Ashwin Srinivasan

Ashwin Srinivasan, A Baskar, Tirtharaj Dash et al.

Relational machine learning programs like those developed in Inductive Logic Programming (ILP) offer several advantages: (1) The ability to model complex relationships amongst data instances; (2) The use of domain-specific relations during model construction; and (3) The models constructed are human-readable, which is often one step closer to being human-understandable. However, these ILP-like methods have not been able to capitalise fully on the rapid hardware, software and algorithmic developments fuelling current developments in deep neural networks. In this paper, we treat relational features as functions and use the notion of generalised composition of functions to derive complex functions from simpler ones. We formulate the notion of a set of $\text{M}$-simple features in a mode language $\text{M}$ and identify two composition operators ($ρ_1$ and $ρ_2$) from which all possible complex features can be derived. We use these results to implement a form of "explainable neural network" called Compositional Relational Machines, or CRMs, which are labelled directed-acyclic graphs. The vertex-label for any vertex $j$ in the CRM contains a feature-function $f_j$ and a continuous activation function $g_j$. If $j$ is a "non-input" vertex, then $f_j$ is the composition of features associated with vertices in the direct predecessors of $j$. Our focus is on CRMs in which input vertices (those without any direct predecessors) all have $\text{M}$-simple features in their vertex-labels. We provide a randomised procedure for constructing and learning such CRMs. Using a notion of explanations based on the compositional structure of features in a CRM, we provide empirical evidence on synthetic data of the ability to identify appropriate explanations; and demonstrate the use of CRMs as 'explanation machines' for black-box models that do not provide explanations for their predictions.

Vishwa Shah, Aditya Sharma, Gautam Shroff et al.

Analogical Reasoning problems challenge both connectionist and symbolic AI systems as these entail a combination of background knowledge, reasoning and pattern recognition. While symbolic systems ingest explicit domain knowledge and perform deductive reasoning, they are sensitive to noise and require inputs be mapped to preset symbolic features. Connectionist systems on the other hand can directly ingest rich input spaces such as images, text or speech and recognize pattern even with noisy inputs. However, connectionist models struggle to include explicit domain knowledge for deductive reasoning. In this paper, we propose a framework that combines the pattern recognition abilities of neural networks with symbolic reasoning and background knowledge for solving a class of Analogical Reasoning problems where the set of attributes and possible relations across them are known apriori. We take inspiration from the 'neural algorithmic reasoning' approach [DeepMind 2020] and use problem-specific background knowledge by (i) learning a distributed representation based on a symbolic model of the problem (ii) training neural-network transformations reflective of the relations involved in the problem and finally (iii) training a neural network encoder from images to the distributed representation in (i). These three elements enable us to perform search-based reasoning using neural networks as elementary functions manipulating distributed representations. We test this on visual analogy problems in RAVENs Progressive Matrices, and achieve accuracy competitive with human performance and, in certain cases, superior to initial end-to-end neural-network based approaches. While recent neural models trained at scale yield SOTA, our novel neuro-symbolic reasoning approach is a promising direction for this problem, and is arguably more general, especially for problems where domain knowledge is available.

Shreyas Bhat Brahmavar, Rohit Rajesh, Tirtharaj Dash et al.

Deep neural network (DNN) models for retinopathy have estimated predictive accuracies in the mid-to-high 90%. However, the following aspects remain unaddressed: State-of-the-art models are complex and require substantial computational infrastructure to train and deploy; The reliability of predictions can vary widely. In this paper, we focus on these aspects and propose a form of iterative knowledge distillation(IKD), called IKD+ that incorporates a tradeoff between size, accuracy and reliability. We investigate the functioning of IKD+ using two widely used techniques for estimating model calibration (Platt-scaling and temperature-scaling), using the best-performing model available, which is an ensemble of EfficientNets with approximately 100M parameters. We demonstrate that IKD+ equipped with temperature-scaling results in models that show up to approximately 500-fold decreases in the number of parameters than the original ensemble without a significant loss in accuracy. In addition, calibration scores (reliability) for the IKD+ models are as good as or better than the base mode

