SlowGuess/ACL_2020_OCR huggingface dataset:
The most similar previous channel model (Norris and McQueen 2008) was based on Dutch gating data (Smits et al. 2003) comparable to that used here. Norris and McQueen (2008) did not construct a triphone-to-uniphone channel model, but made use of all gates and also allowed investigation of word boundary identification.
3.5 Statistical methods
Prior to any analyses, the Switchboard and Buckeye corpora were each randomly divided into evenly-sized Training and Test sets. The Training sets were used for exploratory statistical analyses, and for determining the values of several model hyperparameters. Following this, all parameters and statistical analyses were frozen, and preregistered with the Open Science Foundation.[8]
We perform several linear regressions in order to determine the effect of confusability on word duration. Contextual confusability is defined throughout using Equation 9. Word durations are log-transformed. The following covariates are standard in the literature, and are included in our analyses: speaker identity; part of speech; unigram prior surprisal; speech rate (the average rate of speech, in syllables per second, of the utterance containing the target word); word length (measured by number of segments and syllables). Several covariates that are included are more non-trivial, and are discussed in more detail below: segmental inventory factors; forward and backward surprisal; neighborhood size and log weighted neighborhood density; and unigram confusability.
The segmental inventory variables code each word as a 'bag-of-segments.' A separate variable is defined for each phoneme in the segmental lexicon of the corpus. Each variable counts the number of times the corresponding phoneme occurs in the word. This is a variant of the baseline model
used in previous work (Bell et al. 2009, Gahl et al. 2012).
Certain segments take longer to pronounce than others, and the baseline model is used in case the confusability scores contain information about segment identities within a word. Note, however, that this is a conservative baseline, as segment identity has an effect on confusability; certain segments are, individually, harder to perceive than others. The model will be used to predict word durations after these segmental effects have been factored out.
The forward language-model surprisal of a word is the surprisal of the word given preceding words in the context, and its backward surprisal is the surprisal given the following words in the context. Previous work in English has found backward surprisal to be a stronger predictor of spoken word duration than forward surprisal (Bell et al. 2009, Seyfarth 2014). Word confusability is expected to be correlated with surprisal, as more surprising words will be more difficult for the listener to recover in the presence of noise.
Neighborhood size and log weighted neighborhood density are measures of the number of words adjacent (within Levenshtein distance 1) to a target word. These measures have been extensively studied as explanatory variables for word duration (see Gahl et al. 2012, Vitevitch and Luce 2016 for review), and are expected to correlate with word confusability: words with more neighbors are expected to be more confusable. We evaluate whether there is any residual effect of confusability beyond its impact on these variables.
Unigram confusability measures the confusability of a word (Equation 9) given a unigram (word frequency) language model. This is a measure of the out-of-context confusability of a word, as discussed below.
All variables are treated as fixed effects, and OLS is used for regressions. Confidence intervals and p-values are calculated using the bias-corrected bootstrap. Bootstrapping is used to address possible heteroskedasticity in the data. Random effects are not used due to potential issues arising in observational studies like the current one. In particular, random effects may correlate with predictors in an observational study, leading to incorrect estimates of uncertainty and the potential for bias (Bafumi and Gelman 2006, Wooldridge 2010).
The preregistered analyses are available at the following link: https://osf.io/gj3ph/?view_only=6c5bd9b1211e4b798d2268fb8a8f5842
9While Bafumi and Gelman (2006) propose a solution to
(a) Switchboard
(b)Buckeye
Figure 1: Confusability vs. log duration on the Test sets of the Switchboard and Buckeye corpora. Error bars are  $95\%$  confidence intervals (non-bootstrapped). As illustrated in Figure 2, data are sparse beyond 18 bits, resulting in large confidence intervals in this range.
Figure 2: Histogram of contextual confusability scores on the Test sets.
All analyses were performed in two ways: using the raw values for each variable, and with rank-transformed values for the continuous variables. The rank-transformed analyses provide a test of the papers hypothesis that greater (i.e. higher-rank) confusability is associated with longer (higherrank) duration. The analyses eliminate the potentially questionable parametric assumption of a linear relationship between confusability (in bits) and
duration (in log seconds). The rank-transformed analyses are intended as sensitivity analyses for the non-transformed analyses; if the two analyses provide different results, this provides evidence of a problem with the statistical methods.[10]
Four model hyperparameters were selected using the Switchboard and Buckeye Training sets: the order and direction of the n-gram model, the diphoneto-diphone channel pseudocounts, and the noise factor  $\lambda$ . Backward bigram language models were found to perform best on the Training sets, possibly due to distributional differences between these corpora and the Fisher corpus, which was used for language model estimation. This is consistent with prior work in the area (e.g. Bell et al. 2009, Seyfarth 2014). Pseudocounts were set to 0.01, and the term  $\lambda$  was set to  $2^{-6}$ .
