Do LLMs "know" internally when they follow instructions?

Instruction-following is crucial for building AI agents with large language models (LLMs), as these models must adhere strictly to user-provided constraints and guidelines. However, LLMs often fail to follow even simple and clear instructions. To improve instruction-following behavior and prevent undesirable outputs, a deeper understanding of how LLMs' internal states relate to these outcomes is required. Our analysis of LLM internal states reveal a dimension in the input embedding space linked to successful instruction-following. We demonstrate that modifying representations along this dimension improves instruction-following success rates compared to random changes, without compromising response quality. Further investigation reveals that this dimension is more closely related to the phrasing of prompts rather than the inherent difficulty of the task or instructions. This discovery also suggests explanations for why LLMs sometimes fail to follow clear instructions and why prompt engineering is often effective, even when the content remains largely unchanged. This work provides insight into the internal workings of LLMs' instruction-following, paving the way for reliable LLM agents.

PaCE: Parsimonious Concept Engineering for Large Language Models

Large Language Models (LLMs) are being used for a wide variety of tasks. While they are capable of generating human-like responses, they can also produce undesirable output including potentially harmful information, racist or sexist language, and hallucinations. Alignment methods are designed to reduce such undesirable output, via techniques such as fine-tuning, prompt engineering, and representation engineering. However, existing methods face several challenges: some require costly fine-tuning for every alignment task; some do not adequately remove undesirable concepts, failing alignment; some remove benign concepts, lowering the linguistic capabilities of LLMs. To address these issues, we propose Parsimonious Concept Engineering (PaCE), a novel activation engineering framework for alignment. First, to sufficiently model the concepts, we construct a large-scale concept dictionary in the activation space, in which each atom corresponds to a semantic concept. Then, given any alignment task, we instruct a concept partitioner to efficiently annotate the concepts as benign or undesirable. Finally, at inference time, we decompose the LLM activations along the concept dictionary via sparse coding, to accurately represent the activation as a linear combination of the benign and undesirable components. By removing the latter ones from the activation, we reorient the behavior of LLMs towards alignment goals. We conduct experiments on tasks such as response detoxification, faithfulness enhancement, and sentiment revising, and show that PaCE achieves state-of-the-art alignment performance while maintaining linguistic capabilities.

Learning Interpretable Queries for Explainable Image Classification with Information Pursuit

Information Pursuit (IP) is an explainable prediction algorithm that greedily selects a sequence of interpretable queries about the data in order of information gain, updating its posterior at each step based on observed query-answer pairs. The standard paradigm uses hand-crafted dictionaries of potential data queries curated by a domain expert or a large language model after a human prompt. However, in practice, hand-crafted dictionaries are limited by the expertise of the curator and the heuristics of prompt engineering. This paper introduces a novel approach: learning a dictionary of interpretable queries directly from the dataset. Our query dictionary learning problem is formulated as an optimization problem by augmenting IP's variational formulation with learnable dictionary parameters. To formulate learnable and interpretable queries, we leverage the latent space of large vision and language models like CLIP. To solve the optimization problem, we propose a new query dictionary learning algorithm inspired by classical sparse dictionary learning. Our experiments demonstrate that learned dictionaries significantly outperform hand-crafted dictionaries generated with large language models.

Knowledge Pursuit Prompting for Zero-Shot Multimodal Synthesis

Hallucinations and unfaithful synthesis due to inaccurate prompts with insufficient semantic details are widely observed in multimodal generative models. A prevalent strategy to align multiple modalities is to fine-tune the generator with a large number of annotated text-image pairs. However, such a procedure is labor-consuming and resource-draining. The key question we ask is: can we enhance the quality and faithfulness of text-driven generative models beyond extensive text-image pair annotations? To address this question, we propose Knowledge Pursuit Prompting (KPP), a zero-shot framework that iteratively incorporates external knowledge to help generators produce reliable visual content. Instead of training generators to handle generic prompts, KPP employs a recursive knowledge query process to gather informative external facts from the knowledge base, instructs a language model to compress the acquired knowledge for prompt refinement, and utilizes text-driven generators for visual synthesis. The entire process is zero-shot, without accessing the architectures and parameters of generative models. We evaluate the framework across multiple text-driven generative tasks (image, 3D rendering, and video) on datasets of different domains. We further demonstrate the extensibility and adaptability of KPP through varying foundation model bases and instructions. Our results show that KPP is capable of generating faithful and semantically rich content across diverse visual domains, offering a promising solution to improve multimodal generative models.