A. Baskar, Ashwin Srinivasan, Michael Bain et al.

Machine Learning (ML) has emerged as a powerful form of data modelling with widespread applicability beyond its roots in the design of autonomous agents. However, relatively little attention has been paid to the interaction between people and ML systems. In this paper we view interaction between humans and ML systems within the broader context of communication between agents capable of prediction and explanation. We formalise the interaction model by taking agents to be automata with some special characteristics and define a protocol for communication between such agents. We define One- and Two-Way Intelligibility as properties that emerge at run-time by execution of the protocol. The formalisation allows us to identify conditions under which run-time sequences are bounded, and identify conditions under which the protocol can correctly implement an axiomatic specification of intelligible interaction between a human and an ML system. We also demonstrate using the formal model to: (a) identify instances of One- and Two-Way Intelligibility in literature reports on humans interacting with ML systems providing logic-based explanations, as is done in Inductive Logic Programming (ILP); and (b) map interactions between humans and machines in an elaborate natural-language based dialogue-model to One- or Two-Way Intelligible interactions in the formal model.

S I Harini, Gautam Shroff, Ashwin Srinivasan et al.

We model short-duration (e.g. day) trading in financial markets as a sequential decision-making problem under uncertainty, with the added complication of continual concept-drift. We, therefore, employ meta reinforcement learning via the RL2 algorithm. It is also known that human traders often rely on frequently occurring symbolic patterns in price series. We employ logical program induction to discover symbolic patterns that occur frequently as well as recently, and explore whether using such features improves the performance of our meta reinforcement learning algorithm. We report experiments on real data indicating that meta-RL is better than vanilla RL and also benefits from learned symbolic features.

Ashwin Srinivasan, Michael Bain, Enrico Coiera

Recent engineering developments in specialised computational hardware, data-acquisition and storage technology have seen the emergence of Machine Learning (ML) as a powerful form of data analysis with widespread applicability beyond its historical roots in the design of autonomous agents. However -- possibly because of its origins in the development of agents capable of self-discovery -- relatively little attention has been paid to the interaction between people and ML. In this paper we are concerned with the use of ML in automated or semi-automated tools that assist one or more human decision makers. We argue that requirements on both human and machine in this context are significantly different to the use of ML either as part of autonomous agents for self-discovery or as part statistical data analysis. Our principal position is that the design of such human-machine systems should be driven by repeated, two-way intelligibility of information rather than one-way explainability of the ML-system's recommendations. Iterated rounds of intelligible information exchange, we think, will characterise the kinds of collaboration that will be needed to understand complex phenomena for which neither man or machine have complete answers. We propose operational principles -- we call them Intelligibility Axioms -- to guide the design of a collaborative decision-support system. The principles are concerned with: (a) what it means for information provided by the human to be intelligible to the ML system; and (b) what it means for an explanation provided by an ML system to be intelligible to a human. Using examples from the literature on the use of ML for drug-design and in medicine, we demonstrate cases where the conditions of the axioms are met. We describe some additional requirements needed for the design of a truly collaborative decision-support system.

Vedant Shah, Aditya Agrawal, Lovekesh Vig et al.

We are interested in neurosymbolic systems consisting of a high-level symbolic layer for explainable prediction in terms of human-intelligible concepts; and a low-level neural layer for extracting symbols required to generate the symbolic explanation. Real data is often imperfect meaning that even if the symbolic theory remains unchanged, we may still need to address the problem of mapping raw data to high-level symbols, each time there is a change in the data acquisition environment or equipment. Manual (re-)annotation of the raw data each time this happens is laborious and expensive; and automated labelling methods are often imperfect, especially for complex problems. NEUROLOG proposed the use of a semantic loss function that allows an existing feature-based symbolic model to guide the extraction of feature-values from raw data, using `abduction'. However, the experiments demonstrating the use of semantic loss through abduction appear to rely heavily on a domain-specific pre-processing step that enables a prior delineation of feature locations in the raw data. We examine the use of semantic loss in domains where such pre-processing is not possible, or is not obvious. We show that without any prior information about the features, the NEUROLOG approach can continue to predict accurately even with substantially incorrect feature predictions. We show also that prior information about the features in the form of even imperfect pre-training can help correct this situation. These findings are replicated on the original problem considered by NEUROLOG, without the use of feature-delineation. This suggests that symbolic explanations constructed for data in a domain could be re-used in a related domain, by `feature-adaptation' of pre-trained neural extractors using the semantic loss function constrained by abductive feedback.

Emmanuel Aboah Boateng, Cassiano O. Becker, Nabiha Asghar et al.

