NeurIPS 2026 Papers

Value alignment of Large Language Models (LLMs) requires us to empirically measure these models' actual, acquired representation of value. Among the characteristics of value representation in humans is that they distinguish among value of different kinds. We investigate whether LLMs likewise distinguish three different kinds of good: moral, grammatical, and economic. By probing model behavior, embeddings, and residual stream activations, we report pervasive cases of value entanglement: a conflation between these distinct representations of value. Specifically, both grammatical and economic valuation was found to be overly influenced by moral value, relative to human norms. This conflation was repaired by selective ablation of the activation vectors associated with morality.

Large Language Models (LLMs) have achieved remarkable progress across a wide range of tasks, but remain vulnerable to safety risks such as harmful content generation and jailbreak attacks. Existing safety techniques---including external guardrails, inference-time guidance, and post-training alignment---each face limitations in balancing safety, utility, and controllability. In this work, we propose UpSafe℃, a unified framework for enhancing LLM safety through safety-aware upcycling. Our approach first identifies safety-critical layers and upcycles them into a sparse Mixture-of-Experts (MoE) structure, where the router acts as a soft guardrail that selectively activates original MLPs and added safety experts. We further introduce a two-stage SFT strategy to strengthen safety discrimination while preserving general capabilities. To enable flexible control at inference time, we introduce a safety temperature mechanism, allowing dynamic adjustment of the trade-off between safety and utility. Experiments across multiple benchmarks, base model, and model scales demonstrate that UpSafe℃ achieves robust safety improvements against harmful and jailbreak inputs, while maintaining competitive performance on general tasks. Moreover, analysis shows that safety temperature provides fine-grained inference-time control that achieves controllable trade-off between utility and safety. Our results highlight a new direction for LLM safety: moving from static alignment toward dynamic, modular, and inference-aware control. Code: https://anonymous.4open.science/r/UpCycle-70B3.

Canonical Correlation Analysis (CCA) is a fundamental method for multiview shared space learning. However, its strict reliance on paired data poses a significant limitation, as such data is often difficult to obtain or entirely unavailable. In this paper, we present Unpaired CCA (UCCA), a novel method that learns linear projections to maximize the correlation of the true underlying pairing without access to any paired samples during training. We first establish theoretical results connecting the Quadratic Assignment Problem (QAP) to CCA. Leveraging these theoretical insights, we derive a practical method to maximize correlation exclusively from unpaired data. To the best of our knowledge, UCCA is the first approach to learn maximally correlated projections in a strictly unpaired setting. We validate UCCA on real-world multi-modal datasets, demonstrating that it significantly outperforms recent unpaired alignment baselines in recovering the underlying true correlation. This work fills a critical gap between traditional statistical multiview learning and the growing field of unpaired data learning.

Pruning and quantization are two dominant techniques that effectively address the computational and storage burdens of large language model (LLM) inference on edge devices. Recently, one-shot pruning has gained particular attention for its ability to identify weight supports via optimization without retraining. However, integrating such methods seamlessly with quantization for further model lightweighting is non-trivial. The discreteness of quantization shatters their required variable continuity, inevitably collapsing this integration into a decoupled pruning-quantization pipeline with inherently suboptimal outcomes. To tackle this problem, we propose Quantization-aware One-shot Pruning (QOP), which directly optimizes the quantized weights under sparsity and discreteness constraints, thereby explicitly capturing the impact of quantization on pruning within its objective. Specifically, QOP generalizes the alternating direction method of multipliers to sparse-constrained discrete optimization, enabling the identification of the high-quality support and the update of quantized weights. Theoretically, via the well-conditioned approximation obtained by a slight perturbation, we establish convergence to a stationary feasible point and provide the convergence rate. Extensive experiments across various LLMs, sparsity levels, and quantization settings demonstrate that QOP consistently outperforms existing baselines in terms of both average accuracy and perplexity under weight quantization.

