NeurIPS 2026 Papers

We introduce a new measure of robustness for statistical estimators, which we call empirical sensitivity. An estimator $\hat \mu$ has bounded empirical sensitivity if, with high probability over a dataset $X = (X_1, \dots, X_n) \sim \mathcal{D}^{\otimes n}$, for any dataset $Y$ obtained by modifying at most $\eta n$ points in $X$, we have that $\hat \mu(Y)$ is close to $\hat \mu(X)$. We study bounds on this quantity for the prototypical problem of Gaussian mean estimation. We prove new lower bounds, showing that for any estimator $\hat \mu$ which achieves an optimal $\ell_2$-error bound of $O(\sqrt{d/n})$, the empirical sensitivity is at least $\Omega(\eta + \sqrt{\eta d/n})$. The two terms arise due to obstructions on the mean and variance (via an Efron-Stein argument) of such an estimator. We show that this bound is tight up to logarithmic factors, by employing recent results for robust empirical mean estimation.

Standard ensemble methods can improve robustness by mitigating individual model stochasticity, but they frequently fail to generalize beyond the training distribution, leaving systems vulnerable to out-of-distribution (OOD) data. We introduce the Robust Satisficing Ensemble (RSE), a scalable probabilistic aggregation framework designed to secure model combinations by minimizing their fragility against distributional changes. By bridging a robust satisficing objective with a quadratic risk surrogate, RSE derives a closed-form analytical inner adversary. This fundamental reformulation enables highly efficient weight updates without the computational bottleneck of standard minimax optimization, crucially decoupling optimization complexity from sample size to scale effectively to large datasets. In particular, we prove a geometrically decaying truncation error for the fragility approximation via Lagrange-Bürmann expansion and show that the proximal RSE updates converge to a stationary point. We evaluate RSE across a comprehensive spectrum of distribution shifts, including adversarial label shift (SST-5, TREC), natural subpopulation and temporal shifts (CivilComments, HuffPost). Our results demonstrate that RSE consistently outperforms strong robust baselines, including GroupDRO, IRM, and SRM. These findings establish RSE as a practical, theoretically grounded safeguard for reliable model aggregation in dynamic environments.

Domain generalization (DG) aims to learn predictive models that can generalize to unseen domains. Most existing DG approaches focus on learning domain-invariant representations under the assumption of conditional distribution shift (i.e., primarily addressing changes in $P(X\mid Y)$ while assuming $P(Y)$ remains stable). However, real-world scenarios with multiple domains often involve compound distribution shifts where both the marginal label distribution $P(Y)$ and the conditional distribution $P(X\mid Y)$ vary simultaneously. To address this, we propose a unified framework for robust domain generalization under divergent marginal and conditional distributions. We derive a novel risk bound for unseen domains by explicitly decomposing the joint distribution into marginal and conditional components and characterizing risk gaps arising from both sources of divergence. To operationalize this bound and prevent it from becoming vacuous, we explicitly enforce feature-space $\ell_2$-normalization. We then design a meta-learning procedure that minimizes and validates the proposed risk bound across seen domains, ensuring strong generalization to unseen ones. Empirical evaluations demonstrate that our method achieves competitive performance not only on conventional DG benchmarks but also in challenging multi-domain long-tailed recognition settings where both marginal and conditional shifts are pronounced.

Approximate Nearest Neighbor Search (ANN) is an important algorithmic primitive that has found a plethora of applications in machine learning and information retrieval. The classic approach to this problem due to Indyk and Motwani (1998) leverages Locality Sensitive Hashing (LSH) by sampling multiple hash functions that are likely to identify similar data points. This approach has, however, been demonstrated to be vulnerable to adaptive queries and updates which may not be independent of its internal randomness (Kapralov et al. 2024). While differential-privacy-based techniques have yielded robust versions of randomized algorithms and data structures for estimation problems (Hassidim et al., 2022), ANN is a search problem: the algorithm must return an actual dataset point, without obfuscating the output by adding noise or rounding it. Feng et al. (2025) circumvent this limitation by relying on a density assumption that bounds the number of points near each query point. We study a stronger worst-case model in which the adversary chooses both the initial dataset and an adaptive query sequence. For LSH-equipped metric spaces, we give adversarially robust ANN algorithms with sublinear query time whose guarantees do not depend on any structural assumption on the dataset. The main technical challenge is to preserve sublinear search time when the adversary selects a dataset with arbitrarily many points near a query. Rather than applying differential-privacy robustification as a black box, we develop search-specific mechanisms: fairness as a route to adaptive security, a bucketing reduction from search to robust decision, and a concentric annuli construction that improves the query-time exponent. Moreover, for low-dimensional spaces, we give algorithms with a strong ``for-all'' guarantee, which are correct for every possible query.

