Source-linked AI summary
Inferring Algorithmic Patterns with Stack-Augmented Recurrent Nets
Armand Joulin, Tomas Mikolov
TL;DR
The paper examines algorithmically generated sequence patterns that standard recurrent networks may not learn, especially patterns requiring counting and memorization. It augments recurrent networks with trainable structured memory, showing that basic algorithms can be learned from sequential data and that stacks and lists support these tasks. The approach remains bounded by restricted pattern scope, input formats, and fixed memory topology.
Problem
The paper asks which algorithmic sequence patterns are difficult for standard deep models, focusing on patterns involving counting and memorization.
Method
The paper augments recurrent networks with trainable structured memory, using stack and list topologies controlled through multiplicative gating.
Results
The model learns basic counting and memorization algorithms from sequential data, while Stack RNN and List RNN learn memorization that RNN and LSTM do not generalize to.
Takeaways & Limitations
Structured, potentially unlimited memory can enable recurrent networks to solve difficult pattern-recognition problems and may extend to more complex memory structures.
Takeaways & Limitations
The study is limited to patterns whose symbols can be predicted in one computational step, excluding sorting and dynamic programming.
Abstract
from arXiv · showhide
Despite the recent achievements in machine learning, we are still very far from achieving real artificial intelligence. In this paper, we discuss the limitations of standard deep learning approaches and show that some of these limitations can be overcome by learning how to grow the complexity of a model in a structured way. Specifically, we study the simplest sequence prediction problems that are beyond the scope of what is learnable with standard recurrent networks, algorithmically generated sequences which can only be learned by models which have the capacity to count and to memorize sequences. We show that some basic algorithms can be learned from sequential data using a recurrent network associated with a trainable memory.
1 Introduction
The paper asks which patterns standard deep models struggle to represent and learn, focusing on algorithmically generated symbol sequences. It proposes recurrent networks with trainable structured memory to learn counting and memorization operations.
- Motivation: The paper investigates patterns that are difficult for current methods to represent and learn, following earlier breakthroughs from identifying limits such as XOR and parity.These examples motivated nonlinear hidden layers, kernel methods, and deeper architectures.
- Problem: Algorithmically generated sequences are difficult for some advanced deep learning methods, including recurrent networks.The study focuses on regularities in sequences of symbols generated by simple algorithms.
- Approach: The proposed approach augments recurrent networks with an infinite structured memory whose topology can be a pushdown stack or a list.The memory is intended to increase learning capabilities for sequence patterns involving counting and memorization.
- Approach: Multiplicative gates control the structured memory, allowing the network to perform operations such as PUSH and POP on a stack.The memory is implemented by constraining part of the recurrent matrix and using learnable controllers.
- Related work: The paper positions this memory-augmented approach alongside neural and earlier memory-augmented networks, while emphasizing a return to structured-memory models.Related approaches include Neural Turing Machines, Memory Networks, and work from the early nineties.
2 Algorithmic Patterns
The paper studies predictive modeling of concatenated sequences generated by short algorithms, especially discrete patterns involving counting and memorization. Its setting withholds sequence boundaries and focuses on patterns whose symbols can be predicted in one computational step.
- Task setting: The task concatenates sequences generated by a given algorithm into a stream, without exposing the boundaries between sequences.The model receives only the resulting data stream during training.
- Pattern class: The studied algorithmic patterns involve counting and memorization, with examples represented mainly in unary and binary numeral systems.The simplified representations isolate whether a model can learn the underlying algorithms.
- Pattern class: The paper targets sequential patterns with short descriptions in a general Turing-complete computational system, beyond patterns expressible only as context-free grammars.This defines a broader pattern class than context-free grammars alone.
- Scope: The study is limited to patterns whose symbols can be predicted in a single computational step, excluding algorithms such as sorting and dynamic programming.This is an explicit scope boundary for the studied sequence problems.
3 Related work
Prior work includes recurrent models for grammatical sequences, LSTMs with gating, hardwired symbolic networks, and external-memory architectures. The paper distinguishes its approach by learning a general model for multiple challenging unsupervised problems.
- Symbolic and recurrent models: Hardwired symbolic recurrent networks can handle recursive patterns in computational linguistics but are often designed separately for each grammar.These systems provide continuous implementations of symbolic structures.
- Recurrent models: Simple recurrent networks can learn a^nb^n over a limited range, but the cited work reports reliance on memorization rather than true counting.Related architectures do not generalize to longer sequences generated by the same algorithm.
