Table of Links Abstract and 1. Introduction Abstract and 1. Introduction Background


Method


Experiments
4.1 Multi-hop Reasoning Performance
4.2 Reasoning with Distractors
4.3 Generalization to Real-World knowledge
4.4 Run-time Analysis
4.5 Memorizing Knowledge


Related Work


Conclusion, Acknowledgements, and References Background Background Background Method Method Method Experiments
4.1 Multi-hop Reasoning Performance
4.2 Reasoning with Distractors
4.3 Generalization to Real-World knowledge
4.4 Run-time Analysis
4.5 Memorizing Knowledge Experiments Experiments 4.1 Multi-hop Reasoning Performance 4.1 Multi-hop Reasoning Performance 4.2 Reasoning with Distractors 4.2 Reasoning with Distractors 4.3 Generalization to Real-World knowledge 4.3 Generalization to Real-World knowledge 4.4 Run-time Analysis 4.4 Run-time Analysis 4.5 Memorizing Knowledge 4.5 Memorizing Knowledge Related Work Related Work Related Work Conclusion, Acknowledgements, and References Conclusion, Acknowledgements, and References Conclusion, Acknowledgements, and References A. Dataset Dataset B. In-context Reasoning with Distractors B. In-context Reasoning with Distractors C. Implementation Details C. Implementation Details D. Adaptive Learning Rate D. Adaptive Learning Rate E. Experiments with Large Language Models E. Experiments with Large Language Models C Implementation Details We select GPT-2-base [59] as the model for our method and all the baselines. We use the version implemented by the Huggingface Transformers library [78]. All the experiments for RECKONING are conducted on a cluster with NVIDIA A100 (40GB) GPUs. All the baseline experiments are conducted on a local machine with NVIDIA RTX 3090 GPU (24GB). Fine-tuned In-context Reasoning We set the train batch size to 16 and train the model for 6 epochs with early stopping based on the validation label accuracy. We set the learning rate to 3e-5 and use the AdamW optimizer with ϵ set to 1e-8. We validate the model on the development set for every epoch and select the best checkpoint using the validation accuracy as the metric. Fine-tuned In-context Reasoning RECKONING In the inner loop, we generally perform 4 gradient steps for lower-hop questions (2, 3, 4-hop) and 5 gradient steps for higher-hop questions (5 and 6-hop). We select the AdamW [46] as the optimizer for the inner loop since the main task is language modeling. The inner-loop learning rate is set to 3e-5 before training, and the algorithm dynamically learns a set of optimal learning rates when converged. In our experiments and analysis, we only report the results from RECKONING with a multi-task objective since its performance is better than the single-task objective. In the outer loop, we also use the AdamW with a learning rate of 3e-5. For both optimizers, we set ϵ to 1e-8. We set the train batch size to 2 due to memory limitations. We apply the technique of gradient accumulation and set the accumulation step to 2. We train the model for 6 epochs with early stopping. For each epoch, we validate the model twice: once in the middle and once at the end. We select the best model checkpoint based on the validation label accuracy RECKONING Authors:
(1) Zeming Chen, EPFL (zeming.chen@epfl.ch);
(2) Gail Weiss, EPFL (antoine.bosselut@epfl.ch);
(3) Eric Mitchell, Stanford University (eric.mitchell@cs.stanford.edu)';
(4) Asli Celikyilmaz, Meta AI Research (aslic@meta.com);
(5) Antoine Bosselut, EPFL (antoine.bosselut@epfl.ch). Authors: Authors: (1) Zeming Chen, EPFL (zeming.chen@epfl.ch); (2) Gail Weiss, EPFL (antoine.bosselut@epfl.ch); (3) Eric Mitchell, Stanford University (eric.mitchell@cs.stanford.edu)'; (4) Asli Celikyilmaz, Meta AI Research (aslic@meta.com); (5) Antoine Bosselut, EPFL (antoine.bosselut@epfl.ch). This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv available on arxiv

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Technical Setup for RECKONING: Inner Loop Gradient Steps, Learning Rates, and Hardware Specification

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