arXiv subjects

Andreas Loukas

Publications and source records attributed to Andreas Loukas.

At least 19 recordsLinked to original sources

arXiv2024

Generalizing to any diverse distribution: uniformity, gentle finetuning and rebalancing

As training datasets grow larger, we aspire to develop models that generalize well to any diverse test distribution, even if the latter deviates significantly from the training data. Various approaches like domain adaptation, domain generalization, and robust optimization attempt to address the out-of-distribution challenge by posing assumptions about the relation between training and test distribution. Differently, we adopt a more conservative perspective by accounting for the worst-case error across all sufficiently diverse test distributions within a known domain. Our first finding is that training on a uniform distribution over this domain is optimal. We also interrogate practical remedies when uniform samples are unavailable by considering methods for mitigating non-uniformity through finetuning and rebalancing. Our theory provides a mathematical grounding for previous observations on the role of entropy and rebalancing for o.o.d. generalization and foundation model training. We also provide new empirical evidence across tasks involving o.o.d. shifts which illustrate the broad applicability of our perspective.

cs.LG↗

arXiv2024

Generalization within in silico screening

In silico screening uses predictive models to select a batch of compounds with favorable properties from a library for experimental validation. Unlike conventional learning paradigms, success in this context is measured by the performance of the predictive model on the selected subset of compounds rather than the entire set of predictions. By extending learning theory, we show that the selectivity of the selection policy can significantly impact generalization, with a higher risk of errors occurring when exclusively selecting predicted positives and when targeting rare properties. Our analysis suggests a way to mitigate these challenges. We show that generalization can be markedly enhanced when considering a model's ability to predict the fraction of desired outcomes in a batch. This is promising, as the primary aim of screening is not necessarily to pinpoint the label of each compound individually, but rather to assemble a batch enriched for desirable compounds. Our theoretical insights are empirically validated across diverse tasks, architectures, and screening scenarios, underscoring their applicability.

stat.ML↗

arXiv2024

Implicitly Guided Design with PropEn: Match your Data to Follow the Gradient

Across scientific domains, generating new models or optimizing existing ones while meeting specific criteria is crucial. Traditional machine learning frameworks for guided design use a generative model and a surrogate model (discriminator), requiring large datasets. However, real-world scientific applications often have limited data and complex landscapes, making data-hungry models inefficient or impractical. We propose a new framework, PropEn, inspired by ``matching'', which enables implicit guidance without training a discriminator. By matching each sample with a similar one that has a better property value, we create a larger training dataset that inherently indicates the direction of improvement. Matching, combined with an encoder-decoder architecture, forms a domain-agnostic generative framework for property enhancement. We show that training with a matched dataset approximates the gradient of the property of interest while remaining within the data distribution, allowing efficient design optimization. Extensive evaluations in toy problems and scientific applications, such as therapeutic protein design and airfoil optimization, demonstrate PropEn's advantages over common baselines. Notably, the protein design results are validated with wet lab experiments, confirming the competitiveness and effectiveness of our approach.

cs.LG↗

arXiv2024

AbDiffuser: Full-Atom Generation of in vitro Functioning Antibodies

We introduce AbDiffuser, an equivariant and physics-informed diffusion model for the joint generation of antibody 3D structures and sequences. AbDiffuser is built on top of a new representation of protein structure, relies on a novel architecture for aligned proteins, and utilizes strong diffusion priors to improve the denoising process. Our approach improves protein diffusion by taking advantage of domain knowledge and physics-based constraints; handles sequence-length changes; and reduces memory complexity by an order of magnitude, enabling backbone and side chain generation. We validate AbDiffuser in silico and in vitro. Numerical experiments showcase the ability of AbDiffuser to generate antibodies that closely track the sequence and structural properties of a reference set. Laboratory experiments confirm that all 16 HER2 antibodies discovered were expressed at high levels and that 57.1% of the selected designs were tight binders.

