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",[353,354,262],"h1",{"className":355,"id":357},[356],"page-title__main","reasoning-you-can-check",[359,360,364],"h2",{"className":361,"id":363},[362],"page-title__sub","coupling-language-models-with-classical-solvers-and-where-the-trust-actually-lives","Coupling Language Models with Classical Solvers, and Where the Trust Actually Lives",[347,366,368,369],{"style":367},"width: 100%; padding: 2%;","\n    ",[370,371],"img",{"src":372,"alt":373,"style":374},"https:\u002F\u002Fimages.unsplash.com\u002Fphoto-1501594907352-04cda38ebc29?w=1200&auto=format&fit=crop","The Golden Gate Bridge stretching across open water to the far shore, analogous to carrying a vague human question across to a machine that can answer it exactly, where the whole crossing depends on how well each end is anchored","width: 100%; height: auto;",[376,377,378],"p",{},"A language model guesses the next word. A solver proves a fact. The first is fluent and often wrong in ways that are hard to spot. The second is rigid and, when it answers at all, answers in a way another program can double-check. The obvious move is to put them together, let the model read the messy human sentence and hand the actual working-out to a solver. A solver is an exact, rule-crunching program, the kind of thing behind a Sudoku helper or an airline scheduler, and it only ever returns an answer that provably follows from the rules it was handed. The reasoning step then comes with a guarantee the model alone cannot give. The interesting part is what that guarantee does and does not cover.",[376,380,381],{},"A bridge captures the shape of it. The far bank is the solver, fixed and dependable, the same crossing every time. The near bank is the language model, fluent and fast and willing to say almost anything. The hard part is the connection at each end, carrying the question over without dropping what it meant, and that is where the surprises hide.",[359,383,385],{"id":384},"the-pattern-and-what-it-buys","The Pattern and What It Buys",[376,387,388,389,397,398,404],{},"The dominant setup is the simplest one. Treat the solver as a tool. The model rewrites a plain-language problem as a precise specification, a solver works it out, and the model turns the result back into ordinary prose. Logic-LM is a clean instance. It sends each problem to whichever engine fits, a logic programming engine, a theorem prover, a constraint solver for puzzles with many interacting rules, or Z3, a widely used engine that also handles arithmetic. Across five reasoning datasets, the approach reported an average gain of 39.2 percent over a model prompted directly and 18.4 percent over chain-of-thought prompting, which is the practice of asking the model to write out its intermediate steps ",[390,391,392],"sup",{},[393,394,396],"a",{"href":395},"#source-1","[1]",". SatLM makes the same bet through declarative prompting, parsing a question into a satisfiability problem and letting Z3 plan the actual inference, so the solver guarantees the execution is correct as long as the specification is ",[390,399,400],{},[393,401,403],{"href":402},"#source-2","[2]",".",[376,406,407,408,414,415,421],{},"The same shape appears outside pure logic. LINC translates premises and a conclusion into first-order logic, the formal language of \"for all\" and \"there exists\". A theorem prover named Prover9 handles the inference, and a vote across several translations smooths out the noise ",[390,409,410],{},[393,411,413],{"href":412},"#source-3","[3]",". Planning fits the mold too. LLM+P rewrites the task in PDDL, a standard planning format, then hands it to a classical planner that searches for a correct or optimal route ",[390,416,417],{},[393,418,420],{"href":419},"#source-4","[4]",". On its own the model could not draft even a workable plan. With the planner doing the search, it produced optimal ones. The lesson keeps repeating. The model is a good reader and a poor calculator, and the split plays to both.",[376,423,424,425,429],{},"A practical question follows immediately. What happens when the solver returns unsatisfiable, its way of reporting that no answer can possibly fit the rules, or simply runs out of time. Logic-LM is candid about this. When the generated program cannot be executed, the system falls back to chain-of-thought output, and when even that is unavailable it guesses ",[390,426,427],{},[393,428,396],{"href":395},". The guarantee, in other words, is conditional on getting a runnable, faithful specification in the first place.",[359,431,433],{"id":432},"the-trust-moves-to-the-edges","The Trust Moves to the Edges",[376,435,436,437,404],{},"The solver makes the middle step sound, which mostly relocates the problem. The remaining errors pile up at the two edges, translating in and reporting out. A study of compositional translation found that models struggle to capture the logic hidden in ordinary sentences, the every or some that is implied rather than spelled out, the exception buried in a side clause. Its answer was to parse each sentence into a dependency structure first, translate the pieces in sequence, and then use the satisfiability solver itself to compare candidate translations and throw out the inconsistent ones, topping seven reasoning benchmarks ",[390,438,439],{},[393,440,442],{"href":441},"#source-5","[5]",[347,444,368,445],{"style":367},[370,446],{"src":447,"alt":448,"style":374},"https:\u002F\u002Fimages.unsplash.com\u002Fphoto-1457369804613-52c61a468e7d?w=1200&auto=format&fit=crop","Several open books fanned out on a surface, analogous to the ordinary human writing a language model has read by the shelfload, in contrast with the strict solver notation it has barely seen and therefore writes unreliably",[376,450,451,452,458],{},"Stacked open books make the imbalance plain. A model has read ordinary human writing by the shelfload, and the strict notation a solver expects almost not at all. Those exact code formats show up rarely in the text a model learns from, so asking it to write them directly produces frequent mistakes, the equivalent of a comma in the wrong place