Coding agents are increasingly deployed in real software development, where a single version iteration requires months of coordinated work across many files. However, most existing benchmarks focus predominantly on single-issue bug fixes from Python repositories, with coarse pass/fail evaluation outcomes, and thus fail to capture long-horizon, multi-target development at real engineering scale. To address this gap, we present ROADMAPBENCH, a benchmark of 115 long-horizon coding tasks grounded in real open-source version upgrades across 17 repositories and 5 programming languages. Each task places the agent on a source-version code snapshot and provides a multi-target roadmap instruction requiring it to implement the functionality introduced in the target version, with a median modification of 3700 lines across 51 files. We conduct a systematic evaluation on thirteen frontier models and find that even the strongest, Claude-Opus-4.7, resolves only 39.1% of tasks, while the weakest achieves merely 5.2%, in stark contrast to the high scores these models attain on existing bug-fix benchmarks, suggesting that long-horizon software development remains a largely unsolved problem.

In learnable logic gate networks, each neuron implements a $k$-input Boolean function. The dominant setting $k{=}2$ was chosen for tractability. We ask: when does wider fan-in help? At fixed parameter budget, each gate costs $2^k$ parameters, so increasing $k$ exponentially reduces width. Combined with the depth--fan-in bound $L \geq \lceil \log_k d \rceil$, this partitions tasks into two regimes: width-dominated (image classification), where more gates beat richer gates, and degree-dominated (parity, arithmetic), where $k{>}2$ is necessary. Our main finding is that representability does not imply learnability: at the regime boundary, the selection mechanism determines training success at identical architecture, and the optimal mechanism inverts between regimes. We formalize this via a Jacobian analysis: the softmax mechanism's positive-semidefinite (PSD) structure gives basin attraction absent from sigmoid. We train multilinear coefficients with exact gradients and Möbius-transform snapping (zero deployment error), and validate on 28 tasks and 5 real-world datasets across multiple selection mechanisms.

Single-task RL agents are typically trained under a fixed reward function, which limits their robustness to reward misspecification and their ability to adapt to changing preferences. We introduce Reward-Conditioned Reinforcement Learning (RCRL), an off-policy method that conditions agents on reward parameterizations while collecting experience under a single nominal objective. By recomputing counterfactual rewards from shared replay data, RCRL exposes the agent to multiple reward objectives without additional environment interaction, connecting single-task RL with ideas from multi-objective and multi-task learning. Across single-task, multi-task, and vision-based benchmarks, RCRL improves sample efficiency under the nominal reward parameterization, enables efficient adaptation to new parameterizations, and supports zero-shot behavioral adjustment at deployment. Our results show that RCRL provides a scalable mechanism for learning robust, steerable policies without sacrificing the simplicity of single-task training.

Incremental learning is usually evaluated through the final classifier or LM head, but this interface does not indicate where forgetting occurs. A drop in accuracy may reflect representation degradation in the backbone, readout mismatch in the head, or both. We argue that BWT and FWT should therefore be interpreted as interface-dependent quantities rather than as single model-level properties. We study three evaluation interfaces: the sequentially trained head, a newly optimized probing classifier, and a classifier-free backbone separability diagnostic based on clustering. These interfaces answer different questions: deployed performance, recoverable information under a new readout, and representation-level separability. Across CIL experiments with encoder and decoder language backbones, plus discriminative-backbone TIL sanity checks, we find that qualitative conclusions about forgetting and plasticity change substantially with the evaluation interface. Standard heads often indicate severe forgetting, probes often suggest near-complete recoverability, and backbone diagnostics suggest intermediate representation changes and a stability--plasticity pattern. This pattern is consistent across five clustering algorithms and three clustering metrics, suggesting that it is not an artifact of a single diagnostic choice. Finally, we use Just LM-Head Tuning (JLT) as a head-only intervention to quantify recoverable performance on a fixed incrementally trained backbone. The large gap between standard and head-realigned performance suggests that many failures attributed to catastrophic forgetting are better understood as head--backbone mismatch plus partial representation drift. Our results call for reporting where forgetting is measured, not only how much forgetting is observed.

