and targeted cash transfer programs in Ethiopia.

NeurIPS 2026

On the Memorization of Consistency Distillation for Diffusion Models

Bingqing Jiang, Difan Zou

Diffusion models are central to modern generative modeling, and understanding how they balance memorization and generalization is critical for reliable deployment. Recent work has shown that memorization in diffusion models is shaped by training dynamics, with generalization and memorization emerging at different stages of training. However, deployed diffusion models are often further distilled, introducing an additional training phase whose impact on memorization remains unclear. In this work, we analyze how distillation reshapes memorization behavior in diffusion models, taking consistency distillation as a representative framework. Empirically, we show that when applied to a teacher model that has memorized data, consistency distillation significantly reduces transferred memorization in the student while preserving, and sometimes improving, sample quality. To explain this behavior, we provide a theoretical analysis using a random feature neural network model [Bonnaire et al., 2025], showing that consistency distillation suppresses unstable feature directions associated with memorization while preserving stable, generalizable modes. Our findings suggest that distillation can serve not only as an acceleration tool, but also as a mechanism for improving the memorization-generalization trade-off.

NeurIPS 2026

On the Limits of Latent Reuse in Diffusion Models

Yifeng Yu, Lu Yu

Diffusion models are often trained in low-dimensional latent spaces, which are then reused for related but shifted datasets. In this work, we study when such latent reuse remains reliable under distribution shift. We consider a source-target setting in which both datasets are approximately low-dimensional but may lie near different subspaces. We show that freezing and reusing a source latent space induces a target-domain score error governed by two quantities: the principal-angle misalignment between the source and target subspaces, and the target ambient noise amplified by the diffusion time scale. Motivated by these limits, we further study mixed source-target training and characterize how the required shared latent dimension depends on the relative geometry of the two distributions. Our results provide theoretical guidance on when latent reuse is reliable and when learning a shared representation may be necessary.

NeurIPS 2026

On the Last-Iterate Convergence of Clipped Gradient Methods

Zijian Liu

In stochastic (strongly) convex optimization, establishing last-iterate convergence guarantees for first-order methods has recently garnered increasing attention, as this not only deepens the theoretical understanding of these algorithms but also aligns more closely with practice. Notably, people have demonstrated that one of the most famous, simple, and popular methods, Stochastic Gradient Descent ($\mathtt{SGD}$), provably achieves last-iterate convergence. However, the existing results may have limited applicability, since they typically rely on strong conditions on the gradient noise (e.g., an exponentially decaying tail) rather than the more realistic heavy-tailed noise. Unfortunately, when faced with heavy-tailed noise, $\mathtt{SGD}$ is known to exhibit undesirable behavior or even fail to converge. To address the challenge of heavy-tailed noise, people have proposed $\mathtt{Clipped}\text{-}\mathtt{SGD}$, an algorithm that combines $\mathtt{SGD}$ with a simple mechanism, gradient clipping. Although $\mathtt{Clipped}\text{-}\mathtt{SGD}$ performs well in practice, its last-iterate convergence property remains highly underexplored. In this work, we prove the first optimal last-iterate rates in high probability for $\mathtt{Clipped}\text{-}\mathtt{SGD}$ under heavy-tailed noise, thereby closing a gap in the literature.

NeurIPS 2026

On the Information Loss of Multi-Token Prediction: Origin and Solution

Tangyu Jiang, Zhanke Zhou, Haodi Wang, Yiu-ming Cheung, Xiaohua Jia, Bo Han

Multi-token prediction (MTP) accelerates autoregressive decoding through blockwise prediction, but remains vulnerable to error accumulation across sequentially generated blocks. Existing work primarily focuses on improving MTP’s acceleration ratio while largely overlooking the compounding errors that accumulate during block-wise generation. In this work, we study MTP from an information-theoretic perspective and identify the strength of inter-block dependencies as a key factor governing its performance. Building on the cumulative information loss, we theoretically quantify the gap of block-sequence representation. Motivated by the analysis, we propose Dual-MTP, a novel MTP training framework that explicitly models inter-block dependencies from two complementary perspectives, thus reducing the block-sequence representation gap across decoding steps. Specifically, Dual-MTP introduces a dual-perspective training objective with random masking, where each block is jointly trained for forward prediction and masked context reconstruction, encouraging robust block-level representations. Experiments across five model backbones and six tasks spanning math reasoning and GLUE understanding show that Dual-MTP consistently outperforms standard MTP on both quality and efficiency, attaining the highest average accuracy on every backbone with gains of +0.3 to +3.0 points and a 1.4× to 1.9× wall-clock speedup over standard autoregressive decoding.

