Empirical Sufficiency Lower Bounds for Language Modeling with Locally-Bootstrapped Semantic Structures (2023)

Abstract: In this work we build upon negative results from an attempt at language modeling with predicted semantic structure, in order to establish empirical lower bounds on what could have made the attempt successful. More specifically, we design a concise binary vector representation of semantic structure at the lexical level and evaluate in-depth how good an incremental tagger needs to be in order to achieve better-than-baseline performance with an end-to-end semantic-bootstrapping language model. We envision such a system as consisting of a (pretrained) sequential-neural component and a hierarchical-symbolic component working together to generate text with low surprisal and high linguistic interpretability. We find that (a) dimensionality of the semantic vector representation can be dramatically reduced without losing its main advantages and (b) lower bounds on prediction quality cannot be established via a single score alone, but need to take the distributions of signal and noise into account.

## introduction it is well-established by now that large pretrained transformer language models (lms) can obtain detectable knowledge about linguistic structure from raw text distributions @xcite , thus continuing a long line of research in collecting solid empirical evidence for the distributional hypothesis @xcite . this is often presented in stark contrast to symbolic linguistic theories and representations, which put more emphasis on higherlevel structural principles. in practice, purely neural models have achieved groundbreaking performances in a wide range of nlp tasks @xcite in a much more scalable manner than seems to be possible with symbolic ones. still, theoretical linguistic questions 1 our experimental code is available at https:// github.com/jakpra/sufficiencylowerbounds . figure 1 : example of incremental semantic graph slices obtained from a ptg graph and information flow in a (hypothetical) semantic-bootstrapping lm. in this example, the dark-red-shaded token 'to' is the current lm target; the light-yellow-shaded cells to the left and below directly influence the lm decision as in p+22; and the pink arrow marked with ? stands for the intermediate slice prediction step, for which we want to establish sufficiency lower bounds. p+22's results seem to suggest that at least some aspects of symbolic semantic structure may not be contained in the incremental lm's representationi.e., that these aspects might constitute an instance of grounding, which is helpful for language understanding, but not fully learnable from text alone. alternatively, we consider the possibility that the crucial semantic information could be learned, extracted, or induced to a sufficient extent, if only explicit supervision were provided at training time. the notion of sufficiency, in our case, relates to the potential of improving over a baseline lm ( §3). this paints a grand vision of semantic bootstrapping, i.e., a scenario in which the lm first commits to local semantic structure based on the revealed sentence prefix (pink ? arrow in fig. 1 ) and then uses its prediction to reduce the next token's perplexity. the work by p+22 established upper bounds by using an oracle setup where rich semantic structure inputs are known to be correct, not only during training but also at test time. as the main contribution of this work, assuming the local semantic bootstrapping scenario is feasible at all, we look instead for lower bounds on what would constitute sufficient substance and accuracy in predicted semantic structure for such an improved endto-end neuro-symbolic lm. concretely, we conduct two analyses: first, we make p+22's original formulation of semantic graph slices (sgs) more parsimonious ( §5). we extract binary vectors (b-sgs) representing only bare-bones (unlabeled and unanchored) structural relations ( §5.2) and find that they are sufficient for improving lm perplexity over a strong baseline in the oracle setting ( §5.3). second, we measure how the language modeling benefits of b-sgs are affected by increasing levels of noise, aiming to emulate various imperfect taggers ( §6). interestingly, a comparison of two different shuffling mechanisms ( §6.2) as well as a simple pilot tagger ( §6.1) reveals that how errors are distributed throughout the data is much more important than overall error rate. based on our observations, we establish sufficiency lower bounds of b-sgs for use in a semantic bootstrapping lm. we begin by providing the reader with relevant background information from the literature ( §2), defining concisely what we mean by sufficiency lower bounds ( §3), and describing our data set and general experimental setup ( §4). finally, we discuss our findings and limitations within the bigger picture of ongoing research directions ( §7). ## sufficiency lower bounds we introduce the concept of sufficiency 3 lower bounds on the strength of a data signal ξ in order for a system σ, which takes ξ as an input, to reach a certain performance threshold θ. in this work, the system σ is a neuro-symbolic lm as proposed by p+22 ( §2.1), ξ is an sgs vector representation ( §5) for each (sub)word token in a text corpus d, and θ is the baseline lm performance (measured as surprisal, §4.3). establishing such bounds is important because ξ's richness may need to be reduced in one way or another-either by theoretical design (because small, simple representations and models are desirable; §5), or by practical necessity (due to unavoidable noise in predicting ξ; §6). a main takeaway from our exploratory study is that it is important to identify (i.e., define or measure) candidate bounds in a way that considers the signal's configuration as a whole, rather than focusing on a single aggregate metric. 4 approached empirically, this involves computing (multivariate) distributions over ξ as instantiated in a data set d, such that when the system σ is run on d, the quality of its output is at least θ (i.e., it outperforms a baseline). simply put, if the signal ξ surpasses the sufficiency lower bound in d, it will likely enable the system σ to reach performance θ or better. ## discussion and conclusions we proposed a general framework for semanticallyenriched language modeling. our proposal aims to provide a new perspective on qualitative distributional linguistic analysis, expanding upon prior work in linguistic analysis of neural models in several ways ( §7.1). we implemented and tested this framework with gpt-2 and semantic graph slices (sgs) from two formalisms, finding interesting patterns with potential impact for meaning representation design and low-resource modeling ( §7.2).