arXiv subjects

Paul Smolensky

Publications and source records attributed to Paul Smolensky.

At least 19 recordsLinked to original sources

arXiv2026

The Emergent Symbolic Structure of Artificial Neural Networks

Modern systems in artificial intelligence (AI) somehow excel in domains for which they seem poorly suited. Intelligence has traditionally been modeled as operating over structured combinations of symbols, such as logical formulas. However, the strongest modern AI systems are based on neural networks, which instead represent information in continuous vectors. Vectors seem inadequate for capturing the structure of language, logic, and other cognitive domains, yet neural networks achieve impressive performance in these areas. How do they do it? In this work, we propose a potential answer: Despite appearances, perhaps the internal representations of neural networks implicitly realize symbolic structure. In support of this hypothesis, we show that the vector representations of a variety of neural networks can be closely approximated with symbolic structures: we can replace the network's entire representation-generating process with a closed-form equation instantiating a symbolic structure, and the network's behavior remains largely unchanged. This finding holds for both small-scale neural networks trained to manipulate lists as well as large language models (LLMs) operating in four domains that are central in symbolic traditions: arithmetic, logic, computer code, and language. Further, our symbolic approximation allows us to modify an LLM's behavior in targeted ways via precise interventions on its internal representations, showing that the LLM's behavior is reliant on the symbolic structures we have identified. This work provides a potential way to reconcile longstanding symbolic conceptions of intelligence with the vector-based nature of modern AI.

cs.CL↗

arXiv2026

GFlowRL: Scaling Distribution-Matching RL to Large Language Models

Generative Flow Networks (GFlowNets) offer a promising alternative to reward-maximizing reinforcement learning (RL) for large reasoning models, encouraging diverse reasoning paths by matching reward distributions rather than collapsing to dominant modes. Recent work shows promise on math and code, but scaling GFlowNet-style RL to modern post-training pipelines remains difficult: as model size, rollout horizon, reward noise, and distributed-systems complexity grow together, a learned prompt-conditional partition function becomes a source of gradient instability and engineering overhead rather than a useful normalizer. Through systematic analysis, we find that the learned partition function, previously treated as essential, can be replaced by an in-batch Monte Carlo estimate computed from the rollout group already required for training. We propose GFlowRL, a streamlined GFlowNet-style RL algorithm that removes the auxiliary partition network entirely while preserving the reward-distribution-matching objective, completed by two stabilizers: importance-sampling correction for rollout/trainer drift and asymmetric flow-gap clipping for outlier residuals. GFlowRL exceeds all counterparts on math, code, and adversarial red-teaming benchmarks, reaching a Codeforces rating of 2048 at the 14B scale (within 25 Elo of o3-mini) and attaining the highest average ASR@1 on AdvBench and HarmBench, outperforming the previous SOTA multi-turn attacker in a regime where FlowRL, a prior GFlowNet-style method, diverges. The same recipe transfers to all evaluated MoE configurations up to 235B parameters, where FlowRL again fails to converge. To our knowledge, GFlowRL is the first GFlowNet-style RL algorithm to scale stably across both dense and sparse architectures. Code will be at: https://github.com/microsoft/gflowrl

cs.CL↗

arXiv2025

Mechanisms of Symbol Processing for In-Context Learning in Transformer Networks

Large Language Models (LLMs) have demonstrated impressive abilities in symbol processing through in-context learning (ICL). This success flies in the face of decades of critiques asserting that artificial neural networks cannot master abstract symbol manipulation. We seek to understand the mechanisms that can enable robust symbol processing in transformer networks, illuminating both the unanticipated success, and the significant limitations, of transformers in symbol processing. Borrowing insights from symbolic AI and cognitive science on the power of Production System architectures, we develop a high-level Production System Language, PSL, that allows us to write symbolic programs to do complex, abstract symbol processing, and create compilers that precisely implement PSL programs in transformer networks which are, by construction, 100% mechanistically interpretable. The work is driven by study of a purely abstract (semantics-free) symbolic task that we develop, Templatic Generation (TGT). Although developed through study of TGT, PSL is, we demonstrate, highly general: it is Turing Universal. The new type of transformer architecture that we compile from PSL programs suggests a number of paths for enhancing transformers' capabilities at symbol processing. We note, however, that the work we report addresses computability, and not learnability, by transformer networks. Note: The first section provides an extended synopsis of the entire paper.

