Satwik Bhattamishra

Satwik Bhattamishra, Arkil Patel, Varun Kanade et al. · mila

Despite the widespread success of Transformers on NLP tasks, recent works have found that they struggle to model several formal languages when compared to recurrent models. This raises the question of why Transformers perform well in practice and whether they have any properties that enable them to generalize better than recurrent models. In this work, we conduct an extensive empirical study on Boolean functions to demonstrate the following: (i) Random Transformers are relatively more biased towards functions of low sensitivity. (ii) When trained on Boolean functions, both Transformers and LSTMs prioritize learning functions of low sensitivity, with Transformers ultimately converging to functions of lower sensitivity. (iii) On sparse Boolean functions which have low sensitivity, we find that Transformers generalize near perfectly even in the presence of noisy labels whereas LSTMs overfit and achieve poor generalization accuracy. Overall, our results provide strong quantifiable evidence that suggests differences in the inductive biases of Transformers and recurrent models which may help explain Transformer's effective generalization performance despite relatively limited expressiveness.

Arkil Patel, Satwik Bhattamishra, Phil Blunsom et al. · mila

Compositional generalization is a fundamental trait in humans, allowing us to effortlessly combine known phrases to form novel sentences. Recent works have claimed that standard seq-to-seq models severely lack the ability to compositionally generalize. In this paper, we focus on one-shot primitive generalization as introduced by the popular SCAN benchmark. We demonstrate that modifying the training distribution in simple and intuitive ways enables standard seq-to-seq models to achieve near-perfect generalization performance, thereby showing that their compositional generalization abilities were previously underestimated. We perform detailed empirical analysis of this phenomenon. Our results indicate that the generalization performance of models is highly sensitive to the characteristics of the training data which should be carefully considered while designing such benchmarks in future.

Arkil Patel, Satwik Bhattamishra, Siva Reddy et al. · mila

Humans possess a remarkable ability to assign novel interpretations to linguistic expressions, enabling them to learn new words and understand community-specific connotations. However, Large Language Models (LLMs) have a knowledge cutoff and are costly to finetune repeatedly. Therefore, it is crucial for LLMs to learn novel interpretations in-context. In this paper, we systematically analyse the ability of LLMs to acquire novel interpretations using in-context learning. To facilitate our study, we introduce MAGNIFICo, an evaluation suite implemented within a text-to-SQL semantic parsing framework that incorporates diverse tokens and prompt settings to simulate real-world complexity. Experimental results on MAGNIFICo demonstrate that LLMs exhibit a surprisingly robust capacity for comprehending novel interpretations from natural language descriptions as well as from discussions within long conversations. Nevertheless, our findings also highlight the need for further improvements, particularly when interpreting unfamiliar words or when composing multiple novel interpretations simultaneously in the same example. Additionally, our analysis uncovers the semantic predispositions in LLMs and reveals the impact of recency bias for information presented in long contexts.

Amey Agrawal, Sameer Reddy, Satwik Bhattamishra et al. · gatech

With the increase in the scale of Deep Learning (DL) training workloads in terms of compute resources and time consumption, the likelihood of encountering in-training failures rises substantially, leading to lost work and resource wastage. Such failures are typically offset by a checkpointing mechanism, which comes at the cost of storage and network bandwidth overhead. State-of-the-art approaches involve lossy model compression mechanisms, which induce a tradeoff between the resulting model quality (accuracy) and compression ratio. Delta compression is then used to further reduce the overhead by only storing the difference between consecutive checkpoints. We make a key enabling observation that the sensitivity of model weights to compression varies during training, and different weights benefit from different quantization levels (ranging from retaining full precision to pruning). We propose (1) a non-uniform quantization scheme that leverages this variation, (2) an efficient search mechanism that dynamically finds the best quantization configurations, and (3) a quantization-aware delta compression mechanism that rearranges weights to minimize checkpoint differences, thereby maximizing compression. We instantiate these contributions in Inshrinkerator - a framework for DL workload checkpoint compression. Our experiments show that Inshrinkerator consistently achieves a better tradeoff between accuracy and compression ratios compared to prior works, enabling a compression ratio up to 39x and withstanding up to 10 restores with negligible accuracy impact for fault-tolerant training. Inshrinkerator achieves at least an order of magnitude reduction in checkpoint storage overhead for training failure recovery as well as transfer learning use cases without any loss of accuracy.

