Systematic generalization refers to the capacity to understand and generate novel combinations from known components. Despite recent progress by large language models (LLMs) across various domains, these models often fail to extend their knowledge to novel compositional scenarios, revealing notable limitations in systematic generalization. There has been an ongoing debate about whether neural networks possess the capacity for systematic generalization, with recent studies suggesting that meta-learning approaches designed for compositionality can significantly enhance this ability. However, these insights have largely been confined to linguistic problems, leaving their applicability to other tasks an open question. In this study, we extend the approach of meta-learning for compositionality to the domain of abstract spatial reasoning. To this end, we introduce $\textit{SYGAR}$-a dataset designed to evaluate the capacity of models to systematically generalize from known geometric transformations (e.g., translation, rotation) of two-dimensional objects to novel combinations of these transformations (e.g., translation+rotation). Our results show that a transformer-based encoder-decoder model, trained via meta-learning for compositionality, can systematically generalize to previously unseen transformation compositions, significantly outperforming state-of-the-art LLMs, including o3-mini, GPT-4o, and Gemini 2.0 Flash, which fail to exhibit similar systematic behavior. Our findings highlight the effectiveness of meta-learning in promoting systematicity beyond linguistic tasks, suggesting a promising direction toward more robust and generalizable models.
The integration of explicit Chain-of-Thought (CoT) reasoning into training large language models (LLMs) has advanced their reasoning capabilities, yet the mechanisms by which CoT enhances generalization remain poorly understood. This work investigates (1) \textit{how} CoT training reshapes internal model representations and (2) \textit{why} it improves both in-distribution (ID) and out-of-distribution (OOD) reasoning generalization. Through controlled experiments and theoretical analysis, we derive the following key insights. \textbf{1)} Structural Advantage: CoT training internalizes reasoning into a two-stage generalizing circuit, where the number of stages corresponds to the explicit reasoning steps during training. Notably, CoT-trained models resolve intermediate results at shallower layers compared to non-CoT counterparts, freeing up deeper layers to specialize in subsequent reasoning steps. \textbf{2)} Theoretical Analysis: the information-theoretic generalization bounds via distributional divergence can be decomposed into ID and OOD components. While ID error diminishes with sufficient training regardless of CoT, OOD error critically depends on CoT: Non-CoT training fails to generalize to OOD samples due to unseen reasoning patterns, whereas CoT training achieves near-perfect OOD generalization by mastering subtasks and reasoning compositions during training. The identified mechanisms explain our experimental results: CoT training accelerates convergence and enhances generalization from ID to both ID and OOD scenarios while maintaining robust performance even with tolerable noise. These findings are further validated on complex real-world datasets. This paper offers valuable insights for designing CoT strategies to enhance LLM reasoning robustness.
Sample efficiency and systematic generalization are two long-standing challenges in reinforcement learning. Previous studies have shown that involving natural language along with other observation modalities can improve generalization and sample efficiency due to its compositional and open-ended nature. However, to transfer these properties of language to the decision-making process, it is necessary to establish a proper language grounding mechanism. One approach to this problem is applying inductive biases to extract fine-grained and informative representations from the observations, which makes them more connectable to the language units. We provide architecture-level inductive biases for modularity and sparsity mainly based on Neural Production Systems (NPS). Alongside NPS, we assign a central role to memory in our architecture. It can be seen as a high-level information aggregator which feeds policy/value heads with comprehensive information and simultaneously guides selective attention in NPS through attentional feedback. Our results in the BabyAI environment suggest that the proposed model's systematic generalization and sample efficiency are improved significantly compared to previous models. An extensive ablation study on variants of the proposed method is conducted, and the effectiveness of each employed technique on generalization, sample efficiency, and training stability is specified.
Grounding the instruction in the environment is a key step in solving language-guided goal-reaching reinforcement learning problems. In automated reinforcement learning, a key concern is to enhance the model's ability to generalize across various tasks and environments. In goal-reaching scenarios, the agent must comprehend the different parts of the instructions within the environmental context in order to complete the overall task successfully. In this work, we propose CAREL (Cross-modal Auxiliary REinforcement Learning) as a new framework to solve this problem using auxiliary loss functions inspired by video-text retrieval literature and a novel method called instruction tracking, which automatically keeps track of progress in an environment. The results of our experiments suggest superior sample efficiency and systematic generalization for this framework in multi-modal reinforcement learning problems. Our code base is available here.