Shapley values are a cornerstone of explainable AI, yet their proliferation into competing formulations has created a fragmented landscape with little consensus on practical deployment. While theoretical differences are well-documented, evaluation remains reliant on quantitative proxies whose alignment with human utility is unverified. In this work, we use a unified amortized framework to isolate semantic differences between eight Shapley variants under the low-latency constraints of operational risk workflows. We conduct a large-scale empirical evaluation across four risk datasets and a realistic fraud-detection environment involving professional analysts and 3,735 case reviews. Our results reveal a fundamental misalignment: standard quantitative metrics, such as sparsity and faithfulness, are decoupled from human-perceived clarity and decision utility. Furthermore, while no formulation improved objective analyst performance, explanations consistently increased decision confidence, signaling a critical risk of automation bias and overconfidence in high-stakes settings. These findings demonstrate that current evaluation proxies are insufficient for predicting human impact, motivating our release of interaction measurements to support research into behaviorally grounded XAI evaluation.

Sparse autoencoders (SAEs) were originally motivated by discovering monosemantic features, a property that characterizes individual features but does not specify what the learned feature set should look like as a whole. As SAEs have increasingly been adopted for attribution, circuit discovery, and intervention, researchers have begun evaluating metrics that describe global properties of the feature set, such as sparsity, dead feature rates, reconstruction fidelity, and disentanglement, a diverse set that extends far beyond monosemanticity. However, this implicit shift beyond monosemanticity has not been formalized as a clear, well-defined objective that comes before these evaluation metrics. Without such an objective, existing metrics remain ad hoc, with their necessity unjustified. In this work, we formalize this ultimate objective by introducing a new paradigm for SAE evaluation: requiring that SAE features, and more generally dictionary-based decompositions of model representations, form an atomic interpretable unit basis, a coordinate system for semantically meaningful explanation. Under this paradigm, we organize existing and new measurements such as DAME (Dominance-Aware Monosemanticity Evaluation) as proxy metrics and introduce a comprehensive benchmarking framework. Evaluating hundreds of SAEs across multiple architectures and model families, we uncover failure modes in which some SAEs appear monosemantic under existing evaluation metrics while remaining functionally polysemantic: the most dominant features, those contributing most to model computation, are systematically less interpretable and more redundant. These failure modes warrant attention from SAE researchers as targets for improved training and architectures, and motivate dominance-aware evaluation as a standard check for practitioners before SAE features are deployed for attribution, circuit tracing, or intervention.

Multimodal LLMs are typically trained by first aligning a vision encoder with a language model via projector training on large image-caption datasets, followed by joint training of the full multimodal model. Despite its widespread use, the role of the projector training stage remains poorly understood. Does it learn fine-grained visual-language correspondences, or mainly maps visual features into a compatible input space for the language model? We find that (i) using only $10$ to $20\%$ of the data for training the projector already recovers most downstream performance gains, and (ii) projectors trained on different datasets can be linearly interpolated while largely preserving performance. These results suggest that projector training acts primarily as a coarse alignment within a large solution space. Motivated by these findings, we propose PORTAL, a training-free projector initialization that requires neither paired image-caption data nor gradient-based optimization, but only per-modality summary statistics. PORTAL computes an optimal-transport-based map between Gaussian approximations of the vision and language feature distributions on a shared principal subspace, enabling completely skipping projector pretraining. Despite using no paired data, while the standard approach relies on 0.5M image–caption pairs, PORTAL matches the default trained pipeline across six LLM backbones, two vision encoders, and 16 benchmarks, outperforming it in $3$ of $7$ (vision, LLM) settings, and remaining within $1.6$ average points across all other settings.

Efficient long-video understanding with vision-language models (VLMs) has largely been treated as informative token selection at fixed native resolution: which frames or which visual tokens to retain under a token budget. We argue this framing leaves two axes unused --- per-frame resolution itself can be traded for denser temporal coverage, and front-end decoding latency scales with the candidate pool, not the token budget. Through an empirical study across multiple VLMs and long-video benchmarks, we distill three lessons: (i) dense low-resolution sampling outperforms sparse native-resolution sampling at matched token budgets; (ii) some tasks are resolution-sensitive and benefit from high-resolution frames; and (iii) front-end decoding dominates wall time on hour-scale clips. These lessons motivate LoHi, a training-free, single-pass framework that pairs a dense low-resolution video stream with a sparse set of high-resolution image streams, processed through the VLM's native video and image pathways. Two plug-and-play selectors choose Hi-I frames at near-zero or low overhead: LoHi-Anchor uses codec-level I-frame metadata, and LoHi-SemDiv uses a query-relevance and visual-diversity DPP over CLIP features. On three long-video benchmarks, LoHi improves over the vanilla native-resolution baseline by +10.6% on average at matched token budget and over the strongest prior efficiency methods by +5.2%, while reducing front-end decoding latency by up to 7x on hour-scale clips.