Hand-crafting high quality prompts to optimize the performance of language models is a complicated and labor-intensive process. Furthermore, when migrating to newer, smaller, or weaker models (possibly due to latency or cost gains), prompts need to be updated to re-optimize the task performance. We propose Concept Distillation (CD), an automatic prompt optimization technique for enhancing weaker models on complex tasks. CD involves: (1) collecting mistakes made by weak models with a base prompt (initialization), (2) using a strong model to generate reasons for these mistakes and create rules/concepts for weak models (induction), and (3) filtering these rules based on validation set performance and integrating them into the base prompt (deduction/verification). We evaluated CD on NL2Code and mathematical reasoning tasks, observing significant performance boosts for small and weaker language models. Notably, Mistral-7B's accuracy on Multi-Arith increased by 20%, and Phi-3-mini-3.8B's accuracy on HumanEval rose by 34%. Compared to other automated methods, CD offers an effective, cost-efficient strategy for improving weak models' performance on complex tasks and enables seamless workload migration across different language models without compromising performance.

Harshvardhan Mestha, Karan Bania, Shreyas V Sathyanarayana et al. · cmu

Our interest is in the design of software systems involving a human-expert interacting -- using natural language -- with a large language model (LLM) on data analysis tasks. For complex problems, it is possible that LLMs can harness human expertise and creativity to find solutions that were otherwise elusive. On one level, this interaction takes place through multiple turns of prompts from the human and responses from the LLM. Here we investigate a more structured approach based on an abstract protocol described in [3] for interaction between agents. The protocol is motivated by a notion of "two-way intelligibility" and is modelled by a pair of communicating finite-state machines. We provide an implementation of the protocol, and provide empirical evidence of using the implementation to mediate interactions between an LLM and a human-agent in two areas of scientific interest (radiology and drug design). We conduct controlled experiments with a human proxy (a database), and uncontrolled experiments with human subjects. The results provide evidence in support of the protocol's capability of capturing one- and two-way intelligibility in human-LLM interaction; and for the utility of two-way intelligibility in the design of human-machine systems. Our code is available at https://github.com/karannb/interact.

Riya Naik, Ashwin Srinivasan, Swati Agarwal et al.

Many of us now treat LLMs as modern-day oracles asking it almost any kind of question. However, consulting an LLM does not have to be a single turn activity. But long multi-turn interactions can get tedious if it is simply to clarify contextual information that can be arrived at through reasoning. In this paper, we examine the use of agent-based architecture to bolster LLM-based Question-Answering systems with additional reasoning capabilities. We examine the automatic resolution of potential incompleteness or ambiguities in questions by transducers implemented using LLM-based agents. We focus on several benchmark datasets that are known to contain questions with these deficiencies to varying degrees. We equip different LLMs (GPT-3.5-Turbo and Llama-4-Scout) with agents that act as specialists in detecting and resolving deficiencies of incompleteness and ambiguity. The agents are implemented as zero-shot ReAct agents. Rather than producing an answer in a single step, the model now decides between 3 actions a) classify b) resolve c) answer. Action a) decides if the question is incomplete, ambiguous, or normal. Action b) determines if any deficiencies identified can be resolved. Action c) answers the resolved form of the question. We compare the use of LLMs with and without the use of agents with these components. Our results show benefits of agents with transducer 1) A shortening of the length of interactions with human 2) An improvement in the answer quality and 3) Explainable resolution of deficiencies in the question. On the negative side we find while it may result in additional LLM invocations and in some cases, increased latency. But on tested datasets, the benefits outweigh the costs except when questions already have sufficient context. Suggesting the agent-based approach could be a useful mechanism to harness the power of LLMs to develop more robust QA systems.

Atharv Sonwane, Gautam Shroff, Lovekesh Vig et al.

We consider a class of visual analogical reasoning problems that involve discovering the sequence of transformations by which pairs of input/output images are related, so as to analogously transform future inputs. This program synthesis task can be easily solved via symbolic search. Using a variation of the `neural analogical reasoning' approach of (Velickovic and Blundell 2021), we instead search for a sequence of elementary neural network transformations that manipulate distributed representations derived from a symbolic space, to which input images are directly encoded. We evaluate the extent to which our `neural reasoning' approach generalizes for images with unseen shapes and positions.