Figure 2 shows the frequency of model-computed confusability scores on the Switchboard and Buckeye Test sets. Figure 1 shows the relationship between confusability and word duration on the Test sets.
The first set of analyses include all of the co
this problem by decorrelating the fixed effect from random effects, the method produces identical estimates for the fixed effect, and is primarily useful when the random effect estimates themselves are of interest.
10Model and analysis code is available at: https:// github.com/emeinhardt/wr
11The language model order was the same across all covariates where it was used.
Dataset	Rank	β	95% CI	p-value
SWBD	No	0.006	(0.004, 0.008)	0.001
SWBD	Yes	0.086	(0.067, 0.109)	0.001
Buckeye	No	0.005	(0.001, 0.008)	0.01
Buckeye	Yes	0.123	(0.080, 0.130)	0.001
Table 1: Effect of contextual confusability on log word duration, not controlling for unigram confusability. Estimates from the Test sets. Rank indicates whether continuous variables were rank-transformed. p-values are upper-bounds.
Dataset	Rank	β	95% CI	p-value
SWBD	No	0.009	(0.006, 0.011)	0.001
SWBD	Yes	0.132	(0.095, 0.130)	0.001
Buckeye	No	0.007	(0.003, 0.011)	0.001
Buckeye	Yes	0.148	(0.106, 0.164)	0.001
Table 2: Effect of contextual confusability on log word duration, controlling for unigram confusability. Estimates from the Test sets.
variates from Section 3.5, except for unigram confusability. This allows us to determine whether there is an effect of word confusability on duration, independent of whether this effect is sensitive to context. Greater confusability is associated with longer word durations on both the Switchboard and Buckeye Training sets (p<0.001 for all analyses). Table 1 shows results of the same analyses performed on the Test sets. The effects replicate on the Test sets, and are qualitatively similar when continuous variables are rank-transformed.
These analyses provide evidence that higher confusability is associated with longer word duration. In the second set of analyses, we investigate whether a context-sensitive measure of confusability is necessary for explaining this effect, or whether an out-of-context measure suffices. In order to do this, we include unigram confusability as a covariate in the analyses, in addition to the previous covariates. Unigram confusability is identical to our target measure of word confusability, except that the language model is replaced with a unigram model. The measure calculates a word's confusability based on its acoustic properties and its phonological similarity to other words. It therefore does not take into account top-down expectations based on a word's context.
After controlling for unigram confusability, contextual confusability remains associated with longer word durations on both the Switchboard and Buckeye Training sets  $(p < 0.001$  for all analyses). Table 2 shows the same analyses on the Test sets. The effects replicate on both Test sets, and similarly for the rank-transformed analyses.
4.1 Neighborhood density
We report the results of several unplanned analyses. Confidence intervals and p-values reported in this section are non-bootstrapped.
We evaluate the effect of neighborhood density on word duration in the Test sets. Weighted neighborhood density is associated with lower word duration in all analyses. (See Appendix B.) The results provide evidence that the neighborhood density effects identified in previous work remain qualitatively similar, after adjusting for contextual confusability.
We draw two main conclusions from our results. First, we provide evidence that speakers lengthen words that are more confusable. This supports the hypothesis that variation and structure in natural languages are shaped not only by pressures for efficient signals, but also pressures for effective communication of the speaker's intended message in the face of noise and uncertainty (Lindblom 1990, Lindblom et al. 1995, Hall et al. 2018).
Second, we provide large scale, naturalistic evidence for reduction and enhancement driven by contextual confusability. Conversational context may make a speaker's intended message easier or harder to recover from ambiguous acoustics. The results suggest that speakers modulate their utterances in a manner that is sensitive to this effect of context, increasing duration when context makes the intended utterance harder to recover.
The results complement previous work which demonstrates reduction and enhancement driven by contextual predictability (see e.g. Seyfarth 2014). They also complement work which shows confusability-driven reduction and enhancement in targeted experimental manipulations (see e.g. Kirov and Wilson 2012, Schertz 2013, Seyfarth et al. 2016, Buz et al. 2016).