- LSTM models: LSTM networks can learn simple context-free and context-sensitive grammars through multiplicative gating that permits potentially linear hidden units.The cited work connects this capability to counting-like behavior.
- External memory: External-memory recurrent models have used discrete or continuous stacks, but prior work often focused on isolated supervised problems.The paper instead develops a general model for multiple challenging unsupervised problems.
4 Model
The model extends recurrent networks with trainable structured memories whose controllers learn operations over stacks or lists. These memories increase capacity for sequence prediction, while training uses gradient methods and, for harder tasks, search-based optimization.
- Simple recurrent network: The base RNN updates hidden state from the current token and previous hidden state, then predicts the next-token probability vector.The hidden layer stores information about previous tokens; the output uses a softmax over tokens.
- Pushdown network: A Stack RNN adds a pushdown memory controlled by learned PUSH, POP, and optionally NO-OP actions.The stack can grow on demand, stores its top element at position 0, and feeds top elements back to the hidden layer.
- Pushdown network: Multiple stacks can operate in parallel and interact through the hidden layer, enabling processing of more challenging patterns.The extension addresses the limitation that a single stack can perform only one action at each time step.
- Doubly-linked lists: The same framework extends to a doubly-linked list with a movable read/write head and INSERT, LEFT, RIGHT, and NO-OP operations.Each list node connects to left and right neighbors, allowing the head to move and insert values.
- Optimization: The continuous memory models can be trained with stochastic gradient descent and back-propagation through time, but harder controllers may require random-restart search.Discretizing controllers at test time partially reduces numerical issues from long continuous stack sequences.
5 Experiments and results
The experiments test whether recurrent models can learn algorithmic sequence rules, including counting, memorization, binary addition, and language modeling. Stack RNNs generalize on several algorithmic tasks and outperform standard RNNs on Penn Treebank, though LSTM and SRCN perform better there.
- Experimental setting: The study trains models on concatenated sequences from short algorithms and tests whether they generalize to unseen, longer sequences.Training uses n up to N < 20, while testing uses n up to 60; sequence boundaries are unavailable during training.
- Counting: RNNs fail to generalize on counting tasks, whereas LSTMs and Stack RNNs generalize beyond the training lengths.The authors attribute LSTM's counting ability to linear hidden units; rounding improves Stack RNN performance on anbmcn+m.
- Counting: Two interacting stacks solve anb2n by tracking the a-count, consuming b symbols, and switching behavior when the first stack empties.The second stack also stores a special value, 0.56, to track sequence length.
- Memorization: Stack RNN and List RNN learn memorization, while RNN and LSTM do not appear to generalize; List RNN is less stable and overfits more often.The memorization comparison uses a two-element dictionary, with Stack RNN using 100 units and 10 stacks and List RNN using 10 lists.
- Binary addition: A learned Stack RNN generalizes binary addition by distributing sequence position, operands, lengths, stored values, and carry across multiple stacks.The learned procedure reads symbols left to right and produces the result in reverse order.
- Language modeling: On Penn Treebank, Stack RNN outperforms a comparably parameterized RNN but underperforms LSTM and SRCN.The models use one hidden layer with 100 units; Stack RNN empirically learns an exponentially decaying bag-of-words-like memory.
6 Discussion and future work
The discussion highlights unresolved issues in learning algorithmic patterns with continuous models and structured memory. Future work includes combining continuous and discrete optimization, using more flexible memory operations, and composing simpler algorithms.
- Continuous versus discrete model and search: Although continuous optimization learns some algorithmic patterns, it remains unclear whether continuous representations are appropriate for these problems.The authors suggest combining continuous and discrete optimization in future approaches.
- Long-term memory: Multiple stacks are theoretically Turing complete, but learning intricate stack interactions and requiring correctly formatted sequences limits their practical scope.The paper notes that memorization, for example, requires reversed ordering, and proposes more flexible memory and multi-step operations.
7 Conclusion
The paper shows that difficult pattern-recognition problems can be solved by recurrent networks augmented with structured, growing memory. It also identifies broader memory designs and learned topology as future directions.
- Structured, growing, potentially unlimited memory enables recurrent networks to solve certain difficult pattern-recognition problems.
- The experiments studied simple structured memories, including stacks and lists.
- The same approach could extend to more complex memory structures, such as a multi-dimensional tape.
- The long-term memory topology is fixed in the current work but could be learned from data in future systems.