public void createGradFunction() {
        if(lossVariables.isEmpty()){
            if(trainingConfig != null && trainingConfig.getLossVariables() != null && !trainingConfig.getLossVariables().isEmpty()){
                lossVariables.addAll(trainingConfig.getLossVariables());
            } else {
                List<String> outputs = outputs();
                if (outputs.size() == 1) {
                    String outName = outputs.get(0);
                    String opName = variables.get(outName).getOutputOfOp();
                    if(opName == null || !(ops.get(opName).getOp() instanceof ExternalErrorsFunction)){
                        log.info("Inferring output \"{}\" as loss variable as none were previously set. Use SameDiff.setLossVariables() to override", outputs.get(0));
                    }
                    lossVariables.add(outputs.get(0));
                }
            }
        }

        Preconditions.checkState(!lossVariables.isEmpty(), "Cannot create gradient function: " +
                "No loss variables (variables to minimize) have been specified. Loss variables are the variables that" +
                " represent the loss/cost/score to be minimized during training, and that all gradients are calculated with respect to.\n" +
                " Losses can be specified either in TrainingConfiguration (Builder.minimize(...)) or via SameDiff.setLossVariables()/addLossVariable()");

        if (log.isTraceEnabled()) {
            log.trace("Defining function \"grad\"");
        }


        /*
        Defining gradient function:

        Starting point:
        (a) Set of loss function variables - i.e., one or more variables representing loss to be minimized
        (b) Set of floating point variables we want to train (Variable type SDVariables only - not constants, arrays, placeholders)

        Observation: A trainable parameter only has a gradient defined if there is a floating point path between the variable and the loss.
        for example: X(fp) -> cast(int) -> cast(fp) -> loss - X has no gradient defined

        Algorithm for backprop:

        Step 1: Determine if variable requires a gradient (is trainable)
        How? Walk backward on op graph starting at loss variable(s), along FP variables only.
        Collect FP variables in set as we go.
        This gives us a subgraph "connected to loss by FP path" - gradient for FP variable is defined only if it's in that set/subgraph.


        Step 2: Determine minimal set of variables (including array type SDVariables - i.e., activations) we need gradients for
        Consider following graph: X(fp) -> cast(int) -> cast(fp) -> lots of FP ops -> loss
        unless we need them for other variables, there's zero point calculating the activation gradients for the "cast(fp) -> lots of FP ops" part of the graph, as the gradient from that branch won't go anywhere.
        How to determine minimal subset? Start with FP graph from step 1... then keep pruning leaves until the only remaining leaves are those FP variables that we need gradients for.

        Step 3: Differentiate ops in minimal subgraph
        The only major issue here is with multiple output ops, where only one of the outputs lead to the loss.
        For example, X -> slice -> (A,B); B -> loss, with A being unused (in that it doesn't contribute to the loss function)
        But to do split op backprop, we need gradient variables/arrays for both outputs (A and B).
        We know the shape and type of dL/dA must be exactly the same as A; we also know that the loss function doesn't depend on A. Hence, dL/dA == zerosLike(A)

         */



        final SameDiff outer = this;
        defineFunction("grad", new SameDiffFunctionDefinition() {

            @Override
            public SDVariable[] define(SameDiff sameDiff, Map<String, INDArray> inputs, SDVariable[] variableInputs) {
                //Propagate graph to this samediff instance which will also contain the backward
                if (SameDiff.this.debugMode) {
                    sameDiff.enableDebugMode();
                }

                outer.invokeGraphOn(sameDiff);
                if (debugMode) {
                    //Expect incoming args and outgoing args to be the same
                    Preconditions.checkState(sameDiff.ops.keySet().equals(ops.keySet()), "ops keysets not equal");
                }

