from bokeh.io import curdoc from bokeh.layouts import column, row from bokeh.models import Slider, Select, ColumnDataSource, Span, Div, Button, LogColorMapper, ColorBar, LogTicker from bokeh.models.tools import CrosshairTool from bokeh.plotting import figure from bokeh.events import Tap from bokeh.transform import log_cmap import pandas as pd from scipy.spatial import ConvexHull from scipy.optimize import curve_fit from time import sleep from utils import * from conversions import * ######################################################################################################################## # Basic dimensions ######################################################################################################################## plot_width = 1200 plot_height = 400 sidebar_width = 400 in_text_plot_width = 800 in_text_plot_height = 300 ######################################################################################################################## # Set up data ######################################################################################################################## df = pd.read_csv("optimal_training/static/loss_vs_compute.csv") loss_keys = [key for key in df.keys() if "loss" in key] losses_per_run = {key: np.array(clean_run(list(zip(df["global_step"], df[key])))) for key in loss_keys} losses_per_run = {k: v for k, v in losses_per_run.items() if len(v) > 5} bounds_per_run = {key: [min(value[:, 0]), max(value[:, 0])] for key, value in losses_per_run.items()} params_per_run = {key: param_count(run) for key, run in losses_per_run.items()} ordered_keys = sorted(losses_per_run, key=lambda x: params_per_run[x]) losses_per_run = [losses_per_run[key] for key in ordered_keys] bounds_per_run = [bounds_per_run[key] for key in ordered_keys] params_per_run = [params_per_run[key] for key in ordered_keys] palette = "Viridis256" color_mapper = LogColorMapper(palette=palette, low=min(params_per_run), high=max(params_per_run)) general_bounds = bounds_per_run[2][0], bounds_per_run[-2][1] print("{:.4e}, {:.4e}".format(general_bounds[0] * day_ratio, general_bounds[1] * day_ratio)) color_list = ["#000000" in params_per_run] # there's a bogus point of small coordinates at position 0 to get the ConvexHull facing the origin # hacky, but it's the syntax here, qhull_options=QG0 means the ConvexHull facing point 0 bounded_points = np.array([(10e8, 3, -1)] + [(a, b, i) for i, run in enumerate(losses_per_run) for a, b in run if general_bounds[0] < a < general_bounds[1]]) all_points = np.array([(a, b, i) for i, run in enumerate(losses_per_run) for a, b in run]) all_hull = ConvexHull(bounded_points[:, :2], qhull_options='QG0') log_points = np.array([(np.log(a), b) for a, b, i in bounded_points]) log_hull = ConvexHull(log_points, qhull_options='QG0') indexed_runs = [np.array([(a, b) for a, b in run]) for run in losses_per_run] ######################################################################################################################## # Set up loss_plot ######################################################################################################################## color_bar = ColorBar(color_mapper=color_mapper, ticker=LogTicker(), label_standoff=12, border_line_color=None, location=(0, 0), title="Num of params") loss_plot = figure(plot_height=plot_height, plot_width=plot_width, title="Validation loss during training for an array of models of different sizes", tools="pan,reset,save,wheel_zoom,tap", active_scroll="wheel_zoom", x_range=[min(all_points[:, 0]) * day_ratio, max(all_points[:, 0]) * day_ratio], y_range=[min(all_points[:, 1]), max(all_points[:, 1])], x_axis_type="log", y_axis_type="log", x_axis_label="Floating-point operations (excluding embeddings & softmax)", y_axis_label="Validation loss on Wikitext-103", output_backend="webgl") loss_plot.add_tools(CrosshairTool(dimensions="width", line_alpha=0.2)) loss_plot.add_layout(color_bar, "left") # for i, run in indexed_runs.items(): # source = ColumnDataSource(data=dict(x=run[:, 0] * day_ratio, y=run[:, 1])) # loss_plot.line('x', 'y', source=source, line_width=1, line_alpha=0.6, color=color_list[i]) # loss_plot.scatter('x', 'y', source=source, line_width=1, line_alpha=0.6, color=color_list[i]) source = ColumnDataSource(data=dict( xs=[run[:, 0] * day_ratio for run in indexed_runs], # x coords for each line (list of lists) ys=[run[:, 1] for run in indexed_runs], # y coords for each line (list of lists) params=params_per_run # data to use for colormapping )) loss_plot.multi_line('xs', 'ys', source=source, color=log_cmap('params', palette, min(params_per_run), max(params_per_run))) source = ColumnDataSource(data=dict( x=[compute for run in indexed_runs for compute in run[:, 0] * day_ratio], # x coords for each line (list of lists) y=[loss for run in indexed_runs for loss in run[:, 1]], # y coords for each line (list of lists) params=[repeated_params for i, params in enumerate(params_per_run) for repeated_params in [params] * len(indexed_runs[i])] # data to use for colormapping )) loss_plot.scatter('x', 'y', source=source, color=log_cmap('params', palette, min(params_per_run), max(params_per_run)), size=3) hull_indices = set(index for pair in all_hull.simplices[all_hull.good] for index in pair) hull_indices = sorted(hull_indices, key=lambda x: bounded_points[x, 0]) ######################################################################################################################## # Fit frontier ######################################################################################################################## hull_points = np.array([bounded_points[index] for index in hull_indices]) loss_popt, loss_pcov = curve_fit(loss_fit, hull_points[:, 0], hull_points[:, 1]) a, b, c = loss_popt print(a, b, c) display_abscisses = np.array([min(all_points[:, 0]) / 1.25] + sorted(list(all_points[:, 0])) + [max(all_points[:, 0]) * 1.25]) source = ColumnDataSource( data=dict(x=sorted(display_abscisses * day_ratio), y=loss_fit(sorted(display_abscisses), *loss_popt))) loss_plot.line('x', 'y', source=source, line_width=1, line_alpha=0.8, color="red") ######################################################################################################################## # Set up param_plot ######################################################################################################################## param_plot = figure(plot_height=plot_height, plot_width=plot_width, title="Optimal number of non-embedding parameters per floating-point operations budget", tools="pan,reset,save,wheel_zoom,tap", active_scroll="wheel_zoom", x_range=loss_plot.x_range, y_range=[min(params_per_run), max(params_per_run)], x_axis_type="log", y_axis_type="log", x_axis_label="Floating-point operations (excluding embeddings & softmax)", y_axis_label="Optimal number of non-embedding parameters", output_backend="webgl") param_plot.add_tools(CrosshairTool(dimensions="width", line_alpha=0.2)) param_plot.add_layout(color_bar, "left") logspace_points = convert_to_logspace(bounded_points, *loss_popt) logspace_losses_per_run = [convert_to_logspace(run, *loss_popt) for run in losses_per_run] passing_points = [] for run_index, log_run in enumerate(logspace_losses_per_run): current_point = None passed = False difference = log_run[:, 1] - log_run[:, 0] passing_points.append(np.argmax(difference)) compute_at_passing_points = np.array([(losses_per_run[i][passing_point, 0], params_per_run[i]) for i, passing_point in enumerate(passing_points)]) compute_at_hull = np.array([(losses_per_run[i][passing_point, 0], params_per_run[i]) for i, passing_point in enumerate(passing_points) if i in set(hull_points[:, 2])]) run_indices_at_hull = [i for i, passing_point in enumerate(passing_points) if i in set(hull_points[:, 2])] param_popt, param_pcov = curve_fit(param_fit, compute_at_hull[:, 0], np.log(compute_at_hull[:, 1])) d, e, f = param_popt source = ColumnDataSource(data=dict(x=compute_at_hull[:, 0] * day_ratio, y=compute_at_hull[:, 1], params=[params for i, params in enumerate(params_per_run) if i in set(hull_points[:, 2])])) param_plot.scatter('x', 'y', source=source, color=log_cmap('params', palette, min(params_per_run), max(params_per_run))) display_abscisses = np.array([min(compute_at_hull[:, 0]) / 1.25] + sorted(list(compute_at_hull[:, 0])) + [max(compute_at_hull[:, 0]) * 1.25]) source = ColumnDataSource(data=dict(x=display_abscisses * day_ratio, y=safe_flo_to_param(display_abscisses, d, e, f))) param_plot.line('x', 