Title: Memorizing Transformers
Authors: Yuhuai Wu
Markus Norman Rabe
DeLesley Hutchins
Christian Szegedy
Venue: ICLR 2022
Keywords: Transformer
architecture
memorization.

Abstract: Language models typically need to be trained or finetuned in order to acquire new knowledge, which involves updating their weights.  
We instead envision language models that can simply read and memorize new data at inference time, thus acquiring new knowledge immediately. In this work, we extend language models with the ability to memorize the internal representations of past inputs. We demonstrate that an approximate $k$NN lookup into a non-differentiable memory of recent (key, value) pairs improves language modeling across various benchmarks and tasks, including generic webtext (C4), math papers (arXiv), books (PG-19), code (Github), as well as formal theorems (Isabelle). We show that the performance steadily improves when we increase the size of memory up to 262K tokens. 
On benchmarks including code and mathematics, we find that the model is capable of making use of newly defined functions and theorems during test time.


Review discussion:
Strengths:
1. The method proposed is novel, intuitive and simple to implement. This is a huge advantage in the language modeling space. We’ve seen many memory-augmented transformers in the past few years, and most of them have failed to have significant impact because they are too complicated to replicate or take too many resources to train.
2. The results on the C4 dataset seem significant and show that  memory augmentation could really improve transformer language modeling.
3. The analysis is super interesting, and it shows the potential of this simple approximate attention method to find very relevant contexts to retrieve from the recent past, and how these retrievals aid in improving the LM.
4. The paper is well-written and easy to understand.
Weaknesses:
1. The authors do not compare their model to any previously published model. Throughout the paper the authors only compare their model to baselines that they designed and trained. Doing this for some of the datasets is fine, but not even having one dataset in which you compare to strong, previously published models makes it harder to convince the reader that you have found something interesting. You did show results for PG19, which has been used before in LMing papers, so it’s not clear why you haven’t compared to previously published models on that dataset, such as the compressive transformer?
The numbers in the compressive transformer are very different from the numbers your models obtain, so I’m assuming that you preprocessed that dataset differently and so have a different vocabulary, making those results incomparable? Could you re-train your model using the same settings as the compressive transformer so that we could compare the results of your method and theirs?
2. The baseline has just 6 layers, which is significantly smaller than the current transformer LMs that are being discussed by the community. I’m definitely not expecting to see GPT-3 sized models in every research paper (or even close to that) but I think 16 layers would make more sense for such an exploration. I’m afraid the gains shown here would not transfer to larger models.
On the other hand, larger models might produce better representations resulting in even bigger gains.
3. The authors do not show standard deviation numbers for any of the baselines on the various datasets. This makes understanding the results on each dataset, for the different models, harder.
For example, on the arxiv dataset the authors talk about a drop from 2.927 to 2.877 perplexity between two different models, but is a 0.05 perplexity difference really statistically significant here?
4. The authors don’t provide any speed or memory usage statistics.
Of course, it’s totally fine if this model runs slower or uses more memory than the baseline- I expect such preliminary investigations to potentially be nonoptimal, with later work making it an actually viable model. I would not penalize this paper for having slow runtime or using too much memory.
But I think it's important to discuss these things.
Misc:
1.
Although the perplexity improvements on many of the datasets are quite small (<=.1 perplexity) this could be a non-issue, and more of a problem with the perplexity metric than with the model. The perplexity metric, and most of the data that we train our LMs on, heavily incentivizes models to get short term dependencies right. Getting the model to look back into the past is both hard and barely incentivized, and so these small initial gains that are attained in this paper might be improved when we find a better loss function that incentivizes looking back more, or when we find data that has more long-term dependencies and less short-term ones.
2. The way I see it, there are two different ways to augment the transformer with a memory module. The memory module could be ‘global’ or ‘local’. Local memory transformers have a memory module that can only access the recent past.
So models like the compressive transformer or Transformer-XL are local memory transformers.
