Rethinking Evaluation of Sparse Autoencoders through the Representation of Polysemous Words

Sparse autoencoders (SAEs) have gained a lot of attention as a promising tool to improve the interpretability of large language models (LLMs) by mapping the complex superposition of polysemantic neurons into monosemantic features and composing a sparse dictionary of words. However, traditional performance metrics like Mean Squared Error and L0 sparsity ignore the evaluation of the semantic representational power of SAEs -- whether they can acquire interpretable monosemantic features while preserving the semantic relationship of words. For instance, it is not obvious whether a learned sparse feature could distinguish different meanings in one word. In this paper, we propose a suite of evaluations for SAEs to analyze the quality of monosemantic features by focusing on polysemous words. Our findings reveal that SAEs developed to improve the MSE-L0 Pareto frontier may confuse interpretability, which does not necessarily enhance the extraction of monosemantic features. The analysis of SAEs with polysemous words can also figure out the internal mechanism of LLMs; deeper layers and the Attention module contribute to distinguishing polysemy in a word. Our semantics focused evaluation offers new insights into the polysemy and the existing SAE objective and contributes to the development of more practical SAEs.

ADOPT: Modified Adam Can Converge with Any $β_2$ with the Optimal Rate

Adam is one of the most popular optimization algorithms in deep learning. However, it is known that Adam does not converge in theory unless choosing a hyperparameter, i.e., $\beta_2$, in a problem-dependent manner. There have been many attempts to fix the non-convergence (e.g., AMSGrad), but they require an impractical assumption that the gradient noise is uniformly bounded. In this paper, we propose a new adaptive gradient method named ADOPT, which achieves the optimal convergence rate of $\mathcal{O} ( 1 / \sqrt{T} )$ with any choice of $\beta_2$ without depending on the bounded noise assumption. ADOPT addresses the non-convergence issue of Adam by removing the current gradient from the second moment estimate and changing the order of the momentum update and the normalization by the second moment estimate. We also conduct intensive numerical experiments, and verify that our ADOPT achieves superior results compared to Adam and its variants across a wide range of tasks, including image classification, generative modeling, natural language processing, and deep reinforcement learning. The implementation is available at https://github.com/iShohei220/adopt.

Which Programming Language and What Features at Pre-training Stage Affect Downstream Logical Inference Performance?

Recent large language models (LLMs) have demonstrated remarkable generalization abilities in mathematics and logical reasoning tasks. Prior research indicates that LLMs pre-trained with programming language data exhibit high mathematical and reasoning abilities; however, this causal relationship has not been rigorously tested. Our research aims to verify which programming languages and features during pre-training affect logical inference performance. Specifically, we pre-trained decoder-based language models from scratch using datasets from ten programming languages (e.g., Python, C, Java) and three natural language datasets (Wikipedia, Fineweb, C4) under identical conditions. Thereafter, we evaluated the trained models in a few-shot in-context learning setting on logical reasoning tasks: FLD and bAbi, which do not require commonsense or world knowledge. The results demonstrate that nearly all models trained with programming languages consistently outperform those trained with natural languages, indicating that programming languages contain factors that elicit logic inference performance. In addition, we found that models trained with programming languages exhibit a better ability to follow instructions compared to those trained with natural languages. Further analysis reveals that the depth of Abstract Syntax Trees representing parsed results of programs also affects logical reasoning performance. These findings will offer insights into the essential elements of pre-training for acquiring the foundational abilities of LLMs.

Answer When Needed, Forget When Not: Language Models Pretend to Forget via In-Context Knowledge Unlearning

As large language models (LLMs) are applied across diverse domains, the ability to selectively unlearn specific information has become increasingly essential. For instance, LLMs are expected to provide confidential information to authorized internal users, such as employees or trusted partners, while withholding it from external users, including the general public and unauthorized entities. In response to this challenge, we propose a novel method termed ``in-context knowledge unlearning'', which enables the model to selectively forget information in test-time based on the context of the query. Our method fine-tunes pre-trained LLMs to enable prompt unlearning of target knowledge within the context, while preserving other knowledge. Experiments on the TOFU and AGE datasets using Llama2-7B/13B and Mistral-7B models show our method achieves up to 95% forgetting accuracy while retaining 80% of unrelated knowledge, significantly outperforming baselines in both in-domain and out-of-domain scenarios. Further investigation into the model's internal behavior revealed that while fine-tuned LLMs generate correct predictions in the middle layers and maintain them up to the final layer, they make the decision to forget at the last layer, i.e., ``LLMs pretend to forget''. Our findings offer valuable insights into enhancing the robustness of unlearning mechanisms in LLMs, setting a foundation for future research in the field.

Language Models Do Hard Arithmetic Tasks Easily and Hardly Do Easy Arithmetic Tasks

The ability (and inability) of large language models (LLMs) to perform arithmetic tasks has been the subject of much theoretical and practical debate. We show that LLMs are frequently able to correctly and confidently predict the first digit of n-digit by m-digit multiplication tasks without using chain of thought reasoning, despite these tasks require compounding operations to solve. Simultaneously, LLMs in practice often fail to correctly or confidently predict the last digit of an n-digit by m-digit multiplication, a task equivalent to 1-digit by 1-digit multiplication which can be easily learned or memorized. We show that the latter task can be solved more robustly when the LLM is conditioned on all of the correct higher-order digits, which on average increases the confidence of the correct last digit on 5-digit by 5-digit multiplication tasks using Llama 2-13B by over 230% (0.13 to 0.43) and Mistral-7B by 150% (0.22 to 0.55).