'y', source=source, line_width=1, line_alpha=0.8, color="orange") ######################################################################################################################## # Set up widgets ######################################################################################################################## hours_end = 24 hours_initial = 3.23 gpu_dropdown = Select(title="GPU", options=["V100", "P100", "P4", "K80", ], value="V100", width=sidebar_width, sizing_mode="stretch_width") amp_mode_dropdown = Select(title="AMP mode", options=["O0", "O1", "O2"], value="O0", width=sidebar_width, sizing_mode="stretch_width") tipping_width = tipping_point(gpu_dropdown.value, amp_mode_dropdown.value, param_popt) tip = {} update_tip(tip, tipping_width, gpu_dropdown.value, amp_mode_dropdown.value, loss_popt, param_popt) hours_slider = Slider(title="Wall time (hours)", value=hours_initial, start=tip["hours"], end=hours_end, step=1 / 100, width=sidebar_width, sizing_mode="stretch_width") dollars_slider = Slider(title="Budget (dollars)", value=hours_to_dollars(hours_initial, gpu_dropdown.value), start=dollars_to_hours(tip["hours"], gpu_dropdown.value), end=hours_to_dollars(hours_end, gpu_dropdown.value), step=1 / 100, width=sidebar_width, sizing_mode="stretch_width") input_buffer = Div(text="", width=sidebar_width, height=10, style={"display": "block", "margin": "0 auto", "width": f"{sidebar_width}px", "text-align": 'center'}) top_sidebar_div_style = {"display": "block", "margin": "0 auto", 'font-size': "125%", "width": f"{sidebar_width}px", "text-align": 'center'} energy_text = Div(text=energy_fill(hours_to_kWh(hours_slider.value, gpu_dropdown.value), hours_to_co2(hours_slider.value, gpu_dropdown.value)), width=sidebar_width, height=45, style=top_sidebar_div_style) slider_moves = {"hours": 0, "dollars": 0, "kWh": 0, "co2": 0} n_sliders = len(slider_moves) width = hours_to_width(hours_slider.value, gpu_dropdown.value, amp_mode_dropdown.value, param_popt) flo = width_to_flo(width, *param_popt) optimal_params = safe_flo_to_param(flo / 24 / 3600, *param_popt) final_loss = loss_fit(flo / 24 / 3600, *loss_popt) example_shape = {} example_shape['example_depth'], example_shape['example_width'] = optimal_model_shape(width, optimal_params) example_shape['alternate_depth'], example_shape['alternate_width'] = alternate_model_shape(width, optimal_params) flo_line = Span(location=flo, line_alpha=0.7, dimension='height', line_color='purple', line_dash='dashed', line_width=1) loss_line = Span(location=final_loss, line_alpha=0.7, dimension='width', line_color='red', line_dash='dashed', line_width=1) param_line = Span(location=optimal_params, line_alpha=0.7, dimension='width', line_color='orange', line_dash='dashed', line_width=1) loss_plot.add_layout(flo_line) loss_plot.add_layout(loss_line) param_plot.add_layout(flo_line) param_plot.add_layout(param_line) sidebar_div_style = {"display": "block", "margin": "0 auto", "width": f"{sidebar_width}px", "text-align": 'center'} big_sidebar_div_style = {"display": "block", "margin": "0 auto", "width": f"{sidebar_width}px", "text-align": 'center', 'font-size': "200%", 'font-weight': "bold"} static_loss_text = Div(text="Expected wt-103 validation loss:", width=sidebar_width, height=10, style=sidebar_div_style) optimal_loss_text = Div(text="{:.2f}".format(final_loss), width=sidebar_width, height=45, style={"display": "block", "margin": "0 auto", 'font-size': "200%", 'font-weight': "bold", "width": f"{sidebar_width}px", "text-align": 'center'}) static_param_text = Div(text="Optimal number of non-embedding parameters:", width=sidebar_width, height=10, style=sidebar_div_style) optimal_param_text = Div(text="{:.2e}".format(optimal_params), width=sidebar_width, height=45, style=big_sidebar_div_style) static_shape_text = Div(text="For example, this could be a model of", width=sidebar_width, height=10, style=sidebar_div_style) optimal_shape_text = Div(text=f"{example_shape['example_depth']} layers of {example_shape['example_width']} dimensions", width=sidebar_width, height=30, style=big_sidebar_div_style) static_altshape_text = Div(text="Or a model of", width=sidebar_width, height=10, style=sidebar_div_style) optimal_altshape_text = Div( text=f"{example_shape['alternate_depth']} layers of {example_shape['alternate_width']} dimensions", width=sidebar_width, height=30, style=big_sidebar_div_style) def compare_and_update(width): if width >= tip["width"]: update_width(width) hours = width_to_hours(width, gpu_dropdown.value, amp_mode_dropdown.value, param_popt) hours_slider.value = hours else: width = min(tip["width"], width + 5) update_width(width) compare_and_update(width) def update_width(width): flo = width_to_flo(width, *param_popt) flo_line.location = flo optimal_params = safe_flo_to_param(flo / 24 / 3600, *param_popt) final_loss = loss_fit(flo / 24 / 3600, *loss_popt) loss_line.location = final_loss param_line.location = optimal_params example_shape['example_depth'], example_shape['example_width'] = optimal_model_shape(width, optimal_params) example_shape['alternate_depth'], example_shape['alternate_width'] = alternate_model_shape(width, optimal_params) optimal_shape_text.text = f"{example_shape['example_depth']} layers of {example_shape['example_width']} dimensions" optimal_altshape_text.text = f"{example_shape['alternate_depth']} layers of {example_shape['alternate_width']} dimensions" optimal_param_text.text = "{:.2e}".format(optimal_params) optimal_loss_text.text = "{:.2f}".format(final_loss) def hours_update(attrname, old, new): slider_moves["hours"] += 1 # if hours was the first updated slider if sum(slider_moves.values()) <= n_sliders * slider_moves["hours"] - n_sliders + 1: dollars_slider.value = hours_to_dollars(hours_slider.value, gpu_dropdown.value) energy_text.text = energy_fill(hours_to_kWh(hours_slider.value, gpu_dropdown.value), hours_to_co2(hours_slider.value, gpu_dropdown.value)) width = hours_to_width(hours_slider.value, gpu_dropdown.value, amp_mode_dropdown.value, param_popt) update_width(width) def dollars_update(attrname, old, new): slider_moves["dollars"] += 1 # if hours was the first updated slider if sum(slider_moves.values()) <= n_sliders * slider_moves["dollars"] - n_sliders + 1: hours_slider.value = dollars_to_hours(dollars_slider.value, gpu_dropdown.value) energy_text.text = energy_fill(hours_to_kWh(hours_slider.value, gpu_dropdown.value), hours_to_co2(hours_slider.value, gpu_dropdown.value)) def gpu_update(attrname, old, new): update_tip(tip, tipping_point(gpu_dropdown.value, amp_mode_dropdown.value, param_popt), gpu_dropdown.value, amp_mode_dropdown.value, loss_popt, param_popt) hours_slider.start = tip["hours"] dollars_slider.start = hours_to_dollars(tip["hours"], gpu_dropdown.value) if dollars_to_hours(dollars_slider.value, gpu_dropdown.value) == hours_slider.value: width = hours_to_width(hours_slider.value, gpu_dropdown.value, amp_mode_dropdown.value, param_popt) compare_and_update(width) else: dollars_slider.end = hours_to_dollars(hours_end, new) hours_slider.value = dollars_to_hours(dollars_slider.value, gpu_dropdown.value) energy_text.text = energy_fill(hours_to_kWh(hours_slider.value, gpu_dropdown.value), hours_to_co2(hours_slider.value, gpu_dropdown.value)) def amp_update(attrname, old, new): update_tip(tip, tipping_point(gpu_dropdown.value, amp_mode_dropdown.value, param_popt), gpu_dropdown.value, amp_mode_dropdown.value, loss_popt, param_popt) width = hours_to_width(hours_slider.value, gpu_dropdown.value, amp_mode_dropdown.value, param_popt) hours_slider.start = tip["hours"] dollars_slider.start = hours_to_dollars(tip["hours"], gpu_dropdown.value) compare_and_update(width) energy_text.text = energy_fill(hours_to_kWh(hours_slider.value, gpu_dropdown.value), hours_to_co2(hours_slider.value, gpu_dropdown.value)) def loss_tap(event): _, loss = event.x, event.y flo = loss_to_flo(loss, *loss_popt) param_number = safe_flo_to_param(flo, *param_popt) width = param_to_width(param_number) compare_and_update(width) loss_plot.on_event(Tap, loss_tap) def param_tap(event): _, param_number = event.x, event.y width = param_to_width(param_number) hours = width_to_hours(width, gpu_dropdown.value, amp_mode_dropdown.value, param_popt) hours_slider.value = hours param_plot.on_event(Tap, param_tap) hours_slider.on_change('value', hours_update) dollars_slider.on_change('value', dollars_update) gpu_dropdown.on_change("value", gpu_update) amp_mode_dropdown.on_change("value", amp_update) ######################################################################################################################## # Buttons ######################################################################################################################## def on_optimal_click(): code_box.text = hf_code(example_shape['example_width'], example_shape['example_depth']) def on_alternate_click(): code_box.text = hf_code(example_shape['alternate_width'], example_shape['alternate_depth']) input_text = Div(text="Choose a GPU, AMP mode, and budget:", width=sidebar_width, height=30, style={"display": "block", "margin": "0 auto", 'font-size': "125%", 'font-weight': "bold", "width": f"{sidebar_width}px", "text-align": 'center'}) initialize_optimal = Button(width=175, label="Initialize in 🤗transformers!") initialize_optimal.align = "center" initialize_optimal.on_click(on_optimal_click) results_buffer = Div(text="", width=sidebar_width, height=5, style=sidebar_div_style) initialize_alternate = Button(width=175, label="Initialize in 🤗transformers!") initialize_alternate.align = "center" initialize_alternate.on_click(on_alternate_click) code_box_style = {"display": "block", "margin": "0 auto", "width": f"{sidebar_width + plot_width}px", "text-align": 'center', "white-space": "pre-wrap", "background": "#f4f4f4", "border": "1px solid #ddd", "border-left": "3px solid #f36d33", "color": "#666", "page-break-inside": "avoid", "font-family": "monospace", "font-size": "15px", "line-height": "1.6", "max-width": "100%", "overflow": "hidden", "min-height": "30px", "word-wrap": "break-word"} code_box = Div(text="Find the right model for you with the curves and sliders then click the buttons to display the " "corresponding 🤗transformers code here!", width=sidebar_width + plot_width, style=code_box_style, sizing_mode="scale_width") code_box.align = "center" ######################################################################################################################## # Add write-up text ######################################################################################################################## text_width = "800px" main_text_style = {"min-height": "100px", "overflow": "hidden", "display": "block", "margin": "auto", "width": text_width, "font-size": "18px"} formula_img_style_1 = {"min-height": "25px", "display": "block", "margin": "0 auto", "width": text_width, "height": "auto", "max-width": "100%", "max-height": "100%"} formula_img_style_2 = {"min-height": "50px", "display": "block", "margin": "0 auto", "width": text_width, "height": "auto", "max-width": "100%", "max-height": "100%"} text_1 = Div(text=md1, style=main_text_style) text_2 = Div(text=md2, style=main_text_style) text_3 = Div(text=md3, style=main_text_style) text_4 = Div(text=md4, style=main_text_style) ######################################################################################################################## # Loss plot in write-up ######################################################################################################################## in_text_loss_plot = figure(plot_height=in_text_plot_height, plot_width=in_text_plot_width, title="Validation loss during training for an array of models of different sizes", tools="pan,reset,save,wheel_zoom,tap", active_scroll="wheel_zoom", x_range=[min(all_points[:, 0]) * day_ratio, max(all_points[:, 0]) * day_ratio], y_range=[min(all_points[:, 1]), max(all_points[:, 1])], x_axis_type="log", y_axis_type="log", x_axis_label="Floating-point operations (excluding embeddings & softmax)", y_axis_label="Validation loss on Wikitext-103", output_backend="webgl") in_text_loss_plot.add_layout(color_bar, "left") in_text_loss_plot.align = "center" source = ColumnDataSource(data=dict( xs=[run[:, 0] * day_ratio for run in indexed_runs], # x coords for each line (list of lists) ys=[run[:, 1] for run in indexed_runs], # y coords for each line (list of lists) params=params_per_run # data to use for colormapping )) in_text_loss_plot.multi_line('xs', 'ys', source=source, color=log_cmap('params', palette, min(params_per_run), max(params_per_run))) source = ColumnDataSource(data=dict( x=[compute for run in indexed_runs for compute in run[:, 0] * day_ratio], # x coords for each line (list of lists) y=[loss for run in indexed_runs for loss in run[:, 1]], # y coords for each