NeurIPS 2026 Papers

Multi-agent LLM systems exchange messages whose communicative necessity varies widely, yet no systematic evaluation protocol determines which messages can be safely removed. We introduce, to our knowledge, the first message-level functional analysis protocol for evaluating communication in two-agent LLM systems. The protocol comprises three reusable stages (annotate, perturb, prune), each deployable to new backbones, domains, and topologies without task-specific training data. We release a 21,661-message annotated corpus across 3 backbones and 4 reasoning domains with a five-class taxonomy for mechanism exploration, a zero-shot annotation pipeline using constrained decoding, and a statistical hypothesis-testing framework combining TOST equivalence, non-inferiority, and McNemar's tests. Human validation (N=225) confirms annotation reliability (κ = 0.81 binary ack/non-ack, underpinning all pruning claims; 0.76 five-class); the cross-model annotation pipeline achieves κ=0.72. Applying the protocol across 18 configurations spanning 7B–72B scale, 4 reasoning domains, and 3 topology variants, with 10-seed replication for flagship settings, we surface a perturbation–pruning dissociation: the most disruptive message type under single removal is safe to remove in bulk, enabling acknowledgment-targeted pruning that suppresses 36–56% of inter-agent messages from conversation context at non-inferior accuracy under greedy decoding. The protocol further identifies boundary conditions where pruning fails and reveals backbone-dependent communication mechanisms, providing a screening tool for deployment decisions.

A central goal of science is to produce valid explanations of complex systems: high-level causal accounts that faithfully reflect the behavior of lower-level mechanisms. Yet no consensus exists on how to measure whether a proposed high-level explanation is actually valid. We introduce a benchmark of ten complex systems spanning discrete and continuous state spaces and static and dynamical regimes, each equipped with consensual ground-truth causal explanations and invalid contrastive conditions. Within a unified causal abstraction framework, we systematically evaluate over thirty candidate metrics drawn from observational, functional, information-theoretic, and causal families. Our results show that only the latter reliably discriminates valid from invalid abstractions, and only when incorporating faithfulness testing over unmapped variables. Building on these findings, we introduce the Causal Abstraction Error (CAE), a continuous validity metric with an explicit faithfulness test, which passes all discrimination tests across every system and converges with as few as 30 sampled interventions. We offer it as a general-purpose metric for the discovery and validation of high-level explanations of complex systems.

Learning from past experience requires forming abstractions that can be reused in future problems. Recent work on agentic-memory systems has explored a practical route to continuously improving LLM agents after deployment without parameter updates: a textual abstraction is derived from each history and stored in memory, then continuously updated with more interactions. Yet we show that such textual abstractions produced by today's LLMs are often faulty, even when derived from useful experiences. Over time, the memory becomes less useful and even harmful. More surprisingly, even when abstracting from ground-truth solutions, GPT-5.4 fails on 54% of a set of ARC-AGI problems it had previously solved without memory. We attribute this to the iterative update process: the same trajectories yield qualitatively different memories under different update schedules, while an episodic-only control over those trajectories remains competitive with the consolidators we test---pinning the failure on the consolidation step, not the underlying experience. In our ARC-AGI Stream environment designed to trace memory consolidation behavior, when agents are given additional actions, they tend to keep episodic memory and double the accuracy of their forced-consolidation counterparts; removing consolidation entirely (episodic management only) matches this auto mode. These results suggest that current LLMs should not recursively rewrite their own experience into stable long-term knowledge. Robust agent memory should treat raw episodes as first-class evidence and make abstraction selective, delayed, and explicitly gated rather than mandatory after every interaction.

Universal approximation theorems establish the expressive capacity of neural network architectures. For dynamical systems, existing results are limited to finite time horizons or systems with a globally stable equilibrium, leaving multistability and limit cycles unaddressed. We prove that Neural ODEs achieve $\varepsilon$-$\delta$ closeness, i.e., trajectories within error $\varepsilon$ except for initial conditions of measure $< \delta$, over the \emph{infinite} time horizon $[0,\infty)$ for three target classes: (1) Morse-Smale systems (a structurally stable class) with hyperbolic fixed points, (2) Morse-Smale systems with hyperbolic limit cycles via exact period matching, and (3) systems with normally hyperbolic continuous attractors via discretization. We further establish a temporal generalization bound: $\varepsilon$-$\delta$ closeness implies $L^p$ error $\leq \varepsilon^p + \delta \cdot D^p$ for all $t \geq 0$, bridging topological guarantees to training metrics. These results provide the first universal approximation framework for multistable infinite-horizon dynamics.

