Source-linked AI summary
From Machine Learning to Machine Reasoning
Leon Bottou
TL;DR
Formal logical and probabilistic inference do not capture the full range of human reasoning, including an informal middle layer. The paper proposes algebraically enriching trainable learning systems to build reasoning from the ground up, with auxiliary-task systems achieving near state-of-the-art performance at much higher speed.на
Problem
Human reasoning includes an informal middle layer beyond formal logical analysis, motivating alternatives to computationally complex discrete inference.
Method
The paper treats auxiliary tasks and compositions of trainable modules as algebraic operations, then enriches these operations to construct reasoning capabilities incrementally.
Results
The described system achieves near state-of-the-art performance while running hundreds of times faster than comparable natural language processing systems.
Takeaways & Limitations
Algebraically enriching manipulations over trainable systems offers a proposed path toward machine reasoning built from the ground up.
Takeaways & Limitations
Probabilistic reasoning has a recognized limitation in representing causality, particularly the consequences of interventions.
Abstract
from arXiv · showhide
A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes much simpler manipulations commonly used to build large learning systems. For instance, we can build an optical character recognition system by first training a character segmenter, an isolated character recognizer, and a language model, using appropriate labeled training sets. Adequately concatenating these modules and fine tuning the resulting system can be viewed as an algebraic operation in a space of models. The resulting model answers a new question, that is, converting the image of a text page into a computer readable text. This observation suggests a conceptual continuity between algebraically rich inference systems, such as logical or probabilistic inference, and simple manipulations, such as the mere concatenation of trainable learning systems. Therefore, instead of trying to bridge the gap between machine learning systems and sophisticated "all-purpose" inference mechanisms, we can instead algebraically enrich the set of manipulations applicable to training systems, and build reasoning capabilities from the ground up.
1. Introduction
The paper argues that reasoning is more elusive than learning and should not be equated with formal logical inference. It proposes enriching algebraic manipulations among learned systems, using auxiliary tasks as a foundation for building machine reasoning from the ground up.
- Motivation: Reasoning is distinct from learning and remains less well understood despite the widespread use and statistical understanding of machine learning.The introduction contrasts the established nature of statistical learning with the more elusive nature of reasoning.
- Motivation: Human reasoning is not limited to either logical or probabilistic inference.The paper explicitly states that human reasoning displays neither limitation.
- Motivation: Perception and language understanding suggest a middle layer of reasoning that need not involve explicit formal analysis.People can understand scenes and sentences without evidence that formal decomposition necessarily occurs.
- Contribution: Auxiliary tasks can help solve a task of interest, providing a rudimentary form of reasoning in deep and multi-task learning.The paper treats leveraging auxiliary tasks as an algebraic operation that supports more advanced reasoning.
- Contribution: Enriching the algebraic structure of learned systems offers a path to build higher forms of reasoning into machine learning from the ground up.The proposed approach develops reasoning capabilities by progressively expanding the manipulations applicable to learning systems.
2. Auxiliary tasks
Auxiliary tasks address scarce labels for valuable objectives by exploiting abundant data from nearby, less valuable tasks. The section illustrates this strategy for face recognition and natural language processing, where learned intermediate representations support strong downstream performance.
- Motivation: Abundant labels from nearby, less valuable tasks can provide training opportunities when labels for valuable tasks are expensive and scarce.The passage frames label scarcity as task-dependent rather than a general lack of available labels.
- Face recognition: Face recognition can use the easier auxiliary task of determining whether two face images depict the same person.Collecting varied, labeled images for each subject remains expensive, whereas same-person judgments are easier to obtain.
- Face recognition: The face-transfer strategy assembles two preprocessors P and one comparator D, trains them on auxiliary-task labels, and uses a classifier C for person labels.P computes compact face representations, D compares two representations, and C produces the person label.
- Natural language processing: The NLP auxiliary task learns 50-dimensional word representations from fixed-length sequences drawn from a 900M-word corpus, with incorrect sequences made by replacing the central word.The model produces a score whose magnitude indicates whether a word sequence is correct.
- Natural language processing: The resulting NLP system achieves near-state-of-the-art performance while running hundreds of times faster than comparably performing systems.It learns useful features through an essentially unsupervised task trained on a very large corpus, rather than manually designed task-specific input features.
3. Reasoning revisited
The section argues that composition rules for assembling trainable modules form an algebraic system on models and plausibly constitute a form of reasoning. It emphasizes that these rules, rather than only the modules themselves, are central to constructing task-specific learning systems.
- Reasoning revisited: Composition rules for assembling trainable modules form a simple algebraic system on a space of models.The section notes that these rules describe how modules are combined to address particular tasks.
- Reasoning revisited: Reasoning can plausibly mean algebraically manipulating previously acquired knowledge to answer a new question.The section contrasts conventional reasoning over premises and conclusions with composition rules operating on trainable modules.
