## 5 Improved DSR Using Phonological Features in Vocabulary-
### The Implementation of Phonological Features  
Phonological features, as described in previous works [17; 18], are bundles of characteristics used to describe phones. These features encompass various attributes, including major sound class, place and manner of articulation, and glottal states [36; 65]. As PFs are the basic units of the phonological structure shared among phones, their independence from phones and languages allows the recognition of unseen phones in test sets or new languages, provided that the PF representations of the target phones are detected accurately and the PF compositions of the phones are known. To implement PFs in phone recognition, we first discretely represent the PFs of each phone. We utilize the Panphon toolkit [65], which transforms phones in IPA into vector representations of their corresponding PFs. Initially, the PF vector consists of 24 dimensions, each representing a phonological feature as _syllabic_, _sonorant_, _consonantal_, _continuant_, _delayed release_, _lateral_, _nasal_, _strident_, _voiced_, _spread glottis_, _constricted glottis_, _anterior_, _coronal_, _distributed labial_, _labial_, _high_, _low_, _back_, _rounded_, _valeric_, _tense_, _long_, _hitone_, and _hireg_[65]. For phone recognition loss calculation, we augment the vector with an additional dimension dedicated to a _<blk>_ token, resulting in a 25-dimensional vector representation for each phone. Each feature is encoded with a value in the set {-1,0,1}, indicating the absence, irrelevance, and presence of the feature. In this representation, the _<blk>_ token is the only one with a non-zero element in the first dimension, whereas all other dimensions are zero. For example, the vector representation of the PFs for the phone _'[a]'_ is [0, 1, 1, -1, 1, -1, -1, 0, 1, -1, 0, -1, 0, -1, 0, -1, 0, -1, -1, 1, -1, -1, 1, -1, 0, 0]. The first element is 0, indicating that it is not the _<blk>_ token. The second and third elements, both 1, signify that the phone is syllabic and sonorant, respectively. The remaining elements adhere to a similar pattern. When using PFs as the intermediate representation for phone recognition, the recognition involves two steps, as shown in Figure 2. First, the PFs are extracted from the transformer layer output \(\mathbf{x}\) using PF layer \(\mathbf{F}_{\mathit{PFs}}(\cdot)\), resulting in PF logits \(\mathbf{x}_{\mathit{PFs}}=\tanh\left(\mathbf{F}_{\mathit{PFs}}(\mathbf{x})\right)\) after applying _tanh_ activation to limit their range between \(-1\) and \(1\). These vectors are then transformed into phone logits (distribution) \(\mathbf{y}_{\mathit{PFs}}\) via a 'Signature Matrix' [19]. The Signature Matrix \(\mathbf{A}_{\mathit{sig}}\) contains the predefined PFs vector \(\mathbf{a}_{i}\) for each phone \(i\) in the vocabulary, based on prior phonetic knowledge of phone composition. By computing the dot product between the extracted PF vector \(\mathbf{x}_{\mathit{PFs}}\) and the predefined PF vector \(\mathbf{a}_{i}\) for phone \(i\), we obtain the logits of phone \(i\) given the current speech features. When calculating the dot product between \(\mathbf{x}_{\mathit{PFs}}\) and the entire Signature Matrix \(\mathbf{A}_{\mathit{sig}}\), we derive the phone logits across the vocabulary: \(\mathbf{y}_{\mathit{PFs}}=\mathbf{A}_{\mathit{sig}}\times\tanh\left(\mathbf{F}_{\mathit{ PFs}}(\mathbf{x})\right)\). Hence, we do not train directly for PF targets but indirectly via the Signature matrix. This strategy imposes fewer constraints on PF prediction, since zero values in the Signature matrix now really express that we do not care about the predicted PF value, rather than forcing the model to output a zero value. Also, PFs are not always realized as the context-independent PFs would suggest so the actual PF values can adjust accordingly.