We analyze generalization error, uniform stability, and uniform argument stability of gradient descent (GD) and stochastic gradient descent (SGD) over discrete parameter spaces, where each update involves deterministic or stochastic rounding. We show that deterministic rounding degrades the generalization error of GD on convex, Lipschitz, and smooth loss functions, increasing the rate from $O(T/n)$ to $O(T/\sqrt{n})$, and establish matching lower bounds. We further prove that uniform stability of GD becomes $\Omega(T)$, showing that stability-based generalization bounds are vacuous in this setting. In contrast, for the same losses, stochastic gradient descent with deterministic rounding admits nontrivial uniform stability guarantees, which differ qualitatively from the real-valued case and exhibit distinct dependencies on the number of iterations and the dimension: we prove tight bounds $O(T/n)$ for one dimension and $O(T^2/n)$ for higher dimensions. We also show that stochastic rounding can introduce generalization error that increases with the dimension; such a phenomenon is absent in standard real-valued optimization and in the deterministic rounding case. Finally, we provide upper bounds on uniform argument stability for stochastic rounding schemes and show that these bounds are tight when the loss can be represented as a sum of coordinate-wise functions.

Spectral gradient descent (SpecGD) orthogonalizes matrix parameter updates and has inspired practical optimizers such as Muon. They often perform well in large language model training, but their dynamics remain poorly understood, especially in factorized parameterizations where the product matrix does not receive orthogonalized updates. We study such dynamics through matrix factorization (MF), where the orthogonalization is applied separately to the factor updates. We analyze spectral gradient flow (SpecGF)—a continuous-time analog of SpecGD—in the low-rank MF setting and prove "equal-rate" dynamics: all singular values grow at equal rates up to small deviations. Consequently, smaller singular values attain their target values earlier than larger ones, contrasting with the largest-first stepwise learning observed in standard gradient flow. Moreover, we prove that SpecGF in our setting converges to global minima from almost all initializations, provided the factor norms remain bounded; with $\ell_2$ regularization, we obtain global convergence. Empirically, we observe that LoRA fine-tuning with orthogonalization-based optimizers including Muon exhibit near-uniform growth in the product of LoRA adapters, consistent with the mechanism predicted by our MF analysis.

Graph Neural Networks (GNNs) have demonstrated remarkable effectiveness on graph-based tasks. However, their predictive confidence is often miscalibrated, typically exhibiting under-confidence, which harms the reliability of their decisions. Existing calibration methods for GNNs normally introduce additional calibration components, which fail to capture the intrinsic relationship between the model and the prediction confidence, resulting in limited theoretical guarantees and increased computational overhead. To address this issue, we propose a simple yet efficient graph calibration method. We establish a unified theoretical framework revealing that model confidence is jointly governed by class-centroid-level and node-level calibration at the final layer. Based on this insight, we theoretically show that reducing the weight decay of the final-layer parameters alleviates GNN under-confidence by acting on the class-centroid level, while node-level calibration acts as a finer-grained complement to class-centroid level calibration, which encourages each test node to be closer to its predicted class centroid at the final-layer representations. Extensive experiments validate the superiority of our method.

Population analysis methods have become standard for navigating the complexity of neural data. However, these methods often assume a rate code, neglecting information encoded in the precise timing of spikes. Critically, additional information encoded in bursts of action potentials may be missed. Here, we develop a factor analysis method that disentangles the factors associated with bursts and individual spikes. This enables burst codes to be investigated directly from the structure of the data, without requiring external covariates. We demonstrate that analyzing firing rates alone obscures the latent structure and factors underlying bursts. Applying our method to simulated and experimental data, we show that it can infer the correct latent structure and be used to test for the presence of burst coding. By merging the population and burst coding perspectives, we provide a framework for linking changes in bursting to internal variables involved in attention, perception, and learning.

