diff --git a/tutorials/4-caching-persistence.ipynb b/tutorials/4-caching-persistence.ipynb
index 0632d43..ede97ed 100644
--- a/tutorials/4-caching-persistence.ipynb
+++ b/tutorials/4-caching-persistence.ipynb
@@ -271,7 +271,7 @@
     "\n",
     "class SparseLogRegProbaTransformer(BaseTransformer):\n",
     "    def __init__(self):\n",
-    "        self.estimator = LogisticRegression(penalty='l1')\n",
+    "        self.estimator = LogisticRegression(penalty='l1', multi_class='auto', solver='liblinear')\n",
     "        \n",
     "    def fit(self, X, y):\n",
     "        self.estimator.fit(X, y)\n",
@@ -300,7 +300,7 @@
     "                      input_data=['input'],\n",
     "                      adapter=Adapter({'X': E('input', 'text')}),\n",
     "                      experiment_directory=EXPERIMENT_DIR_A,\n",
-    "                      is_trainable=True)\n",
+    "                      is_fittable=True)\n",
     "\n",
     "tfidf_step = Step(name='TF-IDF',\n",
     "                  transformer=StepsTfidfTransformer(),\n",
@@ -308,7 +308,7 @@
     "                  experiment_directory=EXPERIMENT_DIR_A,\n",
     "                  persist_output=True,\n",
     "                  load_persisted_output=True,  # This breaks when switching from training data to val data or test data!\n",
-    "                  is_trainable=True\n",
+    "                  is_fittable=True\n",
     "                  )\n",
     "\n",
     "logreg_step = Step(name='SparseLogReg',\n",
@@ -319,7 +319,7 @@
     "                                    'y': E('input', 'label')\n",
     "                                   }),\n",
     "                   experiment_directory=EXPERIMENT_DIR_A,\n",
-    "                   is_trainable=True)"
+    "                   is_fittable=True)"
    ]
   },
   {
@@ -366,7 +366,7 @@
    "outputs": [],
    "source": [
     "# Bug workaround: manually delete saved output when switching datasets\n",
-    "os.remove(os.path.join(EXPERIMENT_DIR_A, 'outputs', 'TF-IDF'))\n",
+    "os.remove(tfidf_step.experiment_directory_output_step)\n",
     "preds_linear_val = logreg_step.transform(data_val)"
    ]
   },
@@ -436,7 +436,7 @@
     "                                'y': E('input', 'label')\n",
     "                               }),\n",
     "               experiment_directory=EXPERIMENT_DIR_A,\n",
-    "               is_trainable=True)"
+    "               is_fittable=True)"
    ]
   },
   {
@@ -462,8 +462,7 @@
    "outputs": [],
    "source": [
     "# Bug workaround: manually delete saved output when switching datasets\n",
-    "os.remove(os.path.join(EXPERIMENT_DIR_A, 'outputs', 'TF-IDF'))\n",
-    "\n",
+    "os.remove(tfidf_step.experiment_directory_output_step)\n",
     "preds_rf_fit = rf_step.fit_transform(data_fit)"
    ]
   },
@@ -484,8 +483,7 @@
    "outputs": [],
    "source": [
     "# Bug workaround: manually delete saved output when switching datasets\n",
-    "os.remove(os.path.join(EXPERIMENT_DIR_A, 'outputs', 'TF-IDF'))\n",
-    "\n",
+    "os.remove(tfidf_step.experiment_directory_output_step)\n",
     "preds_rf_val = rf_step.transform(data_val)"
    ]
   },
@@ -552,7 +550,7 @@
     "                                 'y_proba_2': E('RF', 'y_proba'),\n",
     "                                }),\n",
     "                experiment_directory=EXPERIMENT_DIR_A,\n",
-    "                is_trainable=True)"
+    "                is_fittable=True)"
    ]
   },
   {
@@ -577,10 +575,10 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "os.remove(os.path.join(EXPERIMENT_DIR_A, 'outputs', 'TF-IDF'))  # Bug workaround: manually delete saved output when switching datasets\n",
