What does it even mean to average neural networks? We investigate the problem of synthesizing a single neural network from a collection of pretrained models, each trained on disjoint data shards, using only their final weights and no access to training data. In forming a definition of neural averaging, we take insight from model soup, which appears to aggregate multiple models into a singular model while enhancing generalization performance. In this work, we reinterpret model souping as a special case of a broader framework: Amortized Model Ensembling (AME) for neural averaging, a data-free meta-optimization approach that treats model differences as pseudogradients to guide neural weight updates. We show that this perspective not only recovers model soup but enables more expressive and adaptive ensembling strategies. Empirically, AME produces averaged neural solutions that outperform both individual experts and model soup baselines, especially in out-of-distribution settings. Our results suggest a principled and generalizable notion of data-free model weight aggregation and defines, in one sense, how to perform neural averaging.

We need some more notation in order to linearize the value function.

Large Language Models (LLMs) have demonstrated notable capabilities across various tasks, showcasing complex problem-solving abilities. Understanding and executing complex rules, along with multi-step planning, are fundamental to logical reasoning and critical for practical LLM agents and decision-making systems. However, evaluating LLMs as effective rule-based executors and planners remains underexplored. In this paper, we introduce LogicGame, a novel benchmark designed to evaluate the comprehensive rule understanding, execution, and planning capabilities of LLMs. Unlike traditional benchmarks, LogicGame provides diverse games that contain a series of rules with an initial state, requiring models to comprehend and apply predefined regulations to solve problems. We create simulated scenarios in which models execute or plan operations to achieve specific outcomes. These game scenarios are specifically designed to distinguish logical reasoning from mere knowledge by relying exclusively on predefined rules. This separation allows for a pure assessment of rule-based reasoning capabilities. The evaluation considers not only final outcomes but also intermediate steps, providing a comprehensive assessment of model performance. Moreover, these intermediate steps are deterministic and can be automatically verified. LogicGame defines game scenarios with varying difficulty levels, from simple rule applications to complex reasoning chains, in order to offer a precise evaluation of model performance on rule understanding and multi-step execution. Utilizing LogicGame, we test various LLMs and identify notable shortcomings in their rule-based logical reasoning abilities.

Synthetic long-context LLM benchmarks (e.g., "needle-in-the-haystack") test only surface-level retrieval capabilities, but how well can long-context LLMs retrieve, synthesize, and reason over information across book-length inputs? We address this question by creating NoCha, a dataset of 1,001 minimally different pairs of true and false claims about 67 recently-published English fictional books, written by human readers of those books. In contrast to existing long-context benchmarks, our annotators confirm that the largest share of pairs in NoCha require global reasoning over the entire book to verify. Our experiments show that while human readers easily perform this task, it is enormously challenging for all ten long-context LLMs that we evaluate: no open-weight model performs above random chance (despite their strong performance on synthetic benchmarks), while GPT-4o achieves the highest accuracy at 55.8%. Further analysis reveals that (1) on average, models perform much better on pairs that require only sentence-level retrieval vs. global reasoning; (2) model-generated explanations for their decisions are often inaccurate even for correctly-labeled claims; and (3) models perform substantially worse on speculative fiction books that contain extensive world-building. The methodology proposed in NoCha allows for the evolution of the benchmark dataset and the easy analysis of future models.

Analogy is one of the core capacities of human cognition; when faced with new situations, we often transfer prior experience from other domains. Most work on computational analogy relies heavily on complex, manually crafted input. In this work, we relax the input requirements, requiring only names of entities to be mapped. We automatically extract commonsense representations and use them to identify a mapping between the entities. Unlike previous works, our framework can handle partial analogies and suggest new entities to be added. Moreover, our method's output is easily interpretable, allowing for users to understand why a specific mapping was chosen. Experiments show that our model correctly maps 81.2% of classical 2x2 analogy problems (guess level=50%). On larger problems, it achieves 77.8% accuracy (mean guess level=13.1%). In another experiment, we show our algorithm outperforms human performance, and the automatic suggestions of new entities resemble those suggested by humans. We hope this work will advance computational analogy by paving the way to more flexible, realistic input requirements, with broader applicability.