On the other hand, models like the kNN-LM or REALM are ‘global’ memory models, since they can access the entire datastore for every prediction, without any kind of limitation that is dependent on the current timestep and the recent previous timesteps.
The model proposed here is clearly a ‘local’ memory transformer, since it performs approximate attention over the recent past. I believe that that is part of what makes this model work, and I think the paper might benefit from a discussion of this and maybe even an empirical test. Does this model improve performance on WikiText-103, where all the articles are in a shuffled ordering? I don’t think it would, and that’s totally fine, but I think readers would benefit from a discussion of this property of the model.
3. I think it could be helpful if the authors had more comparisons where their model and the baseline can access the same amount of tokens for every prediction.
For example, if you train one of the memory models with 2k tokens of memory and 512 tokens of local context it would be interesting to compare it to the baseline model trained on 2.5k tokens.
Of course, since your model performs approximate attention we do expect to see worse perplexity values, but it would be very insightful to see precisely how much using this approximate attention method degrades performance.
4. For section 3.2, consider referencing [CrossBatch] which discusses this distributional shift in section 3.2 of their paper, in the vision domain.
References:
[Compressive Transformer] Jack W. Rae, Anna Potapenko, Siddhant M. Jayakumar, Timothy P. Lillicrap. “Compressive Transformers for Long-Range Sequence Modelling”
[REALM] Kelvin Guu, Kenton Lee, Zora Tung, Panupong Pasupat, Ming-Wei Chang. “REALM: Retrieval-Augmented Language Model Pre-Training”
[CrossBatch] Xun Wang, Haozhi Zhang, Weilin Huang, Matthew R. Scott. “Cross-Batch Memory for Embedding Learning”
NO.
Thank you for the detailed feedback and insights.
*Baselines and Larger Models:* We fully agree the paper would profit from additional baselines and experiments with larger models (more layers). We are adding comprehensive experiments using Transformer-XL with 12 layers. For details please check the general response.
Additionally, we ran experiments with a model with 1B parameters, where the addition of memory also helped significantly. We will report those in the final version of the paper.
*Speed and memory usage:* See common response
*Standard deviation:* See common response.
*“On most of the datasets the gains from using the proposed method are quite small (<=.1 perplexity)”* We fully agree with the reviewer's point on the perplexity metric.  Perplexity is computed as an average over all tokens, and especially for natural language (PG19, C4), the majority of tokens do not necessarily require much long-range context in order to make accurate predictions.
Thus, adding external memory may dramatically improve the predictions for a few tokens (as we found in our case study), while making only small improvements to overall perplexity.
We also would like to point out that the absolute perplexity gain is not a very meaningful measure, as it depends heavily on the tokenization.  As we mention above, datasets with many single-character tokens (e.g. arXiv, Github, Isabelle) will tend have lower perplexity, simply because predicting a single character is only selecting from a small subset of the total vocabulary.  If the perplexity is already low, small improvements can be significant.
For example, one can see that in compressive transformer, the gain of the model on Enwiki8 is from 0.98 (transformer-XL) to 0.97 (compressive transformer) in terms of bits-per-character, which corresponds to a per-character perplexity improvement from 1.972 to 1.959.  This improvement is considered as significant on that dataset.
*“global vs local memory model”:* This is a very intriguing point. The ambition of our research is indeed to explore 'global' memory models. To that extent we have already performed a preliminary experiment on the English to German translation task, where we concatenate many (randomly shuffled) translation pairs into long strings.
While the benefits of the memorizing transformer were less pronounced than in long-document language modeling, we did observe some improvements. This seems to suggest that the model can benefit not only by retrieving relevant context from the recent past, but also by querying the dataset itself.
*"2k tokens of memory and 512 tokens of local context vs 2.5k tokens of local context":* Great idea - we will add this experiment to the final version of the paper.
*CrossBatch:* Thanks for the reference, we will study the paper and reference it in the final version.
Hi reviewer 75xx, as the interactive discussion period is ending soon, we appreciate your time spent reviewing our manuscript and would be grateful if you can confirm whether our response addressed some of the concerns raised in the review? Please let us know if any issues remain and/or if there are any additional clarifications we can provide.