Atharv Sonwane, Sharad Chitlangia, Tirtharaj Dash et al.

The ability to recognise and make analogies is often used as a measure or test of human intelligence. The ability to solve Bongard problems is an example of such a test. It has also been postulated that the ability to rapidly construct novel abstractions is critical to being able to solve analogical problems. Given an image, the ability to construct a program that would generate that image is one form of abstraction, as exemplified in the Dreamcoder project. In this paper, we present a preliminary examination of whether programs constructed by Dreamcoder can be used for analogical reasoning to solve certain Bongard problems. We use Dreamcoder to discover programs that generate the images in a Bongard problem and represent each of these as a sequence of state transitions. We decorate the states using positional information in an automated manner and then encode the resulting sequence into logical facts in Prolog. We use inductive logic programming (ILP), to learn an (interpretable) theory for the abstract concept involved in an instance of a Bongard problem. Experiments on synthetically created Bongard problems for concepts such as 'above/below' and 'clockwise/counterclockwise' demonstrate that our end-to-end system can solve such problems. We study the importance and completeness of each component of our approach, highlighting its current limitations and pointing to directions for improvement in our formulation as well as in elements of any Dreamcoder-like program synthesis system used for such an approach.

Ji Xin, Chenyan Xiong, Ashwin Srinivasan et al.

Dense retrieval (DR) methods conduct text retrieval by first encoding texts in the embedding space and then matching them by nearest neighbor search. This requires strong locality properties from the representation space, i.e, the close allocations of each small group of relevant texts, which are hard to generalize to domains without sufficient training data. In this paper, we aim to improve the generalization ability of DR models from source training domains with rich supervision signals to target domains without any relevant labels, in the zero-shot setting. To achieve that, we propose Momentum adversarial Domain Invariant Representation learning (MoDIR), which introduces a momentum method in the DR training process to train a domain classifier distinguishing source versus target, and then adversarially updates the DR encoder to learn domain invariant representations. Our experiments show that MoDIR robustly outperforms its baselines on 10+ ranking datasets from the BEIR benchmark in the zero-shot setup, with more than 10% relative gains on datasets with enough sensitivity for DR models' evaluation. Source code of this paper will be released.

Tirtharaj Dash, Sharad Chitlangia, Aditya Ahuja et al.

We present a survey of ways in which existing scientific knowledge are included when constructing models with neural networks. The inclusion of domain-knowledge is of special interest not just to constructing scientific assistants, but also, many other areas that involve understanding data using human-machine collaboration. In many such instances, machine-based model construction may benefit significantly from being provided with human-knowledge of the domain encoded in a sufficiently precise form. This paper examines the inclusion of domain-knowledge by means of changes to: the input, the loss-function, and the architecture of deep networks. The categorisation is for ease of exposition: in practice we expect a combination of such changes will be employed. In each category, we describe techniques that have been shown to yield significant changes in the performance of deep neural networks.

Tirtharaj Dash, Ashwin Srinivasan, A Baskar

We present a general technique for constructing Graph Neural Networks (GNNs) capable of using multi-relational domain knowledge. The technique is based on mode-directed inverse entailment (MDIE) developed in Inductive Logic Programming (ILP). Given a data instance $e$ and background knowledge $B$, MDIE identifies a most-specific logical formula $\bot_B(e)$ that contains all the relational information in $B$ that is related to $e$. We represent $\bot_B(e)$ by a "bottom-graph" that can be converted into a form suitable for GNN implementations. This transformation allows a principled way of incorporating generic background knowledge into GNNs: we use the term `BotGNN' for this form of graph neural networks. For several GNN variants, using real-world datasets with substantial background knowledge, we show that BotGNNs perform significantly better than both GNNs without background knowledge and a recently proposed simplified technique for including domain knowledge into GNNs. We also provide experimental evidence comparing BotGNNs favourably to multi-layer perceptrons (MLPs) that use features representing a "propositionalised" form of the background knowledge; and BotGNNs to a standard ILP based on the use of most-specific clauses. Taken together, these results point to BotGNNs as capable of combining the computational efficacy of GNNs with the representational versatility of ILP.

Tirtharaj Dash, Sharad Chitlangia, Aditya Ahuja et al.