Online platforms often struggle with inflated, uninformative user ratings. This issue can be mitigated by better design of the data collection mechanism, for example through changing the phrasing of user questions. Previous work optimizes a single rating scale to best distinguish the inherent qualities of items under binary feedback. In this paper, we demonstrate the power of utilizing different rating scales for different users. First, we show that a designer can always split a single rating scale into two to improve item rankings. Next, we formally characterize the optimal design of multiple scales as a series of 0-1 step functions whose threshold values are evenly spaced. Finally, we consider an adaptive model where subsequent rating scales can depend on the responses from previous users and show that adaptivity leads to even greater distinguishing power. All in all, our theoretical results show that using heterogeneous scales significantly improves item rankings on platforms.

Large Language Model-based Multi-Agent Systems (LLM-MAS) have demonstrated strong capabilities in solving complex tasks but remain vulnerable when agents receive unreliable messages. This vulnerability stems from a fundamental gap: LLM agents treat all incoming messages equally without evaluating their trustworthiness. While some existing studies approach trustworthiness, they focus on a single type of harmfulness rather than analyze it in a holistic approach from multiple trustworthiness perspectives. We address this gap by proposing a comprehensive definition of trustworthiness inspired by human communication theory \citep{grice1975logic}. Our definition identifies six orthogonal trust dimensions that provide interpretable measures of trustworthiness. Building on this definition, we introduce the Attention Trust Score (A‑Trust), a lightweight, attention‑based method for evaluating the trustworthiness of messages. We then develop a principled trust management system (TMS) for LLM‑MAS that supports both message‑level and agent‑level trust assessments. Experiments across diverse multi‑agent settings and tasks demonstrate that our TMS significantly improves robustness against malicious inputs.

Integration against a probability distribution given its unnormalized density is a central task in Bayesian inference and other fields. We introduce new methods for approximating such expectations with a small set of weighted samples---i.e., a quadrature rule---constructed via an interacting particle system that minimizes maximum mean discrepancy (MMD) to the target distribution. These methods extend the classical mean shift algorithm, as well as recent algorithms for optimal quantization of empirical distributions, to the case of continuous distributions. Crucially, our approach creates dynamics for MMD minimization that are invariant to the unknown normalizing constant; they also admit both gradient-free and gradient-informed implementations. The resulting mean shift interacting particle systems converge quickly, capture anisotropy and multi-modality, avoid mode collapse, and scale to high dimensions. We demonstrate their performance on a wide range of benchmark sampling problems, including multi-modal mixtures, Bayesian hierarchical models, PDE-constrained inverse problems, and beyond.

Over the past decade, a growing body of work has established that implicit biases in learning dynamics fundamentally shape the solutions found by neural networks, governing their learned features and generalisation performance. However, despite these strides in deep learning theory, far less is known about representation learning in generative models based on dynamical systems, from normalising flows to diffusion. Importantly, continuous-time generative models can be prone to mode collapse, yet the learning dynamics underpinning such biases remain elusive. To address this, we use tools from dynamical systems and operator theory to show that bounds on the rank of the gradient of the model weights can explain how collapse occurs in generative models. We show that, in both variational inference and flow matching tasks, optimisation induces low-rank biases that encourage parsimonious representation learning but may also cause the learned distribution to collapse. Together these findings point to a trade-off between promoting feature learning while avoiding both memorisation and collapse in dynamical systems-based generative models.

