diff --git a/MARBLE/default_params.yaml b/MARBLE/default_params.yaml
index 5110b4d9..9acd8fd7 100644
--- a/MARBLE/default_params.yaml
+++ b/MARBLE/default_params.yaml
@@ -1,12 +1,12 @@
 #training parameters
-epochs : 20, # optimisation epochs
+epochs : 100 # optimisation epochs
 batch_size : 64 # batch size
 lr: 0.01 # learning rate
 momentum: 0.9
 
 #manifold/signal parameters
 order: 2 # order to which to compute the directional derivatives
-inner_product_features: True
+inner_product_features: False
 diffusion: False
 frac_sampled_nb: -1 # fraction of neighbours to sample for gradient computation (if -1 then all neighbours)
 include_positions: False # include positions as features (warning: this is untested!)
@@ -18,9 +18,9 @@ hidden_channels: [16] # number of hidden channels
 out_channels: 3 # number of output channels (if null, then =hidden_channels)
 bias: True # learn bias parameters in MLP
 vec_norm: False
-batch_norm: False # batch normalisation
+batch_norm: True # batch normalisation
 emb_norm: False # spherical output
-skip_connections: True # use skips in MLP 
+skip_connections: False # use skips in MLP 
 
 # other params
 seed: 0 # seed for reproducibility
diff --git a/MARBLE/geometry.py b/MARBLE/geometry.py
index 06c49342..1a0ea4a8 100644
--- a/MARBLE/geometry.py
+++ b/MARBLE/geometry.py
@@ -18,7 +18,6 @@
 from MARBLE.lib.cknn import cknneighbors_graph  # isort:skip
 from MARBLE import utils  # isort:skip
 
-
 def furthest_point_sampling(x, N=None, stop_crit=0.0, start_idx=0):
     """A greedy O(N^2) algorithm to do furthest points sampling
 
@@ -457,7 +456,9 @@ def compute_laplacian(data, normalization="rw"):
         num_nodes=data.num_nodes
     )
 
-    return PyGu.to_dense_adj(edge_index, edge_attr=edge_attr).squeeze()
+    # return PyGu.to_dense_adj(edge_index, edge_attr=edge_attr).squeeze()
+    n = len(data.x)
+    return sp.coo_array((edge_attr, (edge_index[0], edge_index[1])), shape=(n, n))
 
 
 def compute_connection_laplacian(data, R, normalization="rw"):
@@ -670,11 +671,12 @@ def vector_diffusion(x, t, method="spectral", Lc=None):
     return out
 
 
-def compute_eigendecomposition(A, eps=1e-8):
+def compute_eigendecomposition(A, k=50, eps=1e-8):
     """Eigendecomposition of a square matrix A.
 
     Args:
         A: square matrix A
+        k: number of eigenvectors
         eps: small error term
 
     Returns:
@@ -683,15 +685,22 @@ def compute_eigendecomposition(A, eps=1e-8):
     """
     if A is None:
         return None
-
-    A = A.to_dense()
+    
+    if k >= A.shape[0]:
+        k = None
 
     # Compute the eigenbasis
     failcount = 0
     while True:
         try:
-            evals, evecs = torch.linalg.eigh(A)
+            if k is None:
+                evals, evecs = torch.linalg.eigh(A)
+            else:
+                evals, evecs = sp.linalg.eigsh(A, k=k, which="SM")
+                evals, evecs = torch.tensor(evals), torch.tensor(evecs)
+                
             evals = torch.clamp(evals, min=0.0)
+            evecs *= np.sqrt(len(evecs))
 
             break
         except Exception as e:  # pylint: disable=broad-exception-caught
@@ -702,4 +711,4 @@ def compute_eigendecomposition(A, eps=1e-8):
             print("--- decomp failed; adding eps ===> count: " + str(failcount))
             A += torch.eye(A.shape[0]) * (eps * 10 ** (failcount - 1))
 
-    return evals, evecs
+    return evals, evecs
\ No newline at end of file
diff --git a/MARBLE/main.py b/MARBLE/main.py
index 90903bc4..cf5ee3a9 100644
--- a/MARBLE/main.py
+++ b/MARBLE/main.py
@@ -18,6 +18,7 @@
 from MARBLE import layers
 from MARBLE import utils
 
