On the Utility of Domain-Adjacent Fine-Tuned Model Ensembles for Few-shot Problems

Large Language Models (LLMs) have been observed to perform well on a wide range of downstream tasks when fine-tuned on domain-specific data. However, such data may not be readily available in many applications, motivating zero-shot or few-shot approaches using domain-adjacent models. While several fine-tuned models for various tasks are available, finding an appropriate domain-adjacent model for a given task is often not straight forward. In this paper, we study DAFT-E, a framework that utilizes an Ensemble of Domain-Adjacent Fine-Tuned Foundation Models for few-shot problems. We show that for zero-shot problems, this ensembling method provides an accuracy performance close to that of the single best model. With few-shot problems, this performance improves further, at which point DEFT-E can outperform any single domain-adjacent model while requiring much less data for domain-specific fine-tuning.

The Importance of Positional Encoding Initialization in Transformers for Relational Reasoning

Relational reasoning refers to the ability to infer and understand the relations between multiple entities. In humans, this ability underpins many higher cognitive functions, such as problem solving and decision-making, and has been reliably linked to fluid intelligence. Despite machine learning models making impressive advances across various domains, such as natural language processing and vision, the extent to which such models can perform relational reasoning tasks remains unclear. Here we study the importance of positional encoding (PE) for relational reasoning in the Transformer, and find that a learnable PE outperforms all other commonly-used PEs (e.g., absolute, relative, rotary, etc.). Moreover, we find that when using a PE with a learnable parameter, the choice of initialization greatly influences the learned representations and its downstream generalization performance. Specifically, we find that a learned PE initialized from a small-norm distribution can 1) uncover ground-truth position information, 2) generalize in the presence of noisy inputs, and 3) produce behavioral patterns that are consistent with human performance. Our results shed light on the importance of learning high-performing and robust PEs during relational reasoning tasks, which will prove useful for tasks in which ground truth positions are not provided or not known.

What makes Models Compositional? A Theoretical View: With Supplement

Compositionality is thought to be a key component of language, and various compositional benchmarks have been developed to empirically probe the compositional generalization of existing sequence processing models. These benchmarks often highlight failures of existing models, but it is not clear why these models fail in this way. In this paper, we seek to theoretically understand the role the compositional structure of the models plays in these failures and how this structure relates to their expressivity and sample complexity. We propose a general neuro-symbolic definition of compositional functions and their compositional complexity. We then show how various existing general and special purpose sequence processing models (such as recurrent, convolution and attention-based ones) fit this definition and use it to analyze their compositional complexity. Finally, we provide theoretical guarantees for the expressivity and systematic generalization of compositional models that explicitly depend on our proposed definition and highlighting factors which drive poor empirical performance.

Enhancing In-context Learning via Linear Probe Calibration

In-context learning (ICL) is a new paradigm for natural language processing that utilizes Generative Pre-trained Transformer (GPT)-like models. This approach uses prompts that include in-context demonstrations to generate the corresponding output for a new query input. However, applying ICL in real cases does not scale with the number of samples, and lacks robustness to different prompt templates and demonstration permutations. In this paper, we first show that GPT-like models using ICL result in unreliable predictions based on a new metric based on Shannon entropy. Then, to solve this problem, we propose a new technique called the Linear Probe Calibration (LinC), a method that calibrates the model's output probabilities, resulting in reliable predictions and improved performance, while requiring only minimal additional samples (as few as five labeled data samples). LinC significantly enhances the ICL test performance of GPT models on various benchmark datasets, with an average improvement of up to 21%, and up to a 50% improvement in some cases, and significantly boosts the performance of PEFT methods, especially in the low resource regime. Moreover, LinC achieves lower expected calibration error, and is highly robust to varying label proportions, prompt templates, and demonstration permutations. Our code is available at \url{https://github.com/mominabbass/LinC}.

Compositional Program Generation for Systematic Generalization

Compositional generalization is a key ability of humans that enables us to learn new concepts from only a handful examples. Machine learning models, including the now ubiquitous transformers, struggle to generalize in this way, and typically require thousands of examples of a concept during training in order to generalize meaningfully. This difference in ability between humans and artificial neural architectures, motivates this study on a neuro-symbolic architecture called the Compositional Program Generator (CPG). CPG has three key features: modularity, type abstraction, and recursive composition, that enable it to generalize both systematically to new concepts in a few-shot manner, as well as productively by length on various sequence-to-sequence language tasks. For each input, CPG uses a grammar of the input domain and a parser to generate a type hierarchy in which each grammar rule is assigned its own unique semantic module, a probabilistic copy or substitution program. Instances with the same hierarchy are processed with the same composed program, while those with different hierarchies may be processed with different programs. CPG learns parameters for the semantic modules and is able to learn the semantics for new types incrementally. Given a context-free grammar of the input language and a dictionary mapping each word in the source language to its interpretation in the output language, CPG can achieve perfect generalization on the SCAN and COGS benchmarks, in both standard and extreme few-shot settings.

End-to-end Differentiable Clustering with Associative Memories

Clustering is a widely used unsupervised learning technique involving an intensive discrete optimization problem. Associative Memory models or AMs are differentiable neural networks defining a recursive dynamical system, which have been integrated with various deep learning architectures. We uncover a novel connection between the AM dynamics and the inherent discrete assignment necessary in clustering to propose a novel unconstrained continuous relaxation of the discrete clustering problem, enabling end-to-end differentiable clustering with AM, dubbed ClAM. Leveraging the pattern completion ability of AMs, we further develop a novel self-supervised clustering loss. Our evaluations on varied datasets demonstrate that ClAM benefits from the self-supervision, and significantly improves upon both the traditional Lloyd's k-means algorithm, and more recent continuous clustering relaxations (by upto 60% in terms of the Silhouette Coefficient).