q-bio.BM↗

arXiv2023

Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth

Attention-based architectures have become ubiquitous in machine learning, yet our understanding of the reasons for their effectiveness remains limited. This work proposes a new way to understand self-attention networks: we show that their output can be decomposed into a sum of smaller terms, each involving the operation of a sequence of attention heads across layers. Using this decomposition, we prove that self-attention possesses a strong inductive bias towards "token uniformity". Specifically, without skip connections or multi-layer perceptrons (MLPs), the output converges doubly exponentially to a rank-1 matrix. On the other hand, skip connections and MLPs stop the output from degeneration. Our experiments verify the identified convergence phenomena on different variants of standard transformer architectures.

cs.LG↗

arXiv2023

Protein Discovery with Discrete Walk-Jump Sampling

We resolve difficulties in training and sampling from a discrete generative model by learning a smoothed energy function, sampling from the smoothed data manifold with Langevin Markov chain Monte Carlo (MCMC), and projecting back to the true data manifold with one-step denoising. Our Discrete Walk-Jump Sampling formalism combines the contrastive divergence training of an energy-based model and improved sample quality of a score-based model, while simplifying training and sampling by requiring only a single noise level. We evaluate the robustness of our approach on generative modeling of antibody proteins and introduce the distributional conformity score to benchmark protein generative models. By optimizing and sampling from our models for the proposed distributional conformity score, 97-100% of generated samples are successfully expressed and purified and 70% of functional designs show equal or improved binding affinity compared to known functional antibodies on the first attempt in a single round of laboratory experiments. We also report the first demonstration of long-run fast-mixing MCMC chains where diverse antibody protein classes are visited in a single MCMC chain.

q-bio.BM↗

arXiv2023

Infusing Lattice Symmetry Priors in Attention Mechanisms for Sample-Efficient Abstract Geometric Reasoning

The Abstraction and Reasoning Corpus (ARC) (Chollet, 2019) and its most recent language-complete instantiation (LARC) has been postulated as an important step towards general AI. Yet, even state-of-the-art machine learning models struggle to achieve meaningful performance on these problems, falling behind non-learning based approaches. We argue that solving these tasks requires extreme generalization that can only be achieved by proper accounting for core knowledge priors. As a step towards this goal, we focus on geometry priors and introduce LatFormer, a model that incorporates lattice symmetry priors in attention masks. We show that, for any transformation of the hypercubic lattice, there exists a binary attention mask that implements that group action. Hence, our study motivates a modification to the standard attention mechanism, where attention weights are scaled using soft masks generated by a convolutional network. Experiments on synthetic geometric reasoning show that LatFormer requires 2 orders of magnitude fewer data than standard attention and transformers. Moreover, our results on ARC and LARC tasks that incorporate geometric priors provide preliminary evidence that these complex datasets do not lie out of the reach of deep learning models.

cs.AI↗

arXiv2023

Towards Understanding and Improving GFlowNet Training

Generative flow networks (GFlowNets) are a family of algorithms that learn a generative policy to sample discrete objects $x$ with non-negative reward $R(x)$. Learning objectives guarantee the GFlowNet samples $x$ from the target distribution $p^*(x) \propto R(x)$ when loss is globally minimized over all states or trajectories, but it is unclear how well they perform with practical limits on training resources. We introduce an efficient evaluation strategy to compare the learned sampling distribution to the target reward distribution. As flows can be underdetermined given training data, we clarify the importance of learned flows to generalization and matching $p^*(x)$ in practice. We investigate how to learn better flows, and propose (i) prioritized replay training of high-reward $x$, (ii) relative edge flow policy parametrization, and (iii) a novel guided trajectory balance objective, and show how it can solve a substructure credit assignment problem. We substantially improve sample efficiency on biochemical design tasks.

cs.LG↗

arXiv2022

Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions

Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (1) not naturally amenable to gradient-based optimization, and (2) incompatible with deep learning architectures that rely on representations in high-dimensional vector spaces. In this work, we address both difficulties for set functions, which capture many important discrete problems. First, we develop a framework for extending set functions onto low-dimensional continuous domains, where many extensions are naturally defined. Our framework subsumes many well-known extensions as special cases. Second, to avoid undesirable low-dimensional neural network bottlenecks, we convert low-dimensional extensions into representations in high-dimensional spaces, taking inspiration from the success of semidefinite programs for combinatorial optimization. Empirically, we observe benefits of our extensions for unsupervised neural combinatorial optimization, in particular with high-dimensional representations.