+import warnings
 
 class net(nn.Module):
     """MARBLE neural network.
@@ -60,16 +61,17 @@ def __init__(self, data, loadpath=None, params=None, verbose=True):
         """
         super().__init__()
 
+        device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
+        
         if loadpath is not None:
             if Path(loadpath).is_dir():
                 loadpath = max(glob.glob(f"{loadpath}/best_model*"))
-            self.params = torch.load(loadpath, map_location=torch.device('cuda' if torch.cuda.is_available() else 'cpu'))["params"]
+            self.params = torch.load(loadpath, map_location=device)["params"]
         else:
             if params is not None:
-                if isinstance(params, str) and Path(params).exists():
-                    with open(params, "rb") as f:
-                        params = yaml.safe_load(f)
                 self.params = params
+            else: 
+                self.params = {}
 
         self._epoch = 0  # to resume optimisation
         self.parse_parameters(data)
@@ -217,11 +219,7 @@ def setup_layers(self):
                 bias=self.params["bias"],
             )        
         
-    
         
-
-        
-
     def forward(self, data, n_id, adjs=None):
         """Forward pass.
         Messages are passed to a set target nodes (current batch) from source
@@ -289,8 +287,12 @@ def forward(self, data, n_id, adjs=None):
             emb = F.normalize(emb)   
         
         return emb, mask[: size[1]]
+    
+    def evaluate(self, data): 
+        warnings.warn("MARBLE.evaluate() is deprecated. Use MARBLE.transform() instead.")
+        self.transform(data)
 
-    def evaluate(self, data):
+    def transform(self, data):
         """Forward pass @ evaluation (no minibatches)"""
         with torch.no_grad():
             size = (data.x.shape[0], data.x.shape[0])
@@ -345,8 +347,13 @@ def batch_loss(self, data, loader, train=False, verbose=False, optimizer=None):
         self.eval()
 
         return cum_loss / len(loader), optimizer
-
+    
     def run_training(self, data, outdir=None, verbose=False):
+        warnings.warn("MARBLE.run_training() is deprecated. Use MARBLE.fit() instead.")
+
+        self.fit(data, outdir=outdir, verbose=verbose)
+
+    def fit(self, data, outdir=None, verbose=False):
         """Network training.
 
         Args:
diff --git a/MARBLE/plotting.py b/MARBLE/plotting.py
index 834337fb..86691ff0 100644
--- a/MARBLE/plotting.py
+++ b/MARBLE/plotting.py
@@ -131,8 +131,7 @@ def histograms(data, titles=None, col=2, figsize=(10, 10)):
     """
     assert hasattr(
         data, "clusters"
-    ), "No clusters found. First, run \
-        geometry.cluster(data) or postprocessing(data)!"
+    ), "No clusters found. First, run postprocessing.cluster(data)!"
 
     labels, s = data.clusters["labels"], data.clusters["slices"]
     n_slices = len(s) - 1
@@ -245,9 +244,9 @@ def embedding(
                         ax.scatter(emb_[t, 0], emb_[t, 1], emb_[t, 2], c=cgrad, alpha=alpha, s=s, label=title)  
         else:
             if dim == 2:
-                ax.scatter(emb_[:, 0], emb_[:, 1], c=c_, alpha=alpha, s=s, label=title)
+                ax.scatter(emb_[:, 0], emb_[:, 1], color=c_, alpha=alpha, s=s, label=title)
             elif dim == 3:
-                ax.scatter(emb_[:, 0], emb_[:, 1], emb_[:, 2], c=c, alpha=alpha, s=s, label=title)
+                ax.scatter(emb_[:, 0], emb_[:, 1], emb_[:, 2], color=c_, alpha=alpha, s=s, label=title)
 
     if dim == 2:
         if hasattr(data, "clusters") and clusters_visible:
@@ -296,8 +295,7 @@ def neighbourhoods(
 
     assert hasattr(
         data, "clusters"
-    ), "No clusters found. First, run \
-        geometry.cluster(data) or postprocessing(data)!"
+    ), "No clusters found. First, run postprocessing.cluster(data)!"
 
