arXiv subjects

David Belanger

Publications and source records attributed to David Belanger.

At least 19 recordsLinked to original sources

arXiv2024

Independence and Induction in Reverse Mathematics

We continue the project of the study of reverse mathematics principles inspired by cardinal invariants. In this article in particular we focus on principles encapsulating the existence of large families of objects that are in some sense mutually independent. More precisely, we study the principle $\mathsf{MAD}$ stating that a maximal family of pairwise almost disjoint sets exists; and the principle $\mathsf{MED}$ expressing the existence of a maximal family of functions that are pairwise eventually different. We investigate characterisations of and relations between these principles and some of their variants. It turns out that induction strength at the levels of $\mathsf{B}\mathrm{\Sigma}_2^0$ or $\mathsf{I}\mathrm{\Sigma}_2^0$ is an essential parameter; for instance, over $\mathsf{B}\mathrm{\Sigma}_2^0$, we show that $\neg\mathsf{MAD}$ is equivalent to the principle $\mathsf{DOM}$ expressing that every weakly represented family of functions is dominated by some other function.

math.LO↗

arXiv2021

Constrained Discrete Black-Box Optimization using Mixed-Integer Programming

Discrete black-box optimization problems are challenging for model-based optimization (MBO) algorithms, such as Bayesian optimization, due to the size of the search space and the need to satisfy combinatorial constraints. In particular, these methods require repeatedly solving a complex discrete global optimization problem in the inner loop, where popular heuristic inner-loop solvers introduce approximations and are difficult to adapt to combinatorial constraints. In response, we propose NN+MILP, a general discrete MBO framework using piecewise-linear neural networks as surrogate models and mixed-integer linear programming (MILP) to optimize the acquisition function. MILP provides optimality guarantees and a versatile declarative language for domain-specific constraints. We test our approach on a range of unconstrained and constrained problems, including DNA binding, constrained binary quadratic problems from the MINLPLib benchmark, and the NAS-Bench-101 neural architecture search benchmark. NN+MILP surpasses or matches the performance of black-box algorithms tailored to the constraints at hand, with global optimization of the acquisition problem running in a few minutes using only standard software packages and hardware.

math.OC↗

arXiv2021

Learnability and Positive Equivalence Relations

Prior work of Gavryushkin, Khoussainov, Jain and Stephan investigated what algebraic structures can be realised in worlds given by a positive (= recursively enumerable) equivalence relation which partitions the natural numbers into infinitely many equivalence classes. The present work investigates the infinite one-one numbered recursively enumerable (r.e.) families realised by such relations and asks how the choice of the equivalence relation impacts the learnability properties of these classes when studying learnability in the limit from positive examples, also known as learning from text. For all choices of such positive equivalence relations, for each of the following entries, there are one-one numbered r.e. families which satisfy it: (a) they are behaviourally correctly learnable but not vacillatorily learnable; (b) they are explanatorily learnable but not confidently learnable; (c) they are not behaviourally correctly learnable. Furthermore, there is a positive equivalence relation which enforces that (d) every vacillatorily learnable one-one numbered family of languages closed under this equivalence relation is already explanatorily learnable and cannot be confidently learnable.

cs.LO↗

arXiv2021

The Next Decade of Telecommunications Artificial Intelligence

It has been an exciting journey since the mobile communications and artificial intelligence were conceived 37 years and 64 years ago. While both fields evolved independently and profoundly changed communications and computing industries, the rapid convergence of 5G and deep learning is beginning to significantly transform the core communication infrastructure, network management and vertical applications. The paper first outlines the individual roadmaps of mobile communications and artificial intelligence in the early stage, with a concentration to review the era from 3G to 5G when AI and mobile communications started to converge. With regard to telecommunications artificial intelligence, the paper further introduces in detail the progress of artificial intelligence in the ecosystem of mobile communications. The paper then summarizes the classifications of AI in telecom ecosystems along with its evolution paths specified by various international telecommunications standardization bodies. Towards the next decade, the paper forecasts the prospective roadmap of telecommunications artificial intelligence. In line with 3GPP and ITU-R timeline of 5G & 6G, the paper further explores the network intelligence following 3GPP and ORAN routes respectively, experience and intention driven network management and operation, network AI signalling system, intelligent middle-office based BSS, intelligent customer experience management and policy control driven by BSS and OSS convergence, evolution from SLA to ELA, and intelligent private network for verticals. The paper is concluded with the vision that AI will reshape the future B5G or 6G landscape and we need pivot our R&D, standardizations, and ecosystem to fully take the unprecedented opportunities.

cs.NI↗

arXiv2020

Is Transfer Learning Necessary for Protein Landscape Prediction?