cs.LG↗

arXiv2022

Conditional Diffusion with Less Explicit Guidance via Model Predictive Control

How much explicit guidance is necessary for conditional diffusion? We consider the problem of conditional sampling using an unconditional diffusion model and limited explicit guidance (e.g., a noised classifier, or a conditional diffusion model) that is restricted to a small number of time steps. We explore a model predictive control (MPC)-like approach to approximate guidance by simulating unconditional diffusion forward, and backpropagating explicit guidance feedback. MPC-approximated guides have high cosine similarity to real guides, even over large simulation distances. Adding MPC steps improves generative quality when explicit guidance is limited to five time steps.

cs.LG↗

arXiv2022

A Pareto-optimal compositional energy-based model for sampling and optimization of protein sequences

Deep generative models have emerged as a popular machine learning-based approach for inverse design problems in the life sciences. However, these problems often require sampling new designs that satisfy multiple properties of interest in addition to learning the data distribution. This multi-objective optimization becomes more challenging when properties are independent or orthogonal to each other. In this work, we propose a Pareto-compositional energy-based model (pcEBM), a framework that uses multiple gradient descent for sampling new designs that adhere to various constraints in optimizing distinct properties. We demonstrate its ability to learn non-convex Pareto fronts and generate sequences that simultaneously satisfy multiple desired properties across a series of real-world antibody design tasks.

cs.LG↗

arXiv2022

On the generalization of learning algorithms that do not converge

Generalization analyses of deep learning typically assume that the training converges to a fixed point. But, recent results indicate that in practice, the weights of deep neural networks optimized with stochastic gradient descent often oscillate indefinitely. To reduce this discrepancy between theory and practice, this paper focuses on the generalization of neural networks whose training dynamics do not necessarily converge to fixed points. Our main contribution is to propose a notion of statistical algorithmic stability (SAS) that extends classical algorithmic stability to non-convergent algorithms and to study its connection to generalization. This ergodic-theoretic approach leads to new insights when compared to the traditional optimization and learning theory perspectives. We prove that the stability of the time-asymptotic behavior of a learning algorithm relates to its generalization and empirically demonstrate how loss dynamics can provide clues to generalization performance. Our findings provide evidence that networks that "train stably generalize better" even when the training continues indefinitely and the weights do not converge.

cs.LG↗

arXiv2022

SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators

We approach the graph generation problem from a spectral perspective by first generating the dominant parts of the graph Laplacian spectrum and then building a graph matching these eigenvalues and eigenvectors. Spectral conditioning allows for direct modeling of the global and local graph structure and helps to overcome the expressivity and mode collapse issues of one-shot graph generators. Our novel GAN, called SPECTRE, enables the one-shot generation of much larger graphs than previously possible with one-shot models. SPECTRE outperforms state-of-the-art deep autoregressive generators in terms of modeling fidelity, while also avoiding expensive sequential generation and dependence on node ordering. A case in point, in sizable synthetic and real-world graphs SPECTRE achieves a 4-to-170 fold improvement over the best competitor that does not overfit and is 23-to-30 times faster than autoregressive generators.

cs.LG↗

arXiv2021

Partition and Code: learning how to compress graphs

Can we use machine learning to compress graph data? The absence of ordering in graphs poses a significant challenge to conventional compression algorithms, limiting their attainable gains as well as their ability to discover relevant patterns. On the other hand, most graph compression approaches rely on domain-dependent handcrafted representations and cannot adapt to different underlying graph distributions. This work aims to establish the necessary principles a lossless graph compression method should follow to approach the entropy storage lower bound. Instead of making rigid assumptions about the graph distribution, we formulate the compressor as a probabilistic model that can be learned from data and generalise to unseen instances. Our "Partition and Code" framework entails three steps: first, a partitioning algorithm decomposes the graph into subgraphs, then these are mapped to the elements of a small dictionary on which we learn a probability distribution, and finally, an entropy encoder translates the representation into bits. All the components (partitioning, dictionary and distribution) are parametric and can be trained with gradient descent. We theoretically compare the compression quality of several graph encodings and prove, under mild conditions, that PnC achieves compression gains that grow either linearly or quadratically with the number of vertices. Empirically, PnC yields significant compression improvements on diverse real-world networks.