cs.AI↗

arXiv2025

TRA: Better Length Generalisation with Threshold Relative Attention

Transformers struggle with length generalisation, displaying poor performance even on basic tasks. We test whether these limitations can be explained through two key failures of the self-attention mechanism. The first is the inability to fully remove irrelevant information. The second is tied to position, even if the dot product between a key and query is highly negative (i.e. an irrelevant key) learned positional biases may unintentionally up-weight such information - dangerous when distances become out of distribution. Put together, these two failure cases lead to compounding generalisation difficulties. We test whether they can be mitigated through the combination of a) selective sparsity - completely removing irrelevant keys from the attention softmax and b) contextualised relative distance - distance is only considered as between the query and the keys that matter. We show how refactoring the attention mechanism with these two mitigations in place can substantially improve the generalisation capabilities of decoder only transformers.

cs.LG↗

arXiv2024

Compositional Generalization Across Distributional Shifts with Sparse Tree Operations

Neural networks continue to struggle with compositional generalization, and this issue is exacerbated by a lack of massive pre-training. One successful approach for developing neural systems which exhibit human-like compositional generalization is \textit{hybrid} neurosymbolic techniques. However, these techniques run into the core issues that plague symbolic approaches to AI: scalability and flexibility. The reason for this failure is that at their core, hybrid neurosymbolic models perform symbolic computation and relegate the scalable and flexible neural computation to parameterizing a symbolic system. We investigate a \textit{unified} neurosymbolic system where transformations in the network can be interpreted simultaneously as both symbolic and neural computation. We extend a unified neurosymbolic architecture called the Differentiable Tree Machine in two central ways. First, we significantly increase the model's efficiency through the use of sparse vector representations of symbolic structures. Second, we enable its application beyond the restricted set of tree2tree problems to the more general class of seq2seq problems. The improved model retains its prior generalization capabilities and, since there is a fully neural path through the network, avoids the pitfalls of other neurosymbolic techniques that elevate symbolic computation over neural computation.

cs.AI↗

arXiv2023

Implicit Chain of Thought Reasoning via Knowledge Distillation

To augment language models with the ability to reason, researchers usually prompt or finetune them to produce chain of thought reasoning steps before producing the final answer. However, although people use natural language to reason effectively, it may be that LMs could reason more effectively with some intermediate computation that is not in natural language. In this work, we explore an alternative reasoning approach: instead of explicitly producing the chain of thought reasoning steps, we use the language model's internal hidden states to perform implicit reasoning. The implicit reasoning steps are distilled from a teacher model trained on explicit chain-of-thought reasoning, and instead of doing reasoning "horizontally" by producing intermediate words one-by-one, we distill it such that the reasoning happens "vertically" among the hidden states in different layers. We conduct experiments on a multi-digit multiplication task and a grade school math problem dataset and find that this approach enables solving tasks previously not solvable without explicit chain-of-thought, at a speed comparable to no chain-of-thought.

cs.CL↗

arXiv2023

Differentiable Tree Operations Promote Compositional Generalization

In the context of structure-to-structure transformation tasks, learning sequences of discrete symbolic operations poses significant challenges due to their non-differentiability. To facilitate the learning of these symbolic sequences, we introduce a differentiable tree interpreter that compiles high-level symbolic tree operations into subsymbolic matrix operations on tensors. We present a novel Differentiable Tree Machine (DTM) architecture that integrates our interpreter with an external memory and an agent that learns to sequentially select tree operations to execute the target transformation in an end-to-end manner. With respect to out-of-distribution compositional generalization on synthetic semantic parsing and language generation tasks, DTM achieves 100% while existing baselines such as Transformer, Tree Transformer, LSTM, and Tree2Tree LSTM achieve less than 30%. DTM remains highly interpretable in addition to its perfect performance.

cs.CL↗

arXiv2022

Uncontrolled Lexical Exposure Leads to Overestimation of Compositional Generalization in Pretrained Models

Human linguistic capacity is often characterized by compositionality and the generalization it enables -- human learners can produce and comprehend novel complex expressions by composing known parts. Several benchmarks exploit distributional control across training and test to gauge compositional generalization, where certain lexical items only occur in limited contexts during training. While recent work using these benchmarks suggests that pretrained models achieve impressive generalization performance, we argue that exposure to pretraining data may break the aforementioned distributional control. Using the COGS benchmark of Kim and Linzen (2020), we test two modified evaluation setups that control for this issue: (1) substituting context-controlled lexical items with novel character sequences, and (2) substituting them with special tokens represented by novel embeddings. We find that both of these setups lead to lower generalization performance in T5 (Raffel et al., 2020), suggesting that previously reported results have been overestimated due to uncontrolled lexical exposure during pretraining. The performance degradation is more extreme with novel embeddings, and the degradation increases with the amount of pretraining data, highlighting an interesting case of inverse scaling.

