arXiv subjects

Navin Goyal

Publications and source records attributed to Navin Goyal.

At least 19 recordsLinked to original sources

arXiv2025

Shape of Thought: When Distribution Matters More than Correctness in Reasoning Tasks

We present the surprising finding that a language model's reasoning capabilities can be improved by training on synthetic datasets of chain-of-thought (CoT) traces from more capable models, even when all of those traces lead to an incorrect final answer. Our experiments show this approach can yield better performance on reasoning tasks than training on human-annotated datasets. We hypothesize that two key factors explain this phenomenon: first, the distribution of synthetic data is inherently closer to the language model's own distribution, making it more amenable to learning. Second, these `incorrect' traces are often only partially flawed and contain valid reasoning steps from which the model can learn. To further test the first hypothesis, we use a language model to paraphrase human-annotated traces -- shifting their distribution closer to the model's own distribution -- and show that this improves performance. For the second hypothesis, we introduce increasingly flawed CoT traces and study to what extent models are tolerant to these flaws. We demonstrate our findings across various reasoning domains like math, algorithmic reasoning and code generation using MATH, GSM8K, Countdown and MBPP datasets on various language models ranging from 1.5B to 9B across Qwen, Llama, and Gemma models. Our study shows that curating datasets that are closer to the model's distribution is a critical aspect to consider. We also show that a correct final answer is not always a reliable indicator of a faithful reasoning process.

cs.AI↗

arXiv2025

CurLL: A Developmental Framework to Evaluate Continual Learning in Language Models

We introduce a comprehensive continual learning dataset and benchmark (CurlL) grounded in human developmental trajectories from ages 5-10, enabling systematic and fine-grained assessment of models' ability to progressively acquire new skills. CurlL spans five developmental stages (0-4) covering ages 5-10, supported by a skill graph that breaks down broad skills into smaller abilities, concrete goals, and measurable indicators, while also capturing which abilities build on others. We generate a 23.4B-token synthetic dataset with controlled skill progression, vocabulary complexity, and format diversity, comprising paragraphs, comprehension-based QA (CQA), skill-testing QA (CSQA), and instruction-response (IR) pairs. Stage-wise token counts range from 2.12B to 6.78B tokens, supporting precise analysis of forgetting, forward transfer, and backward transfer. Using a 135M-parameter transformer trained under independent, joint, and sequential (continual) setups, we show trade-offs in skill retention and transfer efficiency. By mirroring human learning patterns and providing fine-grained control over skill dependencies, this work advances continual learning evaluations for language models.

cs.CL↗

arXiv2025

Characterizing Deep Research: A Benchmark and Formal Definition

Information tasks such as writing surveys or analytical reports require complex search and reasoning, and have recently been grouped under the umbrella of \textit{deep research} -- a term also adopted by recent models targeting these capabilities. Despite growing interest, the scope of the deep research task remains underdefined and its distinction from other reasoning-intensive problems is poorly understood. In this paper, we propose a formal characterization of the deep research (DR) task and introduce a benchmark to evaluate the performance of DR systems. We argue that the core defining feature of deep research is not the production of lengthy report-style outputs, but rather the high fan-out over concepts required during the search process, i.e., broad and reasoning-intensive exploration. To enable objective evaluation, we define DR using an intermediate output representation that encodes key claims uncovered during search-separating the reasoning challenge from surface-level report generation. Based on this formulation, we propose a diverse, challenging benchmark LiveDRBench with 100 challenging tasks over scientific topics (e.g., datasets, materials discovery, prior art search) and public interest events (e.g., flight incidents, movie awards). Across state-of-the-art DR systems, F1 score ranges between 0.02 and 0.72 for any sub-category. OpenAI's model performs the best with an overall F1 score of 0.55. Analysis of reasoning traces reveals the distribution over the number of referenced sources, branching, and backtracking events executed by current DR systems, motivating future directions for improving their search mechanisms and grounding capabilities. The benchmark is available at https://github.com/microsoft/LiveDRBench.

cs.CL↗

arXiv2024

Exploring Continual Fine-Tuning for Enhancing Language Ability in Large Language Model