NeurIPS 2026

On the Importance of Gating: Memorization vs. In-Context Learning in State Space Models

William Tong, Aryo Lotfi, Emmanuel Abbe, Konstantinos Vaggelakos, Vishnu Banna, Etai Littwin, Joshua Susskind, eran malach

State Space Models (SSMs) have emerged as a compelling alternative to Transformers, enabling sequence modeling with constant memory and linear compute. While SSMs excel in certain settings like length generalization, they continue to lag behind Transformers on tasks that require in-context learning and precise retrieval, slowing their adoption for large-scale language modeling. In this work, we demonstrate that both the success and failure of SSMs in these domains can be explained by studying the role of the gating mechanism, a prevalent component in modern recurrent networks. Specifically, we show through theory and experiments that this gating mechanism causes SSMs to first learn an in-weights ``memorization'' solution, while delaying, or even preventing, convergence to a correct in-context learning solution. Importantly, this happens even in cases where there are no fundamental limitations due to the architecture or its memory capacity. On the other hand, we find that gating is often beneficial for improving generalization to long sequence lengths. Our results illuminate the crucial role of the gating mechanism in shaping both the training dynamics and generalization of SSMs, and provide a basis for understanding and improving linear-time models.

NeurIPS 2026

On the Impact of Side-Information in Bandit Learning: More is Not Always Merrier

Ramakrishnan Krishnamurthy

More data is commonly assumed to improve learning performance. We show that this intuition can fail in sequential decision-making. Motivated by multi-agent collaborative learning, we study stochastic bandits with exogenous side information, and ask if free and unbiased reward samples are guaranteed to reduce regret. We introduce a formal notion of non-degradation under side information and demonstrate that the widely used UCB algorithm violates this property: there exist benign side-information designs under which UCB incurs strictly higher regret than when run without side information. We contrast this behavior with Thompson Sampling and Explore-Then-Commit, which benefit from the same information. Constructively, we further propose a meta-algorithm that enforces non-degradation for a broad class of bandit algorithms. Finally, experiments in recommender systems scenarios show that data sharing among different groups of users under UCB can yield diminishing and even negative returns for individual groups.

NeurIPS 2026

On the Geometry and Latent-Space Composition of Hypernetwork-Generated LoRAs

Yanlai Yang, Minki Kang, Divyam Madaan, Sung Ju Hwang, Mengye Ren

Recent work proposes hypernetworks that convert a document into a low-rank parameter update (LoRA) in a single forward pass, enabling fast injection of new knowledge into a frozen LLM. However, storing separate LoRA adapters for each document can be unsustainable in streaming settings. In this paper, we study the problem of composing hypernetwork-generated LoRAs using two representative systems, Doc-to-LoRA and SHINE. We show that hypernetwork-generated LoRAs have a geometry sharply different from directly fine-tuned LoRAs. Hypernetwork-generated LoRAs are highly spectrally concentrated and strongly aligned, while next-token prediction and QA fine-tuned adapters are diffuse and nearly orthogonal across documents. This suggests that hypernetwork-generated LoRAs are not arbitrary low-rank weight updates, but decoded points on a structured adapter manifold. Guided by this observation, we propose latent-space LoRA merging: instead of merging in the weight space, we compose the intermediate hypernetwork latents and then decode the merged latent through the frozen LoRA-generation head. We show that latent-space merging techniques consistently improve over weight-space and factor-space baselines while preserving a single fixed-rank adapter. These results establish latent-space composition as a promising mechanism for bounded accumulation of hypernetwork-generated LoRAs in long document sequences.