Hi!
> "absolute perplexity gain is not a very meaningful measure"
You are totally correct. I'm used to seeing results on datasets that have larger standard deviation so the absolute differences here seemed small but now that you've added the STD it makes everything more clear!
Overall I believe the ideas in this paper are simple and interesting and I strongly recommend accepting this work.
Dear authors,
This is really great work and I was excited reading it!
When would you plan to release the source code?
I tried to reproduce the model on my own but can not achieve a comparable PPL.
I suspect tokenization and attention sliding window are the source of differences.
Could you please provide more information about the tokenizer?
In particularly, what is it trained on; what is the frequency threshold; how many tokens (train/valid/test) did you end up with after tokenizing data; what is the renormalized word-level perplexity?
Could you also please clarify whether the first 2 rows in Table-4 still has the trick of "use a sliding-window causal mask (Beltagy et al., 2020) so that each token has a local context that includes the previous 512 tokens"?
Thank you very much!
Best,
Dear Hongyuan, we released the source code as part of the meliad repository: [https://github.com/google-research/meliad](https://github.com/google-research/meliad).
Pros:
- propose a non-differentiable cache mechanism to reuse keys and values coming from prior training steps.
- comprehensive experiments are conducted to evaluate the effectiveness of the proposed memory-based method.
Cons:
- there are some benchmarks that require models to be able to handle long inputs, such as document-level QA datasets and document-level retrieval.
Besides the LM task, it could be better if more document-level downstream tasks could be evaluated to verify the usefulness of the proposed approach.
NO.
Thank you for the feedback.
*“More document-level downstream tasks could be evaluated to verify the usefulness of the proposed approach.”*
We agree that additional evaluation would be helpful, but we would like to argue that language modeling already is a very diverse task.
For example, the GPT papers have shown that language modeling alone equips models with a wide range of abilities.
Instead of focussing on downstream tasks, we chose to demonstrate improvements across several datasets, which differ greatly in the kind of data they contain.
I would like to very strongly state that I fully agree with the authors here. Language modeling papers that do __just__ language modeling are super interesting and should not be rejected or penalized for not having results on downstream tasks. The authors need to focus on a clear and sharp contribution, and in most cases page limits, deadlines and amount of authors and compute resources limit the scope of a paper.
Of course every paper would be stronger if it had more experiments, but we know how hard it is to write a paper, so we should be very conservative and understanding with what we ask authors to present.
The paper proposes a novel method to connect a k-NN based memory with transformers for language modeling. The idea seems interesting and somewhat novel and evaluated empirically. The previous work is nicely identified, although the work of Rae et al. (ICLR 2020) could be described there as well.
Strong points:
- The memory seems to be usefully working and having a positive effect.
- Practically, seems to work.
- Relevant work to this community.
Weak points:
- Section 3 could see more formalization and better description on what are the input for searching the kNN, how the model is trained (maybe, an algorithm figure).
- Experimentation could be greatly improved: no hyperparameter search or reasoning behind the selection, no baselines with other memory architectures showing differences either performance or specific use-cases (beyond plain transformers).
- Memory sizes are too big for the data selected. It is unclear why such big memories are still improving the model.
- The results on PG-19 doesn't seem to replicate previous work (original paper shows 33.6 for Compressive transformer, whereas this work shows ~19 for plain transformers).
- Results are very close for each memory size and there are no error measurements (e.g., std dev). It is hard to conclude anything about memory sizes and their effectiveness.
- Hard to replicate: several proposed datasets are downloaded from the web, it will be hard to download the same files.
- No details on the specific hardware and software used.
Minor:
- What do you refer with "16 attention heads of size 64"?
- Describe the content of the figures in the caption (e.g., what is the architecture about?)
Yes, Legal compliance (e.g., GDPR, copyright, terms of use)
Some of the experiments in the paper were implemented on data downloaded online.
This data includes scientific papers from arXiv, code from github, and mathematical proofs from another repository. It is unclear if the authors have rights to apply their work on these papers.