Graph-based machine learning models for materials properties show great potential to accelerate virtual high-throughput screening of large chemical spaces. However, in their simplest forms, graph-based models do not include any 3D information and are unable to distinguish stereoisomers such as those arising from different orderings of ligands around a metal center in coordination complexes. In this work we present a modification to revised autocorrelation descriptors, our molecular graph featurization method for machine learning various spin state dependent properties of octahedral transition metal complexes (TMCs). Inspired by analytical semi-empirical models for TMCs, the new modeling strategy is based on the many-body expansion (MBE) and allows one to tune the captured stereoisomer information by changing the truncation order of the MBE. We present the necessary modifications to include this approach in two commonly used machine learning methods, kernel ridge regression and feed-forward neural networks. On a test set composed of all possible isomers of binary transition metal complexes, the best MBE models achieve mean absolute errors of 2.75 kcal/mol on spin-splitting energies and 0.26 eV on frontier orbital energy gaps, a 30-40% reduction in error compared to models based on our previous approach. We also observe improved generalization to previously unseen ligands where the best-performing models exhibit mean absolute errors of 4.00 kcal/mol (i.e., a 0.73 kcal/mol reduction) on the spin-splitting energies and 0.53 eV (i.e., a 0.10 eV reduction) on the frontier orbital energy gaps. Because the new approach incorporates insights from electronic structure theory, such as ligand additivity relationships, these models exhibit systematic generalization from homoleptic to heteroleptic complexes, allowing for efficient screening of TMC search spaces.
A number of machine learning models have been proposed with the goal of achieving systematic generalization: the ability to reason about new situations by combining aspects of previous experiences. These models leverage compositional architectures which aim to learn specialized modules dedicated to structures in a task that can be composed to solve novel problems with similar structures. While the compositionality of these architectures is guaranteed by design, the modules specializing is not. Here we theoretically study the ability of network modules to specialize to useful structures in a dataset and achieve systematic generalization. To this end we introduce a minimal space of datasets motivated by practical systematic generalization benchmarks. From this space of datasets we present a mathematical definition of systematicity and study the learning dynamics of linear neural modules when solving components of the task. Our results shed light on the difficulty of module specialization, what is required for modules to successfully specialize, and the necessity of modular architectures to achieve systematicity. Finally, we confirm that the theoretical results in our tractable setting generalize to more complex datasets and non-linear architectures.
Developing models that can learn to reason is a notoriously challenging problem. We focus on reasoning in relational domains, where the use of Graph Neural Networks (GNNs) seems like a natural choice. However, previous work on reasoning with GNNs has shown that such models tend to fail when presented with test examples that require longer inference chains than those seen during training. This suggests that GNNs lack the ability to generalize from training examples in a systematic way, which would fundamentally limit their reasoning abilities. A common solution is to instead rely on neuro-symbolic methods, which are capable of reasoning in a systematic way by design. Unfortunately, the scalability of such methods is often limited and they tend to rely on overly strong assumptions, e.g.\ that queries can be answered by inspecting a single relational path. In this paper, we revisit the idea of reasoning with GNNs, showing that systematic generalization is possible as long as the right inductive bias is provided. In particular, we argue that node embeddings should be treated as epistemic states and that GNN should be parameterised accordingly. We propose a simple GNN architecture which is based on this view and show that it is capable of achieving state-of-the-art results. We furthermore introduce a benchmark which requires models to aggregate evidence from multiple relational paths. We show that existing neuro-symbolic approaches fail on this benchmark, whereas our considered GNN model learns to reason accurately.