     vector = data.x.shape[1] > 1
     clusters = data.clusters
diff --git a/MARBLE/postprocessing.py b/MARBLE/postprocessing.py
index 3011ad8b..8084635f 100644
--- a/MARBLE/postprocessing.py
+++ b/MARBLE/postprocessing.py
@@ -4,6 +4,21 @@
 from MARBLE import geometry as g
 
 
+def cluster(data, cluster_typ="kmeans", n_clusters=15, seed=0):
+    
+    clusters = g.cluster(data.emb, cluster_typ, n_clusters, seed)
+    clusters = g.relabel_by_proximity(clusters)
+    
+    clusters["slices"] = data._slice_dict["x"]  # pylint: disable=protected-access
+
+    if data.number_of_resamples > 1:
+        clusters["slices"] = clusters["slices"][:: data.number_of_resamples]
+        
+    data.clusters = clusters
+    
+    return data
+
+
 def distribution_distances(data, cluster_typ="kmeans", n_clusters=None, seed=0):
     """Return distance between datasets.
 
@@ -18,21 +33,13 @@ def distribution_distances(data, cluster_typ="kmeans", n_clusters=None, seed=0):
 
     if n_clusters is not None:
         # k-means cluster
-        clusters = g.cluster(emb, cluster_typ, n_clusters, seed)
-        clusters = g.relabel_by_proximity(clusters)
-
-        clusters["slices"] = data._slice_dict["x"]  # pylint: disable=protected-access
-
-        if data.number_of_resamples > 1:
-            clusters["slices"] = clusters["slices"][:: data.number_of_resamples]
+        data = cluster(data, cluster_typ, n_clusters, seed)
 
         # compute distances between clusters
         data.dist, data.gamma = g.compute_distribution_distances(
-            clusters=clusters, slices=clusters["slices"]
+            clusters=data.clusters, slices=data.clusters["slices"]
         )
 
-        data.clusters = clusters
-
     else:
         data.emb = emb
         data.dist, _ = g.compute_distribution_distances(
diff --git a/MARBLE/preprocessing.py b/MARBLE/preprocessing.py
index 66deae3e..48c76877 100644
--- a/MARBLE/preprocessing.py
+++ b/MARBLE/preprocessing.py
@@ -1,5 +1,4 @@
-"""Prepare module."""
-import numpy as np
+"""Preprocessing module."""
 import torch
 from torch_geometric.data import Batch
 from torch_geometric.data import Data
@@ -14,16 +13,12 @@ def construct_dataset(
     labels=None,
     mask=None,
     graph_type="cknn",
-    k=15,
-    n_geodesic_nb=10,
+    k=20,
+    frac_geodesic_nb=1.5,
     stop_crit=0.0,
     number_of_resamples=1,
-    compute_laplacian=False,
-    compute_connection_laplacian=False,
-    return_spectrum=True,
     var_explained=0.9,
     local_gauges=False,
-    dim_man=None,
     delta=1.0,
 ):
     """Construct PyG dataset from node positions and features.
@@ -34,16 +29,13 @@ def construct_dataset(
         labels: any additional data labels used for plotting only
         graph_type: type of nearest-neighbours graph: cknn (default), knn or radius
         k: number of nearest-neighbours to construct the graph
-        n_geodesic_nb: number of geodesic neighbours to fit the gauges to
-        to map to tangent space
+        frac_geodesic_nb: number of geodesic neighbours to fit the gauges to
+        to map to tangent space k*frac_geodesic_nb
         stop_crit: stopping criterion for furthest point sampling
         number_of_resamples: number of furthest point sampling runs to prevent bias (experimental)
-        compute_laplacian: set to True to compute laplacian
-        compute_connection_laplacian: set to True to compute the connection laplacian
         var_explained: fraction of variance explained by the local gauges
         local_gauges: is True, it will try to compute local gauges if it can (signal dim is > 2,
             embedding dimension is > 2 or dim embedding is not dim of manifold)
-        dim_man: if the manifold dimension is known, it can be set here or it will be estimated
         delta: argument for cknn graph construction to decide the radius for each points.
     """
 
