Neural Programmer-Interpreters. Scott Reed and Nando de Freitas
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1 Neural Programmer-Interpreters Scott Reed and Nando de Freitas
2 Neural Programmer Interpreter (NPI) goals: 1. Long-term prediction: Model potentially long sequences of actions by exploiting compositional structure. 2. Continual learning: Learn new programs by composing previouslylearned programs, rather than from scratch. 3. Data efficiency: Learn generalizable programs from a small number of example traces. 4. Interpretability: By looking at NPI s generated commands, we can understand what it is doing at multiple levels of temporal abstraction.
3 Model
4 NPI training data Traces: environment observation program indices program args return bit
5 NPI single step of computation
6 NPI single step of computation
7 NPI single step of computation
8 NPI single step of computation
9 Demos
10 Adding numbers together - environment input 1 input 2 carry output Addition environment interface: Scratch pad with the two numbers to be added, a carry row and output row. LEFT, RIGHT programs that can move a pointer left or right, respectively. WRITE program that writes a specified value to the location of a specified pointer. 4 read/write pointers; one per row.
11 Adding numbers together learned programs Program Description Calls ADD Multi-digit addition ADD1, LSHIFT ADD1 Single-digit add CARRY, ACT CARRY Mark a 1 in the carry row 1 step left. ACT, LSHIFT, RSHIFT LSHIFT Shift specified pointer 1 step left. ACT RSHIFT Shift specified pointer 1 step right. ACT ACT Move pointer or write to the scratch pad -
12 Adding numbers together MEDICINE: AGI SCIENTISTS KNOWLEDGE ACQUISION DECISION SUPPORT ROBOTICS AND AUTOMATION
13 Bubble sort - environment array t= t=1 t= Sorting environment interface: Scratch pad with the array to be sorted. Read/write pointers. LEFT, RIGHT programs that can move a specified pointer left or right, respectively. SWAP program that swaps the values at two specified pointer locations. t=
14 Bubble sort learned programs Program Description Calls BUBBLESORT Sort numbers in ascending order BUBBLE, RESET BUBBLE Perform one sweep of bubble sort BSTEP, ACT RESET Move pointers all back to the left LSHIFT BSTEP Conditionally swap and advance pointers COMPSWAP, RSHIFT COMPSWAP Conditionally swap two pointer values ACT LSHIFT Shift specified pointer 1 step left. ACT RSHIFT Shift specified pointer 1 step right. ACT ACT Perform a swap or move a pointer. -
15 Bubble sort
16 3D car models - environment 3D cars environment interface: Rendering of the car (pixels). Target angle and elevation coordinates. LEFT, RIGHT, UP, DOWN programs that can move the car 15 degrees at a time. The current car pose is NOT provided.
17 3D car models learned programs Program Description Calls GOTO Change 3D car pose to match target HGOTO, VGOTO HGOTO Move horizontally to target angle LGOTO, RGOTO LGOTO Move left to target ACT RGOTO Move right to target ACT VGOTO Move vertically to target elevation UGOTO, DGOTO UGOTO Move up to target ACT DGOTO Move down to target ACT ACT Move 15 degrees up, down, left or right. -
18 Canonicalizing the view of 3D car models
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30 Experiments
31 Data Efficiency Sorting Seq2Seq LSTM and NPI used the same number of layers and hidden units. Trained on length 20 arrays of single-digit numbers. NPI benefits from mining multiple subprogram examples per sorting instance, and additional paramete rs of the program memory.
32 Generalization Sorting For each length, we provided 64 example bubble sort traces, for a total of 1,216 examples. Then, we evaluated whether the network can learn to sort arrays beyond length 20 Training sequence lengths
33 Generalization Addition Example problem: = 250, we could represent the sequence as: 90X160X250 and solve addition via sequence prediction, e.g. Learning to Execute paper.
34 Generalization Addition problems To make it easier, we can reverse and stack the inputs. (s2s-stack) output: XXXX250 input 1: 090XXXX input 2: 061XXXX Even easier version: computation is entirely local. (s2s-easy) output: 052 input 1: 090 input 2: 061
35 Generalization Addition problems Trained on problem sizes 1,..,20 digits.
36 Generalization Addition problems s2s-stack
37 Generalization Addition problems s2s-easy
38 Generalization Addition problems NPI
39 Multi-task NPI Core is shared across all programs
40 Learning new programs with a fixed NPI core Toy example: Maximum-finding in an array. Simple (not optimal) way: Call BUBBLESORT and then take the right-most element of the array. Two new programs: RJMP: Move all pointers to the rightmost position in the array by repeatedly calling RSHIFT program. MAX: Call BUBBLESORT and then RJMP Expand program memory by adding 2 slots. Randomly initialize, then learn by backpropagation with the NPI core and all other parameters fixed.
41 Learning new programs with a fixed NPI core Protocol: 1. Randomly initialize new program vectors in memory 2. Freeze core and other program vectors 3. Backpropagate gradients to new program vectors
42 Quantitative Results Per-sequence % accuracy. + Max indicates performance after addition of MAX program to memory. unseen uses a test set with disjoint car models from the training set.
43 Conclusions & Next Steps A single NPI can learn multiple programs in dissimilar environments with different affordances. NPI sorting and addition programs exhibit strong generalization compared to baseline Seq2Seq models. A trained NPI with a fixed core can continue to learn new programs without forgetting already learned programs. Next steps: reduce supervision, scale up #programs, integrate new perception modules and affordances.
44 Related work Too much to cover in 20 minutes! Sigma-Pi Units (Rumelhart, 1986): activations of one network become th e weights of a second network. Slowly changing network learns to contro l rapidly-changing network (Schmidhuber, 1992). Hierarchical RL (Sutton 1999, Dietterich 2000, Andre and Sutton 2001). Recent extensions of Seq2Seq: NTM, Pointer Networks, Memory Networks, Stack/Queue/Dequeue-augmented recurrent networks. Several other ICLR 16 papers on neural program induction. Main differen ce is that NPI explicitly incorporates compositional program structure. Recent models of prefrontal cognitive control (Donnarumma 2015). Learning to Execute (Zaremba 2014)
45 Thanks!
46 NPI single time step computation Traces: LSTM core input LSTM output pred. return prob next program key next program args
47 NPI single time step computation Traces: selected prog inde x program key memory program memory
48 NPI single time step computation Traces: Next environment observation; depends on selected program and arguments. (Not controlled by NPI parameters)
49 NPI learning Traces: Objective:
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