In 2021, Adam Zsolt Wagner proposed an approach to disprove conjectures in graph theory using Reinforcement Learning (RL). Wagner's idea can be framed as follows: consider a conjecture, such as a certain quantity f(G) < 0 for every graph G; one can then play a single-player graph-building game, where at each turn the player decides whether to add an edge or not. The game ends when all edges have been considered, resulting in a certain graph G_T, and f(G_T) is the final score of the game; RL is then used to maximize this score. This brilliant idea is as simple as innovative, and it lends itself to systematic generalization. Several different single-player graph-building games can be employed, along with various RL algorithms. Moreover, RL maximizes the cumulative reward, allowing for step-by-step rewards instead of a single final score, provided the final cumulative reward represents the quantity of interest f(G_T). In this paper, we discuss these and various other choices that can be significant in Wagner's framework. As a contribution to this systematization, we present four distinct single-player graph-building games. Each game employs both a step-by-step reward system and a single final score. We also propose a principled approach to select the most suitable neural network architecture for any given conjecture, and introduce a new dataset of graphs labeled with their Laplacian spectra. Furthermore, we provide a counterexample for a conjecture regarding the sum of the matching number and the spectral radius, which is simpler than the example provided in Wagner's original paper. The games have been implemented as environments in the Gymnasium framework, and along with the dataset, are available as open-source supplementary materials.
Neuro-symbolic neural networks have been extensively studied to integrate symbolic operations with neural networks, thereby improving systematic generalization. Specifically, Tensor Product Representation (TPR) framework enables neural networks to perform differentiable symbolic operations by encoding the symbolic structure of data within vector spaces. However, TPR-based neural networks often struggle to decompose unseen data into structured TPR representations, undermining their symbolic operations. To address this decomposition problem, we propose a Discrete Dictionary-based Decomposition (D3) layer designed to enhance the decomposition capabilities of TPR-based models. D3 employs discrete, learnable key-value dictionaries trained to capture symbolic features essential for decomposition operations. It leverages the prior knowledge acquired during training to generate structured TPR representations by mapping input data to pre-learned symbolic features within these dictionaries. D3 is a straightforward drop-in layer that can be seamlessly integrated into any TPR-based model without modifications. Our experimental results demonstrate that D3 significantly improves the systematic generalization of various TPR-based models while requiring fewer additional parameters. Notably, D3 outperforms baseline models on the synthetic task that demands the systematic decomposition of unseen combinatorial data.
Learning modular object-centric representations is crucial for systematic generalization. Existing methods show promising object-binding capabilities empirically, but theoretical identifiability guarantees remain relatively underdeveloped. Understanding when object-centric representations can theoretically be identified is crucial for scaling slot-based methods to high-dimensional images with correctness guarantees. To that end, we propose a probabilistic slot-attention algorithm that imposes an aggregate mixture prior over object-centric slot representations, thereby providing slot identifiability guarantees without supervision, up to an equivalence relation. We provide empirical verification of our theoretical identifiability result using both simple 2-dimensional data and high-resolution imaging datasets.
In recent research, Tensor Product Representation (TPR) is applied for the systematic generalization task of deep neural networks by learning the compositional structure of data. However, such prior works show limited performance in discovering and representing the symbolic structure from unseen test data because their decomposition to the structural representations was incomplete. In this work, we propose an Attention-based Iterative Decomposition (AID) module designed to enhance the decomposition operations for the structured representations encoded from the sequential input data with TPR. Our AID can be easily adapted to any TPR-based model and provides enhanced systematic decomposition through a competitive attention mechanism between input features and structured representations. In our experiments, AID shows effectiveness by significantly improving the performance of TPR-based prior works on the series of systematic generalization tasks. Moreover, in the quantitative and qualitative evaluations, AID produces more compositional and well-bound structural representations than other works.
Human visual reasoning is characterized by an ability to identify abstract patterns from only a small number of examples, and to systematically generalize those patterns to novel inputs. This capacity depends in large part on our ability to represent complex visual inputs in terms of both objects and relations. Recent work in computer vision has introduced models with the capacity to extract object-centric representations, leading to the ability to process multi-object visual inputs, but falling short of the systematic generalization displayed by human reasoning. Other recent models have employed inductive biases for relational abstraction to achieve systematic generalization of learned abstract rules, but have generally assumed the presence of object-focused inputs. Here, we combine these two approaches, introducing Object-Centric Relational Abstraction (OCRA), a model that extracts explicit representations of both objects and abstract relations, and achieves strong systematic generalization in tasks (including a novel dataset, CLEVR-ART, with greater visual complexity) involving complex visual displays.
