Inartificial intelligence, adifferentiable neural computer (DNC) is a memory augmentedneural network architecture (MANN), which is typically (but not by definition) recurrent in its implementation. The model was published in 2016 byAlex Graves et al. ofDeepMind.^[1]

DNC indirectly takes inspiration fromVon-Neumann architecture, making it likely to outperform conventional architectures in tasks that are fundamentally algorithmic that cannot be learned by finding adecision boundary.

So far, DNCs have been demonstrated to handle only relatively simple tasks, which can be solved using conventional programming. But DNCs don't need to be programmed for each problem, but can instead be trained. This attention span allows the user to feed complexdata structures such asgraphs sequentially, and recall them for later use. Furthermore, they can learn aspects ofsymbolic reasoning and apply it to working memory. The researchers who published the method see promise that DNCs can be trained to perform complex, structured tasks^[1][2] and address big-data applications that require some sort of reasoning, such as generating video commentaries or semantic text analysis.^[3][4]

DNC can be trained to navigaterapid transit systems, and apply that network to a different system. A neural network without memory would typically have to learn about each transit system from scratch. On graph traversal and sequence-processing tasks withsupervised learning, DNCs performed better than alternatives such aslong short-term memory or aneural turing machine.^[5] With areinforcement learning approach to a block puzzle problem inspired bySHRDLU, DNC was trained via curriculum learning, and learned to make aplan. It performed better than a traditionalrecurrent neural network.^[5]

DNC networks were introduced as an extension of theNeural Turing Machine (NTM), with the addition of memory attention mechanisms that control where the memory is stored, and temporal attention that records the order of events. This structure allows DNCs to be more robust and abstract than a NTM, and still perform tasks that have longer-term dependencies than some predecessors such as Long Short Term Memory (LSTM). The memory, which is simply a matrix, can be allocated dynamically and accessed indefinitely. The DNC isdifferentiable end-to-end (each subcomponent of the model is differentiable, therefore so is the whole model). This makes it possible to optimize them efficiently usinggradient descent.^[3][6][7]

The DNC model is similar to theVon Neumann architecture, and because of the resizability of memory, it isTuring complete.^[8]

This sectionmay beconfusing or unclear to readers. In particular, a list of equations (without, e.g., anexhaustive association with a complete diagram of the DNC) is not a digestible description for many readers of this article. Please helpclarify the section. There might be a discussion about this onthe talk page.(October 2017) (Learn how and when to remove this message)

DNC, as originally published^[1]

