Refine README paper references and wording

README.md

@@ -1,6 +1,9 @@
 # SLiCEs
 
-`slices` is a small PyTorch package providing **Structured Linear CDE (SLiCE)** recurrences.
+`slices` is a PyTorch implementation of **Structured Linear CDEs (SLiCEs)** with parallel-in-time computation.
+
+It provides expressive, scalable sequence layers based on the methods developed in
+[*Structured Linear CDEs: Maximally Expressive and Parallel-in-Time Sequence Models*](https://arxiv.org/abs/2505.17761).
 
 ## Mathematical form
 
@@ -36,15 +39,15 @@ Or install from source:
 pip install git+https://github.com/datasig-ac-uk/slices.git
 ```
 
-## What's included
+## Components
 
 - **`SLiCE`**: the core structured recurrence
-- **`SLiCELayer`**: a residual SLiCE layer with RMSNorm + GELU MLP by default
-- **`StackedSLiCE`**: stacks multiple `SLiCELayer`s with an embedding + output projection (supports tokens or continuous inputs)
+- **`SLiCELayer`**: a residual sequence layer built around `SLiCE`, with RMSNorm and a GELU MLP by default
+- **`StackedSLiCE`**: a full sequence model that stacks `SLiCELayer`s with input and output projections for token or continuous inputs
 
 `SLiCE` supports both:
-- **Recurrent execution** (step-by-step update)
-- **Parallel chunked scan execution** using `torch.associative_scan`
+- **Recurrent execution** for step-by-step updates
+- **Parallel chunked scan execution** via `torch.associative_scan`
 
 ## Structured transition matrices
 
@@ -55,7 +58,8 @@ Set:
 - `diagonal_dense=False`
 - `block_size=1`
 
-Then $A(X_i)$ is diagonal, which aligns with the approach used by Mamba (see [here](https://arxiv.org/abs/2505.17761) for more details).
+Then $A(X_i)$ is diagonal, matching the diagonal state-transition setting used by Mamba (as discussed in
+[*Structured Linear CDEs: Maximally Expressive and Parallel-in-Time Sequence Models*](https://arxiv.org/abs/2505.17761)).
 
 ### 2) Block-diagonal
 Set:
@@ -95,8 +99,8 @@ y = layer(x)  # (8, 128, 64)
 print(y.shape)
 ```
 
-Execution mode is configured via constructor arguments (`use_parallel`, `chunk_size`).
-`path_mode` determines how `SLiCE` treats the sequence you pass in.
+Execution mode is controlled by `use_parallel` and `chunk_size`.
+`path_mode` determines whether the input sequence is interpreted as path values or increments.
 
 ### Use `SLiCELayer` as a residual sequence layer
 
@@ -115,21 +119,21 @@ layer = SLiCELayer(
 y = layer(x)  # (4, 256, 64)
 ```
 
-`SLiCELayer` defaults to this structure:
+`SLiCELayer` uses the following default structure:
 - RMSNorm -> SLiCE -> residual
 - RMSNorm -> Linear -> GELU -> Linear -> residual
 
-Optional toggle for the post-norm wrapper:
+To use a post-norm wrapper:
 - `prenorm=False`
 
-Optional toggles for the LayerNorm + single-stage wrapper include:
+Other configuration options include:
 - `norm_type="layernorm"`
 - `ff_style="single"`
 - `ff_mult=1`
 - `ff_activation="glu"` or `ff_activation="tanh"`
 - `dropout_position="output"`
 
-### Stack layers for a full model
+### Build a full model with stacked layers
 
 #### Token sequence mode (`tokens=True`)
 
@@ -182,15 +186,14 @@ y = model(x)  # (16, 100, 10)
 
 ## Training Example
 
-`examples/language_disambiguation.py` is a simple example of training a
-`StackedSLiCE` model end-to-end on a real dataset.
+`examples/language_disambiguation.py` trains a `StackedSLiCE` model end-to-end on a real dataset.
 
-This example:
+The example:
 - uses a real dataset (**wikimedia/wikipedia**, English/French subset) for
   **character-level language disambiguation**
 - trains a compact token-mode `StackedSLiCE` end-to-end
 - evaluates validation accuracy every `--eval-every` training steps
-- prints sample predictions so you can inspect model behaviour quickly
+- prints sample predictions for quick qualitative inspection
 
 To run it, first install the example dependencies:
 
@@ -213,7 +216,7 @@ Useful flags:
 
 ## Benchmarking
 
-To compare recurrent vs parallel throughput across sequence lengths and hidden dimensions:
+To compare recurrent and parallel throughput across sequence lengths and hidden dimensions:
 
 ```bash
 uv run python examples/benchmark_parallel_vs_recurrent.py
@@ -222,7 +225,7 @@ uv run python examples/benchmark_parallel_vs_recurrent.py
 This script:
 - benchmarks all four SLiCE matrix modes (`diagonal`, `block_diagonal`, `diagonal_dense`, `dense`)
 - uses the default value-path semantics unless `path_mode="increments"` is set in code
-- prints timing/speedup tables
+- prints timing and speedup tables
 - saves a combined 3D plot to `examples/images/parallel_vs_recurrent_speedup_3d_all_modes.png`
 
 For plotting in development, install development dependencies (includes `matplotlib`):