As agent systems scale, skills accumulate into large reusable libraries, yet their scaling laws remain poorly understood. Across 15 frontier LLMs, 1,141 real-world skills, and over 3M routing or execution decisions, we identify two coupled laws. Routing law: single-step routing accuracy decays logarithmically with library size ($R^2{>}0.97$ for all models), with errors progressing from local skill competition to cross-family drift and capture by overly general ``black-hole skills''. Execution law: before state realization, joint routing is approximately multiplicative, whereas correct execution can improve difficult downstream decisions by about $4{\times}$. A single parameter, the routing logarithmic decay slope $b$, couples the two laws: routing-side fits predict execution-side rescue across models, showing that the same library property controls both pre-execution collapse and downstream recoverability. The laws are actionable: law-guided optimization raises held-out routing accuracy from 71.3% to 91.7%, reduces hijack from 22.4% to 4.1%, and transfers directionally to downstream ClawBench and ClawMark execution settings, improving mean pass rate from 49.3% to 61.6% on ClawBench and from 28.4% to 34.5% on ClawMark. These results show that agent performance depends not only on model capability, but also on the structure, granularity, and exposure policy of the skill library.

Frontier AI systems function as \emph{constitutional institutions}: each deployed model encodes an implicit ranking among safety, helpfulness, honesty, autonomy, and equity. We ask whether the supply of frontier constitutional types covers human demand. Combining a paraphrase-controlled audit of $23$ frontier LLM archetypes with a pairwise-tradeoff study of $1{,}649$ humans on the same instrument, we report three facts. Demand is broad: it spans all five values, with the largest constituency under one-third. Supply is narrow and drifting: the $23$-archetype hull occupies $0.10\%$ of the demand hull, and across six model families autonomy decreases in $5/6$, equity increases in $5/6$, and safety increases in $4/6$. The importance of this drift is not that the frontier moves but that it moves away from a value that is already undercovered, mechanically worsening the welfare floor for the users least well served by the static menu. The fix is sparse: a $2$-vertex menu $\{e_{\mathrm{HON}}, e_{\mathrm{AUT}}\}$ beats the full $23$-archetype frontier by $47$ percent on mean regret ($95$ percent); three vertex additions cut mean regret by up to $81$ percent and worst-group regret by up to $64$ percent. We formalize these findings as a budgeted-pluralism trilemma and show the binding regime is empirically realized.

Tourism is a high-stakes setting for conversational recommender systems (CRS): a plausible-sounding suggestion can waste real money and trip time once a traveler acts on it. Existing CRS benchmarks primarily evaluate systems with a single Recall@$k$ score over entity mentions, and tourism-specific resources add spatial or knowledge-graph context, yet none of them couple multi-turn recommendation with verbatim review-span evidence and rejection recovery. This leaves an evaluation gap for tourism recommendation that is simultaneously *trustworthy*, *verifiable*, and *adaptive*: recommend the right point of interest (POI) for multi-aspect preferences (such as cuisine, price, atmosphere, walking distance), justify each suggestion with verifiable evidence from prior visitors so the traveler can act without trial and error, and recover when the first recommendation is rejected mid-dialogue. We introduce **TRACE**, where each item is *a multi-turn tourism recommendation dialogue with review-span citations and explicit rejection turns*: 10,000 dialogues over 2,400 Yelp POIs and 34,208 reviews across eight U.S. cities, paired with 14 retrieval, planning, and LLM baselines, along with 25 metrics organized under *Accuracy*, *Grounding*, and *Recovery*. Across these baselines, TRACE reveals the **Three-Competency Gap**: LLM Zero-Shot leads in closed-set Recall@1 and rejection recovery but cites less densely than retrievers; non-LLM retrievers achieve surface-verbatim grounding but with low accuracy; Multi-Review Synthesis fails on Recovery. The Grounding Score agrees with human citation precision (Spearman $\rho = +0.80$, $p < 10^{-20}$), and paired $t$-tests reproduce the per-baseline ranking ($p < 0.01$ on the dominant contrasts). TRACE reframes accountable tourism recommendation as a joint target (right POI, verifiable evidence, adaptive repair) rather than a single-axis leaderboard.

