Enhancing Length Extrapolation in Sequential Models with Pointer-Augmented Neural Memory

Thank you for your insightful review. We address your concerns and questions point by point below.

Summary

"First, I want to highlight ...". Could you specify the amendment you expected to see in our paper? We will try to address them if they are appropriate.

Weaknesses

1. Thank you for sharing your opinions. We appreciate your insights and agree that expanding the evaluation tasks to a wider range of NLU and NLG applications would be beneficial. However, we do not think that lacking wider NLP evaluations is a good reason to reject a paper that focuses on improving the symbol-processing capability of general deep learning models. Generalization to longer sequences is a crucial aspect with far-reaching implications in various AI applications, particularly in addressing the core limitation of current deep learning architecture. While we acknowledge the importance of broader evaluations, we believe that our paper makes a meaningful contribution by emphasizing and advancing the field's understanding of symbol processing and length extrapolation within the context of general deep learning models. Further, we included experiments on question-answering and machine translation to prove the broad application of our approach. In total, we have conducted experiments on 4 major categories of tasks with 12 different datasets and compared our method with 16 baselines where our method consistently outperforms other models. Therefore, we believe that our evaluation is convincing and comprehensive.
2. As explained in Appendix D's Baseline choice section, our baselines are competitive with SOTA in the considered tasks. Regarding your mention of LLM, could you clarify the setting when LLM with 10B could outperform our method? If the LLM is not finetuned on the task, we have shown that Chat-GPT with 175B still fails in our task, and can be considered to underperform our method (Appendix D6). In case the setting is to finetune LLM to the task, we need to conduct experiments to confirm that the finetuned LLM could perform our PANM+LLM, and this task is not trivial because finetuning LLM of 10B requires huge computing resources.
3. We spent a paragraph in Appendix A to compare positional encoding and our physical pointers. Similarly, we highlighted the difference between our attention and softmax attention used by Transformer in the introduction and Sec. 2.3.1. In this revision, we have added another table (Appendix A Table 3) to summarize the difference between Transformer and our method (see below). | Difference | Transformer | PANM (Our) | | ----------- | ----------- |-----------| | Key Generation | Keys are computed based on input data. Hence, when meeting novel data during testing, Transformer will observe novel keys, and cannot work properly. | The keys in our approach are generated as fixed numbers, specifically physical memory addresses. These keys are entirely separate from the data.| |Extendable to Longer Sequences|The dimension of attention weights varies with input length, making arithmetic transformations on these attention weights infeasible as the sequence length increases.|The fixed nature of our physical addresses allows our pointers to be easily manipulated and extendable to longer sequences.| |Symbol Processing Advantages| The use of attention weights as implicit pointers may lack the explicitness needed for effective symbol processing.| Using physical addresses as keys in our approach is crucial for symbol processing as it explicitly allows pointer assignment, dereference, and arithmetic operations.| |Physical Address vs Positional Encoding| Positional encoding can be generated independently from data. However, they are not separated from the input data as our physical addresses. There is no explicit mechanism in Transformer to attend only to these | Our physical addresses are detached from the data, supporting the transformation of pointers through timesteps and isolating pointer manipulation from the input.|

Thank you for your valuable feedback. We address your concerns and questions point by point below.

• "While PANM is proposed ...". As explained in Appendix D's Baseline choice section, we have compared with competitive and SOTA baselines in the task we considered. In particular, we have compared our method with 16 baselines across tasks. Most of them are memory-based models and designed for symbolic generalization. We note that, as explained in Related Work's second paragraph, we have not compared our model with task-specific methods using reinforcement learning or neural-symbolic architecture. Our focus is improving the systematic generalization of fundamental differentiable models.
• "The paper focuses on ...". The reason we focus more on symbolic processing tasks is that these tasks remain very challenging for current deep neural networks and urgently demand new approaches like our solution. That said, as shown in Sec 3.4, we have tested our methods on practical NLP tasks such as Question Answering (QA) and Machine Translation (MT). The significant gains, ranging from 1-6% in QA and 5-40 perplexity scores in MT, show the potential of extending our method to practical NLP domains.
• "More related work for ...". Thank you for your suggestions on the related works. We have incorporated the below discussion in our section "More Discussion on Related Works" (Appendix A). Among your suggested papers, the last two works on reasoning and generalization using image inputs, which is beyond the scope of our paper only targeting generalization for longer sequences of text/discrete inputs. The other two papers are more relevant. The approach by Lake et al., 2019 addresses systematic generalization with meta-learning training while our method adopts standard supervised training. The two approaches are complementary rather than competing. By focusing on improving the model architecture rather than the training procedures, our method can be used in various settings, not just SCAN tasks. The study conducted by Hu et al., 2020 targets a different problem-syntactic generalization, while our paper focuses on length extrapolation with different benchmarks. Some baselines such as LSTM and Transformer examined in the paper have been chosen as baselines in our paper.