cs.CL↗

arXiv2022

Structural Biases for Improving Transformers on Translation into Morphologically Rich Languages

Machine translation has seen rapid progress with the advent of Transformer-based models. These models have no explicit linguistic structure built into them, yet they may still implicitly learn structured relationships by attending to relevant tokens. We hypothesize that this structural learning could be made more robust by explicitly endowing Transformers with a structural bias, and we investigate two methods for building in such a bias. One method, the TP-Transformer, augments the traditional Transformer architecture to include an additional component to represent structure. The second method imbues structure at the data level by segmenting the data with morphological tokenization. We test these methods on translating from English into morphologically rich languages, Turkish and Inuktitut, and consider both automatic metrics and human evaluations. We find that each of these two approaches allows the network to achieve better performance, but this improvement is dependent on the size of the dataset. In sum, structural encoding methods make Transformers more sample-efficient, enabling them to perform better from smaller amounts of data.

cs.CL↗

arXiv2022

Neurocompositional computing: From the Central Paradox of Cognition to a new generation of AI systems

What explains the dramatic progress from 20th-century to 21st-century AI, and how can the remaining limitations of current AI be overcome? The widely accepted narrative attributes this progress to massive increases in the quantity of computational and data resources available to support statistical learning in deep artificial neural networks. We show that an additional crucial factor is the development of a new type of computation. Neurocompositional computing adopts two principles that must be simultaneously respected to enable human-level cognition: the principles of Compositionality and Continuity. These have seemed irreconcilable until the recent mathematical discovery that compositionality can be realized not only through discrete methods of symbolic computing, but also through novel forms of continuous neural computing. The revolutionary recent progress in AI has resulted from the use of limited forms of neurocompositional computing. New, deeper forms of neurocompositional computing create AI systems that are more robust, accurate, and comprehensible.

cs.AI↗

arXiv2021

How much do language models copy from their training data? Evaluating linguistic novelty in text generation using RAVEN

Current language models can generate high-quality text. Are they simply copying text they have seen before, or have they learned generalizable linguistic abstractions? To tease apart these possibilities, we introduce RAVEN, a suite of analyses for assessing the novelty of generated text, focusing on sequential structure (n-grams) and syntactic structure. We apply these analyses to four neural language models (an LSTM, a Transformer, Transformer-XL, and GPT-2). For local structure - e.g., individual dependencies - model-generated text is substantially less novel than our baseline of human-generated text from each model's test set. For larger-scale structure - e.g., overall sentence structure - model-generated text is as novel or even more novel than the human-generated baseline, but models still sometimes copy substantially, in some cases duplicating passages over 1,000 words long from the training set. We also perform extensive manual analysis showing that GPT-2's novel text is usually well-formed morphologically and syntactically but has reasonably frequent semantic issues (e.g., being self-contradictory).

cs.CL↗

arXiv2021

Scalable knowledge base completion with superposition memories

We present Harmonic Memory Networks (HMem), a neural architecture for knowledge base completion that models entities as weighted sums of pairwise bindings between an entity's neighbors and corresponding relations. Since entities are modeled as aggregated neighborhoods, representations of unseen entities can be generated on the fly. We demonstrate this with two new datasets: WNGen and FBGen. Experiments show that the model is SOTA on benchmarks, and flexible enough to evolve without retraining as the knowledge graph grows.

cs.CL↗

arXiv2021

Distributed neural encoding of binding to thematic roles

A framework and method are proposed for the study of constituent composition in fMRI. The method produces estimates of neural patterns encoding complex linguistic structures, under the assumption that the contributions of individual constituents are additive. Like usual techniques for modeling compositional structure in fMRI, the proposed method employs pattern superposition to synthesize complex structures from their parts. Unlike these techniques, superpositions are sensitive to the structural positions of constituents, making them irreducible to structure-indiscriminate ("bag-of-words") models of composition. Reanalyzing data from a study by Frankland and Greene (2015), it is shown that comparison of neural predictive models with differing specifications can illuminate aspects of neural representational contents that are not apparent when composition is not modelled. The results indicate that the neural instantiations of the binding of fillers to thematic roles in a sentence are non-orthogonal, and therefore spatially overlapping.