Generating inputs for systems that process highly structured data, such as compilers, is difficult due to the dual of syntactic and semantic constraints. Traditional approaches rely on manually crafted rules that require deep domain expertise and are difficult to maintain, while modern machine learning methods have to learn syntax and semantics simultaneously which is challenging. We present Synsema, a novel approach that combines insights from both worlds by reformulating the generation of semantically valid programs as a syntax-guided reinforcement learning task. By guaranteeing syntactic validity through the grammar, the agent needs to only learn the language's semantic rules, sampling from a drastically reduced space. We implement our approach in the context of Java and Rust which both exhibit strict semantic requirements, and train an agent to generate interesting and well-formed programs using fine-grained semantic feedback. Applied to compiler testing, we systematically compare different syntax-guided generation procedures with an unconstrained baseline and show that by restricting the sampling space, Synsema learns semantic rules efficiently. While an average of only 0.03% of programs generated by the baseline are semantically valid, Synsema produces a diverse set of programs with a 7.29% success rate that trigger 2.6x more compiler behaviors. In addition, Synsema discovered 5 previously unknown bugs in production compilers, validating the practical impact of our approach.

Programmable photonic circuits are a natural platform for physical learning, where the learned computation is performed by the hardware itself rather than by a digital model. We propose a physical learning algorithm and architecture for continuous-variable quantum systems where a photonic circuit is configured in situ to invert an unknown lossless Gaussian quantum operation. Our contributions are threefold. (i) Theory: we prove that generic $S \in \mathrm{Sp}(2 N, \mathbb{R})$ admits a triangular decomposition into two-mode and single-mode symplectic gates. (ii) Architecture: we introduce the symplectic Reck mesh, a triangular array of two-mode symplectic gates that physically realizes this factorization, generalizing the unitary Reck mesh widely used in optical neural networks. (iii) Physical learning: when placed after an unknown Gaussian unitary, the mesh is trained in situ by nulling local response blocks one at a time using simple optical probes and measurements. We identify a measure that predicts when training becomes hard and numerically demonstrate finite-shot training and robustness to gate errors. Our work extends self-configuring optical networks from unitary to symplectic transformations, bringing physical learning to continuous-variable quantum photonic hardware.

The modeling and simulation of infinite-dimensional Hamiltonian systems are central problems in mathematical physics and engineering, but they pose significant computational and structural challenges for standard data-driven architectures. In this work, we introduce the Symplectic Neural Operator, a neural operator architecture designed to preserve the symplectic structure intrinsic to Hamiltonian PDEs. We provide a theoretical characterization of their symplecticity and establish a rigorous long-term stability result based on the combination of symplectic structure preservation and learning accuracy. Numerical experiments on canonical Hamiltonian PDEs corroborate this theoretical result and show that SNOs exhibit improved energy behavior compared with non-structure-preserving neural operators.

Passenger-order cancellation is a critical source of uncertainty in on-demand ride-sharing systems, where requests, assignments, and vehicle routes evolve continuously in real time. Due to shared capacity and coupled routes, a single cancellation may propagate through downstream matching and routing decisions, degrading system efficiency and service reliability. However, cancellation prediction in on-demand ride-sharing remains difficult to study systematically due to the lack of large-scale longitudinal datasets, standardized evaluation protocols, and fine-grained real-time benchmarks. In this work, we introduce SurvCancel, a real-world longitudinal dataset and benchmark for dynamic passenger-order cancellation prediction in on-demand ride-sharing systems. Constructed from operational logs collected across four service regions in the real world, SurvCancel contains 173K released orders and 7.9M time-dependent snapshots. Each order is represented as a longitudinal sequence of system states, capturing both order-level attributes and the evolving supply-demand environment throughout its lifecycle. We formulate cancellation prediction as a stage-conditioned dynamic survival task: at each landmark time, models estimate short-term cancellation risk from the historical state sequence observed so far. We evaluate representative survival and dynamic-risk models under both in-distribution and distribution-shift protocols. Our results show stage-dependent model behavior in the in-distribution setting and reveal distinct robustness patterns under regional and temporal distribution shifts.