Taking code for a dataset requires proper licenses, and same goes for arXiv papers that may have different licenses (different CC types, etc).
The authors don't mention how they deal with copyrights.
Update:
Thanks to the authors for clarifying how they deal with these aspects.
Thank you for the detailed suggestions on how to improve the paper. We are addressing the points and will upload a revised version soon.
*“Could you clarify how did you choose the hyperparameters and justify them?”* See "Hyperparameters" in the common response.
*"What is being used as search in k-NN? The output of the layer connected to the memory? Are the keys used in the search or both key/values?"*  We will try to clarify the description in Subsection 3.1. The local context contains keys and values from tokens for the current training step, while the external memory contains keys and values for tokens from previous training steps. The kNN-augmented layer combines the results of attention over both local context and external memory -- for each query in the current set of tokens, it returns a weighted sum of values from both the local context, and from external memory.
*"Why did you choose k=128 in k-NN?"*: In preliminary experiments, we determined that k=128 is a safe approximation of attention.  Lower values of k may reduce the accuracy of the approximation, while higher values can become quite expensive.  We plan to include an ablation with k=32 in the final version.
*"Why do you use one layer of memory, if two improve the results?"*: Thank you for raising this point. There is a point of diminishing returns, and the benefits of adding additional retrieval layers do not necessarily justify the memory and computational costs.
*"Add std dev. values"*: See “statistical significance” in the common response.
*"Please explain why does the arXiv dataset have such a low perplexity?"*: We believe this is primarily the result of tokenization.  LaTeX source code includes many special characters that are tokenized individually, especially for math papers, so their perplexity per-token is closer to what a character-level sequence model might produce, rather than a typical word-level model.  (Character-level models have a much smaller vocabulary, and thus a lower perplexity.)   Note that other datasets which use lots of special characters, such as code (Github) or theorem proving (Isabelle) similarly have lower perplexity than of natural language (C4, PG-19).
*"How many sequences are used for training, validation and testing?"* PG-19, for example, includes 28,752 books (sequences), of which 50 are used for validation and 100 are used for testing. We will add detailed statistics about the number of tokens and sequences in each dataset to the Appendix.
Except for the Isabelle dataset, the number of sequences was large enough so that overfitting was not an issue.
*Experiments section:* We fully agree that the paper would profit from additional experiments as you suggested. Please find additional baselines and experiments in the common response.
*"Memory sizes are too big for the data selected."* All our datasets contain some very long documents (see Appendix A). Note that the very long documents contribute a disproportionate amount of tokens to the dataset and therefore may have a larger impact on the perplexity than one might expect.
*"Hard to replicate."* For easy replication of the results, we included C4 and PG-19, two widely available datasets. We believe the results on the other datasets can be replicated approximately with using publicly available data sources.
*"No details on the specific hardware and software used."* We used two hardware setups: 32 TPU chips and 256 TPU chips.  Our models are implemented in Jax and Flax, starting from the Flax WMT transformer example (and for our new Transformer-XL baseline we started from the T5 codebase). We will add a detailed description of the setup to the paper and plan to release the code in the future.
*"What do you refer with '16 attention heads of size 64'?"* Each of the 16 attention heads uses query, key, and value vectors of dimension 64.
*"the work of Rae et al. (ICLR 2020) could be described"*: Thanks for noticing this oversight. We are now discussing their work in the related work section.
Hi reviewer eMDi, as the interactive discussion period is ending soon, we appreciate your time spent reviewing our manuscript and would be grateful if you can confirm whether our response addressed some of the concerns raised in the review? Please let us know if any issues remain and/or if there are any additional clarifications we can provide.
Thank you for taking time to respond to my questions. I also took time to read the other reviews and responses.
I would like to see some of your answers in the paper before the end of the discussion. This is a unique opportunity you have during the ICLR review.
1. Quick follow up on Section 3.1: How do you define a vector in the k-NN memory for later find the neighbors? Is it a concatenation of the key and value, or only one of them?