- Reasoning revisited: Learned internal representations in auxiliary tasks can support target tasks and function as reasoning abstractions.This parallel is illustrated through face recognition and natural language processing examples.
- Reasoning revisited: Composition rules range from ad hoc combinations based on semantic interpretations to explicit rules in structured learning systems.Graph transformer networks are cited as an example of more explicit composition rules defining recognition and training architectures.
4. Probabilistic Models
Probabilistic models derive their appeal from probability theory’s algebra for combining and interpreting conditional distributions, while graphical models factor joint distributions into parametrized elementary conditionals under conditional-independence assumptions. Richer notations and languages extend this structure to repeated parameterized models and knowledge bases.
- Algebraic structure: Probability theory provides rules for combining conditional distributions and interpreting their combinations, motivating probabilistic models in machine learning.Constructing an algebraic structure for probabilistic models also requires specifying how probability distributions are parametrized.
- Graphical models: Graphical models factor joint distributions into elementary conditional distributions under specific conditional-independence assumptions, with inference inducing relations among models over arbitrary variable subsets.The factorization supports individual parametrization of the elementary conditional distributions.
- Parameterization: Plate notation compactly represents large graphical models with repeated structures that usually share parameters.Treating parameters as random variables makes the parametrization more explicit.
- Richer languages: Probabilistic Relational Models and Relational Dependency Networks derive graphical probabilistic models from frame-based knowledge bases, while Markov Logic Networks derive them from first-order logic clauses.These approaches use richer languages for describing large graphical probabilistic models.
- Illustration: Figure 5 illustrates Bayesian inference over a factorized model extended with a training set {(x_i,y_i)} and model parameters θ, yielding P(y | x, {(x_i,y_i)}).The underlying factorization is P(x,y)=P(x).P(y | x).
5. Reasoning systems
A reasoning system consists of an algebraic space of models and composition rules linking that space to questions of interest. Such systems vary in expressive power, predictive ability, and computational requirements, motivating empirical exploration of domain-specific algebraic structures for language and vision.
- Definition: A reasoning system combines an algebraic space of models with composition rules establishing a homomorphic correspondence to a space of questions.This marks a shift from fitting simple statistical models toward manipulating a more complex structured object.
- Diversity: Reasoning systems are arbitrary in their expressive power, predictive abilities, and computational requirements.The paper illustrates this diversity through logical, probabilistic, causal, mechanical, spatial, social, and non-falsifiable examples.
- Causal reasoning: Causal reasoning extends probabilistic reasoning with interventions represented by P(X|do(Y=y)), addressing limits of observational correlation.The intervention construction represents the distribution of X when an intervention enforces Y=y, unlike P(X|Y=y), which conditions on observation.
- Research strategy: Because no universally dominant and computationally feasible framework is known, the paper advocates embracing reasoning-system diversity.First-order symbolic reasoning did not fulfill hopes for a single powerful framework, while probabilistic reasoning is more practical but less expressive.
- Application domains: The paper proposes empirically exploring algebraic structures for specific applications, including trainable modules for hierarchical representations in language and vision.The following sections discuss natural-language-processing results and potential vision directions.
6 Association and dissociation
The section develops continuous vector representations for arbitrary sentence segments through recursively composed association modules, with saliency-based bracketing and unsupervised ranking-loss training. Dissociation modules invert meaningful compositions, enabling hierarchical traversal and broader transformations across language and vision representations.
- Association: Association modules recursively combine word vectors into representations of sentence meanings and their intermediate fragments.For a segment of n words, n−1 association applications reduce it to one vector, while intermediate vectors represent corresponding fragments.
- Association: A saliency module scores intermediate representations, allowing the system to select the bracketing whose summed scores maximize sentence meaningfulness.Different application sequences correspond to different bracketings and segmentations; parsing algorithms determine the maximizing structure.
- Training: Unsupervised training replaces a corpus word with a random vocabulary word and uses a ranking loss to score genuine sentence fragments above corrupted ones.All module parameters are adjusted by gradient descent within a stochastic gradient procedure.
- Experiments: Preliminary experiments found meaningful phrase embeddings from five-word English Wikipedia segments, while supervised WSJ training also placed semantically related phrases near one another.The unsupervised setup used a 600M-word corpus and a 1000-word vocabulary; supervised work used about 1M words from the Penn TreeBank.
- Dissociation: Dissociation modules split a meaningful composed vector back into its two constituents, forming an auto-encoder with association and enabling traversal of hierarchical representations.These operations parallel Lisp’s cons and car/cdr primitives, but operate on continuous vectors rather than discrete pointers and atoms.