Independent variables
${\displaystyle {\mathbf{x}}_t}$	Input vector
${\displaystyle {\mathbf{z}}_t}$	Target vector
Controller
${\displaystyle {\mathit{\chi }}_t=[{\mathbf{x}}_t;{\mathbf{r}}_{t-1}^1;\cdots ;{\mathbf{r}}_{t-1}^R]}$	Controller input matrix
Deep (layered) LSTM	${\displaystyle \mathrm{\forall }0\le l\le L}$
${\displaystyle {\mathbf{i}}_t^l=\sigma (W_i^l[{\mathit{\chi }}_t;{\mathbf{h}}_{t-1}^l;{\mathbf{h}}_t^{l-1}]+{\mathbf{b}}_i^l)}$	Input gate vector
${\displaystyle {\mathbf{o}}_t^l=\sigma (W_o^l[{\mathit{\chi }}_t;{\mathbf{h}}_{t-1}^l;{\mathbf{h}}_t^{l-1}]+{\mathbf{b}}_o^l)}$	Output gate vector
${\displaystyle {\mathbf{f}}_t^l=\sigma (W_f^l[{\mathit{\chi }}_t;{\mathbf{h}}_{t-1}^l;{\mathbf{h}}_t^{l-1}]+{\mathbf{b}}_f^l)}$	Forget gate vector
${\displaystyle {\mathbf{s}}_t^l={\mathbf{f}}_t^l{\mathbf{s}}_{t-1}^l+{\mathbf{i}}_t^l\tanh (W_s^l[{\mathit{\chi }}_t;{\mathbf{h}}_{t-1}^l;{\mathbf{h}}_t^{l-1}]+{\mathbf{b}}_s^l)}$	State gate vector, ${\displaystyle s_0=0}$
${\displaystyle {\mathbf{h}}_t^l={\mathbf{o}}_t^l\tanh ({\mathbf{s}}_t^l)}$	Hidden gate vector, ${\displaystyle h_0=0;h_t^0=0\mathrm{\forall }t}$
${\displaystyle {\mathbf{y}}_t=W_y[{\mathbf{h}}_t^1;\cdots ;{\mathbf{h}}_t^L]+W_r[{\mathbf{r}}_t^1;\cdots ;{\mathbf{r}}_t^R]}$	DNC output vector
Read & Write heads
${\displaystyle {\xi }_t=W_{\xi }[h_t^1;\cdots ;h_t^L]}$	Interface parameters
${\displaystyle =[{\mathbf{k}}_t^{r,1};\cdots ;{\mathbf{k}}_t^{r,R};{\hat{\beta }}_t^{r,1};\cdots ;{\hat{\beta }}_t^{r,R};{\mathbf{k}}_t^w;\widehat{{\beta }_t^w};{\hat{\mathbf{e}}}_t;{\mathbf{v}}_t;\widehat{f_t^1};\cdots ;\widehat{f_t^R};{\hat{g}}_t^a;{\hat{g}}_t^w;{\hat{\mathit{\pi }}}_t^1;\cdots ;{\hat{\mathit{\pi }}}_t^R]}$
Read heads	${\displaystyle \mathrm{\forall }1\le i\le R}$
${\displaystyle {\mathbf{k}}_t^{r,i}}$	Read keys
${\displaystyle {\beta }_t^{r,i}=\text{oneplus}({\hat{\beta }}_t^{r,i})}$	Read strengths
${\displaystyle f_t^i=\sigma ({\hat{f}}_t^i)}$	Free gates
${\displaystyle {\mathit{\pi }}_t^i=\text{softmax}({\hat{\mathit{\pi }}}_t^i)}$	Read modes, ${\displaystyle {\mathit{\pi }}_t^i\in {\mathbb{R}}^3}$
Write head
${\displaystyle {\mathbf{k}}_t^w}$	Write key
${\displaystyle {\beta }_t^w={\hat{\beta }}_t^w}$	Write strength
${\displaystyle {\mathbf{e}}_t=\sigma ({\hat{\mathbf{e}}}_t)}$	Erase vector
${\displaystyle {\mathbf{v}}_t}$	Write vector
${\displaystyle g_t^a=\sigma ({\hat{g}}_t^a)}$	Allocation gate
${\displaystyle g_t^w=\sigma ({\hat{g}}_t^w)}$	Write gate
Memory
${\displaystyle M_t=M_{t-1}\circ (E-{\mathbf{w}}_t^w{\mathbf{e}}_t^{⊺})+{\mathbf{w}}_t^w{\mathbf{v}}_t^{⊺}}$	Memory matrix, Matrix of ones${\displaystyle E\in {\mathbb{R}}^{N\times W}}$
${\displaystyle {\mathbf{u}}_t=({\mathbf{u}}_{t-1}+{\mathbf{w}}_{t-1}^w-{\mathbf{u}}_{t-1}\circ {\mathbf{w}}_{t-1}^w)\circ {\mathit{\psi }}_t}$	Usage vector
${\displaystyle {\mathbf{p}}_t=\left(1-\sum _i{\mathbf{w}}_t^w[i]\right){\mathbf{p}}_{t-1}+{\mathbf{w}}_t^w}$	Precedence weighting, ${\displaystyle {\mathbf{p}}_0=\mathbf{0}}$