Variational Information Pursuit with Large Language and Multimodal Models for Interpretable Predictions

Variational Information Pursuit (V-IP) is a framework for making interpretable predictions by design by sequentially selecting a short chain of task-relevant, user-defined and interpretable queries about the data that are most informative for the task. While this allows for built-in interpretability in predictive models, applying V-IP to any task requires data samples with dense concept-labeling by domain experts, limiting the application of V-IP to small-scale tasks where manual data annotation is feasible. In this work, we extend the V-IP framework with Foundational Models (FMs) to address this limitation. More specifically, we use a two-step process, by first leveraging Large Language Models (LLMs) to generate a sufficiently large candidate set of task-relevant interpretable concepts, then using Large Multimodal Models to annotate each data sample by semantic similarity with each concept in the generated concept set. While other interpretable-by-design frameworks such as Concept Bottleneck Models (CBMs) require an additional step of removing repetitive and non-discriminative concepts to have good interpretability and test performance, we mathematically and empirically justify that, with a sufficiently informative and task-relevant query (concept) set, the proposed FM+V-IP method does not require any type of concept filtering. In addition, we show that FM+V-IP with LLM generated concepts can achieve better test performance than V-IP with human annotated concepts, demonstrating the effectiveness of LLMs at generating efficient query sets. Finally, when compared to other interpretable-by-design frameworks such as CBMs, FM+V-IP can achieve competitive test performance using fewer number of concepts/queries in both cases with filtered or unfiltered concept sets.

Variational Information Pursuit for Interpretable Predictions

There is a growing interest in the machine learning community in developing predictive algorithms that are "interpretable by design". Towards this end, recent work proposes to make interpretable decisions by sequentially asking interpretable queries about data until a prediction can be made with high confidence based on the answers obtained (the history). To promote short query-answer chains, a greedy procedure called Information Pursuit (IP) is used, which adaptively chooses queries in order of information gain. Generative models are employed to learn the distribution of query-answers and labels, which is in turn used to estimate the most informative query. However, learning and inference with a full generative model of the data is often intractable for complex tasks. In this work, we propose Variational Information Pursuit (V-IP), a variational characterization of IP which bypasses the need for learning generative models. V-IP is based on finding a query selection strategy and a classifier that minimizes the expected cross-entropy between true and predicted labels. We then demonstrate that the IP strategy is the optimal solution to this problem. Therefore, instead of learning generative models, we can use our optimal strategy to directly pick the most informative query given any history. We then develop a practical algorithm by defining a finite-dimensional parameterization of our strategy and classifier using deep networks and train them end-to-end using our objective. Empirically, V-IP is 10-100x faster than IP on different Vision and NLP tasks with competitive performance. Moreover, V-IP finds much shorter query chains when compared to reinforcement learning which is typically used in sequential-decision-making problems. Finally, we demonstrate the utility of V-IP on challenging tasks like medical diagnosis where the performance is far superior to the generative modelling approach.

Unsupervised Manifold Linearizing and Clustering

Clustering data lying close to a union of low-dimensional manifolds, with each manifold as a cluster, is a fundamental problem in machine learning. When the manifolds are assumed to be linear subspaces, many methods succeed using low-rank and sparse priors, which have been studied extensively over the past two decades. Unfortunately, most real-world datasets can not be well approximated by linear subspaces. On the other hand, several works have proposed to identify the manifolds by learning a feature map such that the data transformed by the map lie in a union of linear subspaces, even though the original data are from non-linear manifolds. However, most works either assume knowledge of the membership of samples to clusters, or are shown to learn trivial representations. In this paper, we propose to simultaneously perform clustering and learn a union-of-subspace representation via Maximal Coding Rate Reduction. Experiments on synthetic and realistic datasets show that the proposed method achieves clustering accuracy comparable with state-of-the-art alternatives, while being more scalable and learning geometrically meaningful representations.

