Alan Polyak

Can LLMs strengthen LP relaxations and speed up solver convergence on MILPs? This is a question that we (Milad Yazdani, Samin Aref, Zirui Zhou, and I) explored in our recent work, and the results are promising. In this year’s IMO, leading AI systems (from OpenAI, Google/DeepMind) achieved a gold-medal–level score by solving 5 out of 6 problems, yet P6 (a notoriously difficult problem) remained unsolved. We modeled P6 as an integer program (LLMs, with some guidance, also produced correct formulations). Still, top MILP solvers did not converge in a reasonable time, suggesting a weak LP relaxation. Our method: EvoCut. EvoCut combines evolutionary search + LLMs to automatically discover problem-specific cuts (valid inequalities) that strengthen the relaxation. Results: - ~55% average gap reduction at the same runtime - Order-of-magnitude faster convergence in many instances We also observed similar improvements on other combinatorial problems across different domains. Read more & try EvoCut: - Paper: EvoCut: Strengthening Integer Programs via Evolution-Guided Language Models (https://lnkd.in/g6Kydtp6) - Code: Test EvoCut on your own MILP (https://lnkd.in/g42wMy4s) #MILP #OperationsResearch #Optimization #AI #LLMs #CuttingPlanes #Combinatorics #IMO #LinearProgramming

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Andrew Ng is right: the bottleneck in AI isn’t coding anymore—it’s product management. At Foot Locker and in my grad work in AI, I’ve seen how quickly AI tools can accelerate prototyping and delivery. The challenge isn’t building faster—it’s aligning on what to build, how to validate user needs quickly, and ensuring the right feedback loops are in place. The role of product managers has never been more critical. We’re not just writing specs; we’re orchestrating speed, empathy, and strategy in a world where execution is no longer the slowest part.

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If you’re building with LLMs, these are 10 toolkits I highly recommend getting familiar with 👇 Whether you’re an engineer, researcher, PM, or infra lead, these tools are shaping how GenAI systems get built, debugged, fine-tuned, and scaled today. They form the core of production-grade AI, across RAG, agents, multimodal, evaluation, and more. → AI-Native IDEs (Cursor, JetBrains Junie, Copilot X) Modern IDEs now embed LLMs to accelerate coding, testing, and debugging. They go beyond autocomplete, understanding repo structure, generating unit tests, and optimizing workflows. → Multi-Agent Frameworks (CrewAI, AutoGen, LangGraph) Useful when one model isn’t enough. These frameworks let you build role-based agents (e.g. planner, retriever, coder) that collaborate and coordinate across complex tasks. → Inference Engines (Fireworks AI, vLLM, TGI) Designed for high-throughput, low-latency LLM serving. They handle open models, fine-tuned variants, and multimodal inputs, essential for scaling to production. → Data Frameworks for RAG (LlamaIndex, Haystack, RAGflow) Builds the bridge between your data and the LLM. These frameworks handle parsing, chunking, retrieval, and indexing to ground model outputs in enterprise knowledge. → Vector Databases (Pinecone, Weaviate, Qdrant, Chroma) Backbone of semantic search. They store embeddings and power retrieval in RAG, recommendations, and memory systems using fast nearest-neighbor algorithms. → Evaluation & Benchmarking (Fireworks AI Eval Protocol, Ragas, TruLens) Lets you test for accuracy, hallucinations, regressions, and preference alignment. Core to validating model behavior across prompts, versions, or fine-tuning runs. → Memory Systems (MEM-0, LangChain Memory, Milvus Hybrid) Enables agents to retain past interactions. Useful for building persistent assistants, session-aware tools, and long-term personalized workflows. → Agent Observability (LangSmith, HoneyHive, Arize AI Phoenix) Debugging LLM chains is non-trivial. These tools surface traces, logs, and step-by-step reasoning so you can inspect and iterate with confidence. → Fine-Tuning & Reward Stacks (PEFT, LoRA, Fireworks AI RLHF/RLVR) Supports adapting base models efficiently or aligning behavior using reward models. Great for domain tuning, personalization, and safety alignment. → Multimodal Toolkits (CLIP, BLIP-2, Florence-2, GPT-4o APIs) Text is just one modality. These toolkits let you build agents that understand images, audio, and video, enabling richer input/output capabilities. If you're deep in AI infra or systems, print this out, build a test project around each, and experiment with how they fit together. You’ll learn more in a weekend with these tools than from hours of reading docs. What’s one tool you’d add to this list? 👇 〰️〰️〰️ Follow me (Aishwarya Srinivasan) for more AI infrastructure insights, and subscribe to my newsletter for deeper technical breakdowns: 🔗 https://lnkd.in/dpBNr6Jg

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How do LLMs really compare to the human brain? In a sequence of studies, our team at Google Research and partners at Princeton, HUJI and NYU have been exploring this question, aligning brain activity with the internal contextual embeddings of speech and language within LLMs as they process everyday conversations. What have we discovered? AI language models and the human brain share underlying organizational principles for representing words. Specifically, the internal representations used by these AI systems correspond to the neural activity patterns observed in brain regions crucial for both understanding and generating speech, hinting at potential shared computational mechanisms, all in all demonstrating the power of deep language model’s embeddings to act as a framework for understanding how the human brain processes language. Thank you to our research partners: Hasson Lab at Princeton University, the DeepCognitionLab at the Hebrew University, and researchers from the NYU Langone Comprehensive Epilepsy Center. Google Research Blog Post, authored by Mariano Schain and Ariel Goldstein: https://lnkd.in/d9cbP4Ee Nature Human Behaviour Paper: https://lnkd.in/dCbvdC-A Nature Communications Paper: https://lnkd.in/dbPCGY_m Nature Neuroscience Paper: https://lnkd.in/dvWjEg3C Hasson Lab, Princeton: https://lnkd.in/diMh8RA4 DeepCognitionLab at the Hebrew University: https://lnkd.in/dFPDuM7x  NYU Langone Comprehensive Epilepsy Center: https://lnkd.in/dU8rWe5e

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