diff --git a/include/xgboost/objective.h b/include/xgboost/objective.h
index dcf244987..3e722a18f 100644
--- a/include/xgboost/objective.h
+++ b/include/xgboost/objective.h
@@ -53,7 +53,7 @@ class ObjFunction : public Configurable {
    * \brief transform prediction values, this is only called when Prediction is called
    * \param io_preds prediction values, saves to this vector as well
    */
-  virtual void PredTransform(HostDeviceVector<bst_float>*) {}
+  virtual void PredTransform(HostDeviceVector<bst_float>*) const {}
 
   /*!
    * \brief transform prediction values, this is only called when Eval is called,
diff --git a/plugin/example/custom_obj.cc b/plugin/example/custom_obj.cc
index c42e21c8b..a18d8aecc 100644
--- a/plugin/example/custom_obj.cc
+++ b/plugin/example/custom_obj.cc
@@ -58,7 +58,7 @@ class MyLogistic : public ObjFunction {
   const char* DefaultEvalMetric() const override {
     return "logloss";
   }
-  void PredTransform(HostDeviceVector<bst_float> *io_preds) override {
+  void PredTransform(HostDeviceVector<bst_float> *io_preds) const override {
     // transform margin value to probability.
     std::vector<bst_float> &preds = io_preds->HostVector();
     for (auto& pred : preds) {
diff --git a/src/objective/aft_obj.cu b/src/objective/aft_obj.cu
index fadd449dc..95e4f4c55 100644
--- a/src/objective/aft_obj.cu
+++ b/src/objective/aft_obj.cu
@@ -102,7 +102,7 @@ class AFTObj : public ObjFunction {
     }
   }
 
-  void PredTransform(HostDeviceVector<bst_float> *io_preds) override {
+  void PredTransform(HostDeviceVector<bst_float> *io_preds) const override {
     // Trees give us a prediction in log scale, so exponentiate
     common::Transform<>::Init(
         [] XGBOOST_DEVICE(size_t _idx, common::Span<bst_float> _preds) {
diff --git a/src/objective/hinge.cu b/src/objective/hinge.cu
index 8e37aa0db..0c8c2f317 100644
--- a/src/objective/hinge.cu
+++ b/src/objective/hinge.cu
@@ -68,7 +68,7 @@ class HingeObj : public ObjFunction {
             out_gpair, &preds, &info.labels_, &info.weights_);
   }
 
-  void PredTransform(HostDeviceVector<bst_float> *io_preds) override {
+  void PredTransform(HostDeviceVector<bst_float> *io_preds) const override {
     common::Transform<>::Init(
         [] XGBOOST_DEVICE(size_t _idx, common::Span<bst_float> _preds) {
           _preds[_idx] = _preds[_idx] > 0.0 ? 1.0 : 0.0;
diff --git a/src/objective/multiclass_obj.cu b/src/objective/multiclass_obj.cu
index 4286b6c40..6ffa6eac2 100644
--- a/src/objective/multiclass_obj.cu
+++ b/src/objective/multiclass_obj.cu
@@ -121,7 +121,7 @@ class SoftmaxMultiClassObj : public ObjFunction {
       }
     }
   }
-  void PredTransform(HostDeviceVector<bst_float>* io_preds) override {
+  void PredTransform(HostDeviceVector<bst_float>* io_preds) const override {
     this->Transform(io_preds, output_prob_);
   }
   void EvalTransform(HostDeviceVector<bst_float>* io_preds) override {
@@ -131,10 +131,9 @@ class SoftmaxMultiClassObj : public ObjFunction {
     return "mlogloss";
   }
 