On the Multilingual Ability of Decoder-based Pre-trained Language Models: Finding and Controlling Language-Specific Neurons

Current decoder-based pre-trained language models (PLMs) successfully demonstrate multilingual capabilities. However, it is unclear how these models handle multilingualism. We analyze the neuron-level internal behavior of multilingual decoder-based PLMs, Specifically examining the existence of neurons that fire ``uniquely for each language'' within decoder-only multilingual PLMs. We analyze six languages: English, German, French, Spanish, Chinese, and Japanese, and show that language-specific neurons are unique, with a slight overlap (< 5%) between languages. These neurons are mainly distributed in the models' first and last few layers. This trend remains consistent across languages and models. Additionally, we tamper with less than 1% of the total neurons in each model during inference and demonstrate that tampering with a few language-specific neurons drastically changes the probability of target language occurrence in text generation.

Interpreting Grokked Transformers in Complex Modular Arithmetic

Grokking has been actively explored to reveal the mystery of delayed generalization. Identifying interpretable algorithms inside the grokked models is a suggestive hint to understanding its mechanism. In this work, beyond the simplest and well-studied modular addition, we observe the internal circuits learned through grokking in complex modular arithmetic via interpretable reverse engineering, which highlights the significant difference in their dynamics: subtraction poses a strong asymmetry on Transformer; multiplication requires cosine-biased components at all the frequencies in a Fourier domain; polynomials often result in the superposition of the patterns from elementary arithmetic, but clear patterns do not emerge in challenging cases; grokking can easily occur even in higher-degree formulas with basic symmetric and alternating expressions. We also introduce the novel progress measure for modular arithmetic; Fourier Frequency Sparsity and Fourier Coefficient Ratio, which not only indicate the late generalization but also characterize distinctive internal representations of grokked models per modular operation. Our empirical analysis emphasizes the importance of holistic evaluation among various combinations.

Unnatural Error Correction: GPT-4 Can Almost Perfectly Handle Unnatural Scrambled Text

While Large Language Models (LLMs) have achieved remarkable performance in many tasks, much about their inner workings remains unclear. In this study, we present novel experimental insights into the resilience of LLMs, particularly GPT-4, when subjected to extensive character-level permutations. To investigate this, we first propose the Scrambled Bench, a suite designed to measure the capacity of LLMs to handle scrambled input, in terms of both recovering scrambled sentences and answering questions given scrambled context. The experimental results indicate that most powerful LLMs demonstrate the capability akin to typoglycemia, a phenomenon where humans can understand the meaning of words even when the letters within those words are scrambled, as long as the first and last letters remain in place. More surprisingly, we found that only GPT-4 nearly flawlessly processes inputs with unnatural errors, even under the extreme condition, a task that poses significant challenges for other LLMs and often even for humans. Specifically, GPT-4 can almost perfectly reconstruct the original sentences from scrambled ones, decreasing the edit distance by 95%, even when all letters within each word are entirely scrambled. It is counter-intuitive that LLMs can exhibit such resilience despite severe disruption to input tokenization caused by scrambled text.

Grokking Tickets: Lottery Tickets Accelerate Grokking

Grokking is one of the most surprising puzzles in neural network generalization: a network first reaches a memorization solution with perfect training accuracy and poor generalization, but with further training, it reaches a perfectly generalized solution. We aim to analyze the mechanism of grokking from the lottery ticket hypothesis, identifying the process to find the lottery tickets (good sparse subnetworks) as the key to describing the transitional phase between memorization and generalization. We refer to these subnetworks as ''Grokking tickets'', which is identified via magnitude pruning after perfect generalization. First, using ''Grokking tickets'', we show that the lottery tickets drastically accelerate grokking compared to the dense networks on various configurations (MLP and Transformer, and an arithmetic and image classification tasks). Additionally, to verify that ''Grokking ticket'' are a more critical factor than weight norms, we compared the ''good'' subnetworks with a dense network having the same L1 and L2 norms. Results show that the subnetworks generalize faster than the controlled dense model. In further investigations, we discovered that at an appropriate pruning rate, grokking can be achieved even without weight decay. We also show that speedup does not happen when using tickets identified at the memorization solution or transition between memorization and generalization or when pruning networks at the initialization (Random pruning, Grasp, SNIP, and Synflow). The results indicate that the weight norm of network parameters is not enough to explain the process of grokking, but the importance of finding good subnetworks to describe the transition from memorization to generalization. The implementation code can be accessed via this link: \url{https://github.com/gouki510/Grokking-Tickets}.

Open X-Embodiment: Robotic Learning Datasets and RT-X Models

Large, high-capacity models trained on diverse datasets have shown remarkable successes on efficiently tackling downstream applications. In domains from NLP to Computer Vision, this has led to a consolidation of pretrained models, with general pretrained backbones serving as a starting point for many applications. Can such a consolidation happen in robotics? Conventionally, robotic learning methods train a separate model for every application, every robot, and even every environment. Can we instead train generalist X-robot policy that can be adapted efficiently to new robots, tasks, and environments? In this paper, we provide datasets in standardized data formats and models to make it possible to explore this possibility in the context of robotic manipulation, alongside experimental results that provide an example of effective X-robot policies. We assemble a dataset from 22 different robots collected through a collaboration between 21 institutions, demonstrating 527 skills (160266 tasks). We show that a high-capacity model trained on this data, which we call RT-X, exhibits positive transfer and improves the capabilities of multiple robots by leveraging experience from other platforms. More details can be found on the project website $\href{https://robotics-transformer-x.github.io}{\text{robotics-transformer-x.github.io}}$.