Model Sparsification Can Simplify Machine Unlearning

Recent data regulations necessitate machine unlearning (MU): The removal of the effect of specific examples from the model. While exact unlearning is possible by conducting a model retraining with the remaining data from scratch, its computational cost has led to the development of approximate but efficient unlearning schemes. Beyond data-centric MU solutions, we advance MU through a novel model-based viewpoint: sparsification via weight pruning. Our results in both theory and practice indicate that model sparsity can boost the multi-criteria unlearning performance of an approximate unlearner, closing the approximation gap, while continuing to be efficient. With this insight, we develop two new sparsity-aware unlearning meta-schemes, termed `prune first, then unlearn' and `sparsity-aware unlearning'. Extensive experiments show that our findings and proposals consistently benefit MU in various scenarios, including class-wise data scrubbing, random data scrubbing, and backdoor data forgetting. One highlight is the 77% unlearning efficacy gain of fine-tuning (one of the simplest approximate unlearning methods) in the proposed sparsity-aware unlearning paradigm. Codes are available at https://github.com/OPTML-Group/Unlearn-Sparse.

What Is Missing in IRM Training and Evaluation? Challenges and Solutions

Invariant risk minimization (IRM) has received increasing attention as a way to acquire environment-agnostic data representations and predictions, and as a principled solution for preventing spurious correlations from being learned and for improving models' out-of-distribution generalization. Yet, recent works have found that the optimality of the originally-proposed IRM optimization (IRM) may be compromised in practice or could be impossible to achieve in some scenarios. Therefore, a series of advanced IRM algorithms have been developed that show practical improvement over IRM. In this work, we revisit these recent IRM advancements, and identify and resolve three practical limitations in IRM training and evaluation. First, we find that the effect of batch size during training has been chronically overlooked in previous studies, leaving room for further improvement. We propose small-batch training and highlight the improvements over a set of large-batch optimization techniques. Second, we find that improper selection of evaluation environments could give a false sense of invariance for IRM. To alleviate this effect, we leverage diversified test-time environments to precisely characterize the invariance of IRM when applied in practice. Third, we revisit (Ahuja et al. (2020))'s proposal to convert IRM into an ensemble game and identify a limitation when a single invariant predictor is desired instead of an ensemble of individual predictors. We propose a new IRM variant to address this limitation based on a novel viewpoint of ensemble IRM games as consensus-constrained bi-level optimization. Lastly, we conduct extensive experiments (covering 7 existing IRM variants and 7 datasets) to justify the practical significance of revisiting IRM training and evaluation in a principled manner.

Toward Theoretical Guidance for Two Common Questions in Practical Cross-Validation based Hyperparameter Selection

We show, to our knowledge, the first theoretical treatments of two common questions in cross-validation based hyperparameter selection: (1) After selecting the best hyperparameter using a held-out set, we train the final model using {\em all} of the training data -- since this may or may not improve future generalization error, should one do this? (2) During optimization such as via SGD (stochastic gradient descent), we must set the optimization tolerance $\rho$ -- since it trades off predictive accuracy with computation cost, how should one set it? Toward these problems, we introduce the {\em hold-in risk} (the error due to not using the whole training data), and the {\em model class mis-specification risk} (the error due to having chosen the wrong model class) in a theoretical view which is simple, general, and suggests heuristics that can be used when faced with a dataset instance. In proof-of-concept studies in synthetic data where theoretical quantities can be controlled, we show that these heuristics can, respectively, (1) always perform at least as well as always performing retraining or never performing retraining, (2) either improve performance or reduce computational overhead by $2\times$ with no loss in predictive performance.

Advancing Model Pruning via Bi-level Optimization

The deployment constraints in practical applications necessitate the pruning of large-scale deep learning models, i.e., promoting their weight sparsity. As illustrated by the Lottery Ticket Hypothesis (LTH), pruning also has the potential of improving their generalization ability. At the core of LTH, iterative magnitude pruning (IMP) is the predominant pruning method to successfully find 'winning tickets'. Yet, the computation cost of IMP grows prohibitively as the targeted pruning ratio increases. To reduce the computation overhead, various efficient 'one-shot' pruning methods have been developed, but these schemes are usually unable to find winning tickets as good as IMP. This raises the question of how to close the gap between pruning accuracy and pruning efficiency? To tackle it, we pursue the algorithmic advancement of model pruning. Specifically, we formulate the pruning problem from a fresh and novel viewpoint, bi-level optimization (BLO). We show that the BLO interpretation provides a technically-grounded optimization base for an efficient implementation of the pruning-retraining learning paradigm used in IMP. We also show that the proposed bi-level optimization-oriented pruning method (termed BiP) is a special class of BLO problems with a bi-linear problem structure. By leveraging such bi-linearity, we theoretically show that BiP can be solved as easily as first-order optimization, thus inheriting the computation efficiency. Through extensive experiments on both structured and unstructured pruning with 5 model architectures and 4 data sets, we demonstrate that BiP can find better winning tickets than IMP in most cases, and is computationally as efficient as the one-shot pruning schemes, demonstrating 2-7 times speedup over IMP for the same level of model accuracy and sparsity.