The study may help to resolve questions raised by previous work examining the effects of neighborhood density. That work found negative or null
associations between word duration and neighborhood density and related measures (e.g. Gahl et al. 2012, Gahl and Strand 2016). The proposed confusability measure differs from neighborhood density in three ways: it is sensitive to edit type, words greater than two edits away, and top-down effects.
These differences may account for the discrepancy in the effects of neighborhood density and confusability. Under one hypothesis, neighborhood density effects reflect spillover of activation between words with overlapping subsequences of speech sounds (e.g. Gahl and Strand (2016), Chen and Mirman (2012), Dell (1986), Vitevitch and Luce (2016)). This spillover is potentially sensitive only to Levenshtein distance. In contrast, confusability is sensitive to fine-grained perceptual structure. When lexical neighbors differ in perceptually distinct segments, they will typically be nonconfusable.
A second hypothesis is that the discrepancy arises from the role of top-down expectations in confusability. Neighborhood effects are type-level phenomena: a word has the same neighbors no matter what context it appears in. Confusability, on the other hand, is a token-level phenomenon: contextual expectations will change the confusability of a word. Stable properties of the lexicon may determine which segment sequences undergo frequent articulatory rehearsal, and are reduced as a consequence. The confusability measure picks up on context-dependent variation, which rehearsal processes in the articulatory system may not be sensitive to.
The study suggests several directions for future work. First, while there are advantages of using naturalistic speech data (Gahl et al. 2012), it would be desirable to have experimental validation of the confusability measure and its relationship to speaker reduction. Second, a lower-perplexity neural language model would provide better estimates of a word's confusability, but would first need to be validated on speech data. Third, a more sophisticated channel model would allow for insertions and deletions, and better capture transitional coarticulatory cues (Wright 2004). Because speakers enhance or reduce their speech in ways other than changing duration (see e.g. Kirov and Wilson 2012, Schertz 2013, Seyfarth et al. 2016, Buz et al. 2016), such a model would permit investigation of targeted enhancement and reduction in naturalistic data.
We thank Uriel Cohen Priva and Scott Seyfarth for help reproducing their analyses. We also thank Silas Horton, Todd Williams, and Thanh Nguyen for computing support. The Titan V used for this research was donated by the NVIDIA Corporation.
Anderson, J. R. (1990). The adaptive character of thought. Erlbaum, Hillsdale, NJ.
Anderson, J. R. (1991). Is human cognition adaptive? Behavioral and Brain Sciences, 14:471-517.
Aylett, M. and Turk, A. (2004). The smooth signal redundancy hypothesis: a functional explanation for relationships between redundancy, prosodic prominence, and duration in spontaneous speech. Language and speech, 47(Pt 1):31-56.
Aylett, M. and Turk, A. (2006). Language redundancy predicts syllabic duration and the spectral characteristics of vocalic syllable nuclei. The Journal of the Acoustical Society of America, 119(5 Pt 1):3048-3058.
Bafumi, J. and Gelman, A. (2006). Fitting multilevel models when predictors and group effects correlate. Available at SSRN 1010095.
Bell, A., Brenier, J. M., Gregory, M., Girand, C., and Jurafsky, D. (2009). Predictability effects on durations of content and function words in conversational English. Journal of Memory and Language, 60(1):92-111.
Buz, E., Tanenhaus, M. K., and Jaeger, T. F. (2016). Dynamically adapted context-specific hyperarticulation: Feedback from interlocutors affects speakers' subsequent pronunciations. Journal of Memory and Language, 89:68-86.
Calhoun, S., Carletta, J., Brenier, J. M., Mayo, N., Jurafsky, D., Steedman, M., and Beaver, D. (2010). The NXT-format Switchboard Corpus: A rich resource for investigating the syntax, semantics, pragmatics and prosody of dialogue. In *Language Resources and Evaluation*, volume 44, pages 387-419.
Chen, Q. and Mirman, D. (2012). Competition and cooperation among similar representations: toward a unified account of facilitative and inhibitory effects of lexical neighbors. *Psychological review*, 119(2):417.
Cieri, C., Miller, D., and Walker, K. (2004). The Fisher corpus: a Resource for the Next Generations of Speech-to-Text. Language Resources and Evaluation, 4:69-71.
Cohen Priva, U. (2008). Using information content to predict phone deletion. Proceedings of the 27th West Coast Conference on Formal Linguistics, pages 90-98.
Cohen Priva, U. (2012). Sign and Signal Deriving Linguistic Generalizations From Information Utility. Doctoral dissertation, Stanford University.
Cohen Priva, U. (2015). Informativity affects consonant duration and deletion rates. *Laboratory Phonology*, 6(2):243-278.