line (list of lists) params=[repeated_params for i, params in enumerate(params_per_run) for repeated_params in [params] * len(indexed_runs[i])] # data to use for colormapping )) in_text_loss_plot.scatter('x', 'y', source=source, color=log_cmap('params', palette, min(params_per_run), max(params_per_run)), size=3) # for i, run in indexed_runs.items(): # source = ColumnDataSource(data=dict(x=run[:, 0] * day_ratio, y=run[:, 1])) # in_text_loss_plot.line('x', 'y', source=source, line_width=1, line_alpha=0.6, color=color_list[i]) # in_text_loss_plot.scatter('x', 'y', source=source, line_width=1, line_alpha=0.6, color=color_list[i]) in_text_param_plot = figure(plot_height=in_text_plot_height, plot_width=in_text_plot_width, title="Optimal number of non-embedding parameters per floating-point operations budget", tools="pan,reset,save,wheel_zoom,tap", active_scroll="wheel_zoom", x_range=in_text_loss_plot.x_range, y_range=[min(params_per_run), max(params_per_run)], x_axis_type="log", y_axis_type="log", x_axis_label="Floating-point operations (excluding embeddings & softmax)", y_axis_label="Optimal number of non-embedding parameters", output_backend="webgl") in_text_param_plot.add_layout(color_bar, "left") in_text_param_plot.align = "center" # for i, run_apex in enumerate(compute_at_hull): # source = ColumnDataSource(data=dict(x=[compute_at_hull[i, 0] * day_ratio], y=[compute_at_hull[i, 1]])) # in_text_param_plot.scatter('x', 'y', source=source, color=color_list[run_indices_at_hull[i]]) source = ColumnDataSource(data=dict(x=compute_at_hull[:, 0] * day_ratio, y=compute_at_hull[:, 1], params=[params for i, params in enumerate(params_per_run) if i in set(hull_points[:, 2])])) in_text_param_plot.scatter('x', 'y', source=source, color=log_cmap('params', palette, min(params_per_run), max(params_per_run))) training_button = Button(width=175, label="Fit!") training_button.align = "center" fit_button = Button(width=175, label="Fit!") fit_button.align = "center" def on_train_click(): display_abscisses = np.array([min(all_points[:, 0]) / 1.25] + sorted(list(all_points[:, 0])) + [max(all_points[:, 0]) * 1.25]) source = ColumnDataSource( data=dict(x=sorted(display_abscisses * day_ratio), y=loss_fit(sorted(display_abscisses), *loss_popt))) in_text_loss_plot.line('x', 'y', source=source, line_width=1, line_alpha=1, color="red") def on_fit_click(): display_abscisses = np.array([min(compute_at_hull[:, 0]) / 1.25] + sorted(list(compute_at_hull[:, 0])) + [max(compute_at_hull[:, 0]) * 1.25]) source = ColumnDataSource(data=dict(x=display_abscisses * day_ratio, y=safe_flo_to_param(display_abscisses, d, e, f))) in_text_param_plot.line('x', 'y', source=source, line_width=1, line_alpha=0.8, color="orange") training_button.on_click(on_train_click) fit_button.on_click(on_fit_click) before_text = column(text_1, training_button, in_text_loss_plot, text_2, fit_button, in_text_param_plot, text_3) after_text = column(text_4) ######################################################################################################################## # Set up layouts and add to document ######################################################################################################################## inputs = column(input_text, gpu_dropdown, amp_mode_dropdown, hours_slider, dollars_slider, input_buffer, energy_text, sizing_mode="scale_width", width=sidebar_width, height=plot_height) results = column(static_loss_text, optimal_loss_text, static_param_text, optimal_param_text, static_shape_text, optimal_shape_text, initialize_optimal, results_buffer, static_altshape_text, optimal_altshape_text, initialize_alternate, sizing_mode="scale_width", width=sidebar_width, height=plot_height) # app = column(row(inputs, loss_plot, sizing_mode="scale_width"), row(results, param_plot, sizing_mode="scale_width"), # code_box, sizing_mode="scale_width") app = column(row(column(inputs, results, sizing_mode="fixed"), column(loss_plot, param_plot, sizing_mode="stretch_width", )), code_box, sizing_mode="scale_width") before_text.align = "center" app.align = "center" after_text.align = "center" main_body = column(before_text, app, after_text, sizing_mode="scale_width") curdoc().add_root(main_body) curdoc().title = "How big should my language model be ?"