${\displaystyle L_t=(\mathbf{1}-\mathbf{I})\left[(1-{\mathbf{w}}_t^w[i]-{\mathbf{w}}_t^w[j])L_{t-1}[i,j]+{\mathbf{w}}_t^w[i]{\mathbf{p}}_{t-1}^j\right]}$	Temporal link matrix, ${\displaystyle L_0=\mathbf{0}}$
${\displaystyle {\mathbf{w}}_t^w=g_t^w[g_t^a{\mathbf{a}}_t+(1-g_t^a){\mathbf{c}}_t^w]}$	Write weighting
${\displaystyle {\mathbf{w}}_t^{r,i}={\mathit{\pi }}_t^i[1]{\mathbf{b}}_t^i+{\mathit{\pi }}_t^i[2]c_t^{r,i}+{\mathit{\pi }}_t^i[3]f_t^i}$	Read weighting
${\displaystyle {\mathbf{r}}_t^i=M_t^{⊺}{\mathbf{w}}_t^{r,i}}$	Read vectors
${\displaystyle \mathcal{C}(M,\mathbf{k},\beta )[i]=\frac{\exp \{\mathcal{D}(\mathbf{k},M[i,\cdot ])\beta \}}{\sum _j\exp \{\mathcal{D}(\mathbf{k},M[j,\cdot ])\beta \}}}$	Content-based addressing, Lookup key${\displaystyle \mathbf{k}}$, key strength${\displaystyle \beta }$
${\displaystyle {\varphi }_t}$	Indices of${\displaystyle {\mathbf{u}}_t}$, sorted in ascending order of usage
${\displaystyle {\mathbf{a}}_t[{\varphi }_t[j]]=(1-{\mathbf{u}}_t[{\varphi }_t[j]])\prod _{i=1}^{j-1}{\mathbf{u}}_t[{\varphi }_t[i]]}$	Allocation weighting
${\displaystyle {\mathbf{c}}_t^w=\mathcal{C}(M_{t-1},{\mathbf{k}}_t^w,{\beta }_t^w)}$	Write content weighting
${\displaystyle {\mathbf{c}}_t^{r,i}=\mathcal{C}(M_{t-1},{\mathbf{k}}_t^{r,i},{\beta }_t^{r,i})}$	Read content weighting
${\displaystyle {\mathbf{f}}_t^i=L_t{\mathbf{w}}_{t-1}^{r,i}}$	Forward weighting
${\displaystyle {\mathbf{b}}_t^i=L_t^{⊺}{\mathbf{w}}_{t-1}^{r,i}}$	Backward weighting
${\displaystyle {\mathit{\psi }}_t=\prod _{i=1}^R\left(\mathbf{1}-f_t^i{\mathbf{w}}_{t-1}^{r,i}\right)}$	Memory retention vector
Definitions
${\displaystyle \mathbf{W},\mathbf{b}}$	Weight matrix, bias vector
${\displaystyle \mathbf{0},\mathbf{1},\mathbf{I}}$	Zeros matrix, ones matrix,identity matrix
${\displaystyle \circ }$	Element-wise multiplication
${\displaystyle \mathcal{D}(\mathbf{u},\mathbf{v})=\frac{\mathbf{u}\cdot \mathbf{v}}{\Vert \mathbf{u}\Vert \Vert \mathbf{v}\Vert }}$	Cosine similarity
${\displaystyle \sigma (x)=1/(1+e^{-x})}$	Sigmoid function
${\displaystyle \text{oneplus}(x)=1+\log (1+e^x)}$	Oneplus function
${\displaystyle \text{softmax}(\mathbf{x}{)}_j=\frac{e^{x_j}}{\sum _{k=1}^K{e}^{x_k}}}$    forj = 1, ...,K.	Softmax function

Refinements include sparse memory addressing, which reduces time and space complexity by thousands of times. This can be achieved by using an approximate nearest neighbor algorithm, such asLocality-sensitive hashing, or a randomk-d tree like Fast Library for Approximate Nearest Neighbors fromUBC.^[9] Adding Adaptive Computation Time (ACT) separates computation time from data time, which uses the fact that problem length and problem difficulty are not always the same.^[10] Training using synthetic gradients performs considerably better thanBackpropagation through time (BPTT).^[11] Robustness can be improved with use of layer normalization and Bypass Dropout as regularization.^[12]

• Differentiable programming

• A bit-by-bit guide to the equations governing differentiable neural computers
• DeepMind's Differentiable Neural Network Thinks Deeply

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