Satwik Bhattamishra, Arkil Patel, Phil Blunsom et al. · mila

In order to understand the in-context learning phenomenon, recent works have adopted a stylized experimental framework and demonstrated that Transformers can learn gradient-based learning algorithms for various classes of real-valued functions. However, the limitations of Transformers in implementing learning algorithms, and their ability to learn other forms of algorithms are not well understood. Additionally, the degree to which these capabilities are confined to attention-based models is unclear. Furthermore, it remains to be seen whether the insights derived from these stylized settings can be extrapolated to pretrained Large Language Models (LLMs). In this work, we take a step towards answering these questions by demonstrating the following: (a) On a test-bed with a variety of Boolean function classes, we find that Transformers can nearly match the optimal learning algorithm for 'simpler' tasks, while their performance deteriorates on more 'complex' tasks. Additionally, we find that certain attention-free models perform (almost) identically to Transformers on a range of tasks. (b) When provided a teaching sequence, i.e. a set of examples that uniquely identifies a function in a class, we show that Transformers learn more sample-efficiently. Interestingly, our results show that Transformers can learn to implement two distinct algorithms to solve a single task, and can adaptively select the more sample-efficient algorithm depending on the sequence of in-context examples. (c) Lastly, we show that extant LLMs, e.g. LLaMA-2, GPT-4, can compete with nearest-neighbor baselines on prediction tasks that are guaranteed to not be in their training set.

Kyle Duffy, Satwik Bhattamishra, Phil Blunsom

Large-scale pre-training has made progress in many fields of natural language processing, though little is understood about the design of pre-training datasets. We propose a methodology for obtaining a quantitative understanding of structural overlap between machine translation tasks. We apply our methodology to the natural language to Bash semantic parsing task (NLBash) and show that it is largely reducible to lexical alignment. We also find that there is strong structural overlap between NLBash and natural language to SQL. Additionally, we perform a study varying compute expended during pre-training on the English to German machine translation task and find that more compute expended during pre-training does not always correspond semantic representations with stronger transfer to NLBash.

Satwik Bhattamishra, Kulin Shah, Michael Hahn et al.

We study the problem of learning Transformer-based sequence models with black-box access to their outputs. In this setting, a learner may adaptively query the oracle with any sequence of vectors and observe the corresponding real-valued output. We begin with the simplest case, a single-head softmax-attention regressor. We show that for a model with width $d$, there is an elementary algorithm to learn the parameters of single-head attention exactly with $O(d^2)$ queries. Further, we show that if there exists an algorithm to learn ReLU feedforward networks (FFNs), then the single-head algorithm can be easily adapted to learn one-layer Transformers with single-head attention. Next, motivated by the regime where the head dimension $r \ll d$, we provide a randomised algorithm that learns single-head attention-based models with $O(rd)$ queries via compressed sensing arguments. We also study robustness to noisy oracle access, proving that under mild norm and margin conditions, the parameters can be estimated to $\varepsilon$ accuracy with a polynomial number of queries even when outputs are only provided up to additive tolerance. Finally, we show that multi-head attention parameters are not identifiable from value queries in general -- distinct parameterisations can induce the same input-output map. Hence, guarantees analogous to the single-head setting are impossible without additional structural assumptions.

Xinting Huang, Aleksandra Bakalova, Satwik Bhattamishra et al.

Recent work has shown that the computations of Transformers can be simulated in the RASP family of programming languages. These findings have enabled improved understanding of the expressive capacity and generalization abilities of Transformers. In particular, Transformers have been suggested to length-generalize exactly on problems that have simple RASP programs. However, it remains open whether trained models actually implement simple interpretable programs. In this paper, we present a general method to extract such programs from trained Transformers. The idea is to faithfully re-parameterize a Transformer as a RASP program and then apply causal interventions to discover a small sufficient sub-program. In experiments on small Transformers trained on algorithmic and formal language tasks, we show that our method often recovers simple and interpretable RASP programs from length-generalizing transformers. Our results provide the most direct evidence so far that Transformers internally implement simple RASP programs.