A common challenge towards the adaptability of Large Language Models (LLMs) is their ability to learn new languages over time without hampering the model's performance on languages in which the model is already proficient (usually English). Continual fine-tuning (CFT) is the process of sequentially fine-tuning an LLM to enable the model to adapt to downstream tasks with varying data distributions and time shifts. This paper focuses on the language adaptability of LLMs through CFT. We study a two-phase CFT process in which an English-only end-to-end fine-tuned LLM from Phase 1 (predominantly Task Ability) is sequentially fine-tuned on a multilingual dataset -- comprising task data in new languages -- in Phase 2 (predominantly Language Ability). We observe that the ``similarity'' of Phase 2 tasks with Phase 1 determines the LLM's adaptability. For similar phase-wise datasets, the LLM after Phase 2 does not show deterioration in task ability. In contrast, when the phase-wise datasets are not similar, the LLM's task ability deteriorates. We test our hypothesis on the open-source \mis\ and \llm\ models with multiple phase-wise dataset pairs. To address the deterioration, we analyze tailored variants of two CFT methods: layer freezing and generative replay. Our findings demonstrate their effectiveness in enhancing the language ability of LLMs while preserving task performance, in comparison to relevant baselines.

cs.CL↗

arXiv2024

InversionView: A General-Purpose Method for Reading Information from Neural Activations

The inner workings of neural networks can be better understood if we can fully decipher the information encoded in neural activations. In this paper, we argue that this information is embodied by the subset of inputs that give rise to similar activations. We propose InversionView, which allows us to practically inspect this subset by sampling from a trained decoder model conditioned on activations. This helps uncover the information content of activation vectors, and facilitates understanding of the algorithms implemented by transformer models. We present four case studies where we investigate models ranging from small transformers to GPT-2. In these studies, we show that InversionView can reveal clear information contained in activations, including basic information about tokens appearing in the context, as well as more complex information, such as the count of certain tokens, their relative positions, and abstract knowledge about the subject. We also provide causally verified circuits to confirm the decoded information.

cs.LG↗

arXiv2024

Learning Syntax Without Planting Trees: Understanding Hierarchical Generalization in Transformers

Transformers trained on natural language data have been shown to learn its hierarchical structure and generalize to sentences with unseen syntactic structures without explicitly encoding any structural bias. In this work, we investigate sources of inductive bias in transformer models and their training that could cause such generalization behavior to emerge. We extensively experiment with transformer models trained on multiple synthetic datasets and with different training objectives and show that while other objectives e.g. sequence-to-sequence modeling, prefix language modeling, often failed to lead to hierarchical generalization, models trained with the language modeling objective consistently learned to generalize hierarchically. We then conduct pruning experiments to study how transformers trained with the language modeling objective encode hierarchical structure. When pruned, we find joint existence of subnetworks within the model with different generalization behaviors (subnetworks corresponding to hierarchical structure and linear order). Finally, we take a Bayesian perspective to further uncover transformers' preference for hierarchical generalization: We establish a correlation between whether transformers generalize hierarchically on a dataset and whether the simplest explanation of that dataset is provided by a hierarchical grammar compared to regular grammars exhibiting linear generalization.

cs.CL↗

arXiv2023

Guiding Language Models of Code with Global Context using Monitors

Language models of code (LMs) work well when the surrounding code provides sufficient context. This is not true when it becomes necessary to use types, functionality or APIs defined elsewhere in the repository or a linked library, especially those not seen during training. LMs suffer from limited awareness of such global context and end up hallucinating. Integrated development environments (IDEs) assist developers in understanding repository context using static analysis. We extend this assistance, enjoyed by developers, to LMs. We propose monitor-guided decoding (MGD) where a monitor uses static analysis to guide the decoding. We construct a repository-level dataset PragmaticCode for method-completion in Java and evaluate MGD on it. On models of varying parameter scale, by monitoring for type-consistent object dereferences, MGD consistently improves compilation rates and agreement with ground truth. Further, LMs with fewer parameters, when augmented with MGD, can outperform larger LMs. With MGD, SantaCoder-1.1B achieves better compilation rate and next-identifier match than the much larger text-davinci-003 model. We also conduct a generalizability study to evaluate the ability of MGD to generalize to multiple programming languages (Java, C# and Rust), coding scenarios (e.g., correct number of arguments to method calls), and to enforce richer semantic constraints (e.g., stateful API protocols). Our data and implementation are available at https://github.com/microsoft/monitors4codegen .