2. You haven't addressed my comment before: "The results on PG-19 doesn't seem to replicate previous work (original paper shows 33.6 for Compressive transformer, whereas this work shows ~19 for plain transformers)."
Why is this gap between your paper and Rae et al. in the reporting?
3. Please, could you report the results on the "2k tokens of memory and 512 tokens of local context vs 2.5k tokens of local context" or similar experiment before the end of the discussion period?
1. The memory contains (key, value) pairs. The distance measure used for kNN is the negative dot product between query and key. kNN then returns the (key, value) pairs with the lowest distance (highest dot product) to the queries.
In other words, the kNN returned are the (key, value) pairs that would have received the highest attention scores if we ran full attention over the memory.
2. Apologies for overlooking this point. We measure token-level perplexity, while Rae et al. measured the word-level perplexity.
3. Due to the lack of compute resources, we were not able to run the experiment to completion, but only to around 100k training steps so far.
But we plan to add this ablation to the final version of the paper. We ran three models on the dataset arXiv-math, and here are the results (@100k steps):
| Model | ArXiv-math |
|---|---|
| Transformer 2048 | 2.979 |
| Transformer-XL 2048 | 2.625 |
| Transformer-XL 512 + 1536 Memory | 2.858 |
We can see that the vanilla transformer model with 2048 sequence length performed the worst in this comparison. We believe this is due to the fact that the tokens early in each subsequence can only see a limited window hence lacking of context information, whereas every tokens in the other two models always have the previous 2048 tokens as context. The Transformer-XL 2048 performed the best due to having the ability to backpropagate as well as attending for full layers.
Strengths:
- Integrating kNN module into Transformer is an interesting modeling technique, which would be potentially useful for language generation especially when the context is quite long.
- The kNN layer is integrated into the attention layer, while previous work usually integrates it into FFN blocks.
- The LM experiments are conducted on several corpora.
Weaknesses:
- The method is not compared with previous models in the experiments, such as Transformer-XL, Compressive Transformers, and other efficient Transformers for LM.
- There is no ablation study in terms of modeling.
- I didn't find clear comparisons of training speed and GPU memory usage between different models. It is valuable for the readers to have a sense of what kind of resource is needed to train or host such models.
- Is the application restricted to sequence decoding? Can we finetune the proposed model as BERT on downstream tasks, and how about the performance?
- The above question is related to generalization. Such kind of kNN method seems to suffer from too much memorization instead of generalization. If the model cannot generalize well, it would not be good at zero- or few-shot learning. I agree that language modeling is a meaningful task, but it is more like a testbed for modeling techniques that improve generalization.
Otherwise, the shortcut of memorizing context would hide the real challenge.
- The code seems unavailable. It is unclear how many engineering efforts are required to reproduce the results. The paper writing ignores many details that are helpful for reproducing the method. Even the code would be released, the standalone paper should be informative enough.
- The kNN layer is densely triggered for each position, which seems quite heavy. How about using a gate to determine whether we need to perform kNN?
- Is there any evaluation about the performance of the learned kNN search?
For example, we could conduct some human evaluations to see whether the retrieved knowledge makes sense for prediction.
- The model is only evaluated on the language modeling task. More tasks would be helpful to indicate whether the proposed method is general enough in terms of data distribution.
NO.
*“Is the application restricted to sequence decoding?”* and *"Can we finetune the proposed model as BERT on downstream tasks[...]?"* We agree that additional evaluation would further strengthen the experiments section, but we would also like to argue that language modeling already is a very diverse task.
For example, the GPT papers have shown that language modeling alone equips models with a wide range of abilities. Liu et al. [1] have further shown that we can fine-tune decoder-only language models just as BERT for NLU tasks.
Thus, we believe that general improvements to language modeling should carry over to other tasks as well.
Instead of training the model on several different tasks, we demonstrate improvements across several datasets, which differ greatly in the kind of data they contain.