Recently, there has been great interest in learning how to best represent proteins, specifically with fixed-length embeddings. Deep learning has become a popular tool for protein representation learning as a model's hidden layers produce potentially useful vector embeddings. TAPE introduced a number of benchmark tasks and showed that semi-supervised learning, via pretraining language models on a large protein corpus, improved performance on downstream tasks. Two of the tasks (fluorescence prediction and stability prediction) involve learning fitness landscapes. In this paper, we show that CNN models trained solely using supervised learning both compete with and sometimes outperform the best models from TAPE that leverage expensive pretraining on large protein datasets. These CNN models are sufficiently simple and small that they can be trained using a Google Colab notebook. We also find for the fluorescence task that linear regression outperforms our models and the TAPE models. The benchmarking tasks proposed by TAPE are excellent measures of a model's ability to predict protein function and should be used going forward. However, we believe it is important to add baselines from simple models to put the performance of the semi-supervised models that have been reported so far into perspective.

q-bio.BM↗

arXiv2020

Fixed-Length Protein Embeddings using Contextual Lenses

The Basic Local Alignment Search Tool (BLAST) is currently the most popular method for searching databases of biological sequences. BLAST compares sequences via similarity defined by a weighted edit distance, which results in it being computationally expensive. As opposed to working with edit distance, a vector similarity approach can be accelerated substantially using modern hardware or hashing techniques. Such an approach would require fixed-length embeddings for biological sequences. There has been recent interest in learning fixed-length protein embeddings using deep learning models under the hypothesis that the hidden layers of supervised or semi-supervised models could produce potentially useful vector embeddings. We consider transformer (BERT) protein language models that are pretrained on the TrEMBL data set and learn fixed-length embeddings on top of them with contextual lenses. The embeddings are trained to predict the family a protein belongs to for sequences in the Pfam database. We show that for nearest-neighbor family classification, pretraining offers a noticeable boost in performance and that the corresponding learned embeddings are competitive with BLAST. Furthermore, we show that the raw transformer embeddings, obtained via static pooling, do not perform well on nearest-neighbor family classification, which suggests that learning embeddings in a supervised manner via contextual lenses may be a compute-efficient alternative to fine-tuning.

q-bio.BM↗

arXiv2020

Masked Language Modeling for Proteins via Linearly Scalable Long-Context Transformers

Transformer models have achieved state-of-the-art results across a diverse range of domains. However, concern over the cost of training the attention mechanism to learn complex dependencies between distant inputs continues to grow. In response, solutions that exploit the structure and sparsity of the learned attention matrix have blossomed. However, real-world applications that involve long sequences, such as biological sequence analysis, may fall short of meeting these assumptions, precluding exploration of these models. To address this challenge, we present a new Transformer architecture, Performer, based on Fast Attention Via Orthogonal Random features (FAVOR). Our mechanism scales linearly rather than quadratically in the number of tokens in the sequence, is characterized by sub-quadratic space complexity and does not incorporate any sparsity pattern priors. Furthermore, it provides strong theoretical guarantees: unbiased estimation of the attention matrix and uniform convergence. It is also backwards-compatible with pre-trained regular Transformers. We demonstrate its effectiveness on the challenging task of protein sequence modeling and provide detailed theoretical analysis.

cs.LG↗

arXiv2020

Rethinking Attention with Performers

We introduce Performers, Transformer architectures which can estimate regular (softmax) full-rank-attention Transformers with provable accuracy, but using only linear (as opposed to quadratic) space and time complexity, without relying on any priors such as sparsity or low-rankness. To approximate softmax attention-kernels, Performers use a novel Fast Attention Via positive Orthogonal Random features approach (FAVOR+), which may be of independent interest for scalable kernel methods. FAVOR+ can be also used to efficiently model kernelizable attention mechanisms beyond softmax. This representational power is crucial to accurately compare softmax with other kernels for the first time on large-scale tasks, beyond the reach of regular Transformers, and investigate optimal attention-kernels. Performers are linear architectures fully compatible with regular Transformers and with strong theoretical guarantees: unbiased or nearly-unbiased estimation of the attention matrix, uniform convergence and low estimation variance. We tested Performers on a rich set of tasks stretching from pixel-prediction through text models to protein sequence modeling. We demonstrate competitive results with other examined efficient sparse and dense attention methods, showcasing effectiveness of the novel attention-learning paradigm leveraged by Performers.