Dataset distillation (DD) has emerged as a prominent approach in data centric machine learning, aiming to synthesize compact training sets for efficient training by compressing the information in large datasets into a small number of synthetic samples. However, DD methods are often evaluated under inconsistent evaluation protocols, ranging from standard ERM to single/multi‑teacher supervision, making it difficult to isolate the effectiveness of distilled data from evaluation. Moreover, many prior methods claim that DD outperforms data pruning approaches such as coreset selection (CS), based on the assumption that restricting condensed datasets to subsets of real samples fundamentally limits their expressiveness. In this work, we critically evaluate DD methods through large-scale experiments using standardized datasets and evaluation protocols to assess their intrinsic effectiveness. We benchmark seven state-of-the-art DD methods on ImageNet-1K, ImageNet-100, and ImageNette, using three widely adopted training protocols against three CS strategies. Our results show that while some DD methods fail to outperform even simple random subsets, the SOTA DD approaches are comparable to or worse than coresets on large‑scale datasets and incur a substantially higher cost for construction. Beyond accuracy, we also evaluate the representativeness, diversity, and quality of condensed sets, and find that coresets consistently achieve better coverage of the original data distribution. These findings highlight the limited practical advantages of current DD methods and show that coresets remain competitive and are often a more computationally efficient alternative for data-centric learning.

Large language models trained with Reinforcement Learning (RL) with verifiable rewards exhibit strong reasoning ability and broad generalization, whereas models trained with Supervised Fine-Tuning (SFT) are often viewed as more prone to memorization and limited transfer. This paper rethinks this distinction through the lens of SFT training data. First, we study the role of data source and show that it is critical: a carefully mixed SFT dataset substantially outperforms data generated solely by a larger model. Second, we study the role of data scale and show that matching the number of correct rollouts between SFT and RL greatly improves SFT generalization, while matching the total rollout budget enables SFT to generalize as well as RL. Combining these two factors further enables SFT to generalize even better than RL. Third, by using LLM annotations to characterize the solution methods in training rollouts, we show that larger datasets cover more tail methods and that these tail methods provide generalizable reasoning signals. Finally, we support these empirical findings theoretically by analyzing the training dynamics of shallow transformers under both RL and SFT.

Density Peak Clustering (DPC) focuses on identifying centers and propagates labels at the sample level, which makes density estimation cutoff-sensitive and assignment chain-vulnerable, yielding suboptimal performance under heterogeneous densities and complex cluster structures. This paper argues that density peaks inference should instead be performed on resolution-controlled structural units: density becomes a stable count statistic, relative distance inherits the separation of the enclosing hierarchy, and assignment runs over a compact graph of structural units rather than long sample-to-sample chains. This view is realized in Resolution-Aware Structural Density Peak Clustering (RSDP), which builds a constrained hierarchy, selects an admissible level via a single resolution parameter, and applies a one-pass DPC rule on the selected structural units. Under a faithful-realization condition, it is proved that RSDP's empirical $\gamma$-ranking recovers the dominant population units and that its one-pass assignment recovers the sampled ground-truth partition. On synthetic and real-world datasets, RSDP achieves the highest ACC and NMI against state-of-the-art DPC variants, exceeding the strongest by 19.91% and 9.09% in average ACC and NMI, respectively.