We present a survey of ways in which domain-knowledge has been included when constructing models with neural networks. The inclusion of domain-knowledge is of special interest not just to constructing scientific assistants, but also, many other areas that involve understanding data using human-machine collaboration. In many such instances, machine-based model construction may benefit significantly from being provided with human-knowledge of the domain encoded in a sufficiently precise form. This paper examines two broad approaches to encode such knowledge--as logical and numerical constraints--and describes techniques and results obtained in several sub-categories under each of these approaches.

Rishab Khincha, Soundarya Krishnan, Tirtharaj Dash et al.

In this paper, our focus is on constructing models to assist a clinician in the diagnosis of COVID-19 patients in situations where it is easier and cheaper to obtain X-ray data than to obtain high-quality images like those from CT scans. Deep neural networks have repeatedly been shown to be capable of constructing highly predictive models for disease detection directly from image data. However, their use in assisting clinicians has repeatedly hit a stumbling block due to their black-box nature. Some of this difficulty can be alleviated if predictions were accompanied by explanations expressed in clinically relevant terms. In this paper, deep neural networks are used to extract domain-specific features(morphological features like ground-glass opacity and disease indications like pneumonia) directly from the image data. Predictions about these features are then used to construct a symbolic model (a decision tree) for the diagnosis of COVID-19 from chest X-rays, accompanied with two kinds of explanations: visual (saliency maps, derived from the neural stage), and textual (logical descriptions, derived from the symbolic stage). A radiologist rates the usefulness of the visual and textual explanations. Our results demonstrate that neural models can be employed usefully in identifying domain-specific features from low-level image data; that textual explanations in terms of clinically relevant features may be useful; and that visual explanations will need to be clinically meaningful to be useful.

Tirtharaj Dash, Ashwin Srinivasan, Lovekesh Vig

Our interest is in scientific problems with the following characteristics: (1) Data are naturally represented as graphs; (2) The amount of data available is typically small; and (3) There is significant domain-knowledge, usually expressed in some symbolic form. These kinds of problems have been addressed effectively in the past by Inductive Logic Programming (ILP), by virtue of 2 important characteristics: (a) The use of a representation language that easily captures the relation encoded in graph-structured data, and (b) The inclusion of prior information encoded as domain-specific relations, that can alleviate problems of data scarcity, and construct new relations. Recent advances have seen the emergence of deep neural networks specifically developed for graph-structured data (Graph-based Neural Networks, or GNNs). While GNNs have been shown to be able to handle graph-structured data, less has been done to investigate the inclusion of domain-knowledge. Here we investigate this aspect of GNNs empirically by employing an operation we term "vertex-enrichment" and denote the corresponding GNNs as "VEGNNs". Using over 70 real-world datasets and substantial amounts of symbolic domain-knowledge, we examine the result of vertex-enrichment across 5 different variants of GNNs. Our results provide support for the following: (a) Inclusion of domain-knowledge by vertex-enrichment can significantly improve the performance of a GNN. That is, the performance VEGNNs is significantly better than GNNs across all GNN variants; (b) The inclusion of domain-specific relations constructed using ILP improves the performance of VEGNNs, across all GNN variants. Taken together, the results provide evidence that it is possible to incorporate symbolic domain knowledge into a GNN, and that ILP can play an important role in providing high-level relationships that are not easily discovered by a GNN.

Vinayshekhar Bannihatti Kumar, Ashwin Srinivasan, Aditi Chaudhary et al.

This paper presents the submissions by Team Dr.Quad to the ACL-BioNLP 2019 shared task on Textual Inference and Question Entailment in the Medical Domain. Our system is based on the prior work Liu et al. (2019) which uses a multi-task objective function for textual entailment. In this work, we explore different strategies for generalizing state-of-the-art language understanding models to the specialized medical domain. Our results on the shared task demonstrate that incorporating domain knowledge through data augmentation is a powerful strategy for addressing challenges posed by specialized domains such as medicine.

Vishal Sunder, Ashwin Srinivasan, Lovekesh Vig et al.