Efficient Maximal Coding Rate Reduction by Variational Forms

The principle of Maximal Coding Rate Reduction (MCR$^2$) has recently been proposed as a training objective for learning discriminative low-dimensional structures intrinsic to high-dimensional data to allow for more robust training than standard approaches, such as cross-entropy minimization. However, despite the advantages that have been shown for MCR$^2$ training, MCR$^2$ suffers from a significant computational cost due to the need to evaluate and differentiate a significant number of log-determinant terms that grows linearly with the number of classes. By taking advantage of variational forms of spectral functions of a matrix, we reformulate the MCR$^2$ objective to a form that can scale significantly without compromising training accuracy. Experiments in image classification demonstrate that our proposed formulation results in a significant speed up over optimizing the original MCR$^2$ objective directly and often results in higher quality learned representations. Further, our approach may be of independent interest in other models that require computation of log-determinant forms, such as in system identification or normalizing flow models.

Closed-Loop Data Transcription to an LDR via Minimaxing Rate Reduction

This work proposes a new computational framework for learning an explicit generative model for real-world datasets. In particular we propose to learn {\em a closed-loop transcription} between a multi-class multi-dimensional data distribution and a { linear discriminative representation (LDR)} in the feature space that consists of multiple independent multi-dimensional linear subspaces. In particular, we argue that the optimal encoding and decoding mappings sought can be formulated as the equilibrium point of a {\em two-player minimax game between the encoder and decoder}. A natural utility function for this game is the so-called {\em rate reduction}, a simple information-theoretic measure for distances between mixtures of subspace-like Gaussians in the feature space. Our formulation draws inspiration from closed-loop error feedback from control systems and avoids expensive evaluating and minimizing approximated distances between arbitrary distributions in either the data space or the feature space. To a large extent, this new formulation unifies the concepts and benefits of Auto-Encoding and GAN and naturally extends them to the settings of learning a {\em both discriminative and generative} representation for multi-class and multi-dimensional real-world data. Our extensive experiments on many benchmark imagery datasets demonstrate tremendous potential of this new closed-loop formulation: under fair comparison, visual quality of the learned decoder and classification performance of the encoder is competitive and often better than existing methods based on GAN, VAE, or a combination of both. We notice that the so learned features of different classes are explicitly mapped onto approximately {\em independent principal subspaces} in the feature space; and diverse visual attributes within each class are modeled by the {\em independent principal components} within each subspace.

ReduNet: A White-box Deep Network from the Principle of Maximizing Rate Reduction

This work attempts to provide a plausible theoretical framework that aims to interpret modern deep (convolutional) networks from the principles of data compression and discriminative representation. We argue that for high-dimensional multi-class data, the optimal linear discriminative representation maximizes the coding rate difference between the whole dataset and the average of all the subsets. We show that the basic iterative gradient ascent scheme for optimizing the rate reduction objective naturally leads to a multi-layer deep network, named ReduNet, which shares common characteristics of modern deep networks. The deep layered architectures, linear and nonlinear operators, and even parameters of the network are all explicitly constructed layer-by-layer via forward propagation, although they are amenable to fine-tuning via back propagation. All components of so-obtained ``white-box'' network have precise optimization, statistical, and geometric interpretation. Moreover, all linear operators of the so-derived network naturally become multi-channel convolutions when we enforce classification to be rigorously shift-invariant. The derivation in the invariant setting suggests a trade-off between sparsity and invariance, and also indicates that such a deep convolution network is significantly more efficient to construct and learn in the spectral domain. Our preliminary simulations and experiments clearly verify the effectiveness of both the rate reduction objective and the associated ReduNet. All code and data are available at https://github.com/Ma-Lab-Berkeley.