                List<SameDiffOp> allFunctions = new ArrayList<>(sameDiff.ops.values());
                if (allFunctions.isEmpty()) {
                    throw new ND4JIllegalStateException("No ops found!");
                }

                for (SameDiffOp op : allFunctions) {
                    DifferentialFunction func = op.getOp();
                    if (func instanceof SDVariable) {
                        continue;
                    }

                    val args = func.args();
                    for (val arg : args)
                        arg.setSameDiff(sameDiff);
                    val outputs = func.outputVariables();
                    for (val output : outputs)
                        output.setSameDiff(sameDiff);
                    func.setSameDiff(sameDiff);
                }

                List<SDVariable> finalOutputs = new ArrayList<>(lossVariables.size());
                SDVariable initialGrad = sameDiff.var("one-var", Nd4j.scalar(1.0f));
                for(String s : lossVariables){
                    Preconditions.checkNotNull(s, "Encountered null value in loss variables. Null loss variables are not allowed." +
                            " Use SameDiff.setLossVariables with non-null array names to fix");
                    Preconditions.checkState(variables.containsKey(s), "Specified loss function variable \"%s\" does not exist", s);
                    SDVariable v = variables.get(s).getVariable();
                    Preconditions.checkState(v.dataType().isFPType(), "Specified loss function variable \"%s\" is not a floating" +
                            "point variable (datatype: %s). Only floating point variables may be used as loss function variable", s, v.dataType());
                    v = v.sum();    //If output is not a scalar: we'll use loss = v.sum(), same as adding loss for multiple outputs. We don't always know for sure if output is scalar at this point
                    if(v.dataType() == initialGrad.dataType()){
                        sameDiff.setGradientForVariableName(v.getVarName(), initialGrad);
                    } else {
                        sameDiff.setGradientForVariableName(v.getVarName(), initialGrad.castTo(v.dataType()));
                    }
                    if(finalOutputs.contains(v)){
                        log.warn("Loss function variable \"{}\" appears multiple times in list of loss variables - using only first instance", s);
                    } else {
                        finalOutputs.add(v);
                    }
                }

                if (log.isTraceEnabled()) {
                    String[] initialOutputsStr = allFunctions.get(allFunctions.size() - 1).getOp().outputVariablesNames();
                    String s = initialOutputsStr == null ? "null" : Arrays.toString(initialOutputsStr);
                    log.trace("Defining backward function: initial outputs {}", s);
                }


                //----- Step 1: Determine FP variables connected to loss -----
                // Find all FP variables that are connected to loss by an floating point (FP16/32/64) path
                Set<String> allFpVarsConnectedToLoss = new HashSet<>();
                Queue<String> toProcess = new LinkedList<>();
                for(String s : lossVariables){
                    if(!toProcess.contains(s)){
                        toProcess.add(s);
                    }
                }
                while(!toProcess.isEmpty()){
                    String next = toProcess.remove();
                    if(!allFpVarsConnectedToLoss.contains(next)){
                        Variable v = variables.get(next);
                        if(v.getVariable().dataType().isFPType()){
                            allFpVarsConnectedToLoss.add(v.getName());
                            //Work out what op (if any) this is an output of... and add the inputs to that op to be processed
                            if(v.getOutputOfOp() != null){
                                String opName = v.getOutputOfOp();
                                SameDiffOp op = ops.get(opName);
                                List<String> opInputs = op.getInputsToOp();
                                if(opInputs != null){
                                    for(String s : opInputs){
                                        Variable inputVar = variables.get(s);
                                        if(inputVar.getVariable().dataType().isFPType()){
                                            //Add this connected floating point type to the list to be processed
                                            toProcess.add(s);
                                        }
                                    }
                                }
                            }
                        }
                    }
                }

