Add Makefile + results for MetaMathQA task

These are the first results for the MetaMathQA task and also the first
test of the Makefile used to run these tests.

The Makefile offers the functionality to run individual experiments by
specifying the result you want to have, e.g.
`make results/adalora--llama-3.2-3B-rank32[...].json`. Alternatively
you can simply run `make` for `make all` which runs all experiments
that don't have a result yet or which have outdated configs (comparing
result timestamp and config timestamp).

The results are from the main branch. No errors happened during the run.
There were errors with a compute instance that used a A10G 24GB because
of OOM. L40S with 48GB RAM was fine.

Author: Marian Tietz

method_comparison/MetaMathQA/Makefile

@@ -0,0 +1,88 @@
+# Makefile for running MetaMathQA experiments.
+
+# --- Configuration ---
+PYTHON := python
+RUN_SCRIPT := run.py
+EXPERIMENTS_DIR := experiments
+RESULTS_DIR := results
+
+# --- Automatic Experiment and Result Discovery ---
+
+# 1. Find all experiment directories by looking for adapter_config.json files.
+#    This gives us a list like: experiments/lora/llama-3.2-3B-rank32 ...
+EXPERIMENT_PATHS := $(patsubst %/adapter_config.json,%,$(shell find $(EXPERIMENTS_DIR) -name "adapter_config.json"))
+
+# 2. Define a function to replace all occurrences of a character in a string.
+#    This is needed to replicate the result naming logic from run.py (e.g., "lora/foo" -> "lora-foo").
+#    Usage: $(call replace-all, string, char_to_replace, replacement_char)
+replace-all = $(if $(findstring $(2),$(1)),$(call replace-all,$(subst $(2),$(3),$(1)),$(2),$(3)),$(1))
+
+# 3. Define a function to convert an experiment path to its flat result file path.
+#    e.g., "experiments/lora/llama-3.2-3B-rank32" -> "results/lora-llama-3.2-3B-rank32.json"
+exp_to_res = $(RESULTS_DIR)/$(call replace-all,$(patsubst $(EXPERIMENTS_DIR)/%,%,$(1)),/,-).json
+
+# 4. Generate the list of all target result files we want to build.
+RESULT_FILES := $(foreach exp,$(EXPERIMENT_PATHS),$(call exp_to_res,$(exp)))
+
+
+# --- Main Rules ---
+
+# The default 'all' target depends on all possible result files.
+# Running `make` or `make all` will check and run any outdated or missing experiments.
+all: $(RESULT_FILES)
+
+
+# --- Dynamic Rule Generation ---
+
+# This is the core logic. We dynamically generate a specific Makefile rule for each experiment found.
+# This avoids a complex pattern rule and makes the logic clearer.
+define EXPERIMENT_template
+# Input $1: The full experiment path (e.g., experiments/lora/llama-3.2-3B-rank32)
+
+# Define the rule:
+# The target is the result file (e.g., results/lora-llama-3.2-3B-rank32.json).
+# The dependencies are its config files, code changes need to be audited manually since they can
+# vary in degree of importance. Note that we explicitly ignore when the script fails to run
+# so that the other experiments still have a chance to run.
+$(call exp_to_res,$(1)): $(1)/adapter_config.json $(wildcard $(1)/training_params.json)
+	@echo "---"
+	@echo "Running experiment: $(1)"
+	-$(PYTHON) $(RUN_SCRIPT) -v $(1)
+	@echo "Finished: $$@"
+	@echo "---"
+
+endef
+
+# This command iterates through every found experiment path and evaluates the template,
+# effectively stamping out a unique, explicit rule for each one.
+$(foreach exp_path,$(EXPERIMENT_PATHS),$(eval $(call EXPERIMENT_template,$(exp_path))))
+
+
+# --- Utility Rules ---
+
+.PHONY: all clean list dump_rules
+
+# The 'clean' rule removes all generated results.
+clean:
+	@echo "Cleaning results directory..."
+	@([ -n "$(wildcard $(RESULTS_DIR)/*.json)" ] && rm $(RESULTS_DIR)/*.json) || exit 0
+
+# The 'list' rule is for debugging. It shows the discovered experiments
+# and the result files the Makefile expects to create for them.
+list:
+	@echo "Discovered experiment configurations:"
+	@$(foreach exp,$(EXPERIMENT_PATHS),echo "  - $(exp)/adapter_config.json";)
+	@echo "\nTarget result files:"
+	@$(foreach res,$(RESULT_FILES),echo "  - $(res)";)
+
+# The 'dump_rules' rule is for debugging. It dumps all dynamically defined rules.
+define newline
+
+
+endef
+define DUMPED_RULES
+	$(foreach exp_path,$(EXPERIMENT_PATHS),$(call EXPERIMENT_template,$(exp_path)))
+endef
+
+dump_rules:
+	@echo -e "$(subst $(newline),\n,${DUMPED_RULES})"