cs.CL↗

arXiv2023

In-Context Learning through the Bayesian Prism

In-context learning (ICL) is one of the surprising and useful features of large language models and subject of intense research. Recently, stylized meta-learning-like ICL setups have been devised that train transformers on sequences of input-output pairs $(x, f(x))$. The function $f$ comes from a function class and generalization is checked by evaluating on sequences generated from unseen functions from the same class. One of the main discoveries in this line of research has been that for several function classes, such as linear regression, transformers successfully generalize to new functions in the class. However, the inductive biases of these models resulting in this behavior are not clearly understood. A model with unlimited training data and compute is a Bayesian predictor: it learns the pretraining distribution. In this paper we empirically examine how far this Bayesian perspective can help us understand ICL. To this end, we generalize the previous meta-ICL setup to hierarchical meta-ICL setup which involve unions of multiple task families. We instantiate this setup on a diverse range of linear and nonlinear function families and find that transformers can do ICL in this setting as well. Where Bayesian inference is tractable, we find evidence that high-capacity transformers mimic the Bayesian predictor. The Bayesian perspective provides insights into the inductive bias of ICL and how transformers perform a particular task when they are trained on multiple tasks. We also find that transformers can learn to generalize to new function classes that were not seen during pretraining. This involves deviation from the Bayesian predictor. We examine these deviations in more depth offering new insights and hypotheses.

cs.LG↗

arXiv2023

A Theory of Emergent In-Context Learning as Implicit Structure Induction

Scaling large language models (LLMs) leads to an emergent capacity to learn in-context from example demonstrations. Despite progress, theoretical understanding of this phenomenon remains limited. We argue that in-context learning relies on recombination of compositional operations found in natural language data. We derive an information-theoretic bound showing how in-context learning abilities arise from generic next-token prediction when the pretraining distribution has sufficient amounts of compositional structure, under linguistically motivated assumptions. A second bound provides a theoretical justification for the empirical success of prompting LLMs to output intermediate steps towards an answer. To validate theoretical predictions, we introduce a controlled setup for inducing in-context learning; unlike previous approaches, it accounts for the compositional nature of language. Trained transformers can perform in-context learning for a range of tasks, in a manner consistent with the theoretical results. Mirroring real-world LLMs in a miniature setup, in-context learning emerges when scaling parameters and data, and models perform better when prompted to output intermediate steps. Probing shows that in-context learning is supported by a representation of the input's compositional structure. Taken together, these results provide a step towards theoretical understanding of emergent behavior in large language models.

cs.CL↗

arXiv2022

Towards a Mathematics Formalisation Assistant using Large Language Models

Mathematics formalisation is the task of writing mathematics (i.e., definitions, theorem statements, proofs) in natural language, as found in books and papers, into a formal language that can then be checked for correctness by a program. It is a thriving activity today, however formalisation remains cumbersome. In this paper, we explore the abilities of a large language model (Codex) to help with formalisation in the Lean theorem prover. We find that with careful input-dependent prompt selection and postprocessing, Codex is able to formalise short mathematical statements at undergrad level with nearly 75\% accuracy for $120$ theorem statements. For proofs quantitative analysis is infeasible and we undertake a detailed case study. We choose a diverse set of $13$ theorems at undergrad level with proofs that fit in two-three paragraphs. We show that with a new prompting strategy Codex can formalise these proofs in natural language with at least one out of twelve Codex completion being easy to repair into a complete proof. This is surprising as essentially no aligned data exists for formalised mathematics, particularly for proofs. These results suggest that large language models are a promising avenue towards fully or partially automating formalisation.

cs.CL↗

arXiv2022

When Can Transformers Ground and Compose: Insights from Compositional Generalization Benchmarks