                //----- Step 2: Determine minimal set of FP variables actually required -----
                // Keep removing leaf nodes until only Variable type SDVariables remain
                Set<String> minimalSubgraphVars = new HashSet<>(allFpVarsConnectedToLoss);
                Queue<String> leafFPVars = new LinkedList<>();
                for(String s : allFpVarsConnectedToLoss){
                    //First: determine if is a FP leaf (Array type SDVariable)
                    Variable v = variables.get(s);
                    if(v.getVariable().getVariableType() == VariableType.ARRAY){
                        String opName = v.getOutputOfOp();  //Always defined for array type
                        SameDiffOp op = ops.get(opName);
                        List<String> inputsToOp = op.getInputsToOp();
                        boolean anyInputsInSubgraph = false;
                        if(inputsToOp != null){
                            for(String s2 : inputsToOp){
                                if(allFpVarsConnectedToLoss.contains(s2)){
                                    //Connection s2 -> s exists... therefore s is not a leaf (yet)
                                    anyInputsInSubgraph = true;
                                    break;
                                }
                            }
                        }
                        if(!anyInputsInSubgraph){
                            //Mark s as a leaf to be removed
                            leafFPVars.add(s);
                        }
                    }
                    if(v.getVariable().getVariableType() == VariableType.CONSTANT || v.getVariable().getVariableType() == VariableType.PLACEHOLDER){
                        leafFPVars.add(s);
                    }
                }

                while(!leafFPVars.isEmpty()){
                    String nextLeaf = leafFPVars.remove();
                    Variable v = variables.get(nextLeaf);
                    minimalSubgraphVars.remove(nextLeaf);

                    //Now, after removing: check what this variable is input to...
                    //If nextLeaf is input to some op X, then if none of inputs y->X are present in subgraph, then
                    // output variables X->z must now be leafs
                    //Note that any time we remove a variable, the only possible new leafs are those that this one
                    // is connected to.
                    List<String> inputsTo = v.getInputsForOp();
                    if( inputsTo != null && !inputsTo.isEmpty()) {
                        for (String opName : inputsTo) {
                            SameDiffOp op = ops.get(opName);
                            List<String> inputsToOp = op.getInputsToOp();
                            boolean anyPresent = false;
                            for(String s : inputsToOp){
                                if(minimalSubgraphVars.contains(s)){
                                    anyPresent = true;
                                    break;
                                }
                            }
                            if(!anyPresent){
                                //All inputs to op X are not in subgraph. Therefore outputs of op must be new leaves
                                List<String> outVars = op.getOutputsOfOp();
                                if(outVars != null) {
                                    for (String s : outVars) {
                                        if(!leafFPVars.contains(s)){
                                            //Mark this variable to be processed next
                                            leafFPVars.add(s);
                                        }
                                    }
                                }
                            }
                        }
                    }
                }

                Preconditions.checkState(!minimalSubgraphVars.isEmpty(), "Cannot differentiate graph relative to the specified loss function variables %s:" +
                        " graph does not contain any trainable SDVariables (floating point VARIABLE type SDVariables) that the loss function depend on.", lossVariables);

                //At this point: we know the set of variables that are connected to the loss - these all (and only) need gradients
                Queue<String> availableForDiff = new LinkedList<>();
                for(SDVariable lossVar : finalOutputs){
                    Variable v = sameDiff.variables.get(lossVar.getVarName());
                    if(v.getOutputOfOp() != null){
                        String opName = v.getOutputOfOp();
                        availableForDiff.add(opName);
                    }
                }

                // Collect all the the ops that have to be traversed before we can conclude that the gradient for
                // a variable is fully available
                //For example, if we have  X -> op -> Y, and Y -> (A,B) we need gradient contribution from BOTH
                // Y->A and Y->B connections before we can do differentiation of op "op"
                final HashMap<String, List<String>> prerequisites = new HashMap<>();    //Key: variable name. Value: list of op names
                for(String var : minimalSubgraphVars){
                    Variable variable = variables.get(var);
                    // Copy the collection, as the original one will be modified during backprop
                    final List<String> inputsForOp = variable.getInputsForOp();
                    if (inputsForOp != null) {
                        List<String> req = new ArrayList<>();
                        for(String opName : inputsForOp){
                            //Need to filter ops here
                            //For example, if we have: var -> Op1, and var -> Op2
                            //we might not need to differentiate Op2 if output of Op2 doesn't impact loss function
                            SameDiffOp o = ops.get(opName);
                            List<String> opOutputs = o.getOutputsOfOp();
                            boolean anyOpOutputsRequired = false;
                            if(opOutputs != null) {
                                for (String s : opOutputs) {
                                    if(minimalSubgraphVars.contains(s)) {
                                        anyOpOutputsRequired = true;
                                        break;
                                    }
                                }
                            }
                            if(anyOpOutputsRequired){
                                req.add(opName);
                            }
                        }
                        prerequisites.put(variable.getName(), req);
                    }
                }