cs.LG↗

arXiv2020

Population-Based Black-Box Optimization for Biological Sequence Design

The use of black-box optimization for the design of new biological sequences is an emerging research area with potentially revolutionary impact. The cost and latency of wet-lab experiments requires methods that find good sequences in few experimental rounds of large batches of sequences--a setting that off-the-shelf black-box optimization methods are ill-equipped to handle. We find that the performance of existing methods varies drastically across optimization tasks, posing a significant obstacle to real-world applications. To improve robustness, we propose Population-Based Black-Box Optimization (P3BO), which generates batches of sequences by sampling from an ensemble of methods. The number of sequences sampled from any method is proportional to the quality of sequences it previously proposed, allowing P3BO to combine the strengths of individual methods while hedging against their innate brittleness. Adapting the hyper-parameters of each of the methods online using evolutionary optimization further improves performance. Through extensive experiments on in-silico optimization tasks, we show that P3BO outperforms any single method in its population, proposing higher quality sequences as well as more diverse batches. As such, P3BO and Adaptive-P3BO are a crucial step towards deploying ML to real-world sequence design.

cs.LG↗

arXiv2019

Where Pigeonhole Principles meet König Lemmas

We study the pigeonhole principle for $Σ_2$-definable injections with domain twice as large as the codomain, and the weak König lemma for $Δ^0_2$-definable trees in which every level has at least half of the possible nodes. We show that the latter implies the existence of $2$-random reals, and is conservative over the former. We also show that the former is strictly weaker than the usual pigeonhole principle for $Σ_2$-definable injections.

math.LO↗

arXiv2019

Boundless: Generative Adversarial Networks for Image Extension

Image extension models have broad applications in image editing, computational photography and computer graphics. While image inpainting has been extensively studied in the literature, it is challenging to directly apply the state-of-the-art inpainting methods to image extension as they tend to generate blurry or repetitive pixels with inconsistent semantics. We introduce semantic conditioning to the discriminator of a generative adversarial network (GAN), and achieve strong results on image extension with coherent semantics and visually pleasing colors and textures. We also show promising results in extreme extensions, such as panorama generation.

cs.CV↗

arXiv2019

Rapid Prediction of Electron-Ionization Mass Spectrometry using Neural Networks

When confronted with a substance of unknown identity, researchers often perform mass spectrometry on the sample and compare the observed spectrum to a library of previously-collected spectra to identify the molecule. While popular, this approach will fail to identify molecules that are not in the existing library. In response, we propose to improve the library's coverage by augmenting it with synthetic spectra that are predicted using machine learning. We contribute a lightweight neural network model that quickly predicts mass spectra for small molecules. Achieving high accuracy predictions requires a novel neural network architecture that is designed to capture typical fragmentation patterns from electron ionization. We analyze the effects of our modeling innovations on library matching performance and compare our models to prior machine learning-based work on spectrum prediction.

physics.chem-ph↗

arXiv2018

Learning Latent Permutations with Gumbel-Sinkhorn Networks

Permutations and matchings are core building blocks in a variety of latent variable models, as they allow us to align, canonicalize, and sort data. Learning in such models is difficult, however, because exact marginalization over these combinatorial objects is intractable. In response, this paper introduces a collection of new methods for end-to-end learning in such models that approximate discrete maximum-weight matching using the continuous Sinkhorn operator. Sinkhorn iteration is attractive because it functions as a simple, easy-to-implement analog of the softmax operator. With this, we can define the Gumbel-Sinkhorn method, an extension of the Gumbel-Softmax method (Jang et al. 2016, Maddison2016 et al. 2016) to distributions over latent matchings. We demonstrate the effectiveness of our method by outperforming competitive baselines on a range of qualitatively different tasks: sorting numbers, solving jigsaw puzzles, and identifying neural signals in worms.

stat.ML↗

arXiv2017

Synthesizing Normalized Faces from Facial Identity Features

We present a method for synthesizing a frontal, neutral-expression image of a person's face given an input face photograph. This is achieved by learning to generate facial landmarks and textures from features extracted from a facial-recognition network. Unlike previous approaches, our encoding feature vector is largely invariant to lighting, pose, and facial expression. Exploiting this invariance, we train our decoder network using only frontal, neutral-expression photographs. Since these photographs are well aligned, we can decompose them into a sparse set of landmark points and aligned texture maps. The decoder then predicts landmarks and textures independently and combines them using a differentiable image warping operation. The resulting images can be used for a number of applications, such as analyzing facial attributes, exposure and white balance adjustment, or creating a 3-D avatar.

