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One-step secant backpropagation

`net.trainFcn = 'trainoss'`

[net,tr] = train(net,...)

`trainoss`

is a network training function that
updates weight and bias values according to the one-step secant method.

`net.trainFcn = 'trainoss'`

sets the network `trainFcn`

property.

`[net,tr] = train(net,...)`

trains the network
with `trainoss`

.

Training occurs according to `trainoss`

training
parameters, shown here with their default values:

`net.trainParam.epochs` | `1000` | Maximum number of epochs to train |

`net.trainParam.goal` | `0` | Performance goal |

`net.trainParam.max_fail` | `6` | Maximum validation failures |

`net.trainParam.min_grad` | `1e-10` | Minimum performance gradient |

`net.trainParam.searchFcn` | `'srchbac'` | Name of line search routine to use |

`net.trainParam.show` | `25` | Epochs between displays ( |

`net.trainParam.showCommandLine` | `false` | Generate command-line output |

`net.trainParam.showWindow` | `true` | Show training GUI |

`net.trainParam.time` | `inf` | Maximum time to train in seconds |

Parameters related to line search methods (not all used for all methods):

`net.trainParam.scal_tol` | `20` | Divide into |

`net.trainParam.alpha` | `0.001` | Scale factor that determines sufficient reduction in |

`net.trainParam.beta` | `0.1` | Scale factor that determines sufficiently large step size |

`net.trainParam.delta` | `0.01` | Initial step size in interval location step |

`net.trainParam.gama` | `0.1` | Parameter to avoid small reductions in performance, usually
set to |

`net.trainParam.low_lim` | `0.1` | Lower limit on change in step size |

`net.trainParam.up_lim` | ` 0.5` | Upper limit on change in step size |

`net.trainParam.maxstep` | `100` | Maximum step length |

`net.trainParam.minstep` | `1.0e-6` | Minimum step length |

`net.trainParam.bmax` | `26` | Maximum step size |

You can create a standard network that uses `trainoss`

with `feedforwardnet`

or `cascadeforwardnet`

.
To prepare a custom network to be trained with `trainoss`

:

Set

`net.trainFcn`

to`'trainoss'`

. This sets`net.trainParam`

to`trainoss`

's default parameters.Set

`net.trainParam`

properties to desired values.

In either case, calling `train`

with the resulting
network trains the network with `trainoss`

.

`trainoss`

can train any network as long as
its weight, net input, and transfer functions have derivative functions.

Backpropagation is used to calculate derivatives of performance `perf`

with
respect to the weight and bias variables `X`

. Each
variable is adjusted according to the following:

X = X + a*dX;

where `dX`

is the search direction. The parameter `a`

is
selected to minimize the performance along the search direction. The
line search function `searchFcn`

is used to locate
the minimum point. The first search direction is the negative of the
gradient of performance. In succeeding iterations the search direction
is computed from the new gradient and the previous steps and gradients,
according to the following formula:

dX = -gX + Ac*X_step + Bc*dgX;

where `gX`

is the gradient, `X_step`

is
the change in the weights on the previous iteration, and `dgX`

is
the change in the gradient from the last iteration. See Battiti (*Neural
Computation, *Vol. 4, 1992, pp. 141–166) for a more
detailed discussion of the one-step secant algorithm.

Training stops when any of these conditions occurs:

The maximum number of

`epochs`

(repetitions) is reached.The maximum amount of

`time`

is exceeded.Performance is minimized to the

`goal`

.The performance gradient falls below

`min_grad`

.Validation performance has increased more than

`max_fail`

times since the last time it decreased (when using validation).

Battiti, R., "First and second order methods for learning:
Between steepest descent and Newton's method," *Neural
Computation*, Vol. 4, No. 2, 1992, pp. 141–166

`trainbfg`

| `traincgb`

| `traincgf`

| `traincgp`

| `traingda`

| `traingdm`

| `traingdx`

| `trainlm`

| `trainrp`

| `trainscg`

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