Humans can reason compositionally whilst grounding language utterances to the real world. Recent benchmarks like ReaSCAN use navigation tasks grounded in a grid world to assess whether neural models exhibit similar capabilities. In this work, we present a simple transformer-based model that outperforms specialized architectures on ReaSCAN and a modified version of gSCAN. On analyzing the task, we find that identifying the target location in the grid world is the main challenge for the models. Furthermore, we show that a particular split in ReaSCAN, which tests depth generalization, is unfair. On an amended version of this split, we show that transformers can generalize to deeper input structures. Finally, we design a simpler grounded compositional generalization task, RefEx, to investigate how transformers reason compositionally. We show that a single self-attention layer with a single head generalizes to novel combinations of object attributes. Moreover, we derive a precise mathematical construction of the transformer's computations from the learned network. Overall, we provide valuable insights about the grounded compositional generalization task and the behaviour of transformers on it, which would be useful for researchers working in this area.

cs.CL↗

arXiv2022

Revisiting the Compositional Generalization Abilities of Neural Sequence Models

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.

cs.CL↗

arXiv2021

Learning and Generalization in Overparameterized Normalizing Flows

In supervised learning, it is known that overparameterized neural networks with one hidden layer provably and efficiently learn and generalize, when trained using stochastic gradient descent with a sufficiently small learning rate and suitable initialization. In contrast, the benefit of overparameterization in unsupervised learning is not well understood. Normalizing flows (NFs) constitute an important class of models in unsupervised learning for sampling and density estimation. In this paper, we theoretically and empirically analyze these models when the underlying neural network is a one-hidden-layer overparametrized network. Our main contributions are two-fold: (1) On the one hand, we provide theoretical and empirical evidence that for constrained NFs (this class of NFs underlies many NF constructions) with the one-hidden-layer network, overparametrization hurts training. (2) On the other hand, we prove that unconstrained NFs, a recently introduced model, can efficiently learn any reasonable data distribution under minimal assumptions when the underlying network is overparametrized and has one hidden-layer.

cs.LG↗

arXiv2021

Learning and Generalization in RNNs

Simple recurrent neural networks (RNNs) and their more advanced cousins LSTMs etc. have been very successful in sequence modeling. Their theoretical understanding, however, is lacking and has not kept pace with the progress for feedforward networks, where a reasonably complete understanding in the special case of highly overparametrized one-hidden-layer networks has emerged. In this paper, we make progress towards remedying this situation by proving that RNNs can learn functions of sequences. In contrast to the previous work that could only deal with functions of sequences that are sums of functions of individual tokens in the sequence, we allow general functions. Conceptually and technically, we introduce new ideas which enable us to extract information from the hidden state of the RNN in our proofs -- addressing a crucial weakness in previous work. We illustrate our results on some regular language recognition problems.

cs.LG↗

arXiv2021

Analyzing the Nuances of Transformers' Polynomial Simplification Abilities

Symbolic Mathematical tasks such as integration often require multiple well-defined steps and understanding of sub-tasks to reach a solution. To understand Transformers' abilities in such tasks in a fine-grained manner, we deviate from traditional end-to-end settings, and explore a step-wise polynomial simplification task. Polynomials can be written in a simple normal form as a sum of monomials which are ordered in a lexicographic order. For a polynomial which is not necessarily in this normal form, a sequence of simplification steps is applied to reach the fully simplified (i.e., in the normal form) polynomial. We propose a synthetic Polynomial dataset generation algorithm that generates polynomials with unique proof steps. Through varying coefficient configurations, input representation, proof granularity, and extensive hyper-parameter tuning, we observe that Transformers consistently struggle with numeric multiplication. We explore two ways to mitigate this: Curriculum Learning and a Symbolic Calculator approach (where the numeric operations are offloaded to a calculator). Both approaches provide significant gains over the vanilla Transformers-based baseline.

cs.AI↗

arXiv2021

Are NLP Models really able to Solve Simple Math Word Problems?

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.

cs.CL↗

arXiv2020

On the Practical Ability of Recurrent Neural Networks to Recognize Hierarchical Languages

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.

cs.CL↗

arXiv2020

On the Ability and Limitations of Transformers to Recognize Formal Languages

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.

cs.CL↗