@@ -103,24 +95,15 @@ def construct_dataset(
     return _compute_geometric_objects(
         batch,
         local_gauges=local_gauges,
-        compute_laplacian=compute_laplacian,
-        compute_connection_laplacian=compute_connection_laplacian,
-        n_geodesic_nb=n_geodesic_nb,
+        frac_geodesic_nb=frac_geodesic_nb,
         var_explained=var_explained,
-        dim_man=dim_man,
-        return_spectrum=return_spectrum
     )
 
 
-def _compute_geometric_objects(
-    data,
-    n_geodesic_nb=2.0,
+def _compute_geometric_objects(data,
+    frac_geodesic_nb=2.0,
     var_explained=0.9,
-    return_spectrum=True,
     local_gauges=False,
-    compute_laplacian=False,
-    compute_connection_laplacian=False,
-    dim_man=None,
 ):
     """
     Compute geometric objects used later: local gauges, Levi-Civita connections
@@ -157,7 +140,7 @@ def _compute_geometric_objects(
 
     if local_gauges:
         try:
-            gauges, Sigma = g.compute_gauges(data, n_geodesic_nb=n_geodesic_nb)
+            gauges, Sigma = g.compute_gauges(data, n_geodesic_nb=frac_geodesic_nb)
         except Exception as exc:
             raise Exception(
                 "\nCould not compute gauges (possibly data is too sparse or the \
@@ -166,44 +149,30 @@ def _compute_geometric_objects(
     else:
         gauges = torch.eye(dim_emb).repeat(n, 1, 1)
 
-    # Laplacian
-    if compute_laplacian:
-        L = g.compute_laplacian(data)
-    else:
-        L = None
+    L = g.compute_laplacian(data)
 
     if local_gauges:
-        if not dim_man:
-            dim_man = g.manifold_dimension(Sigma, frac_explained=var_explained)
-        data.dim_man = dim_man
-
-        print(f"\n---- Manifold dimension: {dim_man}")
+        data.dim_man = g.manifold_dimension(Sigma, frac_explained=var_explained)
+        print(f"\n---- Manifold dimension: {data.dim_man}")
 
-        gauges = gauges[:, :, :dim_man]
+        gauges = gauges[:, :, :data.dim_man]
         R = g.compute_connections(data, gauges)
 
         print("\n---- Computing kernels ... ", end="")
         kernels = g.gradient_op(data.pos, data.edge_index, gauges)
-        kernels = [utils.tile_tensor(K, dim_man) for K in kernels]
+        kernels = [utils.tile_tensor(K, data.dim_man) for K in kernels]
         kernels = [K * R for K in kernels]
-        print("Done ")
 
-        if compute_connection_laplacian:
-            Lc = g.compute_connection_laplacian(data, R)
-        else:
-            Lc = None
+        Lc = g.compute_connection_laplacian(data, R)
 
     else:
         print("\n---- Computing kernels ... ", end="")
         kernels = g.gradient_op(data.pos, data.edge_index, gauges)
-        print("Done ")
         Lc = None
 
-    if return_spectrum:
-        print("---- Computing eigendecomposition ... ", end="")
-        L = g.compute_eigendecomposition(L)
-        Lc = g.compute_eigendecomposition(Lc)
-        print("Done ")
+    print("---- Computing eigendecomposition ... ", end="")
+    L = g.compute_eigendecomposition(L)
+    Lc = g.compute_eigendecomposition(Lc)
 
     data.kernels = [
         utils.to_SparseTensor(K.coalesce().indices(), value=K.coalesce().values()) for K in kernels
diff --git a/examples/rat_task/Demo_consistency.ipynb b/examples/rat_hippocampus/Demo_consistency.ipynb
similarity index 100%
rename from examples/rat_task/Demo_consistency.ipynb
rename to examples/rat_hippocampus/Demo_consistency.ipynb
diff --git a/examples/rat_task/Demo_decoding.ipynb b/examples/rat_hippocampus/Demo_decoding.ipynb
similarity index 100%
rename from examples/rat_task/Demo_decoding.ipynb
rename to examples/rat_hippocampus/Demo_decoding.ipynb
diff --git a/examples/rat_task/rat_data.pkl b/examples/rat_hippocampus/rat_data.pkl
similarity index 100%
rename from examples/rat_task/rat_data.pkl
rename to examples/rat_hippocampus/rat_data.pkl
diff --git a/examples/rat_task/rat_utils.py b/examples/rat_hippocampus/rat_utils.py
similarity index 100%
rename from examples/rat_task/rat_utils.py
rename to examples/rat_hippocampus/rat_utils.py
diff --git a/examples/ex_scalar_field_flat_surface.py b/examples/toy_examples/ex_scalar_field_flat_surface.py
similarity index 64%
rename from examples/ex_scalar_field_flat_surface.py
rename to examples/toy_examples/ex_scalar_field_flat_surface.py
index adf3ffb4..4cd0e1fe 100644
--- a/examples/ex_scalar_field_flat_surface.py
+++ b/examples/toy_examples/ex_scalar_field_flat_surface.py
@@ -28,38 +28,35 @@ def main():
     x = [dynamics.sample_2d(n, [[-1, -1], [1, 1]], "random") for i in range(4)]
     y = [f0(x[0]), f1(x[1]), f2(x[2]), f3(x[3])]  # evaluated functions
 