*“The code seems unavailable. It is unclear how many engineering efforts are required to reproduce the results.”* We will open source the code as we stated in the reproducibility statement. The engineering efforts to implement our approach are moderate: the major changes to a standard Transformer training setup are (1) that we have to modify the data pipeline to feed the subsequences in the correct order (without shuffling), (2) that we augment the attention layer with the keys and values retrieved using an existing kNN algorithm (see Subsection 3.1), and (3) that we write the keys and values back to the memory after retrieval.
*“I didn't find clear comparisons of training speed and GPU memory usage between different models.”* See our general answer on Speed and Memory Usage.
*"The kNN layer is densely triggered for each position. How about using a gate to determine whether we need to perform kNN?"* We were discussing similar ideas, but decided to keep the approach as simple as possible for our initial publication.
*“could conduct some human evaluations to see whether the retrieved knowledge makes sense for prediction”* We have manually investigated what the kNN model retrieved on arXiv, Github, and the Isabelle dataset. Please see Table 5,9,10 and the Appendix for some examples. We saw that the model achieves the cross-entropy gains by retrieving function/theorem names as well as their body.
[1] Liu et. al., GPT Understands, Too.
Hi reviewer gVad, as the interactive discussion period is ending soon, we appreciate your time spent reviewing our manuscript and would be grateful if you can confirm whether our response addressed some of the concerns raised in the review? Please let us know if any issues remain and/or if there are any additional clarifications we can provide.
Thanks for the reply. I acknowledge the response and update my detailed comments.
We thank all reviewers for their thoughtful and constructive reviews. We feel encouraged by the positive comments on our work, e.g., **“the method is novel, intuitive and simple to implement”**, recognizing **the kNN module has its potential in long context modeling**, with **a comprehensive suite of datasets**. We also acknowledge that our submission can be improved in several ways and we will do our best to incorporate all suggestions made by the reviewers.
In this common response, we address the concerns shared by multiple reviewers, before we answer individual reviewer's questions in separate posts.
**Additional Baselines:** We fully agree that the paper would profit from additional experiments and baselines. We are running a new set of experiments where we compare the regular Transformer and the Transformer-XL both with and without memory. We already see that memory helps both models and across all datasets, but we are still waiting for all the runs to finish.
As suggested by reviewer 75XX, we are also using a larger model (12 layers instead of 6 layers), and have verified that the new perplexity results are comparable to other published results in the literature, and to the T5 model, which we use as baseline.
**Perplexities across datasets**
|Model| ArXiv-math | Github | Isabelle | C4 | PG-19 |
|---|---|---|---|---|---|
| Transformer-512 | 3.320 | 2.832 | 3.200 | 17.427 | 13.971 |
| Transformer-2048 | 2.798 | 2.485 | 2.440 | 15.394 | 12.503 |
| Transformer-512 XL | 2.756 | 2.255 | 2.511 | 15.379 | 12.554 |
| Transformer-512 + 8092 Memory | 2.591 | 2.133 | 2.278 | 15.287 | 12.782 |
| Transformer-512 XL + 8092 Memory | **2.452** | **1.966** | **2.198** | **14.629** | **12.158** |
**Hyperparameters:** Our choice of hyperparameters for the first version of our experiments relied mostly on prior experiments on natural language and formal mathematics. For all three types of models (vanilla transformer, transformer XL, and memory models) we have tried three different learning rates. If there are other hyperparameters that you would like to see explored in detail, we would be happy to follow your suggestions.
**Statistical significance:** We have started 3 runs for some of the experiments to report their standard deviation, which appears to be very low in our preliminary results (much lower than the gain of adding memory). The cost to run a statistically relevant number of runs for all experiments is prohibitive, unfortunately.  On math-arXiv at 120k training steps we observe the following variance:
Transformer XL:  2.904 ± 0.06
Transformer XL + 8k: 2.542 ± 0.05
**Speed and Memory Usage:** Memory overhead of kNN memory is relatively low, since it is not differentiable.  Computation overhead is higher; our current implementation of the memory on TPUs increases the step time by a factor of 2.4 (for Transformer-XL, 32k memory).