Large language models can have hidden propensities: behaviours that arise only in rare contexts. These hidden propensities pose a challenge to alignment audits, which seek to uncover problematic model behaviour but are limited in scope to scenarios anticipated by the auditor. To address this challenge, we explore _limited-parameter finetuning_ (LPF) on examples of a target behaviour. While training 3–15\% of model parameters, LPF reveals whether the model has a hidden propensity, even when standard behavioural evaluations cannot. LPF succeeds on a suite of model organisms with hidden propensities (8B-14B parameters), and also surfaces naturally occurring hidden propensities in open-weight models (27-32B parameters). LPF can thus distinguish between behaviourally equivalent models, even without knowing the context in which the propensity surfaces. LPF provides a novel affordance that may be useful for auditing frontier AI models.

Direct Preference Optimization (DPO) offers a streamlined one-stage alternative to Reinforcement Learning from Human Feedback (RLHF). However, our theoretical analysis reveals a structural distinction between the two: DPO and RLHF optimize alignment on different data distributions with different supervision sources. Specifically, DPO learns from ground-truth human preferences but within the off-policy support of an offline dataset, while RLHF optimizes on the on-policy rollouts but learns from pseudo-labels produced by a reward proxy. This distinction explains how each method may fail: DPO alignment collapses when the policy drifts away from the offline dataset support, and RLHF alignment is biased due to the extrapolation error of the reward proxy on out-of-distribution rollouts. Effective alignment requires avoiding both failure modes, which neither method can do alone. We achieve this via a semi-supervised alignment objective: ground-truth preferences anchor alignment within the dataset support, and pseudo-labels on online rollouts extend it beyond. Applying DPO's reward reparameterization to this objective yields Ultra-DPO, a one-stage algorithm that augments direct human alignment with an online self-alignment mechanism. Across multiple benchmarks, Ultra-DPO consistently outperforms DPO, RLHF, and online preference learning methods.

Sampling from a softmax distribution is a fundamental operation in machine learning, but its linear complexity in the number of items makes exact sampling impractical at scale. Two-level softmax (2LS) sampling is a popular alternative enabling sublinear-time sampling. Assuming items are partitioned into clusters, 2LS first samples a cluster and then an item within it. In this paper, we show that, despite its advantages, 2LS introduces systematic and undesirable sampling biases, which arise from misweighting clusters by ignoring both cluster size imbalance and intra-cluster similarity dispersion. We propose two sampling methods, Size-Corrected 2LS (S-2LS) and Size- and Dispersion-Corrected 2LS (SD-2LS), which correct these biases and provide provably better softmax approximations with negligible to non-existent computational overhead. In-depth experiments on five large-scale datasets validate the improved sampling properties of our methods. We recommend their consistent use in place of standard 2LS in future work.

Training loss and accuracy are the standard signals used to monitor generalization during deep neural network training. Two well-documented phenomena complicate this picture: in grokking, train loss falls rapidly while test performance improves abruptly only after a long delay; in epoch-wise double descent, train loss decreases monotonically while test loss or error rises and falls. Existing accounts are often task-specific, and a task-agnostic analysis framework for diagnosing and explaining these phenomena across realistic tasks and architectures is missing. We address this challenge by analyzing two competing processes that underlie learning dynamics: representation learning in the encoder and readout calibration in the final classifier. Using tools from representational geometry, neural tangent kernels, and linear probing, we show that both processes are active throughout training, with the fluctuations of their relative speed giving rise to seemingly anomalous generalization dynamics. Applying the representation-readout decomposition to grokking across a wide range of tasks and architectures, we find that the readout is train-biased before grokking onset, and representation learning is gradual but not absent—contrary to the lazy-to-rich account. The framework further provides diagnostic signatures distinguishing spurious from genuine generalization: in a previously reported MNIST grokking example and an epoch-wise double descent example, apparent delayed or non-monotone generalization is shown to arise from representation degradation and readout misalignment induced by non-standard training recipes. Together, these results establish the representation-readout decomposition as a top-down framework for understanding learning dynamics and revealing underlying algorithms for interpretability research.