As Embodied Agents System (EAS) move into physical domains such as autonomous navigation and household assistance, reliable execution becomes critical for physical task completion and collaboration trust. Recent EAS reliability evaluation works typically focus on outcome-centric metrics as success rate or safety-only scores to assess an agent's performance, which collapse diverse execution trajectories into coarse outcomes. Therefore they ignore a critical property of EAS -- which we define as the **Resilience** -- that reflects how EASs recover, stabilize, and extend under perturbations and across iterative updates. The lack of resilience is particularly critical in open-world environments due to continuous unexpected disruptions, thus directly affecting the quality of EAS deployment. To address this problem, we gain insight from the resilience-engineering concepts to EAS groundings and propose a novel resilience evaluation framework that can be flexibly applied to any EAS. Specifically, we define the first comprehensive resilience metrics suite for EASs system that exposes *Rebound*, *Stability*, and *Graceful Extensibility* across embodied tasks execution, providing a practical grounding for EAS resilience analysis. We further implement the resilience evaluation layer that transforms execution evidence into assessments for comparison, diagnosis and optimization. Across 400 household tasks with 10 representative EAS baselines, our evaluation reveals process-level distinction hidden by outcome metrics, including recovery cost differences among successful episodes ($\Delta C_{\mathrm{rec}}=25.2$), increased instability under semantic perturbations, and task-family-specific degradation under stress. Metrics-guided optimizations reduce recovery cost by 42.94%, increase stability by 19.87%, and improve graceful extensibility completion by 10.08%, showing the diagnostic effect of resilience evaluation. Beyond these targeted gains, our results reveal trade-offs among resilience characteristics, suggesting that a resilient EAS construction should be evaluated and configured according to deployment-specific requirements. Our code and data are available at .

In a 100-body robot co-design benchmark, the height threshold that resets a falling robot changes which bodies appear optimal. We train PPO controllers for DERL-evolved UNIMAL morphologies under Standard (τ = 0.20), Strict (τ = 0.50), and Reset-free (τ = 0) protocols, then evaluate every policy under a common protocol. Strict and Reset-free training share only 5 of their top-10 bodies and have low rank agreement (Spearman ρ = 0.21). The effect is family-specific, not a uniform penalty: averaging per-body retention ratios, Reset-free training reduces Floor bodies' per-step reward by 45% relative to Standard training but reduces variable-terrain bodies by 16%. Under Strict, the losses are 22% for Floor and 34% for variable-terrain bodies, while multi-task bodies are most stable across protocols. Blocked ANOVA and morphology-level permutation tests support the protocol-by-family interaction. A SAC validation panel planned before analysis finds the same Strict-versus-Reset-free family ordering under a different optimizer. Selecting bodies by their minimum reward across the three training protocols recovers ≥91% of every single-protocol oracle's top-k average reward (k ∈ {5, 10, 20}; all bootstrap lower bounds ≥84.3%). Co-design benchmarks should state the reset rule, audit ranking sensitivity, and report protocol-robust selections when choosing bodies.

Human vision flexibly extracts part-whole hierarchies from visual scenes, but representing such structures remains a key challenge for neural networks. Inspired by the neural syntax hypothesis in neuroscience, we propose a framework for representing hierarchical part-whole relationships through nested neuronal coherence, characterized by its continuous and distributed nature. Nested neuronal coherence refers to dynamical states where distributed activations are temporally correlated to form cell assembly sequences across timescales, argued to represent neural syntax. Building on this framework, we develop a cortical-inspired hybrid model, Composer, which dynamically achieves emergent nestedness when given images. To evaluate the emergent hierarchy, we create four synthetic datasets and three quantitative metrics, demonstrating the model’s ability to parse scenes of varying complexity. Overall, our work advances a systematic paradigm spanning representation, implementation, and evaluation toward building human-like vision in neural networks.

Upgrading a deployed face-recognition model usually makes new query embeddings incompatible with the legacy gallery, forcing costly backfilling of stored embeddings. We show that this incompatibility is often much simpler than it appears: independently trained angular-margin face models exhibit representation rigidity, where their embedding spaces are well approximated by a single global orthogonal transformation. We formalize this phenomenon as Procrustes rigidity, derive a finite-calibration recoverability bound, and estimate the orthogonal adapter from a small paired calibration set via closed-form Procrustes alignment. The resulting deployment protocol is backfill-free: transport upgraded queries into the legacy coordinate system, then reuse the existing gallery without re-embedding stored identities. Across 45 models spanning three architectures, two losses, three data scales, and five seeds, we find strong rigidity within architecture families, non-monotonic scaling with data size, and robust cross-model retrieval. On the 1.6M-image IFRT benchmark, Procrustes-aligned queries recover at least $99.8\%$ of mono-model Rank-1 accuracy for same-family upgrades, while lightweight residual correction substantially narrows the cross-architecture gap.