- Applications: The same algebraic framework could support tense conversion, viewpoint and affine image transformations, and bidirectional image–sentence association.A sentence can be parsed, transformed in representation space, and reconstructed through dissociation; analogous procedures can generate image sketches from sentences.
7. Universal parser
The universal parser treats parsing as a maximization process over a short-term memory of representation vectors. It builds reasoning by inserting vectors and repeatedly associating selected pairs according to saliency, with the memory structure and search strategy adapted to the task.
- Universal parser: The parser maximizes the sum of association scores over intermediate representations.The association module is applied to representation vectors, and each application receives a saliency score.
- Universal parser: Its short-term memory supports two actions: inserting a representation vector or replacing two stored vectors with their associated combination.The memory stores representation vectors, while association reduces two vectors to one combined representation.
- Universal parser: Algorithm design depends on choosing which vectors to insert and associate, which in turn determines the appropriate short-term-memory data structure.The selection criteria are the main design choices for implementing the memory.
- Universal parser: For English, contiguous sentence segments motivate a stack-based shift/reduce parser that shifts words and reduces the top two stack elements.Shift pushes the next word representation onto the stack; reduce applies the association module to the top two elements.
- Universal parser: Beam search efficiently explores the parsing graph, while greedy parsing inserts all words first and repeatedly associates the pair with highest saliency.Beam search can also support more complex memory organizations without dramatically increasing computational complexity.
8. More modules
The paper proposes extending algebraic reasoning with modules that add semantics to representation vectors, including language transformations, visual interventions, and sentence–image bridges. It further sketches modules for first-order logic, anaphora resolution, and context-sensitive instantiation scoring.
- Semantic extensions: Additional modules can encode natural-language transformations, visual reasoning primitives, and bridges between sentence and image representations, enriching representation vectors with semantics.These modules extend the association and dissociation framework beyond its previously discussed core components.
- Natural-language transformations: Association and dissociation modules can replicate Harris’s sentence-transformation operators because they provide tools for navigating sentence structure.Operator grammars describe natural languages through transformation operators applied to elementary sentence forms.
- Visual interventions: Representation-vector modules could model visual consequences of viewpoint changes, including rotations, rescaling, perspective changes, and occlusion.The framework could also represent direct scene interventions such as moving an object.
- First-order logic: Adding variables and quantifiers to the Lisp-equivalent association and dissociation primitives would provide an implementation of first-order logic.The primitives car, cdr, and cons support constructing arbitrarily propositional logic expressions.
- Anaphora resolution: An instantiation module could resolve anaphora by applying a predefined substitution to every occurrence of a designated entity in a tree representation.This corresponds to identifying repeated variables in first-order logic or resolving pronouns in natural language.
- Context-sensitive instantiation: A trainable instantiation-scoring module could assess plausible bindings through isKindOf relations, but ontology judgments depend on context.For example, cats and turtles can both be pets in a household context while belonging to different biological families.
9. Representation space
Representation-space choices substantially affect the computational and practical properties of training algorithms. The section contrasts dense low-dimensional, sparse high-dimensional, and probabilistic representations, while emphasizing the importance of efficient GPU implementation.
- Representation space: Representation spaces can vary while preserving similar algebraic module properties, but their choice considerably affects training algorithms’ computational and practical aspects.The paper identifies investigating these effects as necessary.
- Dense vectors: Dense vectors typically use 20–200 dimensions and often require nonlinear parametrizations trained with back-propagation and stochastic gradient descent.These nonconvex optimization procedures are described as inherently complex.
- Sparse vectors: Sparse vectors in much higher-dimensional spaces can support more linearly parametrized trainable modules and simpler optimization procedures.Sparsity-inducing terms are needed to maintain generalization and computational performance.
- Probability distributions: Probability-distribution representations over discrete random variables require stochastic sampling methods such as Gibbs sampling, MCMC, Contrastive Divergence, or Herding.The passage presents these methods as examples of the required learning algorithms.
- Implementation: GPU implementations can considerably accelerate experimentation, reducing language-model training from three to six weeks on a standard processor to a couple days.The shorter cycle changes the dynamics of experimentation.
Conclusions
The paper proposes building machine reasoning from the ground up by algebraically enriching the manipulations applied to machine-learning systems, rather than bridging them to all-purpose inference mechanisms.
- Conclusions: The research agenda targets practical and conceptual understanding of how machine learning and machine reasoning interact.It is presented as a breakthrough effort toward that understanding.
- Conclusions: Rather than bridging machine-learning systems to sophisticated all-purpose inference mechanisms, the paper proposes algebraically enriching manipulations applicable to training systems.This reframes the relationship between learning and reasoning as an expansion of operations on trained systems.
- Conclusions: The proposed approach aims to build reasoning capabilities from the ground up.This is the stated consequence of enriching the manipulations applied to training systems.