-    # construct PyG data object
-    data = preprocessing.construct_dataset(x, y, graph_type="cknn", k=15)
+    # construct data object
+    data = preprocessing.construct_dataset(x, y)
 
     # train model
     params = {
-        "epochs": 50,  # optimisation epochs
-        "order": 2,  # order of derivatives
-        "hidden_channels": 16,  # number of internal dimensions in MLP
-        "out_channels": 5,
+        "order": 1,  # order of derivatives
         "include_self": False,  # remove feature centers, for testing only, to get the figure in the SI
-        "inner_product_features": False,
     }
 
     model = net(data, params=params)
-    model.run_training(data)
+    model.fit(data)
 
     # evaluate model on data
-    data = model.evaluate(data)
-    n_clusters = 10  # use 15 clusters for simple visualisation
-    data = postprocessing.distribution_distances(data, n_clusters=n_clusters)
+    data = model.transform(data)
+    
+    # embed into 2D for visualisation
+    data = postprocessing.cluster(data, n_clusters=10)
     data = postprocessing.embed_in_2D(data, embed_typ="tsne")
 
     # plot
     titles = ["Constant", "Linear", "Parabola", "Saddle"]
     plotting.fields(data, titles=titles, node_size=20, col=2)
-    # plt.savefig('../results/fields.svg')
+    plt.savefig('fields.png')
     plotting.embedding(data, data.y.numpy(), titles=titles, clusters_visible=True)
-    # plt.savefig('../results/embedding.svg')
+    plt.savefig('embedding.png')
     plotting.histograms(data, titles=titles)
-    # plt.savefig('../results/histogram.svg')
+    plt.savefig('histogram.png')
     plotting.neighbourhoods(data, hops=1, norm=True, figsize=(10, 20))
-    # plt.savefig('../results/neighbourhoods.svg')
+    plt.savefig('neighbourhoods.png')
     plt.show()
 
 
diff --git a/examples/ex_vector_field_curved_surface.py b/examples/toy_examples/ex_vector_field_curved_surface.py
similarity index 76%
rename from examples/ex_vector_field_curved_surface.py
rename to examples/toy_examples/ex_vector_field_curved_surface.py
index fad81da2..08d7bfe0 100644
--- a/examples/ex_vector_field_curved_surface.py
+++ b/examples/toy_examples/ex_vector_field_curved_surface.py
@@ -57,33 +57,29 @@ def main():
 
     # train model
     params = {
-        "epochs": 70,  # optimisation epochs
-        "order": 1,  # first-order derivatives are enough because the vector field have at most first-order features
-        "hidden_channels": 32,  # 16 is enough in this simple example
-        "out_channels": 3,  # 3 is enough in this simple example
+        "order": 1,
         "inner_product_features": True,
     }
 
     model = net(data, params=params)
-    model.run_training(data)
+    model.fit(data)
 
     # evaluate model on data
-    data = model.evaluate(data)
-    n_clusters = 20  # use 15 clusters for simple visualisation
-    data = postprocessing.distribution_distances(data, n_clusters=n_clusters, cluster_typ="kmeans")
+    data = model.transform(data)
+    data = postprocessing.cluster(data)
     data = postprocessing.embed_in_2D(data)
 
