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Abstraction is a desirable capability for deep learning models, which means to induce abstract concepts from concrete instances and flexibly apply them beyond the learning context. At the same time, there is a lack of clear understanding…
Current methods for the interpretability of discriminative deep neural networks commonly rely on the model's input-gradients, i.e., the gradients of the output logits w.r.t. the inputs. The common assumption is that these input-gradients…
Chain-of-Thought (CoT) prompting substantially improves the sample efficiency of transformers, reducing the complexity of tasks like parity learning from exponential to polynomial in the input length. However, generating explicit reasoning…
Understanding the internal mechanisms of GPT-style transformers, particularly their capacity to perform in-context learning (ICL), is critical for advancing AI alignment and interpretability. In-context learning allows transformers to…
Causal transformer language models (LMs), such as GPT-3, typically require some form of positional encoding, such as positional embeddings. However, we show that LMs without any explicit positional encoding are still competitive with…
When trained on tasks requiring an understanding of hierarchical structure, transformers have been found to represent this hierarchy in distinct ways: in the geometry of the residual stream, and in stack-like attention patterns maintaining…
Recent studies suggest that large language models (LLMs) possess the capability to solve graph reasoning tasks. Notably, even when graph structures are embedded within textual descriptions, LLMs can still effectively answer related…
Implicit deep learning prediction rules generalize the recursive rules of feedforward neural networks. Such rules are based on the solution of a fixed-point equation involving a single vector of hidden features, which is thus only…
We introduce a dataset of concept learning tasks that helps uncover implicit biases in large language models. Using in-context concept learning experiments, we found that language models may have a bias toward upward monotonicity in…
Finite element methods typically require a high resolution to satisfactorily approximate micro and even macro patterns of an underlying physical model. This issue can be circumvented by appropriate multiscale strategies that are able to…
Architectural obfuscation - e.g., permuting hidden-state tensors, linearly transforming embedding tables, or remapping tokens - has recently gained traction as a lightweight substitute for heavyweight cryptography in privacy-preserving…
Two pressing topics in the theory of deep learning are the interpretation of feature learning (FL) mechanisms and the determination of implicit bias of networks in the rich regime. Current theories of rich FL often appear in the form of…
With the methodological support of probing (or diagnostic classification), recent studies have demonstrated that Transformers encode syntactic and semantic information to some extent. Following this line of research, this paper aims at…
An extension of Transformers is proposed that enables explicit relational reasoning through a novel module called the Abstractor. At the core of the Abstractor is a variant of attention called relational cross-attention. The approach is…
Linear probes and sparse autoencoders consistently recover meaningful structure from transformer representations -- yet why should such simple methods succeed in deep, nonlinear systems? We show this is not merely an empirical regularity…
Transformer based large language models have achieved tremendous success. However, the significant memory and computational costs incurred during the inference process make it challenging to deploy large models on resource-constrained…
Coinduction occurs in two guises in Horn clause logic: in proofs of self-referencing properties and relations, and in proofs involving construction of (possibly irregular) infinite data. Both instances of coinductive reasoning appeared in…
We propose a framework for reasoning about programs that manipulate coinductive data as well as inductive data. Our approach is based on using equational programs, which support a seamless combination of computation and reasoning, and using…
Algorithmic reasoning requires capabilities which are most naturally understood through recurrent models of computation, like the Turing machine. However, Transformer models, while lacking recurrence, are able to perform such reasoning…
One explanation for the strong generalization ability of neural networks is implicit bias. Yet, the definition and mechanism of implicit bias in non-linear contexts remains little understood. In this work, we propose to characterize…