Our interest in this paper is in meeting a rapidly growing industrial demand for information extraction from images of documents such as invoices, bills, receipts etc. In practice users are able to provide a very small number of example images labeled with the information that needs to be extracted. We adopt a novel two-level neuro-deductive, approach where (a) we use pre-trained deep neural networks to populate a relational database with facts about each document-image; and (b) we use a form of deductive reasoning, related to meta-interpretive learning of transition systems to learn extraction programs: Given task-specific transitions defined using the entities and relations identified by the neural detectors and a small number of instances (usually 1, sometimes 2) of images and the desired outputs, a resource-bounded meta-interpreter constructs proofs for the instance(s) via logical deduction; a set of logic programs that extract each desired entity is easily synthesized from such proofs. In most cases a single training example together with a noisy-clone of itself suffices to learn a program-set that generalizes well on test documents, at which time the value of each entity is determined by a majority vote across its program-set. We demonstrate our two-level neuro-deductive approach on publicly available datasets ("Patent" and "Doctor's Bills") and also describe its use in a real-life industrial problem.

Vishwanath D, Rohit Rahul, Gunjan Sehgal et al.

Recent advancements in the area of Computer Vision with state-of-art Neural Networks has given a boost to Optical Character Recognition (OCR) accuracies. However, extracting characters/text alone is often insufficient for relevant information extraction as documents also have a visual structure that is not captured by OCR. Extracting information from tables, charts, footnotes, boxes, headings and retrieving the corresponding structured representation for the document remains a challenge and finds application in a large number of real-world use cases. In this paper, we propose a novel enterprise based end-to-end framework called DeepReader which facilitates information extraction from document images via identification of visual entities and populating a meta relational model across different entities in the document image. The model schema allows for an easy to understand abstraction of the entities detected by the deep vision models and the relationships between them. DeepReader has a suite of state-of-the-art vision algorithms which are applied to recognize handwritten and printed text, eliminate noisy effects, identify the type of documents and detect visual entities like tables, lines and boxes. Deep Reader maps the extracted entities into a rich relational schema so as to capture all the relevant relationships between entities (words, textboxes, lines etc) detected in the document. Relevant information and fields can then be extracted from the document by writing SQL queries on top of the relationship tables. A natural language based interface is added on top of the relationship schema so that a non-technical user, specifying the queries in natural language, can fetch the information with minimal effort. In this paper, we also demonstrate many different capabilities of Deep Reader and report results on a real-world use case.

Ashwin Srinivasan, Lovekesh Vig, Michael Bain

Our interest in this paper is in the construction of symbolic explanations for predictions made by a deep neural network. We will focus attention on deep relational machines (DRMs, first proposed by H. Lodhi). A DRM is a deep network in which the input layer consists of Boolean-valued functions (features) that are defined in terms of relations provided as domain, or background, knowledge. Our DRMs differ from those proposed by Lodhi, which use an Inductive Logic Programming (ILP) engine to first select features (we use random selections from a space of features that satisfies some approximate constraints on logical relevance and non-redundancy). But why do the DRMs predict what they do? One way of answering this is the LIME setting, in which readable proxies for a black-box predictor. The proxies are intended only to model the predictions of the black-box in local regions of the instance-space. But readability alone may not enough: to be understandable, the local models must use relevant concepts in an meaningful manner. We investigate the use of a Bayes-like approach to identify logical proxies for local predictions of a DRM. We show: (a) DRM's with our randomised propositionalization method achieve state-of-the-art predictive performance; (b) Models in first-order logic can approximate the DRM's prediction closely in a small local region; and (c) Expert-provided relevance information can play the role of a prior to distinguish between logical explanations that perform equivalently on prediction alone.

S Saikia, R Verma, P Agarwal et al.

Loading the containers on the ship from a yard, is an impor- tant part of port operations. Finding the optimal sequence for the loading of containers, is known to be computationally hard and is an example of combinatorial optimization, which leads to the application of simple heuristics in practice. In this paper, we propose an approach which uses a mix of Evolutionary Strategies and Reinforcement Learning (RL) tech- niques to find an approximation of the optimal solution. The RL based agent uses the Policy Gradient method, an evolutionary reward strategy and a Pool of good (not-optimal) solutions to find the approximation. We find that the RL agent learns near-optimal solutions that outperforms the heuristic solutions. We also observe that the RL agent assisted with a pool generalizes better for unseen problems than an RL agent without a pool. We present our results on synthetic data as well as on subsets of real-world problems taken from container terminal. The results validate that our approach does comparatively better than the heuristics solutions available, and adapts to unseen problems better.

Sarmimala Saikia, Lovekesh Vig, Ashwin Srinivasan et al.