Satwik Bhattamishra, Phil Blunsom, Varun Kanade

We study the learnability of languages in the Next Symbol Prediction (NSP) setting, where a learner receives only positive examples from a language together with, for every prefix, (i) whether the prefix itself is in the language and (ii) which next symbols can lead to an accepting string. This setting has been used in prior works to empirically analyze neural sequence models, and additionally, we observe that efficient algorithms for the NSP setting can be used to learn the (truncated) support of language models. We formalize the setting so as to make it amenable to PAC-learning analysis. While the setting provides a much richer set of labels than the conventional classification setting, we show that learning concept classes such as DFAs and Boolean formulas remains computationally hard. The proof is via a construction that makes almost all additional labels uninformative, yielding a reduction from the conventional learning problem to learning with NSP labels. Under cryptographic assumptions, the reduction implies that the problem of learning DFAs is computationally hard in the NSP setting.

Michael Rizvi-Martel, Satwik Bhattamishra, Neil Rathi et al.

Chain-of-thought prompting has popularized step-by-step reasoning in large language models, yet model performance still degrades as problem complexity and context length grow. By decomposing difficult tasks with long contexts into shorter, manageable ones, recent multi-agent paradigms offer a promising near-term solution to this problem. However, the fundamental capacities of such systems are poorly understood. In this work, we propose a theoretical framework to analyze the expressivity of multi-agent systems. We apply our framework to three algorithmic families: state tracking, recall, and $k$-hop reasoning. We derive bounds on (i) the number of agents required to solve the task exactly, (ii) the quantity and structure of inter-agent communication, and (iii) the achievable speedups as problem size and context scale. Our results identify regimes where communication is provably beneficial, delineate tradeoffs between agent count and bandwidth, and expose intrinsic limitations when either resource is constrained. We complement our theoretical analysis with a set of experiments on pretrained LLMs using controlled synthetic benchmarks. Empirical outcomes confirm the tradeoffs between key quantities predicted by our theory. Collectively, our analysis offers principled guidance for designing scalable multi-agent reasoning systems.

Andy Yang, Christopher Watson, Anton Xue et al. · allen-ai, eth-zurich

We present the transformer cookbook: a collection of techniques for directly encoding algorithms into a transformer's parameters. This work addresses the steep learning curve of such endeavors, a problem exacerbated by a fragmented literature where key results are scattered across numerous papers. In particular, we synthesize this disparate body of findings into a curated set of recipes that demonstrate how to implement everything from basic arithmetic in feed-forward layers to complex data routing via self-attention. Our mise en place of formulations is for both newcomers seeking an accessible entry point and experts in need of a systematic reference. This unified presentation of transformer constructions provides a foundation for future work spanning theoretical research in computational complexity to empirical investigations in architecture design and interpretability.

Satwik Bhattamishra, Michael Hahn, Phil Blunsom et al.

Transformer architectures have been widely adopted in foundation models. Due to their high inference costs, there is renewed interest in exploring the potential of efficient recurrent architectures (RNNs). In this paper, we analyze the differences in the representational capabilities of Transformers and RNNs across several tasks of practical relevance, including index lookup, nearest neighbor, recognizing bounded Dyck languages, and string equality. For the tasks considered, our results show separations based on the size of the model required for different architectures. For example, we show that a one-layer Transformer of logarithmic width can perform index lookup, whereas an RNN requires a hidden state of linear size. Conversely, while constant-size RNNs can recognize bounded Dyck languages, we show that one-layer Transformers require a linear size for this task. Furthermore, we show that two-layer Transformers of logarithmic size can perform decision tasks such as string equality or disjointness, whereas both one-layer Transformers and recurrent models require linear size for these tasks. We also show that a log-size two-layer Transformer can implement the nearest neighbor algorithm in its forward pass; on the other hand recurrent models require linear size. Our constructions are based on the existence of $N$ nearly orthogonal vectors in $O(\log N)$ dimensional space and our lower bounds are based on reductions from communication complexity problems. We supplement our theoretical results with experiments that highlight the differences in the performance of these architectures on practical-size sequences.