To lower the expertise barrier in machine learning, the AutoML community has focused on the CASH problem, which jointly automates algorithm selection and hyperparameter tuning. While traditional methods like Bayesian Optimization (BO) struggle with cold-start issues, Large Language Models (LLMs) can mitigate these through semantic priors. However, existing LLM-based optimizers generalize poorly to high-dimensional, structured CASH spaces. In this paper, we propose LB-MCTS, a trajectory-structured optimization framework that uses a Monte Carlo Tree Search tree as a shared state for algorithm selection, hyperparameter refinement, and BO–LLM proposer synergy. Within this shared state, BO provides algorithm-specific surrogate modeling for quantitative search, while the LLM exploits path-aware selective memory to generate semantic proposals and reflections. As the surrogate model improves, a reliability-aware proposer policy adaptively shifts from LLM-driven to BO-driven proposals within a unified search trajectory. Experiments on 104 AMLB datasets demonstrate that LB-MCTS consistently outperforms BO-based, LLM-based, and hybrid baselines.

We study $N$-armed stochastic dueling bandits under the Condorcet-winner assumption, where three widely adopted objectives are considered: best-arm identification (BAI), weak regret, and strong regret. We propose *Tree-Guided Identify-Then-Exploit (TG-ITE)*, the first unified framework to tackle all these objectives to our knowledge. Without requiring stronger assumptions, we propose a shared tree-guided identification approach to find a high-confidence incumbent within $O(N)$ comparisons. We further propose varied exploitation strategies to utilize this warm-start stage to optimize the specific objectives at hand. This methodology enables our approach to (1) achieve $O(N)$ sample complexity in BAI without commonly adopted stronger assumptions; (2) build the first winner-stays-style algorithm to achieve $O(N)$ weak regret; (3) enjoy the same $O(N \log T)$ guarantee as specialized strong-regret approaches; (4) realize the joint optimization of BAI and weak regret with $O(N)$ guarantees for both, eliminating the sub-optimal gap of $O(\log N)$ in the existing approach. Our results provide evidence that the trade-off between BAI and regret minimization is relatively benign in dueling bandits.

It is widely recognized that in many applications, strong predictive performance is not enough to warrant use of a learned model. Additionally, it is required to ascertain whether the model conforms to certain properties such as fairness, robustness or safety. Unfortunately, most learning approaches are not guaranteed to produce a model that adheres to these properties. Model repair addresses this through a post-hoc debugging loop. Approaches such as verification are used to check if the desired property holds for a model; if not they return a counterexample which is used to modify or repair the ML model. We propose a novel repair method for tree ensembles. Our approach is based on a MILP encoding where the objective is to modify the leaf values in the tree ensemble such that it fixes the counterexamples while at the same time preserves predictive performance. The use of constrained optimization over the model parameters is compelling as it is guaranteed to fix a given set of counterexamples. We implement and evaluate our method in two use-case scenarios, classification requiring fairness and action policies in MDPs requiring safety. Results show that our MILP repair of tree ensembles can be feasible computationally, and is often successful in improving the desired property while not degrading performance.

Large language models are increasingly deployed in decisions that require culture-dependent moral judgements, yet they answer as if the whole world thinks with a Western mindset. The Moral Machine experiment showed this is wrong at scale: 40 million judgments across 233 countries reveal that moral preferences are systematically structured by culture, and a model that ignores this variation does not merely underperform, but also imposes one society's intuitions on all others. Existing fixes do not scale to global deployment, as fine-tuning needs per-country preference data and GPU budgets, reward-guided decoding needs per-country reward models, and activation steering needs access to model internals that black-box APIs do not expose. In this work, we focus on this realistic inference-time regime, with no weight updates, no training data, and no internal access. The key observation is that within-country demographic disagreement, not consensus, is the steering signal. When culturally grounded personas agree, the base model is already calibrated. But when they disagree, the spread tells us what to fix and how. We propose DISCA (Disagreement-Informed Steering for Cultural Alignment), which instantiates each country as a panel of four World-Values-Survey-grounded persona agents, converts their disagreement into a bounded, loss-averse correction whose magnitude is set by the panel's variance, and shrinks the correction toward zero when the estimate is unreliable. Across 20 countries and 7 open-weight backbones (2B–70B) from five model families, DISCA reduces cultural misalignment on MultiTP by 10–24% on binary moral dilemmas and 2–7% on open-ended scenarios. Furthermore, a smaller 14B backbone with DISCA reaches lower absolute misalignment than a vanilla 70B model.