Cover, T. M. and Thomas, J. A. (2012). Elements of information theory. John Wiley & Sons.
Dautriche, I., Mahowald, K., Gibson, E., Christophe, A., and Piantadosi, S. T. (2017). Words cluster phonetically beyond phonotactic regularities. Cognition, 163:128-145.
Dell, G. S. (1986). A spreading-activation theory of retrieval in sentence production. Psychological review, 93(3):283.
Demberg, V., Sayeed, A. B., Gorinski, P. J., and Engonopoulos, N. (2012). Syntactic surprisal affects spoken word duration in conversational contexts. Proceedings of the 2012 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning, (July):356-367.
Gahl, S. and Strand, J. F. (2016). Many neighborhoods: Phonological and perceptual neighborhood density in lexical production and perception. Journal of Memory and Language, 89:162-178.
Gahl, S., Yao, Y., and Johnson, K. (2012). Why reduce? Phonological neighborhood density and phonetic reduction in spontaneous speech. Journal of Memory and Language, 66(4):789-806.
Godfrey, J. J. and Holliman, E. (1997). Switchboard-1 Release 2. Technical report, Linguistic Data Consortium.
Grosjean, F. (1980). Spoken word recognition processes and the gating paradigm. Perception & psychophysics, 28(4):267-283.
Hall, K. C., Hume, E., Jaeger, T. F., and Wedel, A. (2018). The Role of Predictability in Shaping Phonological Patterns. Linguistic Vanguard, 4.
Heafield, K. (2011). KenLM: Faster and Smaller Language Model Queries. Proceedings of the Sixth Workshop on Statistical Machine Translation, (2009):187-197.
Jaeger, T. F. and Buz, E. (2018). Signal Reduction and Linguistic Encoding. In The Handbook of Psycholinguistics, pages 38-81. Wiley-Blackwell.
Jurafsky, D., Bell, A., Gregory, M., and Raymond, W. D. (2001). Probabilistic Relations between Words: Evidence from Reduction in Lexical Production. Frequency and the emergence of linguistic structure, pages 229-254.
Kirov, C. and Wilson, C. (2012). The Specificity of Online Variation in Speech Production. Proceedings of the 34th Annual Conference of the Cognitive Science Society, pages 587-592.
Levy, R. (2005). Probabilistic Models of Word Order and Syntactic Discontinuity. Doctoral dissertation, Stanford University.
Levy, R. (2008a). A noisy-channel model of rational human sentence comprehension under uncertain input. In Proceedings of the 2008 Conference on Empirical Methods in Natural Language Processing, pages 234-243.
Levy, R. (2008b). Expectation-based syntactic comprehension. Cognition, 106(3):1126-1177.
Lindblom, B. (1990). Explaining phonetic variation: a sketch of the H&H theory. In Speech Production and Speech Modelling, pages 403-439.
Lindblom, B., Guion, S., Hura, S., Moon, S.-J., and Willerman, R. (1995). Is sound change adaptive? Rivista di Linguistica, 7:5-37.
Lombard, E. (1911). Le signe de l'élevation de la voix. Ann. Mal. de L'Oreille et du Larynx, pages 101-119.
Mahowald, K., Fedorenko, E., Piantadosi, S. T., and Gibson, E. (2013). Info/information theory: Speakers choose shorter words in predictive contexts. Cognition, 126(2):313-318.
Norris, D. and McQueen, J. M. (2008). Shortlist B: a Bayesian model of continuous speech recognition. Psychological Review, 115(2):357-395.
Ohala, J. J. (1990). The phonetics and phonology of aspects of assimilation. In Kingston, J. and Beckman, M. E., editors, *Papers in Laboratory Phonology I: Between the Grammar and Physics of Speech*, chapter 14, pages 258-282.
Pate, J. K. and Goldwater, S. (2015). Talkers account for listener and channel characteristics to communicate efficiently. Journal of Memory and Language, 78.
Piantadosi, S. T., Tily, H., and Gibson, E. (2011). Word lengths are optimized for efficient communication. Proceedings of the National Academy of Sciences, 108(9):3526-3529.
Piantadosi, S. T., Tily, H., and Gibson, E. (2012). The communicative function of ambiguity in language. Cognition, 122(3):280-291.
Picheny, M. A., Durlach, N. I., and Braida, L. D. (1986). Speaking clearly for the hard of hearing ii: Acoustic characteristics of clear and conversational speech. Journal of Speech, Language, and Hearing Research, 29(4):434-446.