Thank you for your positive review. We address your concerns and questions point by point below.

Weaknesses

• "I didn’t understand ...". Firstly, we would like to correct that our method outperforms Universal Transformer. Even with Relational Position Encoding, Universal Transformer (UT) falls short of our PANM in SCAN's most challenging scenarios. Specifically, when training lengths are set at 22, 24, and 25, PANM exhibits performance advantages of 2%, 35%, and 29%, respectively. Similarly, in more demanding mathematical tasks, PANM outshines UT+RPE by 11%. I (Universal Transformer without RPE is even worse). In the QA task, we opted against using UT as the backbone primarily due to its slow speed resulting from recurrent computation. Additionally, in our bAbI setting, Transformer and UT+RPE demonstrate minimal performance differences (see our revised Appendix Table 12), thus, we chose to integrate PANM with Transformer. In the SQUAD task, it is well known that BERT serves as a much stronger baseline compared to Universal Transformer. The successful enhancement of a potent baseline like BERT with PANM substantiates the practical efficacy of our approach. Our objective aligns closely with your second hypothesis: to demonstrate that PANM "can also perform better than existing transformer based approaches that perform well on the considered NLP tasks"
• "How many parameters ...". It depends on the task and choice of the Controller. Usually, PANM's module's size is similar to the size of an attention-layer in Transformer. We report PANM model size in Appendix D1, the final sentence of the fifth paragraph. In the considering task, the whole architecture with PANM has ≈1.1 million parameters.
• "Say I am a ...". As clarified earlier, PANM outperforms U. TRM (with and without RPE) in the toughest generalization testbed. We will clarify the benefit of our approach vs Transformer: | Difference | Transformer | PANM (Our) | | ----------- | ----------- |-----------| | Key Generation | Keys are computed based on input data. Hence, when meeting novel data during testing, Transformer will observe novel keys, and cannot work properly. | The keys in our approach are generated as fixed numbers, specifically physical memory addresses. These keys are entirely separate from the data.| |Extendable to Longer Sequences|The dimension of attention weights varies with input length, making arithmetic transformations on these attention weights infeasible as the sequence length increases.|The fixed nature of our physical addresses allows our pointers to be easily manipulated and extendable to longer sequences.| |Symbol Processing Advantages| The use of attention weights as implicit pointers may lack the explicitness needed for effective symbol processing.| Using physical addresses as keys in our approach is crucial for symbol processing as it explicitly allows pointer assignment, dereference, and arithmetic operations.| |Physical Address vs Positional Encoding| Positional encoding can be generated independently from data. However, they are not separated from the input data as our physical addresses. There is no explicit mechanism in Transformer to attend only to these | Our physical addresses are detached from the data, supporting the transformation of pointers through timesteps and isolating pointer manipulation from the input.|
• "The comparison with Chat-GPT ...." PANM failure will focus on the end of the sequence. When sequence length increases, more characters at the end of the output sequence are likely wrong. For example, in the reverse task, input 123456789, true output 987654321, PANM output can be 987654322. The reason for this failure pattern is that PANM uses a Pointer Unit to recurrently transform the pointer across timestep. As the transformation is not always perfect, there could be error accumulation as the number of timesteps increases. Looking at Fig 2c as an example, attention errors (red) become clearer at the end of the decoding. Although in this example, the majority of attention is still correct, pointing to the right address. As the test length increases, these errors will amplify and possibly make the final prediction incorrect. We explained the reason for not carefully testing ChatGPT on other tasks in Appendix D6's first paragraph. There are two main reasons: (1) the task input is not suitable for text representation. (2) the test data is public and can be seen by ChatGPT. Another reason is the cost of systematically evaluating ChatGPT on these tasks: we have to manually extract the relevant answer from ChatGPT's output to have a reliable evaluation.