+    "os.remove(tfidf_step.experiment_directory_output_step)  # Bug workaround: manually delete saved output when switching datasets\n",
     "preds_ens_val = ens_step.fit_transform(data_val)\n",
     "\n",
-    "os.remove(os.path.join(EXPERIMENT_DIR_A, 'outputs', 'TF-IDF'))  # Bug workaround: manually delete saved output when switching datasets\n",
+    "os.remove(tfidf_step.experiment_directory_output_step)  # Bug workaround: manually delete saved output when switching datasets\n",
     "preds_ens_test = ens_step.transform(data_test)"
    ]
   },
@@ -622,14 +620,15 @@
     "                          input_data=['input'],\n",
     "                          adapter=Adapter({'X': E('input', 'text')}),\n",
     "                          experiment_directory=EXPERIMENT_DIR_B,\n",
-    "                          is_trainable=True)\n",
+    "                          is_fittable=True)\n",
     "\n",
     "new_tfidf_step = Step(name='TF-IDF',\n",
     "                      transformer=StepsTfidfTransformer(),\n",
     "                      input_steps=[new_count_vec_step],        \n",
     "                      experiment_directory=EXPERIMENT_DIR_B,\n",
     "                      cache_output=True,\n",
-    "                      is_trainable=True)\n",
+    "                      force_fitting=False,\n",
+    "                      is_fittable=True)\n",
     "\n",
     "new_logreg_step = Step(name='SparseLogReg',\n",
     "                   transformer=SparseLogRegProbaTransformer(),\n",
@@ -639,7 +638,7 @@
     "                                    'y': E('input', 'label')\n",
     "                                   }),\n",
     "                   experiment_directory=EXPERIMENT_DIR_B,\n",
-    "                   is_trainable=True)\n",
+    "                   is_fittable=True)\n",
     "\n",
     "new_rf_step = Step(name='RF',\n",
     "               transformer=RfClfTransformer(n_estimators=200, max_depth=8),\n",
@@ -649,7 +648,7 @@
     "                                'y': E('input', 'label')\n",
     "                               }),\n",
     "               experiment_directory=EXPERIMENT_DIR_B,\n",
-    "               is_trainable=True)\n",
+    "               is_fittable=True)\n",
     "\n",
     "new_ens_step = Step(name='Ensembler',\n",
     "                transformer=AvgTransformer(),\n",
@@ -658,7 +657,7 @@
     "                                 'y_proba_2': E('RF', 'y_proba')\n",
     "                                }),\n",
     "                experiment_directory=EXPERIMENT_DIR_B,\n",
-    "                is_trainable=True)"
+    "                is_fittable=True)"
    ]
   },
   {
@@ -676,9 +675,8 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "new_ens_step.clean_cache()\n",
-    "new_preds_ens_fit = new_ens_step.fit_transform(data_fit)\n",
-    "new_ens_step.clean_cache()"
+    "new_ens_step.clean_cache_upstream()\n",
+    "new_preds_ens_fit = new_ens_step.fit_transform(data_fit)"
    ]
   },
   {
@@ -694,9 +692,8 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "new_ens_step.clean_cache()\n",
-    "new_preds_ens_val = new_ens_step.transform(data_val)\n",
-    "new_ens_step.clean_cache()"
+    "new_ens_step.clean_cache_upstream()\n",
+    "new_preds_ens_val = new_ens_step.transform(data_val)"
    ]
   },
   {
@@ -705,9 +702,8 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "new_ens_step.clean_cache()\n",
-    "new_preds_ens_test = new_ens_step.transform(data_test)\n",
-    "new_ens_step.clean_cache()"
+    "new_ens_step.clean_cache_upstream()\n",
+    "new_preds_ens_test = new_ens_step.transform(data_test)"
    ]
   },
   {