We thank the reviewer for their prompt reply. Here are our thoughts.
**1. Nonparametric LMs:** We respectfully disagree that previous non-parametric LM research is unrelated to our method. In the context of language models, non-parametric language models are defined as language models whose data distribution is “a function of the available data,” with complexity growing with data (Siegel, 1957; Hollander et al., 2013; Min et al., 2023). We believe that this definition well-encapsulates a language model interpolated with n-gram models. Indeed, we see similar use cases in kNN-LM (Khandelwal et al., 2020) and NPM (Min et al., 2023), which use external datastores that behave like n-gram models - *the sole difference is that they are queried with a representation vector instead of a token sequence.*
Superposed Decoding also can rely on representation vectors for retrieval from a datastore rather than directly doing a dictionary lookup during n-gram filtering. The former is “semantic” while the latter is “syntactic”.
**2. Modes of data:** Yes, the reviewer is right about Superposed Decoding potentially being unable to cover significantly different modes of the data like top-p sampling. However, this is not a concern nor a bug. The goal of Superposed Decoding is to provide multiple drafts at constant compute to help increase coverage. This coverage aids in improving user experience and factuality as shown in the experiments. As we mention, Superposed Decoding is intended for local exploration. More often than not, the greedy top-1 generation solves the problem at hand; further enabling local search and multiple drafts around it supports quite a few use cases.
Having said that, Superposed Decoding can be combined with any sampling method, be top-p or something else, and it can help generate a local set of drafts for each sampling trajectory at no additional compute cost. For instance, if top-p sampling is used to generate $n$ drafts, Superposed Decoding with $k$ local drafts can be spliced in at any timestep to strategically produce $nk$ drafts, where each top-p trajectory is bolstered by $k$ local explorations at no extra cost. We include a sample generation below, using Superposed Decoding to produce three local drafts for each top-p sample; this expands the available options without extra compute or reducing mode coverage.
*SPD denotes Superposed Decoding.*
```
Example of Top-p Sampling w/Superposed Decoding:
│ Prefix: “Melbourne is”
│
└───Top-p: Melbourne is a great city, with
│ │ SPD: Melbourne is a great city, with a lot of things
│ │ SPD: Melbourne is a great city, with a lot to things
│ │ SPD: Melbourne is a great city, with a lot of history
│
└───Top-p: Melbourne is a city of many different
│ │ SPD: Melbourne is a city of many different cultures and relig
│ │ SPD: Melbourne is a city of many different cultures, relig
│ │ SPD: Melbourne is a city of many different cultures and languages
│
└───Top-p: Melbourne is the capital city of Victoria
│ │ SPD: Melbourne is the capital city of Victoria, Australia. It
│ │ SPD: Melbourne is the capital city of Victoria and Australia. It
│ │ SPD: Melbourne is the capital city of Victoria, Australia. The
```
Do let us know if we are missing something here, and we are happy to discuss further. Also, let us know if the concern about optimization potential was resolved through the rebuttal.