Spatial reasoning is a key capability in the field of artificial intelligence, especially crucial in areas such as robotics, computer vision, and natural language understanding. However, evaluating the ability of multimodal large language models (MLLMs) in complex spatial reasoning still faces challenges, particularly in scenarios requiring multi-step reasoning and precise mathematical constraints.

Compiler optimization is essential for improving program performance, yet modern compilers still depend on manually crafted transformation rules over intermediate representations (IRs). As compilers grow in complexity, maintaining these rulebased optimizations becomes increasingly labor-intensive and difficult to scale. Recent advances in large language models (LLMs) offer a promising alternative, but their effectiveness in compiler optimization remains limited - primarily due to the lack of IR-oriented datasets that expose models to diverse transformation samples in real-world scenarios (optimization-sensitive samples), hindering LLMs from learning rich and generalizable optimization strategies. In this paper, we introduce IR-OptSet, the first public optimization-sensitive dataset for advancing LLM-based IR optimizers. It comprises 170KLLVMIR samples from open-source repositories across 8 representative optimization domains. IROptSet defines two core tasks: Code Analysis and Optimized Code Generation, and provides tools for correctness verification, performance evaluation, and dataset expansion. In our experiments, fine-tuning three representative LLMs on IROptSet leads to significant accuracy improvements across both tasks. Moreover, the LLM fine-tuned with IR-OptSet outperforms traditional compiler with the -O3 option in 64 test cases in terms of performance. Further analysis reveals that IROptSet provides greater transformation diversity and representativeness than three widely used IR-oriented datasets, highlighting its potential to drive model-based IR optimization.

Formal reasoning and automated theorem proving constitute a challenging subfield of machine learning, in which machines are tasked with proving mathematical theorems using formal languages like Lean. A formal verification system can check whether a formal proof is correct or not almost instantaneously, but generating a completely correct formal proof with large language models (LLMs) remains a formidable task. The usual approach in the literature is to prompt the LLM many times (up to several thousands) until one of the generated proofs passes the verification system.

Most incremental learners excessively prioritize object classes while neglecting various kinds of states (e.g.

We review the current state of automatic differentiation (AD) for array programming in machine learning (ML), including the different approaches such as operator overloading (OO) and source transformation (ST) used for AD, graph-based intermediate representations for programs, and source languages. Based on these insights, we introduce a new graph-based intermediate representation (IR) which specifically aims to efficiently support fully-general AD for array programming. Unlike existing dataflow programming representations in ML frameworks, our IR naturally supports function calls, higher-order functions and recursion, making ML models easier to implement. The ability to represent closures allows us to perform AD using ST without a tape, making the resulting derivative (adjoint) program amenable to ahead-of-time optimization using tools from functional language compilers, and enabling higher-order derivatives. Lastly, we introduce a proof of concept compiler toolchain called Myia which uses a subset of Python as a front end.

Many machine learning applications involve jointly predicting multiple mutually dependent output variables. Learning to search is a family of methods where the complex decision problem is cast into a sequence of decisions via a search space. Although these methods have shown promise both in theory and in practice, implementing them has been burdensomely awkward. In this paper, we show the search space can be defined by an arbitrary imperative program, turning learning to search into a credit assignment compiler. Altogether with the algorithmic improvements for the compiler, we radically reduce the complexity of programming and the running time. We demonstrate the feasibility of our approach on multiple joint prediction tasks. In all cases, we obtain accuracies as high as alternative approaches, at drastically reduced execution and programming time.

Precise hardware performance models play a crucial role in code optimizations. They can assist compilers in making heuristic decisions or aid autotuners in identifying the optimal configuration for a given program.

Firstly, many machine learning models use optimization algorithms which require access to derivatives of the model.