-  inline void Transform(HostDeviceVector<bst_float> *io_preds, bool prob) {
+  inline void Transform(HostDeviceVector<bst_float> *io_preds, bool prob) const {
     const int nclass = param_.num_class;
     const auto ndata = static_cast<int64_t>(io_preds->Size() / nclass);
-    max_preds_.Resize(ndata);
 
     auto device = io_preds->DeviceIdx();
     if (prob) {
@@ -148,23 +147,22 @@ class SoftmaxMultiClassObj : public ObjFunction {
         .Eval(io_preds);
     } else {
       io_preds->SetDevice(device);
-      max_preds_.SetDevice(device);
+      HostDeviceVector<bst_float> max_preds;
+      max_preds.SetDevice(device);
+      max_preds.Resize(ndata);
       common::Transform<>::Init(
-          [=] XGBOOST_DEVICE(size_t _idx,
-                             common::Span<const bst_float> _preds,
+          [=] XGBOOST_DEVICE(size_t _idx, common::Span<const bst_float> _preds,
                              common::Span<bst_float> _max_preds) {
             common::Span<const bst_float> point =
                 _preds.subspan(_idx * nclass, nclass);
             _max_preds[_idx] =
-                common::FindMaxIndex(point.cbegin(),
-                                     point.cend()) - point.cbegin();
+                common::FindMaxIndex(point.cbegin(), point.cend()) -
+                point.cbegin();
           },
           common::Range{0, ndata}, device, false)
-        .Eval(io_preds, &max_preds_);
-    }
-    if (!prob) {
-      io_preds->Resize(max_preds_.Size());
-      io_preds->Copy(max_preds_);
+          .Eval(io_preds, &max_preds);
+      io_preds->Resize(max_preds.Size());
+      io_preds->Copy(max_preds);
     }
   }
 
@@ -188,7 +186,6 @@ class SoftmaxMultiClassObj : public ObjFunction {
   // parameter
   SoftmaxMultiClassParam param_;
   // Cache for max_preds
-  HostDeviceVector<bst_float> max_preds_;
   HostDeviceVector<int> label_correct_;
 };
 
diff --git a/src/objective/regression_obj.cu b/src/objective/regression_obj.cu
index cb5e0f48e..bb4e7074b 100644
--- a/src/objective/regression_obj.cu
+++ b/src/objective/regression_obj.cu
@@ -109,7 +109,7 @@ class RegLossObj : public ObjFunction {
     return Loss::DefaultEvalMetric();
   }
 
-  void PredTransform(HostDeviceVector<float> *io_preds) override {
+  void PredTransform(HostDeviceVector<float> *io_preds) const override {
     common::Transform<>::Init(
         [] XGBOOST_DEVICE(size_t _idx, common::Span<float> _preds) {
           _preds[_idx] = Loss::PredTransform(_preds[_idx]);
@@ -233,7 +233,7 @@ class PoissonRegression : public ObjFunction {
       }
     }
   }
-  void PredTransform(HostDeviceVector<bst_float> *io_preds) override {
+  void PredTransform(HostDeviceVector<bst_float> *io_preds) const override {
     common::Transform<>::Init(
         [] XGBOOST_DEVICE(size_t _idx, common::Span<bst_float> _preds) {
           _preds[_idx] = expf(_preds[_idx]);
@@ -343,7 +343,7 @@ class CoxRegression : public ObjFunction {
       last_exp_p = exp_p;
     }
   }
-  void PredTransform(HostDeviceVector<bst_float> *io_preds) override {
+  void PredTransform(HostDeviceVector<bst_float> *io_preds) const override {
     std::vector<bst_float> &preds = io_preds->HostVector();
     const long ndata = static_cast<long>(preds.size()); // NOLINT(*)
     common::ParallelFor(ndata, [&](long j) { // NOLINT(*)
@@ -420,7 +420,7 @@ class GammaRegression : public ObjFunction {
       }
     }
   }
-  void PredTransform(HostDeviceVector<bst_float> *io_preds) override {
+  void PredTransform(HostDeviceVector<bst_float> *io_preds) const override {
     common::Transform<>::Init(
         [] XGBOOST_DEVICE(size_t _idx, common::Span<bst_float> _preds) {
           _preds[_idx] = expf(_preds[_idx]);
@@ -523,7 +523,7 @@ class TweedieRegression : public ObjFunction {
       }
     }
   }
-  void PredTransform(HostDeviceVector<bst_float> *io_preds) override {
+  void PredTransform(HostDeviceVector<bst_float> *io_preds) const override {
     common::Transform<>::Init(
         [] XGBOOST_DEVICE(size_t _idx, common::Span<bst_float> _preds) {
           _preds[_idx] = expf(_preds[_idx]);