cs.LG↗

arXiv2021

What training reveals about neural network complexity

This work explores the Benevolent Training Hypothesis (BTH) which argues that the complexity of the function a deep neural network (NN) is learning can be deduced by its training dynamics. Our analysis provides evidence for BTH by relating the NN's Lipschitz constant at different regions of the input space with the behavior of the stochastic training procedure. We first observe that the Lipschitz constant close to the training data affects various aspects of the parameter trajectory, with more complex networks having a longer trajectory, bigger variance, and often veering further from their initialization. We then show that NNs whose 1st layer bias is trained more steadily (i.e., slowly and with little variation) have bounded complexity even in regions of the input space that are far from any training point. Finally, we find that steady training with Dropout implies a training- and data-dependent generalization bound that grows poly-logarithmically with the number of parameters. Overall, our results support the intuition that good training behavior can be a useful bias towards good generalization.

cs.LG↗

arXiv2021

SQALER: Scaling Question Answering by Decoupling Multi-Hop and Logical Reasoning

State-of-the-art approaches to reasoning and question answering over knowledge graphs (KGs) usually scale with the number of edges and can only be applied effectively on small instance-dependent subgraphs. In this paper, we address this issue by showing that multi-hop and more complex logical reasoning can be accomplished separately without losing expressive power. Motivated by this insight, we propose an approach to multi-hop reasoning that scales linearly with the number of relation types in the graph, which is usually significantly smaller than the number of edges or nodes. This produces a set of candidate solutions that can be provably refined to recover the solution to the original problem. Our experiments on knowledge-based question answering show that our approach solves the multi-hop MetaQA dataset, achieves a new state-of-the-art on the more challenging WebQuestionsSP, is orders of magnitude more scalable than competitive approaches, and can achieve compositional generalization out of the training distribution.

cs.LG↗

arXiv2021

Multi-Head Attention: Collaborate Instead of Concatenate

Attention layers are widely used in natural language processing (NLP) and are beginning to influence computer vision architectures. Training very large transformer models allowed significant improvement in both fields, but once trained, these networks show symptoms of over-parameterization. For instance, it is known that many attention heads can be pruned without impacting accuracy. This work aims to enhance current understanding on how multiple heads interact. Motivated by the observation that attention heads learn redundant key/query projections, we propose a collaborative multi-head attention layer that enables heads to learn shared projections. Our scheme decreases the number of parameters in an attention layer and can be used as a drop-in replacement in any transformer architecture. Our experiments confirm that sharing key/query dimensions can be exploited in language understanding, machine translation and vision. We also show that it is possible to re-parametrize a pre-trained multi-head attention layer into our collaborative attention layer. Collaborative multi-head attention reduces the size of the key and query projections by 4 for same accuracy and speed. Our code is public.

cs.LG↗

arXiv2021

Erdos Goes Neural: an Unsupervised Learning Framework for Combinatorial Optimization on Graphs

Combinatorial optimization problems are notoriously challenging for neural networks, especially in the absence of labeled instances. This work proposes an unsupervised learning framework for CO problems on graphs that can provide integral solutions of certified quality. Inspired by Erdos' probabilistic method, we use a neural network to parametrize a probability distribution over sets. Crucially, we show that when the network is optimized w.r.t. a suitably chosen loss, the learned distribution contains, with controlled probability, a low-cost integral solution that obeys the constraints of the combinatorial problem. The probabilistic proof of existence is then derandomized to decode the desired solutions. We demonstrate the efficacy of this approach to obtain valid solutions to the maximum clique problem and to perform local graph clustering. Our method achieves competitive results on both real datasets and synthetic hard instances.

cs.LG↗