Modifying 3D assets requires enacting targeted structural transformations while strictly preserving the geometric identity of unedited regions. While recent probability flow models enable training-free editing, bounding these modifications within a high-dimensional latent space presents severe mathematical challenges. Current inversion-free trajectories rely on global velocity updates, which consistently result in spatial bleed into preserved structures and induce trajectory under-commitment, causing edits to stall mid-path. To resolve these dual failures, we introduce FocusFlow, a segmentation-free framework that structures the integration trajectory into two disjoint phases. During early coarse structure formation, FocusFlow applies Feature-Divergence Localization (FDL) to spatially gate the velocity field using intrinsic cross-attention. During late-stage fine-detail refinement, Reference-Guided Generation (RGG) drives topological convergence by pulling the trajectory toward an explicit clean-latent target. Evaluated on the joint Google Scanned Objects and PartObjaverse-Tiny benchmarks, FocusFlow breaks the traditional preservation-modification trade-off. It achieves superior structural preservation while maximizing edit magnitude. By providing stable, localized geometric control without manual spatial annotations, this phase-scheduled approach removes significant technical barriers to the precise modification of synthetic 3D media.

Recently, Muon has gained substantial attention as an appealing alternative to Adam, with many works highlighting its advantages through spectral normalization and improved conditioning. Yet this positive theoretical narrative contrasts with its empirical performance in large language model (LLM) training, where Muon’s gains over Adam/AdamW are often mixed, schedule-sensitive, and not uniformly superior. To address this gap, we develop a trajectory-level theory characterizing both the strengths and limitations of Muon. We introduce a mixed-spiked matrix sensing model whose sensing operator decomposes into signal, spike, and bulk components, capturing a mixture of anisotropic structure and long-tail information reminiscent of LLM training. On top of it, we adopted a river-valley perspective in which we view the landscape as composed of a river direction flowing to the desired solution and hill directions encoding nuisance or task-irrelevant information. In the momentum-free setting, we show that Muon moves faster along the information-bearing river direction during early optimization, but can converge much more slowly near the river bottom than gradient descent. We then extend the river-valley perspective to general nonconvex objectives with momentum by studying points on the spectral river. There, while Muon converges faster early on, its orthogonalized update removes residual scale information, making it prone to overshooting and oscillation near the target solution. Together, these results suggest that our characterizations extend beyond spiked matrix sensing and motivate switching to GD-like refinement optimizers in the final phase, rather than relying only on a fixed learning-rate schedule for Muon. We also provide preliminary evidence supporting this two-stage approach in language model training experiments.

Large Language Models (LLMs) are increasingly deployed in real-world settings where alignment with diverse human values is essential. However, existing alignment methods are often costly, obscure underlying value heterogeneity, and offer limited interpretability. In this work, we move toward multi-human-value alignment through inference-time intervention by investigating how different values are internally represented within LLMs. We propose a probing-based value localization framework that identifies value-sensitive components, i.e., value heads, which mediate model behavior across multiple moral and normative dimensions such as harmlessness, honesty, and helpfulness. Analyses across multiple LLM families reveal that value heads are universally sparse and exhibit structured interactions, including conflicts among certain values. These components demonstrate clear functional specialization: selectively ablating value heads induces substantial and value-specific behavioral changes. Building on these findings, we introduce an inference-time intervention strategy that enables controllable adaptation of LLMs to single or multiple human value systems, with theoretical support for its effectiveness. Experiments on human-value benchmarks demonstrate that our method improves flexible and faithful value alignment while maintaining overall model performance, highlighting mechanistic interpretability as a foundation for socially aware, pluralistic AI.