"""C.2 Branchability: Hidden Maze. Task (paper, verbatim protocol): a randomly generated rooted tree of maximum depth D; BFS generation samples 0..N children per room at depth < D; trees that reach depth D are retained; the treasure sits at a uniformly sampled deepest leaf. Room/exit IDs are opaque. A worker sees only its current room, its visible exits, the exit back to the preceding room, and dead-end/treasure flags. Every move through a visible exit costs one step, including retraces. Treatments (previous memory read-only in all): flat - memory/paths.jsonl logs all earlier moves; no saved state is restorable; every worker starts at the entrance. unstructured - memory/nodes/ stores one endpoint file per completed trajectory; a worker can copy one to current_state.json but its prompt does not mention this possibility. branch_native - memory/ is a tree of checkpoint directories beneath the endpoint they resumed; the prompt explicitly instructs the worker to inspect the tree, select an endpoint and restore its checkpoint.json before continuing. Restoring an endpoint with existing children creates a sibling branch. A checkpoint can be copied to current_state.json only BEFORE the worker's first move; afterwards it follows one continuous trajectory. The harness validates every restore and commits the final state after the episode. Metrics: treasure discovery, steps to treasure, checkpoint restorations, repeated-move fraction (steps whose directed room-exit pair was traversed by an earlier step, across the whole run). Sweeps (paper): depth sweep N=4, D in {4,6,8,10}, (B,k) = (2,6),(3,9),(4,12), (4,15); branching sweep D=6, N in {2,4,6,8}, (B,k)=(3,9). k > D everywhere. """ import json import os import random import shutil import subprocess from agent import run_worker_episode def generate_maze(seed, D, N): """Random rooted tree, BFS generation, 0..N children, must reach depth D.""" rng = random.Random(seed) while True: rooms = {} root = "room000" rooms[root] = {"parent": None, "children": [], "depth": 0} frontier = [root] deepest = [] while frontier: cur = frontier.pop(0) d = rooms[cur]["depth"] if d < D: n = rng.randint(0, N) if n == 0 and d < D and not any( rooms[o]["children"] for o in frontier): n = 1 # keep the tree alive so it can reach depth D for _ in range(n): rid = f"room{len(rooms):03d}_{rng.randrange(100, 999)}" rooms[rid] = {"parent": cur, "children": [], "depth": d + 1} rooms[cur]["children"].append(rid) frontier.append(rid) if d == D: deepest.append(cur) if deepest: # retained only if it reaches depth D break treasure = rng.choice(deepest) rooms[treasure]["treasure"] = True # opaque exit ids: one per directed edge (room -> child), plus back-exits exits = {} def _new_eid(): while True: eid = f"exit{rng.randrange(10000, 99999)}" if eid not in exits: return eid for rid, r in rooms.items(): r["exits"] = {} for child in r["children"]: eid = _new_eid() exits[eid] = {"from": rid, "to": child, "back": False} r["exits"][eid] = child if r["parent"] is not None: eid = _new_eid() exits[eid] = {"from": rid, "to": r["parent"], "back": True} r["exits"][eid] = r["parent"] return {"rooms": rooms, "exits": exits, "root": root, "treasure": treasure, "D": D, "N": N} def room_state(maze, rid): r = maze["rooms"][rid] dead_end = not r["children"] and rid != maze["treasure"] return { "current_room": rid, "visible_exits": sorted(r["exits"].keys()), "treasure_here": rid == maze["treasure"], "dead_end": dead_end, } def save_state_json(path, maze, rid): with open(path, "w") as f: json.dump(room_state(maze, rid), f, indent=2) def system_prompt(treatment, k, memory_note): restore_txt = "" if treatment == "branch_native": restore_txt = """ CHECKPOINT RESTORATION (important): memory/ holds a TREE of checkpoints from earlier workers. Each endpoint directory contains checkpoint.json -- the exact room state a previous worker stopped at. Inspect the tree (ls -R memory/), select an endpoint, and copy its checkpoint.json over your current_state.json BEFORE you make your first move. Restoring a leaf endpoint continues that branch; restoring an endpoint that already has children starts a sibling branch. After your first move you follow one continuous trajectory