Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2606.23672

Teaching LLMs String Matching, Backtracking, and Error Recovery to Deduce Bases and Truth Tables for the Combinatorially Exploding Bit Manipulation Puzzles

Prateek Agnihotri·Sanchit Jain·Prabhat Agnihotri·Aditya Prasad·Shubham Jain
View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper presents our algorithmic innovations for the NVIDIA Nemotron Model Reasoning Challenge, focusing on Bit Manipulation Puzzles. In this task, the objective is to discover a hidden logical rule transforming input binary strings to outputs, then apply it to unseen inputs. Large Language Models (LLMs) notoriously struggle here; traditional methods force them to simulate complex boolean logic and arithmetic, leading to hallucinations. Furthermore, the search space of bitwise operations (combinations of shifts, rotations, and logic gates) suffers from a severe combinatorial explosion. To overcome this computational intractability, we present a novel approach that abandons arithmetic logic entirely in favor of string similarity, structured search, and autonomous error recovery. Our core contributions are: 1. Bases and Truth Table Formulation: We reframe logic-gate deduction into a base-selection task, leveraging string similarity (minimal bit flips) to isolate primitive transformations ("bases") and deduce truth tables without complex arithmetic. 2. Backtracking DFS and Error Recovery: We formalize a search process that tests candidate bases, detects logical collisions across examples, and backtracks upon failure to perform robust error recovery. 3. Bit Tokenization and Interactive Reasoning SFT: We force the tokenizer to encode binary strings as individual single-bit tokens. We use dynamic masking to simulate external oracle feedback, training the model to hypothesize, self-evaluate, and backtrack natively. Evaluated on bit manipulation puzzles, our approach achieved over 96% validation accuracy. This represents the highest performance in this category. These algorithmic and training innovations ultimately earned our team the Best Fine-tuning Method and Best Data/Synthetic Data Method awards in the contest, alongside a 7th Place overall finish on leaderboard.

Explore related subjects

cs.AI

Keep this discovery

BibTeXRIS

Prateek Agnihotri, Sanchit Jain, Prabhat Agnihotri, Aditya Prasad, Shubham Jain. 2026-06-22. Teaching LLMs String Matching, Backtracking, and Error Recovery to Deduce Bases and Truth Tables for the Combinatorially Exploding Bit Manipulation Puzzles. https://arxiv.org/abs/2606.23672

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Decoupling Readiness from Release for Tail-Aware Scheduling of Agentic LLM Workflows

Agentic LLM workflows consist of sequences of model turns interleaved with tool interactions, so their end-to-end completion time depends not only on inference speed but also on when ready turns are released. Most runtimes release each turn immediately upon readiness. Under contention, this eager release policy can accumulate released but unfinished work; once submitted, those turns can no longer be reordered by the workflow-level policy, increasing tail latency. We present a tail-risk-aware turn release scheduling method that jointly decides which ready turn to release next and how much released but unfinished work to maintain. The method uses a mean--Conditional Value-at-Risk (CVaR) objective to capture the evolving tail risk of unfinished workflows, incorporates online estimates of turn work when prioritizing ready turns, and adapts the released work budget to observed queue pressure. We evaluate the method using real agent execution traces from software engineering tasks across multiple LLMs and workflow arrival rates. The method performs comparably to eager release under light load and substantially reduces the P95 of workflow flow time under contention, achieving up to a \(3.50\times\) speedup.

cs.AI↗
arXiv2026

Demystifying the Privacy-Utility Trade-off in LLM Interactions

The integration of Large Language Models into daily tasks relies on context-rich instructions, inevitably exposing sensitive user information. Current privacy-preserving methods typically employ context-agnostic static rules, causing severe utility degradation. However, the specific mechanisms governing how sanitization impacts downstream performance remain largely underexplored. To address this, we conduct a systematic analysis to deconstruct the privacy-utility trade-off, uncovering three underlying mechanisms: (1) Context-Dependent Utility, which first establishes when to sanitize by revealing that data value shifts from critical constraints to dispensable noise based on user intent; (2) Strategic Adaptation, which subsequently determines how to sanitize by dictating that the choice between removal and replacement depends on the task's reliance on factual integrity versus structural coherence; and (3) Combinatorial Interplay, which finally extends the protection scope by demonstrating that attributes form a semantic web of synergistic dependencies or antagonistic redundancies. Guided by these insights, we introduce an intent-driven local protection framework. By distilling a lightweight model Veilmind-4B to drive a dynamic extraction-sanitization-restoration pipeline, our approach reaches a low-leakage privacy point while preserving substantially higher response utility than existing privacy-oriented baselines, advancing the privacy-utility trade-off toward the Pareto frontier.

cs.AI↗
arXiv2026

Defining AI Agents: A Compendium of Criteria, Metrics, and Benchmarks

The term agent in artificial intelligence lacks a standard definition, complicating the evaluation, comparison, and reproducibility of AI agent research. We address this ambiguity through a survey organized around five dimensions of agenticness: environmental interaction, learning and adaptation, autonomy, goal-directed behavior, and temporal coherence. For each dimension, we examine how the underlying capability has been conceptualized across prior work and synthesize the metrics, benchmarks, and evaluation frameworks used to assess it. This review provides a structured account of the current landscape of agent evaluation, highlighting both established approaches and areas where evaluation remains limited or inconsistent. We additionally introduce the Agent Compendium, a public-facing digital resource that organizes and extends the evaluation methods identified through this review. Together, the survey and compendium provide a common structure for evaluating and comparing agent capabilities across AI systems, supporting more reproducible research, clearer communication, and more systematic study of artificial agents.

cs.AI↗