In multi-task learning, the conventional approach involves training a model on multiple tasks simultaneously. However, the training signals from different tasks can interfere with one another, potentially leading to \textit{negative transfer}. To mitigate this, we investigate if modular language models can facilitate positive transfer and systematic generalization. Specifically, we propose a novel modular language model (\texttt{TensorPoly}), that balances parameter efficiency with nuanced routing methods. For \textit{modules}, we reparameterize Low-Rank Adaptation (\texttt{LoRA}) by employing an entangled tensor through the use of tensor product operations and name the resulting approach \texttt{TLoRA}. For \textit{routing function}, we tailor two innovative routing functions according to the granularity: \texttt{TensorPoly-I} which directs to each rank within the entangled tensor while \texttt{TensorPoly-II} offers a finer-grained routing approach targeting each order of the entangled tensor. The experimental results from the multi-task T0-benchmark demonstrate that: 1) all modular LMs surpass the corresponding dense approaches, highlighting the potential of modular language models to mitigate negative inference in multi-task learning and deliver superior outcomes. 2) \texttt{TensorPoly-I} achieves higher parameter efficiency in adaptation and outperforms other modular LMs, which shows the potential of our approach in multi-task transfer learning.
Learning compositional representation is a key aspect of object-centric learning as it enables flexible systematic generalization and supports complex visual reasoning. However, most of the existing approaches rely on auto-encoding objective, while the compositionality is implicitly imposed by the architectural or algorithmic bias in the encoder. This misalignment between auto-encoding objective and learning compositionality often results in failure of capturing meaningful object representations. In this study, we propose a novel objective that explicitly encourages compositionality of the representations. Built upon the existing object-centric learning framework (e.g., slot attention), our method incorporates additional constraints that an arbitrary mixture of object representations from two images should be valid by maximizing the likelihood of the composite data. We demonstrate that incorporating our objective to the existing framework consistently improves the objective-centric learning and enhances the robustness to the architectural choices.
Abstract visual reasoning is a characteristically human ability, allowing the identification of relational patterns that are abstracted away from object features, and the systematic generalization of those patterns to unseen problems. Recent work has demonstrated strong systematic generalization in visual reasoning tasks involving multi-object inputs, through the integration of slot-based methods used for extracting object-centric representations coupled with strong inductive biases for relational abstraction. However, this approach was limited to problems containing a single rule, and was not scalable to visual reasoning problems containing a large number of objects. Other recent work proposed Abstractors, an extension of Transformers that incorporates strong relational inductive biases, thereby inheriting the Transformer's scalability and multi-head architecture, but it has yet to be demonstrated how this approach might be applied to multi-object visual inputs. Here we combine the strengths of the above approaches and propose Slot Abstractors, an approach to abstract visual reasoning that can be scaled to problems involving a large number of objects and multiple relations among them. The approach displays state-of-the-art performance across four abstract visual reasoning tasks, as well as an abstract reasoning task involving real-world images.
Despite the impressive performance in a variety of complex tasks, modern large language models (LLMs) still have trouble dealing with some math problems that are simple and intuitive for humans, such as addition. While we can easily learn basic rules of addition and apply them to new problems of any length, LLMs struggle to do the same. Instead, they may rely on similar cases seen in the training corpus for help. We define these two different reasoning mechanisms as "rule-based reasoning" and "case-based reasoning". Since rule-based reasoning is essential for acquiring systematic generalization ability, we aim to explore exactly whether transformers use rule-based or case-based reasoning for math problems. Through carefully designed intervention experiments on five math tasks, we confirm that transformers are performing case-based reasoning, no matter whether scratchpad is used, which aligns with the previous observations that transformers use subgraph matching/shortcut learning to reason. To mitigate such problems, we propose a Rule-Following Fine-Tuning (RFFT) technique to teach transformers to perform rule-based reasoning. Specifically, we provide explicit rules in the input and then instruct transformers to recite and follow the rules step by step. Through RFFT, we successfully enable LLMs fine-tuned on 1-5 digit addition to generalize to up to 12-digit addition with over 95% accuracy, which is over 40% higher than scratchpad. The significant improvement demonstrates that teaching LLMs to use rules explicitly helps them learn rule-based reasoning and generalize better in length.