Pitt, M. A., Johnson, K., Hume, E., Kiesling, S., and Raymond, W. (2005). The Buckeye corpus of conversational speech: Labeling conventions and a test of transcriber reliability. Speech Communication, 45(1):89-95.
Schertz, J. (2013). Exaggeration of featural contrasts in clarifications of misheard speech in English. Journal of Phonetics, 41(3-4):249-263.
Seyfarth, S. (2014). Word informativity influences acoustic duration: Effects of contextual predictability on lexical representation. Cognition, 133(1):140-155.
Seyfarth, S., Buz, E., and Jaeger, T. F. (2016). Dynamic hyperarticulation of coda voicing contrasts. The Journal of the Acoustical Society of America, 139(2).
Shannon, C. (1948). A Mathematical Theory of Communication. Bell System Technical Journal, 27(3):379-423.
Smits, R., Warner, N., McQueen, J. M., and Cutler, A. (2003). Unfolding of phonetic information over time: a database of Dutch diphone perception. The Journal of the Acoustical Society of America, 113(January):563-574.
Stolcke, A. (2002). SRILM-An Extensible Language Modeling Toolkit. In 8th International Conference on Spoken Language Processing (INTERSPEECH 2002), volume 2, pages 901-904.
Stolcke, A., Zheng, J., Wang, W., and Abrash, V. (2011). SRILM at Sixteen: Update and Outlook. In Proceedings - IEEE Automatic Speech Recognition and Understanding Workshop.
Turnbull, R., Seyfarth, S., Hume, E., and Jaeger, T. F. (2018). Nasal place assimilation trades off inferability of both target and trigger words. *Laboratory Phonology: Journal of the Association for Laboratory Phonology*, 9(1).
Uther, M., Knoll, M. A., and Burnham, D. (2007). Do you speak e-ng-li-sh? a comparison of foreigner-and infant-directed speech. Speech communication, 49(1):2-7.
Van Son, R. J. J. and Pols, L. C. W. (2003). How efficient is speech? In Proceedings of the Institute of Phonetic Sciences, pages 171-184.
Van Son, R. J. J. H., Koopmans-van Beinum, F. J., and Pols, L. C. W. (1998). Efficiency As An Organizing Principle Of Natural Speech. In Fifth International Conference on Spoken Language Processing.
Vitevitch, M. S. (2002). The influence of phonological similarity neighborhoods on speech production. Journal of Experimental Psychology, Learning, Memory, and Cognition, 28(4):735-747.
Vitevitch, M. S. and Luce, P. A. (2016). Phonological Neighborhood Effects in Spoken Word Perception and Production. Annual Review of Linguistics, 2:75-94.
Warner, N., McQueen, J. M., and Cutler, A. (2014). Tracking perception of the sounds of English. The Journal of the Acoustical Society of America, 135(5):2995-3006.
Warner, N., Smits, R., McQueen, J. M., and Cutler, A. (2005). Phonological and statistical effects on timing of speech perception: Insights from a database of Dutch diphone perception. Speech Communication, 46(1):53-72.
Wooldridge, J. M. (2010). Econometric analysis of cross section and panel data. MIT press.
Wright, R. (2004). A review of perceptual cues and cue robustness. In Hayes, B., Kirchner, R., and Steriade, D., editors, *Phonetically based phonology*, chapter 2. Cambridge University Press.
Zipf, G. K. (1936). The Psychobiology of Language. Routledge, London.
Zipf, G. K. (1949). Human Behavior and the Principle of Least Effort: An Introduction to Human Ecology. Addison-Wesley Press.
A Sensitivity analyses
In this section we present the results of several sensitivity analyses. These analyses are post-hoc, and were not pre-registered with OSF. They are performed in order to assess the sensitivity of the findings to the bootstrapping method that was used for calculating p-values.
The analyses are intended to evaluate the effect of contextual confusability on word duration, and are identical to the analyses in Section 4, except that p-values are calculated using a likelihood ratio test. Each likelihood ratio test compares a pair of OLS models: one model containing contextual confusability as a covariate, and an ablated model which does not use this covariate, but is otherwise identical. The tests evaluate whether the inclusion of contextual confusability improves the prediction of word duration, beyond the contributions of other covariates.
Table 3 and Table 4 show results without and with unigram confusability included as a covariate. All comparisons performed in Section 4 remain significant with the likelihood ratio test.
Dataset	Rank	Likelihood ratio	p-value
SWBD	No	35.4	3x10-9
SWBD	Yes	91.8	3x10-22
Buckeye	No	7.23	0.007
Buckeye	Yes	64.9	8x10-16