NeurIPS 2026

On the Fragility of Latent Knowledge: Layer-wise Influence under Unlearning in Large Language Model

Jianing Zhu, Zongze Li, Chandler Squires, Qizhou Wang, Bo Han, Pradeep Ravikumar

Large language model (LLM) unlearning has emerged as an essential post-training mechanism for erasing specific knowledge or undesirable behaviors. However, forgetting target data often causes an unintended degradation in overall model utility. Although various advanced methods have explored different learning objectives to mitigate the trade-off, it remains unclear how the highly entangled internal representations in LLMs contribute to unlearning. In this work, we introduce the notion of latent knowledge fragility to explore the vulnerability of retained knowledge to unlearning. We develop a unified analytical approach via component-wise parameter patching that isolates and quantifies fragility in terms of different transformer blocks. We observe that the LLM encodes different levels of abstraction, from surface syntax in shallow layers to complex semantics in deeper layers, which align with different degrees of representation disruption and utility degradation. Based on the insights, we propose a lightweight framework called Component-wise Replacement Unlearning (CRU) that restores fragile layers (also extendable to other components) from the original model based on post-hoc validation, which allows us to obtain a hybrid model without additional training. Extensive experiments on various aspects verify that CRU generally improves the trade-off between removal and retention with non-uniform unlearning influence.

NeurIPS 2026

On the Existence of Uniformly Optimal Policies in MDPs under Epistemic Uncertainty

Axel Benyamine, Julien Grand Clement, Marek Petrik, Michael Jordan, Alain Durmus

We study the existence of uniformly optimal stationary policies, which are optimal for any starting distribution in Markov Decision Processes (MDPs) under epistemic (parameter) uncertainty within two complementary frameworks. For robust MDPs, we establish that (s- and sa-) rectangular models are equivalent to the existence of uniformly optimal stationary policies and provide several interesting counterexamples, including a simple r-rectangular instance with only history-dependent optimal policies. For ambiguity-averse MDPs where the uncertain transition kernel is a random variable, and the return is evaluated via a law-invariant risk measure, we show that uniformly optimal stationary policies can only exist for the essential supremum or essential infimum (under mild monotone continuity assumptions), thus excluding other risk measures such as CVaR, VaR, and the Entropic Risk Measure. We conclude our work by relating dynamic programming and the existence of uniformly optimal policies. One of the main takeaways of our impossibility results is the need for new models to go beyond uniformly optimal stationary policies.

NeurIPS 2026

On the Effect of Token Correlations on Semantic Transfer in Transformers

Nevena Lazic, Julian Zimmert, Alan Malek, Tor Lattimore, Csaba Szepesvari, Andras Gyorgy

We study issues which may arise when using transformer models to formally reason about problems stated informally using natural language. In particular, we focus on transfer learning between tasks that are semantically equivalent but phrased differently. We assume that examples with a particular target label are only available for a subset of tasks, and aim to transfer zero-shot the ability to predict this label to other tasks. Using controlled experiments on propositional logic problems, we show that transformers are capable of such transfer, but that it can be impeded by the presence of task-specific tokens, due to the model picking up on correlations between these tokens and the label early in the training. As a simple solution, we show that introducing the target label later in the training dramatically improves transfer.

NeurIPS 2026

On the Design Space of Discrete Diffusion Online Adaptation for Molecular Optimization

Trevor Chen, Ariel Dai, Jason Yang, Riccardo De Santi, Daniel Khalil, Wenda Chu, Nate Gruver, Pranav Murugan, Alexander Goldberg, Maruan Al-Shedivat, Yisong Yue