     # plot
     titles = ["Linear left", "Linear right", "Vortex right", "Vortex left"]
     # plot gauges in black to show that they 'hug' the manifold surface
     plotting.fields(data, titles=titles, col=2, width=3, scale=10, view=[0, 40], plot_gauges=True)
-    # plt.savefig('../results/fields.svg')
+    plt.savefig('fields.png')
     plotting.embedding(data, data.y.numpy(), titles=titles, clusters_visible=True)
-    # plt.savefig('../results/embedding.svg')
+    plt.savefig('embedding.png')
     plotting.histograms(data, titles=titles)
-    # plt.savefig('../results/histogram.svg')
+    plt.savefig('histogram.png')
     plotting.neighbourhoods(data)
-    # plt.savefig('../results/neighbourhoods.svg')
+    plt.savefig('neighbourhoods.png')
     plt.show()
 
 
diff --git a/examples/ex_vector_field_flat_surface.py b/examples/toy_examples/ex_vector_field_flat_surface.py
similarity index 59%
rename from examples/ex_vector_field_flat_surface.py
rename to examples/toy_examples/ex_vector_field_flat_surface.py
index e785ea63..0095b265 100644
--- a/examples/ex_vector_field_flat_surface.py
+++ b/examples/toy_examples/ex_vector_field_flat_surface.py
@@ -8,11 +8,9 @@
 def f0(x):
     return x * 0 + np.array([-1, -1])
 
-
 def f1(x):
     return x * 0 + np.array([1, 1])
 
-
 def f2(x):
     eps = 1e-1
     norm = np.sqrt((x[:, [0]] + 1) ** 2 + x[:, [1]] ** 2 + eps)
@@ -20,7 +18,6 @@ def f2(x):
     v = -(x[:, [0]] + 1) / norm
     return np.hstack([u, v])
 
-
 def f3(x):
     eps = 1e-1
     norm = np.sqrt((x[:, [0]] - 1) ** 2 + x[:, [1]] ** 2 + eps)
@@ -37,36 +34,28 @@ def main():
     x = [dynamics.sample_2d(n, [[-1, -1], [1, 1]], "random") for i in range(4)]
     y = [f0(x[0]), f1(x[1]), f2(x[2]), f3(x[3])]  # evaluated functions
 
-    # construct PyG data object
-    data = preprocessing.construct_dataset(x, y, graph_type="cknn", k=20)
+    # construct data object
+    data = preprocessing.construct_dataset(x, y)
 
     # train model
-    params = {
-        "epochs": 100,  # optimisation epochs
-        "order": 1,  # first-order derivatives are enough because the vector field have at most first-order features
-        "hidden_channels": 32,  # 16 is enough in this simple example
-        "out_channels": 3,  # 3 is enough in this simple example
-        "inner_product_features": False,  # try changing this to False and see how the embeddings change
-    }
-    model = net(data, params=params)
-    model.run_training(data)
+    model = net(data)
+    model.fit(data)
 
     # evaluate model on data
-    data = model.evaluate(data)
-    n_clusters = 15  # use 15 clusters for simple visualisation
-    data = postprocessing.distribution_distances(data, n_clusters=n_clusters, cluster_typ="kmeans")
+    data = model.transform(data)
+    data = postprocessing.cluster(data)
     data = postprocessing.embed_in_2D(data)
 
     # plot results
     titles = ["Linear left", "Linear right", "Vortex right", "Vortex left"]
     plotting.fields(data, titles=titles, col=2)
-    # plt.savefig('../results/fields.svg')
+    plt.savefig('fields.png')
     plotting.embedding(data, data.y.numpy(), titles=titles, clusters_visible=True)
-    plt.savefig('../results/embedding.svg')
+    plt.savefig('mbedding.png')
     plotting.histograms(data, titles=titles)
-    # plt.savefig('../results/histogram.svg')
+    plt.savefig('histogram.png')
     plotting.neighbourhoods(data)
-    # plt.savefig('../results/neighbourhoods.svg')
+    plt.savefig('neighbourhoods.png')
     plt.show()
 
 
diff --git a/examples/toy_examples/outputs/best_model_20231127-112433.pth b/examples/toy_examples/outputs/best_model_20231127-112433.pth
new file mode 100644
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