Due to the size and complexity of modern large language models (LLMs), it has proven challenging to uncover the underlying mechanisms that models use to solve reasoning problems. For instance, is their reasoning for a specific problem localized to certain parts of the network? Do they break down the reasoning problem into modular components that are then executed as sequential steps as we go deeper in the model? To better understand the reasoning capability of LLMs, we study a minimal propositional logic problem that requires combining multiple facts to arrive at a solution. By studying this problem on Mistral and Gemma models, up to 27B parameters, we illuminate the core components the models use to solve such logic problems. From a mechanistic interpretability point of view, we use causal mediation analysis to uncover the pathways and components of the LLMs' reasoning processes. Then, we offer fine-grained insights into the functions of attention heads in different layers. We not only find a sparse circuit that computes the answer, but we decompose it into sub-circuits that have four distinct and modular uses. Finally, we reveal that three distinct models -- Mistral-7B, Gemma-2-9B and Gemma-2-27B -- contain analogous but not identical mechanisms.

Causal language modeling using the Transformer architecture has yielded remarkable capabilities in Large Language Models (LLMs) over the last few years. However, the extent to which fundamental search and reasoning capabilities emerged within LLMs remains a topic of ongoing debate. In this work, we study if causal language modeling can learn a complex task such as solving Sudoku puzzles. To solve a Sudoku, the model is first required to search over all empty cells of the puzzle to decide on a cell to fill and then apply an appropriate strategy to fill the decided cell. Sometimes, the application of a strategy only results in thinning down the possible values in a cell rather than concluding the exact value of the cell. In such cases, multiple strategies are applied one after the other to fill a single cell. We observe that Transformer models trained on this synthetic task can indeed learn to solve Sudokus (our model solves $94.21\%$ of the puzzles fully correctly) when trained on a logical sequence of steps taken by a solver. We find that training Transformers with the logical sequence of steps is necessary and without such training, they fail to learn Sudoku. We also extend our analysis to Zebra puzzles (known as Einstein puzzles) and show that the model solves $92.04 \%$ of the puzzles fully correctly. In addition, we study the internal representations of the trained Transformer and find that through linear probing, we can decode information about the set of possible values in any given cell from them, pointing to the presence of a strong reasoning engine implicit in the Transformer weights.

Mixture-of-Expert (MoE) models, such as the Switch Transformer, allow us to scale model sizes while keeping the amount of compute time fixed.Prior work has established the computational benefits of MoE models.We investigate whether they offer benefits other than scaling up.A core component of these models is a router that routes input tokens to different experts in a layer.We show theoretical and empirical evidence that the router's ability to route intelligently confers a significant advantage to MoE models.We study synthetic settings where the input data is distributed in clusters and show theoretically and empirically that the router learns the cluster structure.Then we perform experiments on real data using the T5X library, where we observe that a trainable router confers a non-trivial benefit instead of a non-trainable router.

It has been well established that increasing scale in deep transformer networks leads to improved quality and performance. However, this increase in scale often comes with prohibitive increases in compute cost and inference latency. We introduce Alternating Updates (AltUp), a simple-to-implement method to increase a model's capacity without the computational burden. AltUp enables the widening of the learned representation, i.e., the token embedding, while only incurring a negligible increase in latency. AltUp achieves this by working on a subblock of the widened representation at each layer and using a predict-and-correct mechanism to update the inactivated blocks. We present extensions of AltUp, such as its applicability to the sequence dimension, and demonstrate how AltUp can be synergistically combined with existing approaches, such as Sparse Mixture-of-Experts models, to obtain efficient models with even higher capacity. Our experiments on benchmark transformer models and language tasks demonstrate the consistent effectiveness of AltUp on a diverse set of scenarios. Notably, on SuperGLUE and SQuAD benchmarks, AltUp enables up to $87\%$ speedup relative to the dense baselines at the same accuracy.

In this paper, we propose a dynamic cascaded encoder Automatic Speech Recognition (ASR) model, which unifies models for different deployment scenarios. Moreover, the model can significantly reduce model size and power consumption without loss of quality. Namely, with the dynamic cascaded encoder model, we explore three techniques to maximally boost the performance of each model size: 1) Use separate decoders for each sub-model while sharing the encoders; 2) Use funnel-pooling to improve the encoder efficiency; 3) Balance the size of causal and non-causal encoders to improve quality and fit deployment constraints. Overall, the proposed large-medium model has 30% smaller size and reduces power consumption by 33%, compared to the baseline cascaded encoder model. The triple-size model that unifies the large, medium, and small models achieves 37% total size reduction with minimal quality loss, while substantially reducing the engineering efforts of having separate models.

Deep and wide neural networks successfully fit very complex functions today, but dense models are starting to be prohibitively expensive for inference. To mitigate this, one promising research direction is networks that activate a sparse subgraph of the network. The subgraph is chosen by a data-dependent routing function, enforcing a fixed mapping of inputs to subnetworks (e.g., the Mixture of Experts (MoE) paradigm in Switch Transformers). However, there is no theoretical grounding for these sparsely activated models. As our first contribution, we present a formal model of data-dependent sparse networks that captures salient aspects of popular architectures. Then, we show how to construct sparse networks that provably match the approximation power and total size of dense networks on Lipschitz functions. The sparse networks use much fewer inference operations than dense networks, leading to a faster forward pass. The key idea is to use locality sensitive hashing on the input vectors and then interpolate the function in subregions of the input space. This offers a theoretical insight into why sparse networks work well in practice. Finally, we present empirical findings that support our theory; compared to dense networks, sparse networks give a favorable trade-off between number of active units and approximation quality.

How do we provably represent images succinctly so that their essential latent attributes are correctly captured by the representation to as high level of detail as possible? While today's deep networks (such as CNNs) produce image embeddings they do not have any provable properties and seem to work in mysterious non-interpretable ways. In this work we theoretically study synthetic images that are composed of a union or intersection of several mathematically specified shapes using thresholded polynomial functions (for e.g. ellipses, rectangles). We show how to produce a succinct sketch of such an image so that the sketch “smoothly” maps to the latent-coefficients producing the different shapes in the image. We prove several important properties such as: easy reconstruction of the image from the sketch, similarity preservation (similar shapes produce similar sketches), being able to index sketches so that other similar images and parts of other images can be retrieved, being able to store the sketches into a dictionary of concepts and shapes so parts of the same or different images that refer to the same shape can point to the same entry in this dictionary of common shape attributes.

Deep learning has shown tremendous success on a variety of problems. However, unlike traditional computational paradigm, most neural networks do not have access to a memory, which might be hampering its ability to scale to large data structures such as graphs, lookup-tables, databases. We propose a neural architecture where sketch based memory is integrated into a neural network in a uniform manner at every layer. This architecture supplements a neural layer by information accessed from the memory before feeding it to the next layer, thereby significantly expanding the capacity of the network to solve larger problem instances. We show theoretically that problems involving key-value lookup that are traditionally stored in standard databases can now be solved using neural networks augmented by our memory architecture. We also show that our memory layer can be viewed as a kernel function. We show benefits on diverse problems such as long tail image classification, language model, large graph multi hop traversal, etc. arguing that they are all build upon the classical key-value lookup problem (or the variant where the keys may be fuzzy).