We investigate solving discrete optimisation problems using the estimation of distribution (EDA) approach via a novel combination of deep belief networks(DBN) and inductive logic programming (ILP).While DBNs are used to learn the structure of successively better feasible solutions,ILP enables the incorporation of domain-based background knowledge related to the goodness of solutions.Recent work showed that ILP could be an effective way to use domain knowledge in an EDA scenario.However,in a purely ILP-based EDA,sampling successive populations is either inefficient or not straightforward.In our Neuro-symbolic EDA,an ILP engine is used to construct a model for good solutions using domain-based background knowledge.These rules are introduced as Boolean features in the last hidden layer of DBNs used for EDA-based optimization.This incorporation of logical ILP features requires some changes while training and sampling from DBNs: (a)our DBNs need to be trained with data for units at the input layer as well as some units in an otherwise hidden layer, and (b)we would like the samples generated to be drawn from instances entailed by the logical model.We demonstrate the viability of our approach on instances of two optimisation problems: predicting optimal depth-of-win for the KRK endgame,and jobshop scheduling.Our results are promising: (i)On each iteration of distribution estimation,samples obtained with an ILP-assisted DBN have a substantially greater proportion of good solutions than samples generated using a DBN without ILP features, and (ii)On termination of distribution estimation,samples obtained using an ILP-assisted DBN contain more near-optimal samples than samples from a DBN without ILP features.These results suggest that the use of ILP-constructed theories could be useful for incorporating complex domain-knowledge into deep models for estimation of distribution based procedures.

Ashwin Srinivasan, Gautam Shroff, Lovekesh Vig et al.

Our interest in this paper is in optimisation problems that are intractable to solve by direct numerical optimisation, but nevertheless have significant amounts of relevant domain-specific knowledge. The category of heuristic search techniques known as estimation of distribution algorithms (EDAs) seek to incrementally sample from probability distributions in which optimal (or near-optimal) solutions have increasingly higher probabilities. Can we use domain knowledge to assist the estimation of these distributions? To answer this in the affirmative, we need: (a)a general-purpose technique for the incorporation of domain knowledge when constructing models for optimal values; and (b)a way of using these models to generate new data samples. Here we investigate a combination of the use of Inductive Logic Programming (ILP) for (a), and standard logic-programming machinery to generate new samples for (b). Specifically, on each iteration of distribution estimation, an ILP engine is used to construct a model for good solutions. The resulting theory is then used to guide the generation of new data instances, which are now restricted to those derivable using the ILP model in conjunction with the background knowledge). We demonstrate the approach on two optimisation problems (predicting optimal depth-of-win for the KRK endgame, and job-shop scheduling). Our results are promising: (a)On each iteration of distribution estimation, samples obtained with an ILP theory have a substantially greater proportion of good solutions than samples without a theory; and (b)On termination of distribution estimation, samples obtained with an ILP theory contain more near-optimal samples than samples without a theory. Taken together, these results suggest that the use of ILP-constructed theories could be a useful technique for incorporating complex domain-knowledge into estimation distribution procedures.

Haimonti Dutta, Ashwin Srinivasan

A particularly successful role for Inductive Logic Programming (ILP) is as a tool for discovering useful relational features for subsequent use in a predictive model. Conceptually, the case for using ILP to construct relational features rests on treating these features as functions, the automated discovery of which necessarily requires some form of first-order learning. Practically, there are now several reports in the literature that suggest that augmenting any existing features with ILP-discovered relational features can substantially improve the predictive power of a model. While the approach is straightforward enough, much still needs to be done to scale it up to explore more fully the space of possible features that can be constructed by an ILP system. This is in principle, infinite and in practice, extremely large. Applications have been confined to heuristic or random selections from this space. In this paper, we address this computational difficulty by allowing features to be constructed in a distributed manner. That is, there is a network of computational units, each of which employs an ILP engine to construct some small number of features and then builds a (local) model. We then employ a consensus-based algorithm, in which neighboring nodes share information to update local models. For a category of models (those with convex loss functions), it can be shown that the algorithm will result in all nodes converging to a consensus model. In practice, it may be slow to achieve this convergence. Nevertheless, our results on synthetic and real datasets that suggests that in relatively short time the "best" node in the network reaches a model whose predictive accuracy is comparable to that obtained using more computational effort in a non-distributed setting (the best node is identified as the one whose weights converge first).