                Set<String> differentiatedOps = new HashSet<>();
                while(!availableForDiff.isEmpty()){
                    String dfName = availableForDiff.remove();
                    DifferentialFunction df = sameDiff.ops.get(dfName).getOp();

                    //Get the inputs and outputs of the op
                    List<String> inputsToOp;
                    List<String> outputsOfOp;
                    if(df instanceof GradientBackwardsMarker){
                        SameDiffOp op = sameDiff.ops.get(df.getOwnName());
                        inputsToOp = op.getInputsToOp();
                        outputsOfOp = Collections.emptyList();
                    } else {
                        inputsToOp = sameDiff.ops.get(df.getOwnName()).getInputsToOp();
                        outputsOfOp = sameDiff.ops.get(df.getOwnName()).getOutputsOfOp();
                    }


                    //Get gradients for all output variables:
                    List<SDVariable> grads = new ArrayList<>();
                    for(String s : outputsOfOp){
                        SDVariable v = sameDiff.getVariable(s);
                        SDVariable g = v.hasGradient() ? v.gradient() : null;

                        if(g == null){
                            //If no gradient exists at this point, 3 possibilities:
                            // (a) we have a bug
                            // (b) output of this op isn't used in calculating the loss
                            // (c) output isn't a FP type
                            //In the FP case, we should create a zero variable to backprop, because we can't perform backprop
                            // for this op otherwise...
                            if(!v.dataType().isFPType()){
                                grads.add(null);
                            } else {
                                //See "Step 3: Differentiate ops in minimal subgraph" above for explanation on why this should be zerosLike here...
                                SDVariable gTemp = sameDiff.zerosLike(v);
                                grads.add(gTemp);
                            }
                        } else {
                            grads.add(g);
                        }
                    }

                    //Differentiate:
                    List<SDVariable> currFnGrads = df.diff(grads);
                    differentiatedOps.add(df.getOwnName());

                    //Check the inputs to this op, see if we can differentiate those ops now (and if so: add to queue)
                    for(String s : inputsToOp){
                        Variable v = sameDiff.variables.get(s);
                        String opName = v.getOutputOfOp();
                        if(opName == null || differentiatedOps.contains(opName)){
                            //Skip placeholder/constant etc; also skip if we've previously differentiated this op
                            continue;
                        }

                        //Next: we've just differentiated OpX
                        //For s -> OpX: we now have gradient for s after df.diff(grads) call earlier
                        //Now, do we also need to differentiate OpY, where OpY -> s?
                        //If any input variables x (x -> OpY) exist, if they are in the minimal subgraph, then we
                        // need to differentiate OpY too
                        //Note that just because we *need to* doesn't mean we *can* yet

                        boolean isRequiredOp = false;
                        SameDiffOp op = ops.get(opName);
                        if(op.getInputsToOp() != null){
                            List<String> opInputs = op.getInputsToOp();
                            boolean anyInputsRequired = false;
                            for(String s2 : opInputs){
                                if(minimalSubgraphVars.contains(s2)){
                                    anyInputsRequired = true;
                                    break;
                                }
                            }
                            if(anyInputsRequired){
                                if(!differentiatedOps.contains(op.getName())){
                                    isRequiredOp = true;
                                }
                            }
                        }