The advent of the Transformer has led to the development of large language models (LLM), which appear to demonstrate human-like capabilities. To assess the generality of this class of models and a variety of other base neural network architectures to multimodal domains, we evaluated and compared their capacity for multimodal generalization. We introduce a multimodal question-answer benchmark to evaluate three specific types of out-of-distribution (OOD) generalization performance: distractor generalization (generalization in the presence of distractors), systematic compositional generalization (generalization to new task permutations), and productive compositional generalization (generalization to more complex tasks structures). We found that across model architectures (e.g., RNNs, Transformers, Perceivers, etc.), models with multiple attention layers, or models that leveraged cross-attention mechanisms between input domains, fared better. Our positive results demonstrate that for multimodal distractor and systematic generalization, either cross-modal attention or models with deeper attention layers are key architectural features required to integrate multimodal inputs. On the other hand, neither of these architectural features led to productive generalization, suggesting fundamental limitations of existing architectures for specific types of multimodal generalization. These results demonstrate the strengths and limitations of specific architectural components underlying modern neural models for multimodal reasoning. Finally, we provide Generic COG (gCOG), a configurable benchmark with several multimodal generalization splits, for future studies to explore.
Strong inductive biases enable learning from little data and help generalization outside of the training distribution. Popular neural architectures such as Transformers lack strong structural inductive biases for seq2seq NLP tasks on their own. Consequently, they struggle with systematic generalization beyond the training distribution, e.g. with extrapolating to longer inputs, even when pre-trained on large amounts of text. We show how a structural inductive bias can be efficiently injected into a seq2seq model by pre-training it to simulate structural transformations on synthetic data. Specifically, we inject an inductive bias towards Finite State Transducers (FSTs) into a Transformer by pre-training it to simulate FSTs given their descriptions. Our experiments show that our method imparts the desired inductive bias, resulting in improved systematic generalization and better few-shot learning for FST-like tasks. Our analysis shows that fine-tuned models accurately capture the state dynamics of the unseen underlying FSTs, suggesting that the simulation process is internalized by the fine-tuned model.
Compositional generalization is a key ability of humans that enables us to learn new concepts from only a handful examples. Neural machine learning models, including the now ubiquitous Transformers, struggle to generalize in this way, and typically require thousands of examples of a concept during training in order to generalize meaningfully. This difference in ability between humans and artificial neural architectures, motivates this study on a neuro-symbolic architecture called the Compositional Program Generator (CPG). CPG has three key features: \textit{modularity}, \textit{composition}, and \textit{abstraction}, in the form of grammar rules, that enable it to generalize both systematically to new concepts in a few-shot manner, as well as productively by length on various sequence-to-sequence language tasks. For each input, CPG uses a grammar of the input language and a parser to generate a parse in which each grammar rule is assigned its own unique semantic module, a probabilistic copy or substitution program. Instances with the same parse are always processed with the same composed modules, while those with different parses may be processed with different modules. CPG learns parameters for the modules and is able to learn the semantics for new rules and types incrementally, without forgetting or retraining on rules it's already seen. It achieves perfect generalization on both the SCAN and COGS benchmarks using just 14 examples for SCAN and 22 examples for COGS -- state-of-the-art accuracy with a 1000x improvement in sample efficiency.
Systematic generalization is a crucial aspect of intelligence, which refers to the ability to generalize to novel tasks by combining known subtasks and concepts. One critical factor that has been shown to influence systematic generalization is the diversity of training data. However, diversity can be defined in various ways, as data have many factors of variation. A more granular understanding of how different aspects of data diversity affect systematic generalization is lacking. We present new evidence in the problem of Visual Question Answering (VQA) that reveals that the diversity of simple tasks (i.e. tasks formed by a few subtasks and concepts) plays a key role in achieving systematic generalization. This implies that it may not be essential to gather a large and varied number of complex tasks, which could be costly to obtain. We demonstrate that this result is independent of the similarity between the training and testing data and applies to well-known families of neural network architectures for VQA (i.e. monolithic architectures and neural module networks). Additionally, we observe that neural module networks leverage all forms of data diversity we evaluated, while monolithic architectures require more extensive amounts of data to do so. These findings provide a first step towards understanding the interactions between data diversity design, neural network architectures, and systematic generalization capabilities.