cs.CV↗

arXiv2017

Low-Rank Hidden State Embeddings for Viterbi Sequence Labeling

In textual information extraction and other sequence labeling tasks it is now common to use recurrent neural networks (such as LSTM) to form rich embedded representations of long-term input co-occurrence patterns. Representation of output co-occurrence patterns is typically limited to a hand-designed graphical model, such as a linear-chain CRF representing short-term Markov dependencies among successive labels. This paper presents a method that learns embedded representations of latent output structure in sequence data. Our model takes the form of a finite-state machine with a large number of latent states per label (a latent variable CRF), where the state-transition matrix is factorized---effectively forming an embedded representation of state-transitions capable of enforcing long-term label dependencies, while supporting exact Viterbi inference over output labels. We demonstrate accuracy improvements and interpretable latent structure in a synthetic but complex task based on CoNLL named entity recognition.

cs.CL↗

arXiv2017

Fast and Accurate Entity Recognition with Iterated Dilated Convolutions

Today when many practitioners run basic NLP on the entire web and large-volume traffic, faster methods are paramount to saving time and energy costs. Recent advances in GPU hardware have led to the emergence of bi-directional LSTMs as a standard method for obtaining per-token vector representations serving as input to labeling tasks such as NER (often followed by prediction in a linear-chain CRF). Though expressive and accurate, these models fail to fully exploit GPU parallelism, limiting their computational efficiency. This paper proposes a faster alternative to Bi-LSTMs for NER: Iterated Dilated Convolutional Neural Networks (ID-CNNs), which have better capacity than traditional CNNs for large context and structured prediction. Unlike LSTMs whose sequential processing on sentences of length N requires O(N) time even in the face of parallelism, ID-CNNs permit fixed-depth convolutions to run in parallel across entire documents. We describe a distinct combination of network structure, parameter sharing and training procedures that enable dramatic 14-20x test-time speedups while retaining accuracy comparable to the Bi-LSTM-CRF. Moreover, ID-CNNs trained to aggregate context from the entire document are even more accurate while maintaining 8x faster test time speeds.

cs.CL↗

arXiv2017

End-to-End Learning for Structured Prediction Energy Networks

Structured Prediction Energy Networks (SPENs) are a simple, yet expressive family of structured prediction models (Belanger and McCallum, 2016). An energy function over candidate structured outputs is given by a deep network, and predictions are formed by gradient-based optimization. This paper presents end-to-end learning for SPENs, where the energy function is discriminatively trained by back-propagating through gradient-based prediction. In our experience, the approach is substantially more accurate than the structured SVM method of Belanger and McCallum (2016), as it allows us to use more sophisticated non-convex energies. We provide a collection of techniques for improving the speed, accuracy, and memory requirements of end-to-end SPENs, and demonstrate the power of our method on 7-Scenes image denoising and CoNLL-2005 semantic role labeling tasks. In both, inexact minimization of non-convex SPEN energies is superior to baseline methods that use simplistic energy functions that can be minimized exactly.

stat.ML↗

arXiv2017

Chains of Reasoning over Entities, Relations, and Text using Recurrent Neural Networks

Our goal is to combine the rich multistep inference of symbolic logical reasoning with the generalization capabilities of neural networks. We are particularly interested in complex reasoning about entities and relations in text and large-scale knowledge bases (KBs). Neelakantan et al. (2015) use RNNs to compose the distributed semantics of multi-hop paths in KBs; however for multiple reasons, the approach lacks accuracy and practicality. This paper proposes three significant modeling advances: (1) we learn to jointly reason about relations, entities, and entity-types; (2) we use neural attention modeling to incorporate multiple paths; (3) we learn to share strength in a single RNN that represents logical composition across all relations. On a largescale Freebase+ClueWeb prediction task, we achieve 25% error reduction, and a 53% error reduction on sparse relations due to shared strength. On chains of reasoning in WordNet we reduce error in mean quantile by 84% versus previous state-of-the-art. The code and data are available at https://rajarshd.github.io/ChainsofReasoning

cs.CL↗