                        if(!isRequiredOp){
                            continue;
                        }

                        //Now that we know we need this op - check if we can actually differentiate it...
                        //We can differentiate it if, for all variables that are outputs of this op:
                        //(a) we have gradient already, OR
                        //(b) it's not a FP variable, OR
                        //(c) it's a FP variable but not one that the loss depends on
                        //Note that for "output array is used multiple times" case (i.e., X->opY->Y, X->opZ->Z) we need all gradient
                        // contributions - i.e., we need to have differentiated both opY and opZ

                        boolean allAvailable = true;
                        SameDiffOp o = sameDiff.ops.get(opName);
                        for(String opOutput : o.getOutputsOfOp()){
                            Variable outVar = variables.get(opOutput);
                            if(outVar.getVariable().dataType().isFPType()){
                                if(minimalSubgraphVars.contains(outVar.getName())){
                                    //Need gradient for this variable to be available before we can differentiate
                                    if(outVar.getVariable().gradient() == null){
                                        allAvailable = false;
                                        break;
                                    }
                                    //However, when a variable is used multiple times, we need ALL gradient contributions available:
                                    List<String> prereqs = prerequisites.get(outVar.getName());
                                    if(prereqs != null){
                                        allAvailable &= differentiatedOps.containsAll(prereqs);
                                        if(!allAvailable)
                                            break;
                                    }
                                }
                                //If in't not in the minimal subgraph, loss doesn't depend on it, so we don't care about it
                            }
                        }

                        if(allAvailable && !availableForDiff.contains(o.getOp().getOwnName())){
                            availableForDiff.add(o.getOp().getOwnName());
                        }
                    }
                }

                //Let's validate we actually differentiated everything correctly:
                for(String s : minimalSubgraphVars){
                    if(lossVariables.contains(s))
                        continue;
                    SDVariable g = variables.get(s).getVariable().gradient();
                    if(g == null){
                        throw new IllegalStateException("Error encountered during differentiation: no gradient for required variable \"" + s + "\" was calculated");
                    }
                }


                return new SDVariable[]{sameDiff.var("grad", org.nd4j.linalg.api.buffer.DataType.FLOAT, 1)};
            }
        });