cs.CL↗

arXiv2021

Enriching Transformers with Structured Tensor-Product Representations for Abstractive Summarization

Abstractive summarization, the task of generating a concise summary of input documents, requires: (1) reasoning over the source document to determine the salient pieces of information scattered across the long document, and (2) composing a cohesive text by reconstructing these salient facts into a shorter summary that faithfully reflects the complex relations connecting these facts. In this paper, we adapt TP-TRANSFORMER (Schlag et al., 2019), an architecture that enriches the original Transformer (Vaswani et al., 2017) with the explicitly compositional Tensor Product Representation (TPR), for the task of abstractive summarization. The key feature of our model is a structural bias that we introduce by encoding two separate representations for each token to represent the syntactic structure (with role vectors) and semantic content (with filler vectors) separately. The model then binds the role and filler vectors into the TPR as the layer output. We argue that the structured intermediate representations enable the model to take better control of the contents (salient facts) and structures (the syntax that connects the facts) when generating the summary. Empirically, we show that our TP-TRANSFORMER outperforms the Transformer and the original TP-TRANSFORMER significantly on several abstractive summarization datasets based on both automatic and human evaluations. On several syntactic and semantic probing tasks, we demonstrate the emergent structural information in the role vectors and improved syntactic interpretability in the TPR layer outputs. Code and models are available at https://github.com/jiangycTarheel/TPT-Summ.

cs.CL↗

arXiv2021

Compositional Processing Emerges in Neural Networks Solving Math Problems

A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations (e.g., auditory speech), and use this knowledge to guide the composition of simpler meanings into complex wholes. Recent progress in artificial neural networks has shown that when large models are trained on enough linguistic data, grammatical structure emerges in their representations. We extend this work to the domain of mathematical reasoning, where it is possible to formulate precise hypotheses about how meanings (e.g., the quantities corresponding to numerals) should be composed according to structured rules (e.g., order of operations). Our work shows that neural networks are not only able to infer something about the structured relationships implicit in their training data, but can also deploy this knowledge to guide the composition of individual meanings into composite wholes.

cs.LG↗

arXiv2021

HUBERT Untangles BERT to Improve Transfer across NLP Tasks

We introduce HUBERT which combines the structured-representational power of Tensor-Product Representations (TPRs) and BERT, a pre-trained bidirectional Transformer language model. We show that there is shared structure between different NLP datasets that HUBERT, but not BERT, is able to learn and leverage. We validate the effectiveness of our model on the GLUE benchmark and HANS dataset. Our experiment results show that untangling data-specific semantics from general language structure is key for better transfer among NLP tasks.

cs.CL↗

arXiv2020

Neuro-Symbolic Representations for Video Captioning: A Case for Leveraging Inductive Biases for Vision and Language

Neuro-symbolic representations have proved effective in learning structure information in vision and language. In this paper, we propose a new model architecture for learning multi-modal neuro-symbolic representations for video captioning. Our approach uses a dictionary learning-based method of learning relations between videos and their paired text descriptions. We refer to these relations as relative roles and leverage them to make each token role-aware using attention. This results in a more structured and interpretable architecture that incorporates modality-specific inductive biases for the captioning task. Intuitively, the model is able to learn spatial, temporal, and cross-modal relations in a given pair of video and text. The disentanglement achieved by our proposal gives the model more capacity to capture multi-modal structures which result in captions with higher quality for videos. Our experiments on two established video captioning datasets verifies the effectiveness of the proposed approach based on automatic metrics. We further conduct a human evaluation to measure the grounding and relevance of the generated captions and observe consistent improvement for the proposed model. The codes and trained models can be found at https://github.com/hassanhub/R3Transformer

cs.CV↗

arXiv2020

Discovering the Compositional Structure of Vector Representations with Role Learning Networks

How can neural networks perform so well on compositional tasks even though they lack explicit compositional representations? We use a novel analysis technique called ROLE to show that recurrent neural networks perform well on such tasks by converging to solutions which implicitly represent symbolic structure. This method uncovers a symbolic structure which, when properly embedded in vector space, closely approximates the encodings of a standard seq2seq network trained to perform the compositional SCAN task. We verify the causal importance of the discovered symbolic structure by showing that, when we systematically manipulate hidden embeddings based on this symbolic structure, the model's output is changed in the way predicted by our analysis.

cs.LG↗