Flow matching is an emerging, scalable generative framework for characterizing continuous normalizing flows with wide-range applications. However, state-of-the-art methods are not well-suited for modeling dynamical systems, as they construct conditional paths that are restricted to linear interpolants, a suboptimal supervision signal, which may not capture the system's underlying state evolution. Moreover, constructing unified paths to satisfy multi-marginal constraints across observations is challenging, since naïve higher-order polynomials tend to be unstable and oscillatory. To address these limitations, we introduce SplineFlow, a theoretically grounded flow matching algorithm that jointly models conditional paths across observations via B-spline interpolation. Specifically, SplineFlow exploits the smoothness and stability of B-spline bases to learn the complex underlying dynamics in a structured manner while ensuring the multi-marginal requirements are met. Comprehensive experiments across deterministic and stochastic dynamical systems under various configurations, as well as cellular trajectory inference tasks, demonstrate that SplineFlow outperforms existing baselines, especially when the underlying dynamics are of higher degree or in irregular sampling regimes.

Sample covariance matrices are fundamental objects in machine learning and statistics, with valuable information encoded into their eigenvalues. When treating modern problems, the scale of these matrices can become prohibitive for tractable computation. This creates a critical need for "spectral decompression": a method for inferring the eigenspectrum of a very large-scale model using only information from its smaller realizations. Existing methods fall into two main categories: those relying on spectral inversion; and those that rely on Free Decompression techniques. On one hand, spectral inversion is a fundamentally ill-posed problem that is notoriously unstable, often failing to yield reliable results in finite-size settings. On the other hand, while Free Decompression was recently proposed to address this scaling, its reliance on the Nica-Speicher framework restricts its use to unitarily invariant ensembles, a symmetry condition that subsampled covariance matrices fail to satisfy. In this work, we introduce Deformed Decompression (DD), a novel framework for the stable, forward-extrapolation of spectral densities. By leveraging properties of the companion matrix, DD recasts the spectral decompression problem as a directed evolution of the Stieltjes transform of the companion. This approach bypasses the instabilities of traditional inversion and provides a robust methodology for scaling covariance matrices and even their generalized variants (including Hessian matrices) that lack unitary invariance. We demonstrate the utility of our framework through experiments on a variety of random matrix examples, showing that DD successfully captures the complex spectral signatures of large-scale systems.

Koopman autoencoders (KAEs) seek a higher-dimensional latent representation in which nonlinear dynamics evolve linearly. However, many interesting systems have multiple basins of attraction, and both theoretical and empirical work has shown these multibasin systems cannot generally admit a single finite-dimensional global Koopman embedding under standard assumptions. We posit that encoders with a sparsity-inducing objective encouraging few active latent coefficients will provide latent supports as an inspectable basin-modeling principle for Koopman autoencoders. We use these encoders producing sparse latents in training Sparse Koopman Autoencoders (SKAEs) without basin labels or other regime annotations, and treat the learned latent supports as model-produced regime variables after training. Across a range of procedurally generated multibasin systems and chaotic flows, we show that SKAEs have superior forecasting performance compared to dense-latent KAEs. We also perform a mechanistic study that shows latent supports produced by SKAEs are both essential for the quality of the representation and useful for identifying basins on held-out basin interior states, whereas dense-latent KAEs collapse to an uninformative single family. These results identify sparse latents and their corresponding supports as label-free, interpretable regime variables for Koopman learning in nonlinear systems with multiple local dynamical laws.

Traditional methods for automating recommender system design, such as Neural Architecture Search (NAS), are often constrained by a fixed search space defined by human priors, limiting innovation to pre-defined operators. While recent LLM-driven code evolution frameworks shift fixed search space target to open-ended program spaces, they primarily rely on scalar metrics (e.g., NDCG, Hit Ratio) that fail to provide qualitative insights into model failures or directional guidance for improvement. To address this, we propose Self-EvolveRec, a novel framework that establishes a directional feedback loop by integrating a User Simulator for qualitative critiques and a Model Diagnosis Tool for quantitative internal verification. Furthermore, we introduce a Diagnosis Tool - Model Co-Evolution strategy to ensure that evaluation criteria dynamically adapt as the recommendation architecture evolves. Extensive experiments demonstrate that Self-EvolveRec significantly outperforms state-of-the-art NAS and LLM-driven code evolution baselines in both recommendation performance and user satisfaction. Our code is available at https://anonymous.4open.science/r/selfevolverec-37F5/.