Arkil Patel, Satwik Bhattamishra, Navin Goyal

The problem of designing NLP solvers for math word problems (MWP) has seen sustained research activity and steady gains in the test accuracy. Since existing solvers achieve high performance on the benchmark datasets for elementary level MWPs containing one-unknown arithmetic word problems, such problems are often considered "solved" with the bulk of research attention moving to more complex MWPs. In this paper, we restrict our attention to English MWPs taught in grades four and lower. We provide strong evidence that the existing MWP solvers rely on shallow heuristics to achieve high performance on the benchmark datasets. To this end, we show that MWP solvers that do not have access to the question asked in the MWP can still solve a large fraction of MWPs. Similarly, models that treat MWPs as bag-of-words can also achieve surprisingly high accuracy. Further, we introduce a challenge dataset, SVAMP, created by applying carefully chosen variations over examples sampled from existing datasets. The best accuracy achieved by state-of-the-art models is substantially lower on SVAMP, thus showing that much remains to be done even for the simplest of the MWPs.

Satwik Bhattamishra, Kabir Ahuja, Navin Goyal

While recurrent models have been effective in NLP tasks, their performance on context-free languages (CFLs) has been found to be quite weak. Given that CFLs are believed to capture important phenomena such as hierarchical structure in natural languages, this discrepancy in performance calls for an explanation. We study the performance of recurrent models on Dyck-n languages, a particularly important and well-studied class of CFLs. We find that while recurrent models generalize nearly perfectly if the lengths of the training and test strings are from the same range, they perform poorly if the test strings are longer. At the same time, we observe that recurrent models are expressive enough to recognize Dyck words of arbitrary lengths in finite precision if their depths are bounded. Hence, we evaluate our models on samples generated from Dyck languages with bounded depth and find that they are indeed able to generalize to much higher lengths. Since natural language datasets have nested dependencies of bounded depth, this may help explain why they perform well in modeling hierarchical dependencies in natural language data despite prior works indicating poor generalization performance on Dyck languages. We perform probing studies to support our results and provide comparisons with Transformers.

Satwik Bhattamishra, Kabir Ahuja, Navin Goyal

Transformers have supplanted recurrent models in a large number of NLP tasks. However, the differences in their abilities to model different syntactic properties remain largely unknown. Past works suggest that LSTMs generalize very well on regular languages and have close connections with counter languages. In this work, we systematically study the ability of Transformers to model such languages as well as the role of its individual components in doing so. We first provide a construction of Transformers for a subclass of counter languages, including well-studied languages such as n-ary Boolean Expressions, Dyck-1, and its generalizations. In experiments, we find that Transformers do well on this subclass, and their learned mechanism strongly correlates with our construction. Perhaps surprisingly, in contrast to LSTMs, Transformers do well only on a subset of regular languages with degrading performance as we make languages more complex according to a well-known measure of complexity. Our analysis also provides insights on the role of self-attention mechanism in modeling certain behaviors and the influence of positional encoding schemes on the learning and generalization abilities of the model.

Satwik Bhattamishra, Arkil Patel, Navin Goyal

Transformers are being used extensively across several sequence modeling tasks. Significant research effort has been devoted to experimentally probe the inner workings of Transformers. However, our conceptual and theoretical understanding of their power and inherent limitations is still nascent. In particular, the roles of various components in Transformers such as positional encodings, attention heads, residual connections, and feedforward networks, are not clear. In this paper, we take a step towards answering these questions. We analyze the computational power as captured by Turing-completeness. We first provide an alternate and simpler proof to show that vanilla Transformers are Turing-complete and then we prove that Transformers with only positional masking and without any positional encoding are also Turing-complete. We further analyze the necessity of each component for the Turing-completeness of the network; interestingly, we find that a particular type of residual connection is necessary. We demonstrate the practical implications of our results via experiments on machine translation and synthetic tasks.

Pratik Joshi, Christain Barnes, Sebastin Santy et al.

In this paper, we examine and analyze the challenges associated with developing and introducing language technologies to low-resource language communities. While doing so, we bring to light the successes and failures of past work in this area, challenges being faced in doing so, and what they have achieved. Throughout this paper, we take a problem-facing approach and describe essential factors which the success of such technologies hinges upon. We present the various aspects in a manner which clarify and lay out the different tasks involved, which can aid organizations looking to make an impact in this area. We take the example of Gondi, an extremely-low resource Indian language, to reinforce and complement our discussion.