The runtime overhead on TPUs is dominated by the cost of the `gather` operation in kNN lookup, which is very slow on TPUs due to their memory architecture.
However, there are many different algorithms for kNN search, and our technique can work interchangeably with any of them.  Implementations of kNN search on CPUs (ScaNN library) or GPUs (Faiss library) would have very different overheads.  Both CPUs and GPUs are far more flexible than TPUs, and have much more efficient gather operations.  We do not believe that the computational cost of our current implementation, on TPUs, is representative of what could be achieved on other architectures.
**Perplexity measurements:** Unfortunately, we discovered a mistake in how we had computed perplexity. Our original numbers were computed from the cross-entropy loss with label smoothing turned on (with a coefficient of 0.1).  We have since been re-running all of the experiments with label-smoothing turned off to get the correct perplexity.
While the exact numbers changed, memory still helps across all datasets. The numbers reported above used the corrected measurement.
[Edit log: merged the tables into one.]
We would like to thank all reviewers for their constructive feedback. We have uploaded a newer version of the paper, with changes including:
- We added a paragraph describing the hardware used and speed and memory usage in Section 4.1.
- We expanded on how we compute the datasets from publicly available sources in Sections 4.3 and 4.4, as well as the reproducibility statement.
- We added references [CrossBatch], [REALM], and [Compressive Transformer].
As we are still waiting for some experiments suggested by the reviewers, we decided not to update the experiments in the paper.
However, we plan to add the following experimental results into the final version of the paper:
- Adding the results given by the larger model (12 layers instead of 6 layers, as suggested by reviewer 75xx).
- Adding more baseline comparisons to the Transformer-XL model, with various sequence lengths and memory sizes.
- Adding an ablation study on standard deviation / statistical significance.
- Adding an ablation study to compare memory and standard model while keeping the context window the same (512 + 1536 memory vs. 2048 Transformer-XL).
Since the last update, we have obtained more results using the larger sized model and more comparisons to the baseline model.
In particular, we now have numbers for Transformer-XL 2048, Transformer-XL 512 + 65k memory, and Transformer-XL 2048 + 8k memory.
One can see that (i) 65k memory significantly improves upon 8k, and (ii) using memory helps even with longer sequence models (Transformer-XL 2048).
|Model| ArXiv-math | Github | Isabelle | C4 | PG-19 |
|---|---|---|---|---|---|
| Transformer-512 | 3.320 | 2.832 | 3.200 | 17.427 | 13.971 |
| Transformer-2048 | 2.798 | 2.485 | 2.440 | 15.394 | 12.503 |
| Transformer-512 XL | 2.756 | 2.255 | 2.511 | 15.379 | 12.554 |
| Transformer-512 + 8k Memory | 2.591 | 2.133 | 2.278 | 15.287 | 12.782 |
| Transformer-512 XL + 8k Memory | 2.452 | 1.966 | 2.198 | 14.629 | 12.158 | 
| Transformer-512 XL + 65k Memory | **2.317** | **1.879** |  - | 14.08 |  **11.822** |
| Transformer-2048 XL | 2.422 | 2.154 | - | 14.00 | 11.941 |
| Transformer-2048 XL + 8k Memory | 2.321 | 1.914 | - | **13.76** | 11.834 |
Lastly, we would like to update the standard deviation results.
Also at 500k steps, the deviation between different runs of the same experiment appears to be much smaller than the gap between different models:
Transformer XL: 2.746 ± 0.01
Transformer XL + 8k: 2.445 ± 0.005

Meta-review:
role: PC
data: comment: This paper studies the problem of dealing with long contexts within a Transformer architecture.
The key contribution is a  kNN memory module that works in concert with  a Transformer by integrating upper layers with additional retrieved context.

The idea is simple  but the execution is good.  While the  idea is reminiscent of other recent work on this topic, and novelty is somewhat borderline, it is practically useful.
Overall, though ambivalent, my recommendation is that the paper should probably be accepted

Decision: Accept (Spotlight)