To be robust to surprising developments, an intelligent agent must be able to respond to many different types of unexpected change in the world. To date, there are no general frameworks for defining and characterizing the types of environment changes that are possible. We introduce a formal and theoretical framework for defining and categorizing environment transformations, changes to the world an agent inhabits. We introduce two types of environment transformation: R-transformations which modify environment dynamics and T-transformations which modify the generation process that produces scenarios. We present a new language for describing domains, scenario generators, and transformations, called the Transformation and Simulator Abstraction Language (T-SAL), and a logical formalism that rigorously defines these concepts. Then, we offer the first formal and computational set of tests for eight categories of environment transformations. This domain-independent framework paves the way for describing unambiguous classes of novelty, constrained and domain-independent random generation of environment transformations, replication of environment transformation studies, and fair evaluation of agent robustness.

Subsampling is an important technique to tackle the computational challenges brought by big data. Many subsampling procedures fall within the framework of importance sampling, which assigns high sampling probabilities to the samples appearing to have big impacts. When the noise level is high, those sampling procedures tend to pick many outliers and thus often do not perform satisfactorily in practice. To tackle this issue, we design a new Markov subsampling strategy based on Huber criterion (HMS) to construct an informative subset from the noisy full data; the constructed subset then serves as a refined working data for efficient processing. HMS is built upon a Metropolis-Hasting procedure, where the inclusion probability of each sampling unit is determined using the Huber criterion to prevent over scoring the outliers. Under mild conditions, we show that the estimator based on the subsamples selected by HMS is statistically consistent with a sub-Gaussian deviation bound. The promising performance of HMS is demonstrated by extensive studies on large scale simulations and real data examples.

Evidence often grounds temporal probabilistic relational models over time, which makes reasoning infeasible. To counteract groundings over time and to keep reasoning polynomial by restoring a lifted representation, we present temporal approximate merging (T AMe), which incorporates (i) clustering for grouping submodels as well as (ii) statistical significance checks to test the fitness of the clustering outcome. In exchange for faster runtimes, T AMe introduces a bounded error that becomes negligible over time. Empirical results show that T AMe significantly improves the runtime performance of inference, while keeping errors small. Introduction Temporal probabilistic relational models express relations between objects, modelling uncertainty as well as temporal aspects. Within one time step, a temporal model is considered static. Performing inference on such models requires algorithms to efficiently handle the temporal aspect to be able to efficiently answer queries. Reasoning in lifted representations has a complexity polynomial in domain sizes. But, models dissolve into ground instances through evidence, which no longer permits reasoning in polynomial time, making query answering infeasible for any reasoning algorithm, exact or approximate. Thus, a key challenge during inference in temporal models is to restore a lifted, i.e., non-grounded, representation. Therefore, we formulate and study the problem of keeping reasoning polynomial (KRP) in temporal models to tame the effect of evidence for efficient query answering. First-order probabilistic inference leverages the relational aspect of a static model, using representatives for groups of indistinguishable, known objects, also known as lifting (Poole 2003). Poole (2003) presents parametric factor graphs as relational models and proposes lifted variable elimination (L VE) as an exact inference algorithm on relational models.

Knowledge of the importance of input features towards decisions made by machine-learning models is essential to increase our understanding of both the models and the underlying data. Here, we present a new approach to estimating feature importance with neural networks based on the idea of distributing the features of interest among experts in an attentive mixture of experts (AME). AMEs couple attentive gating networks with a Granger-causal objective to jointly produce accurate predictions as well as estimates of feature importance. Our experiments on an established benchmark and two real-world datasets show (i) that the feature importance estimates provided by AMEs compare favourably to those provided by state-of-the-art methods, (ii) that AMEs are significantly faster than existing methods, and (iii) that the associations discovered by AMEs are consistent with those reported by domain experts. In addition, we analyse the trade-off between predictive performance and estimation accuracy, the degree to which importance estimates of existing methods conform to predictive value, and whether a lower Granger-causal error on held-out data indicates a better feature importance estimation accuracy.

Several recently developed Multi-Agent Path Finding (MAPF) solvers scale to large MAPF instances by searching for MAPF plans on 2 levels: The high-level search resolves collisions between agents, and the low-level search plans paths for single agents under the constraints imposed by the high-level search. We make the following contributions to solve the MAPF problem with imperfect plan execution with small average makespans: First, we formalize the MAPF Problem with Delay Probabilities (MAPF-DP), define valid MAPF-DP plans and propose the use of robust plan-execution policies for valid MAPF-DP plans to control how each agent proceeds along its path. Second, we discuss 2 classes of decentralized robust plan-execution policies (called Fully Synchronized Policies and Minimal Communication Policies) that prevent collisions during plan execution for valid MAPF-DP plans. Third, we present a 2-level MAPF-DP solver (called Approximate Minimization in Expectation) that generates valid MAPF-DP plans.