We study how to design online optimization loops for molecular optimization via adaptation of pre-trained generative models. At test time, we aim to utilize limited oracle feedback to steer generation toward top-molecules achieving high rewards. This creates a design problem coupled across several dimensions, including which candidates receive oracle evaluations, how observed rewards are utilized for model update, and how to overcome pre-trained model biases–to effectively explore over complex design spaces. Despite recent algorithmic progress on each individual component, it remains unclear how they interact in practice, within real-world online adaptation loops. For instance, top-$K$ optimization objectives may make adaptation overly greedy and thereby reduce exploration, while model-debiasing techniques may be unnecessary when exploration is already induced by exploratory acquisition functions, e.g., Thompson sampling. To address this, we conduct a controlled study on discrete-diffusion molecular optimization, finding that well-designed components remain beneficial when combined, indicating that they tackle complementary issues. Together, these components yield an online fine-tuning recipe that outperforms offline fine-tuning and search-augmented baselines across several small-molecule binding affinity and protein fitness optimization tasks, under equal oracle-call budgets and GPU-hour accounting.

NeurIPS 2026

On the Depth of Monotone ReLU Neural Networks and ICNNs

Egor Bakaev, Florestan Brunck, Christoph Hertrich, Daniel Reichman, Amir Yehudayoff

We study two models of $\mathsf{ReLU}$ neural networks: monotone networks ($\mathsf{ReLU}^+$) and input convex neural networks ($\mathsf{ICNN}$). Our focus is on expressivity, mostly in terms of depth and our motivation is to gain better understanding of depth requirement needed to exactly represent functions in terms of neural networks with ReLU activations: a subject that has received a lot of attention lately. We prove several lower bounds on the depth required to represent functions by monotone ReLU networks and $\mathsf{ICNN}$. For the maximum function $\mathsf{MAX}_n$ computing the maximum of $n$ real numbers, we show that $\mathsf{ReLU}^+$ networks cannot compute $\mathsf{MAX}_n$, or even approximate it. We prove a sharp $n$ lower bound on the $\mathsf{ICNN}$ depth complexity of $\mathsf{MAX}_n$. We also prove depth separations between $\mathsf{ReLU}$ networks and $\mathsf{ICNN}$s; for every $k$, there is a depth-$2$ $\mathsf{ReLU}$ network of size $O(k^2)$ that cannot be simulated by a depth-$k$ $\mathsf{ICNN}$. The proofs combine ideas from some structural results for $\mathsf{ReLU}^+$ networks.

NeurIPS 2026

On the Convergence of Success Conditioning for Policy Optimization

Matthew Brun, Andy Sun

Success conditioning is a strategy for improving decision-making policies in stochastic environments; it updates a policy by increasing the probability of taking actions that yield successful outcomes. Success conditioning is common to many reinforcement learning applications, yet its limiting behavior and convergence rates are not well understood. In this work, we demonstrate that success conditioning converges to an optimal policy on a broad class of Markov decision processes (MDP). We also derive convergence rates in some common settings. For discounted MDPs, we prove convergence within $\mathcal{O}(1/\varepsilon^p)$ iterations to an $\varepsilon$-optimal policy, where the exponent $p$ depends on problem data. For single-period MDPs, $\mathcal{O}(1/\varepsilon)$ iterations are required.

NeurIPS 2026

On the Convergence of Multicalibration Gradient Boosting

Daniel Haimovich, Fridolin Linder, Lorenzo Perini, Niek Tax, Milan Vojnovic

Multicalibration gradient boosting has recently emerged as a scalable method that empirically produces approximately multicalibrated predictors and has been deployed at web scale. Despite this empirical success, its convergence properties are not well understood. In this paper, we provide computational guarantees for multicalibration gradient boosting algorithms. We show that the magnitude of successive prediction updates decays at $O(1/\sqrt{T})$, which implies the same convergence rate bound for the empirical multicalibration error over rounds. Under additional smoothness assumptions on the weak learners, this rate improves to linear convergence. We further establish convergence for adaptive variants. Experiments on real-world datasets support our theory and clarify the regimes in which the method achieves fast convergence.

NeurIPS 2026

On the Construction and Implications of Low-Loss Valleys in LoRA-based Bayesian Inference

Daniel Dold, Emanuel Sommer, Julius Kobialka, Oliver Dürr, David Rügamer

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.

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