A Non-Linear Structural Probe (2105.10185v1)

Abstract: Probes are models devised to investigate the encoding of knowledge -- e.g. syntactic structure -- in contextual representations. Probes are often designed for simplicity, which has led to restrictions on probe design that may not allow for the full exploitation of the structure of encoded information; one such restriction is linearity. We examine the case of a structural probe (Hewitt and Manning, 2019), which aims to investigate the encoding of syntactic structure in contextual representations through learning only linear transformations. By observing that the structural probe learns a metric, we are able to kernelize it and develop a novel non-linear variant with an identical number of parameters. We test on 6 languages and find that the radial-basis function (RBF) kernel, in conjunction with regularization, achieves a statistically significant improvement over the baseline in all languages -- implying that at least part of the syntactic knowledge is encoded non-linearly. We conclude by discussing how the RBF kernel resembles BERT's self-attention layers and speculate that this resemblance leads to the RBF-based probe's stronger performance.

• The paper introduces a kernelized non-linear probe to uncover syntactic encodings in contextual models such as BERT.
• It transforms linear structural probes into non-linear variants using polynomial, RBF, and sigmoid kernels without increasing parameter counts.
• Empirical results across six languages show improved UUAS metrics, demonstrating the probe's effectiveness in capturing non-linear syntactic relationships.

A Non-Linear Structural Probe

The paper "A Non-Linear Structural Probe" (2105.10185) presents a novel approach to probing the encoding of syntactic information in contextual representations by introducing a non-linear variant of a structural probe. This new paradigm leverages a kernelized extension for enhancing the expressivity of structural probes without increasing their parameter count, thereby maintaining model simplicity while extracting richer syntactic structures.

Introduction to Probing and Challenges

Probing techniques have long been employed to ascertain the extent of linguistic features encoded in models such as BERT and ELMo. Historically, these probes have been deliberately simplistic to ensure they do not merely learn to solve NLP tasks themselves but rather reveal the presence of linguistic structures within representations. The prevalent use of linearity in probes has restricted their capacity to fully exploit non-linear syntactic encodings—a potential oversight given the complex architectures of models like BERT.

The Structural Probe Framework

The paper revisits the structural probe introduced by Hewitt and Manning, which originally adopted a linear transformation approach to learn syntactic distances in contextual embeddings. By treating the problem as one of metric learning, the authors propose transforming the classical linear probe into a non-linear form via kernelization. This allows the probe to effectively capture non-linear syntactic relationships, thus aligning more closely with the complex, non-linear architecture of models such as BERT.

Kernelized Metric Learning

The non-linear approach employs a variety of kernel functions—namely, polynomial, RBF (radial-basis function), and sigmoid kernels—to expand the probe's capacity without introducing additional parameters. The paper highlights the suitability of the RBF kernel in particular, drawing parallels between its formulation and BERT's self-attention mechanism. This congruence suggests that syntactic structures are encoded in a manner naturally accessible through RBF-like metrics.

Experimental Results

Empirical evaluations conducted across six languages demonstrate the superior performance of the RBF kernel-enhanced probe over its linear predecessor, particularly in unlabeled undirected attachment score (UUAS) metrics. The improvements underscore the hypothesis that non-linear encodings are integral to how BERT processes syntactic information. The analysis further reveals the probe’s sensitivity to proximal syntactic relationships, aligning with known linguistic dependencies where nearby words exhibit higher mutual information.

Implications and Considerations

The paper advances the understanding of how syntactic structures are embedded within contextual representations. By demonstrating that kernelization can provide a more nuanced extraction of syntactic information, the paper posits that models like BERT inherently encode information in complex, non-linear spaces. This insight fosters a deeper comprehension of BERT’s attention mechanisms, suggesting a potential framework for future research into model interpretability and enhancement.

Conclusion

In conclusion, this research highlights significant benefits in adopting a non-linear probing approach to uncovering syntactic encodings in contextual representations. The incorporation of kernelized methods foreshadows broader applications across diverse linguistic tasks and sets a precedent for exploring more intricate relationships within neural network architectures. As research continues to refine these probing techniques, the field moves closer to unraveling the intricacies of LLM representations in AI.