and cannot restore again. Previous memory is read-only.""" elif treatment == "unstructured": restore_txt = """ MEMORY: memory/nodes/ contains files saved by earlier workers, one per endpoint where a previous worker stopped. This directory is read-only.""" return f"""You are an exploration worker in a hidden maze. THE MAZE: a tree of rooms with opaque IDs. You see only your current room (state in current_state.json): its visible exits, the exit back to the preceding room, and whether the room is a dead end or contains the treasure. A treasure is hidden at a deep leaf. Moving through any exit costs one step, including moves that retrace previously explored routes. TOOLS (reply with exactly one JSON object per turn): {{"tool": "move", "args": {{"exit_id": "", "rationale": ""}}}} - Moves through a visible exit; costs one step; updates current_state.json. {{"tool": "bash", "args": {{"command": ""}}}} - Runs a shell command in your working directory (for notes and reading read-only memory). Costs nothing. {{"tool": "yield_worker", "args": {{"summary": ""}}}} - Ends your episode; your final state is committed for later workers. MOVE BUDGET: exactly {k} moves. {memory_note}{restore_txt} """ def treatment_memory_note(treatment): if treatment == "flat": return ("MEMORY: memory/paths.jsonl records every move made by " "earlier workers on this maze (room, exit, resulting room) " "and is read-only. You always start at the entrance; no " "saved position can be resumed, so reaching a known region " "means physically retracing the route there.") if treatment == "unstructured": return ("MEMORY: memory/nodes/ contains files saved by earlier " "workers (read-only).") if treatment == "branch_native": return ("MEMORY: memory/ holds the checkpoint tree of all earlier " "workers (read-only).") raise ValueError(treatment) def run_worker(client, maze, worker_dir, treatment, k, seed, usage, global_steps, valid_restore_rooms): os.makedirs(worker_dir, exist_ok=True) cur_path = os.path.join(worker_dir, "current_state.json") save_state_json(cur_path, maze, maze["root"]) state = {"room": maze["root"], "moves": 0, "steps_this_worker": [], "found_at": None, "restored": False, "moved": False} def validate_restore(room_id): # a restore is legal only to an endpoint a previous worker actually # committed; workers cannot fabricate states return room_id in valid_restore_rooms def move(args): eid = str(args.get("exit_id", "")) if state["moves"] >= k: return "ERROR: move budget exhausted. Call yield_worker now.", False if state["moved"] is False: # apply and validate any pre-first-move restore BEFORE exit # visibility is checked, so a restored worker moves from its # restored room, not from the entrance try: with open(cur_path) as f: st = json.load(f) rid = st.get("current_room") if rid != state["room"]: if not validate_restore(rid): save_state_json(cur_path, maze, state["room"]) return ("ERROR: invalid restored state; reset to " "entrance."), False state["restored"] = True state["resume_room"] = rid state["room"] = rid except Exception: save_state_json(cur_path, maze, state["room"]) ex = maze["exits"].get(eid) if ex is None or ex["from"] != state["room"]: return (f"ERROR: exit '{eid}' is not visible from your current " "room."), False state["moved"] = True state["moves"] += 1 pair = (state["room"], eid) rep = pair in global_steps global_steps.add(pair) state["room"] = ex["to"] save_state_json(cur_path, maze, state["room"]) if state["room"] == maze["treasure"] and state["found_at"] is None: state["found_at"] = state["moves"] state["steps_this_worker"].append( {"room": pair[0], "exit": eid, "to": state["room"], "repeated": rep}) note = " (you already traversed this pair earlier)" if rep else "" if state["room"] == maze["treasure"]: return json.dumps({"moved_to": state["room"], "treasure_found": True}) + note, False return json.dumps({"moved_to": state["room"]}) + note, False def bash(args): p = subprocess.run(["bash", "-lc", str(args.get("command", ""))], cwd=worker_dir, capture_output=True, text=True, timeout=20) return (p.stdout + p.stderr)[:8000] or "(no output)", False def yield_worker(args): state["summary"] = args.get("summary", "") return "Episode committed.", True tools = {"move": move, "bash": bash, "yield_worker": yield_worker} prompt = system_prompt(treatment, k, treatment_memory_note(treatment)) done = run_worker_episode(prompt, tools, usage=usage, client=client) return state def prepare_memory(run_dir, maze, treatment): mem = os.path.join(run_dir, "memory") if treatment == "flat": os.makedirs(mem, exist_ok=True) open(os.path.join(mem, "paths.jsonl"), "a").close() elif treatment == "unstructured": os.makedirs(os.path.join(mem, "nodes"), exist_ok=True) elif treatment == "branch_native": os.makedirs(os.path.join(mem, "tree", maze["root"]), exist_ok=True) return mem def commit_state(run_dir, maze, treatment, worker_dir, state, worker_i): """Harness commits the worker's final state into the shared memory.""" mem = os.path.join(run_dir, "memory") if treatment == "flat": with open(os.path.join(mem, "paths.jsonl"), "a") as f: for s in state["steps_this_worker"]: f.write(json.dumps(s) + "\n") return rid = state["room"] if treatment == "unstructured": d = os.path.join(mem, "nodes") shutil.copytree(worker_dir, os.path.join(d, f"endpoint_{worker_i}_{rid}")) else: # branch_native: checkpoint as a child of the endpoint it resumed # find the checkpoint dir whose room matches the resume point, else root tree = os.path.join(mem, "tree") parent_dir = _find_endpoint_dir(tree, state.get("resume_room", maze["root"])) d = os.path.join(parent_dir, f"branch_{worker_i}_{rid}") os.makedirs(d, exist_ok=True) shutil.copytree(worker_dir, d, ignore=shutil.ignore_patterns("memory"), dirs_exist_ok=True) with open(os.path.join(d, "checkpoint.json"), "w") as f: json.dump(room_state(maze, rid), f) with open(os.path.join(d, "path.json"), "w") as f: json.dump({"room": rid, "steps": len(state["steps_this_worker"]), "resume_room": state.get("resume_room", maze["root"])}, f) def _find_endpoint_dir(tree, rid): """Locate the checkpoint directory for room rid (BFS), else tree root.""" # a room-named container dir (tree/) wins if it exists: commits # resuming a room with no committed checkpoint yet are siblings there cand = os.path.join(tree, rid) if os.path.isdir(cand): return cand for dirpath, dirnames, _ in os.walk(tree): pf = os.path.join(dirpath, "path.json") if os.path.exists(pf): with open(pf) as f: if json.load(f).get("room") == rid: return dirpath # no checkpoint dir for rid yet: create its room container so sibling # commits on the same fresh endpoint land side by side os.makedirs(cand, exist_ok=True) return cand def run_condition(client, out_root, seed, D, N, B, k, treatment, usage=None): maze = generate_maze(seed, D, N) run_dir = os.path.join(out_root, f"maze_D{D}_N{N}_{treatment}_seed{seed}") os.makedirs(run_dir, exist_ok=True) with open(os.path.join(run_dir, "maze.json"), "w") as f: json.dump({"rooms": {r: {"parent": v["parent"], "children": v["children"], "depth": v["depth"], "treasure": v.get("treasure", False)} for r, v in maze["rooms"].items()}, "exits": maze["exits"], "root": maze["root"], "treasure": maze["treasure"], "D": D, "N": N}, f) prepare_memory(run_dir, maze, treatment) global_steps = set() discovered_at = None restorations = 0 total_steps = 0 repeated_steps = 0 valid_restore_rooms = set() for i in range(B): wdir = os.path.join(run_dir, f"worker_{i}") state = run_worker(client, maze, wdir, treatment, k, seed * 100 + i, usage, global_steps, valid_restore_rooms) total_steps += len(state["steps_this_worker"]) repeated_steps += sum(1 for s in state["steps_this_worker"] if s["repeated"]) restorations += int(state["restored"]) if state["found_at"] is not None and discovered_at is None: discovered_at = total_steps if treatment != "flat": valid_restore_rooms.add(state["room"]) commit_state(run_dir, maze, treatment, wdir, state, i) if treatment != "flat": # previous memory is read-only for later workers subprocess.run(["chmod", "-R", "a-w", os.path.join(run_dir, "memory")], check=False) return {"task": "maze", "seed": seed, "D": D, "N": N, "B": B, "k": k, "treatment": treatment, "discovered": discovered_at is not None, "steps_to_treasure": discovered_at, "total_steps": total_steps, "repeated_fraction": (repeated_steps / total_steps if total_steps else 0.0), "checkpoint_restorations": restorations, "run_dir": run_dir}