        associateSameDiffWithOpsAndVariables();
    }
public void createGradFunction ( ) { if ( lossVariables . isEmpty ( ) ) { if ( trainingConfig != null && trainingConfig . getLossVariables ( ) != null && ! trainingConfig . getLossVariables ( ) . isEmpty ( ) ) { lossVariables . addAll ( trainingConfig . getLossVariables ( ) ) ; } else { List < String > outputs = outputs ( ) ; if ( outputs . size ( ) == 1 ) { String outName = outputs . get ( 0 ) ; String opName = variables . get ( outName ) . getOutputOfOp ( ) ; if ( opName == null || ! ( ops . get ( opName ) . getOp ( ) instanceof ExternalErrorsFunction ) ) { log . info ( "Inferring output \"{}\" as loss variable as none were previously set. Use SameDiff.setLossVariables() to override" , outputs . get ( 0 ) ) ; } lossVariables . add ( outputs . get ( 0 ) ) ; } } } Preconditions . checkState ( ! lossVariables . isEmpty ( ) , "Cannot create gradient function: " + "No loss variables (variables to minimize) have been specified. Loss variables are the variables that" + " represent the loss/cost/score to be minimized during training, and that all gradients are calculated with respect to.\n" + " Losses can be specified either in TrainingConfiguration (Builder.minimize(...)) or via SameDiff.setLossVariables()/addLossVariable()" ) ; if ( log . isTraceEnabled ( ) ) { log . trace ( "Defining function \"grad\"" ) ; } final SameDiff outer = this ; defineFunction ( "grad" , new SameDiffFunctionDefinition ( ) { @ Override public SDVariable [ ] define ( SameDiff sameDiff , Map < String , INDArray > inputs , SDVariable [ ] variableInputs ) { if ( SameDiff . this . debugMode ) { sameDiff . enableDebugMode ( ) ; } outer . invokeGraphOn ( sameDiff ) ; if ( debugMode ) { Preconditions . checkState ( sameDiff . ops . keySet ( ) . equals ( ops . keySet ( ) ) , "ops keysets not equal" ) ; } List < SameDiffOp > allFunctions = new ArrayList < > ( sameDiff . ops . values ( ) ) ; if ( allFunctions . isEmpty ( ) ) { throw new ND4JIllegalStateException ( "No ops found!" ) ; } for ( SameDiffOp op : allFunctions ) { DifferentialFunction func = op . getOp ( ) ; if ( func instanceof SDVariable ) { continue ; } val args = func . args ( ) ; for ( val arg : args ) arg . setSameDiff ( sameDiff ) ; val outputs = func . outputVariables ( ) ; for ( val output : outputs ) output . setSameDiff ( sameDiff ) ; func . setSameDiff ( sameDiff ) ; } List < SDVariable > finalOutputs = new ArrayList < > ( lossVariables . size ( ) ) ; SDVariable initialGrad = sameDiff . var ( "one-var" , Nd4j . scalar ( 1.0f ) ) ; for ( String s : lossVariables ) { Preconditions . checkNotNull ( s , "Encountered null value in loss variables. Null loss variables are not allowed." + " Use SameDiff.setLossVariables with non-null array names to fix" ) ; Preconditions . checkState ( variables . containsKey ( s ) , "Specified loss function variable \"%s\" does not exist" , s ) ; SDVariable v = variables . get ( s ) . getVariable ( ) ; Preconditions . checkState ( v . dataType ( ) . isFPType ( ) , "Specified loss function variable \"%s\" is not a floating" + "point variable (datatype: %s). Only floating point variables may be used as loss function variable" , s , v . dataType ( ) ) ; v = v . sum ( ) ; if ( v . dataType ( ) == initialGrad . dataType ( ) ) { sameDiff . setGradientForVariableName ( v . getVarName ( ) , initialGrad ) ; } else { sameDiff . setGradientForVariableName ( v . getVarName ( ) , initialGrad . castTo ( v . dataType ( ) ) ) ; } if ( finalOutputs . contains ( v ) ) { log . warn ( "Loss function variable \"{}\" appears multiple times in list of loss variables - using only first instance" , s ) ; } else { finalOutputs . add ( v ) ; } } if ( log . isTraceEnabled ( ) ) { String [ ] initialOutputsStr = allFunctions . get ( allFunctions . size ( ) - 1 ) . getOp ( ) . outputVariablesNames ( ) ; String s = initialOutputsStr == null ? "null" : Arrays . toString ( initialOutputsStr ) ; log . trace ( "Defining backward function: initial outputs {}" , s ) ; } Set < String > allFpVarsConnectedToLoss = new HashSet < > ( ) ; Queue < String > toProcess = new LinkedList < > ( ) ; for ( String s : lossVariables ) { if ( ! toProcess . contains ( s ) ) { toProcess . add ( s ) ; } } while ( ! toProcess . isEmpty ( ) ) { String next = toProcess . remove ( ) ; if ( ! allFpVarsConnectedToLoss . contains ( next ) ) { Variable v = variables . get ( next ) ; if ( v . getVariable ( ) . dataType ( ) . isFPType ( ) ) { allFpVarsConnectedToLoss . add ( v . getName ( ) ) ; if ( v . getOutputOfOp ( ) != null ) { String opName = v . getOutputOfOp ( ) ; SameDiffOp op = ops . get ( opName ) ; List < String > opInputs = op . getInputsToOp ( ) ; if ( opInputs != null ) { for ( String s : opInputs ) { Variable inputVar = variables . get ( s ) ; if ( inputVar . getVariable ( ) . dataType ( ) . isFPType ( ) ) { toProcess . add ( s ) ; } } } } } } } Set < String > minimalSubgraphVars = new HashSet < > ( allFpVarsConnectedToLoss ) ; Queue < String > leafFPVars = new LinkedList < > ( ) ; for ( String s : allFpVarsConnectedToLoss ) { Variable v = variables . get ( s ) ; if ( v . getVariable ( ) . getVariableType ( ) == VariableType . ARRAY ) { String opName = v . getOutputOfOp ( ) ; SameDiffOp op = ops . get ( opName ) ; List < String > inputsToOp = op . getInputsToOp ( ) ; boolean anyInputsInSubgraph = false ; if ( inputsToOp != null ) { for ( String s2 : inputsToOp ) { if ( allFpVarsConnectedToLoss . contains ( s2 ) ) { anyInputsInSubgraph = true ; break ; } } } if ( ! anyInputsInSubgraph ) { leafFPVars . add ( s ) ; } } if ( v . getVariable ( ) . getVariableType ( ) == VariableType . CONSTANT || v . getVariable ( ) . getVariableType ( ) == VariableType . PLACEHOLDER ) { leafFPVars . add ( s ) ; } } while ( ! leafFPVars . isEmpty ( ) ) { String nextLeaf = leafFPVars . remove ( ) ; Variable v = variables . get ( nextLeaf ) ; minimalSubgraphVars . remove ( nextLeaf ) ; List < String > inputsTo = v . getInputsForOp ( ) ; if ( inputsTo != null && ! inputsTo . isEmpty ( ) ) { for ( String opName : inputsTo ) { SameDiffOp op = ops . get ( opName ) ; List < String > inputsToOp = op . getInputsToOp ( ) ; boolean anyPresent = false ; for ( String s : inputsToOp ) { if ( minimalSubgraphVars . contains ( s ) ) { anyPresent = true ; break ; } } if ( ! anyPresent ) { List < String > outVars = op . getOutputsOfOp ( ) ; if ( outVars != null ) { for ( String s : outVars ) { if ( ! leafFPVars . contains ( s ) ) { leafFPVars . add ( s ) ; } } } } } } } Preconditions . checkState ( ! minimalSubgraphVars . isEmpty ( ) , "Cannot differentiate graph relative to the specified loss function variables %s:" + " graph does not contain any trainable SDVariables (floating point VARIABLE type SDVariables) that the loss function depend on." , lossVariables ) ; Queue < String > availableForDiff = new LinkedList < > ( ) ; for ( SDVariable lossVar : finalOutputs ) { Variable v = sameDiff . variables . get ( lossVar . getVarName ( ) ) ; if ( v . getOutputOfOp ( ) != null ) { String opName = v . getOutputOfOp ( ) ; availableForDiff . add ( opName ) ; } } final HashMap < String , List < String > > prerequisites = new HashMap < > ( ) ; for ( String var : minimalSubgraphVars ) { Variable variable = variables . get ( var ) ; final List < String > inputsForOp = variable . getInputsForOp ( ) ; if ( inputsForOp != null ) { List < String > req = new ArrayList < > ( ) ; for ( String opName : inputsForOp ) { SameDiffOp o = ops . get ( opName ) ; List < String > opOutputs = o . getOutputsOfOp ( ) ; boolean anyOpOutputsRequired = false ; if ( opOutputs != null ) { for ( String s : opOutputs ) { if ( minimalSubgraphVars . contains ( s ) ) { anyOpOutputsRequired = true ; break ; } } } if ( anyOpOutputsRequired ) { req . add ( opName ) ; } } prerequisites . put ( variable . getName ( ) , req ) ; } } Set < String > differentiatedOps = new HashSet < > ( ) ; while ( ! availableForDiff . isEmpty ( ) ) { String dfName = availableForDiff . remove ( ) ; DifferentialFunction df = sameDiff . ops . get ( dfName ) . getOp ( ) ; List < String > inputsToOp ; List < String > outputsOfOp ; if ( df instanceof GradientBackwardsMarker ) { SameDiffOp op = sameDiff . ops . get ( df . getOwnName ( ) ) ; inputsToOp = op . getInputsToOp ( ) ; outputsOfOp = Collections . emptyList ( ) ; } else { inputsToOp = sameDiff . ops . get ( df . getOwnName ( ) ) . getInputsToOp ( ) ; outputsOfOp = sameDiff . ops . get ( df . getOwnName ( ) ) . getOutputsOfOp ( ) ; } List < SDVariable > grads = new ArrayList < > ( ) ; for ( String s : outputsOfOp ) { SDVariable v = sameDiff . getVariable ( s ) ; SDVariable g = v . hasGradient ( ) ? v . gradient ( ) : null ; if ( g == null ) { if ( ! v . dataType ( ) . isFPType ( ) ) { grads . add ( null ) ; } else { SDVariable gTemp = sameDiff . zerosLike ( v ) ; grads . add ( gTemp ) ; } } else { grads . add ( g ) ; } } List < SDVariable > currFnGrads = df . diff ( grads ) ; differentiatedOps . add ( df . getOwnName ( ) ) ; for ( String s : inputsToOp ) { Variable v = sameDiff . variables . get ( s ) ; String opName = v . getOutputOfOp ( ) ; if ( opName == null || differentiatedOps . contains ( opName ) ) { continue ; } boolean isRequiredOp = false ; SameDiffOp op = ops . get ( opName ) ; if ( op . getInputsToOp ( ) != null ) { List < String > opInputs = op . getInputsToOp ( ) ; boolean anyInputsRequired = false ; for ( String s2 : opInputs ) { if ( minimalSubgraphVars . contains ( s2 ) ) { anyInputsRequired = true ; break ; } } if ( anyInputsRequired ) { if ( ! differentiatedOps . contains ( op . getName ( ) ) ) { isRequiredOp = true ; } } } if ( ! isRequiredOp ) { continue ; } boolean allAvailable = true ; SameDiffOp o = sameDiff . ops . get ( opName ) ; for ( String opOutput : o . getOutputsOfOp ( ) ) { Variable outVar = variables . get ( opOutput ) ; if ( outVar . getVariable ( ) . dataType ( ) . isFPType ( ) ) { if ( minimalSubgraphVars . contains ( outVar . getName ( ) ) ) { if ( outVar . getVariable ( ) . gradient ( ) == null ) { allAvailable = false ; break ; } List < String > prereqs = prerequisites . get ( outVar . getName ( ) ) ; if ( prereqs != null ) { allAvailable &= differentiatedOps . containsAll ( prereqs ) ; if ( ! allAvailable ) break ; } } } } if ( allAvailable && ! availableForDiff . contains ( o . getOp ( ) . getOwnName ( ) ) ) { availableForDiff . add ( o . getOp ( ) . getOwnName ( ) ) ; } } } for ( String s : minimalSubgraphVars ) { if ( lossVariables . contains ( s ) ) continue ; SDVariable g = variables . get ( s ) . getVariable ( ) . gradient ( ) ; if ( g == null ) { throw new IllegalStateException ( "Error encountered during differentiation: no gradient for required variable \"" + s + "\" was calculated" ) ; } } return new SDVariable [ ] { sameDiff . var ( "grad" , org . nd4j . linalg . api . buffer . DataType . FLOAT , 1 ) } ; } } ) ; associateSameDiffWithOpsAndVariables ( ) ; }
Create the gradient function (for calculating gradients via {@link #execBackwards(Map)}) if it is not already defined.
Users do not usually need to call this function manually, as it is called as required in the aforementioned method.
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If the gradient function already exists, this method is a no-op.<br>
After this method returns, the SameDiff function instance for the gradient can be accessed using {@link #getFunction(String)}
with name "grad" as the argument.