that stops the whole program. NL2Logic responds by splitting the job in two. One step turns the sentence into a tidy outline of the logic that does not depend on any particular solver, and a second, purely mechanical step turns that outline into solver-ready code. The split reached 99 percent correct syntax and, dropped into Logic-LM in place of its original translator, improved downstream accuracy by 31 percent ",[390,453,454],{},[393,455,457],{"href":456},"#source-6","[6]",". The pattern worth noticing is that the fix is structural rather than a matter of asking the model more nicely.",[376,460,461,462,468],{},"Cleaning up the input edge still leaves the other one exposed. The reporting edge is subtler and easy to miss. One analysis breaks the pipeline into three parts, formalizing the question, deciding it, and narrating the result, and points out that prior work checked the first two and assumed the third was free. It is not. A solver can return a sound verdict with a certificate, an independently checkable proof of an unsatisfiable instance, and the model can still narrate the wrong conclusion to the user. Under prompt injection the authors flipped a verified answer while the underlying verdict stayed correct, a failure that is invisible to anyone auditing only the solver ",[390,463,464],{},[393,465,467],{"href":466},"#source-7","[7]",". Soundness in the engine does not imply soundness in the sentence the user reads.",[359,470,472],{"id":471},"closing-the-loop","Closing the Loop",[376,474,475,476,480,481,487,488,494],{},"If the weak link is translation, the obvious lever is feedback. The solver does not only return an answer, it returns error messages, and those can drive revision. Logic-LM already used a self-refinement step that feeds solver errors back for correction ",[390,477,478],{},[393,479,396],{"href":395},". ChatLogic puts the model at the center as a controller, translating problems into pyDatalog programs and running dedicated semantic and syntax correction modules before execution ",[390,482,483],{},[393,484,486],{"href":485},"#source-8","[8]",". The most pointed result in this direction comes from work pairing models with Answer Set Programming, a style of logic built for rules that hold until something overrides them, the way birds fly unless the bird happens to be a penguin. The system ran the clingo solver in a loop, feeding each round of complaints back for another attempt. Across six benchmarks it needed no task-specific setup and still beat the stricter logic approaches on these exception-laden problems ",[390,489,490],{},[393,491,493],{"href":492},"#source-9","[9]",". The interesting part is what drove those gains. The correction loop did most of the work, with no hand-written domain knowledge required. That speaks to a live question, whether solver feedback can help without fine-tuning, and here the loop carried it alone.",[376,496,497,498,504,505,404],{},"Training is the other route. Thought-Like-Pro has a model generate rules and facts, lets a Prolog engine derive verified reasoning paths to the target, translates only the verified paths into natural language, and fine-tunes the model to imitate them, which improved performance on out-of-distribution reasoning tasks the model had not seen ",[390,499,500],{},[393,501,503],{"href":502},"#source-10","[10]",". The solver here is a labeler that never approves an invalid step. A related concern is expressiveness, since the target language can be too narrow. LoRP, published in a peer-reviewed venue, shows that some basic first-order logic constructs cannot be stated directly in Prolog and supplies a systematic translation from first-order logic into Prolog to widen what the pipeline can represent, reporting stable gains across model architectures ",[390,506,507],{},[393,508,510],{"href":509},"#source-11","[11]",[359,512,514],{"id":513},"proving-code-and-math","Proving Code and Math",[376,516,517,518,524],{},"The strongest version of verifiable reasoning is formal proof, where a machine-checked argument leaves no room for a plausible-sounding mistake. HybridProver targets the Isabelle proof assistant and combines two styles, writing a whole proof at once and building it one small step at a time, with a helper tool called Sledgehammer filling gaps. It reached a 59.4 percent success rate on the miniF2F benchmark of competition mathematics problems, up from a previous best of 56.1 percent for Isabelle ",[390,519,520],{},[393,521,523],{"href":522},"#source-12","[12]",". The same work is honest about scope. Isabelle is often used for system verification rather than mathematics, proofs there depend on extensive project-specific context, and reported numbers on a math benchmark are not the same as proving a real codebase correct. The toolchains exist and are improving, though treating them as turnkey verification for production software would be premature.",[359,526,528],{"id":527},"what-is-settled-and-what-is-not","What Is Settled and What Is Not",[376,530,531,532,536,540],{},"The settled part is that handing the deductive step to a solver removes a real and well-documented class of failure, the model that reasons fluently to a wrong conclusion. The unsettled part is everything around that step. Ambiguous input and underspecified constraints are not fixed by a solver, since the engine faithfully executes whatever specification it is given, including a wrong one. The semantic gap between a probabilistic reader and a deterministic engine is the root problem, and the more durable responses attack it structurally, through compositional parsing, intermediate syntax trees, and verification of the translation itself, rather than through retries and voting alone ",[390,533,534],{},[393,535,442],{"href":441},[390,537,538],{},[393,539,457],{"href":456},". This is also where a parallel research line sits, the differentiable approaches such as logic tensor networks and logical neural networks that fold logic inside the model rather than calling an external engine. Whether those converge with the pipeline approach or remain a separate track is an open question, and the practical reasoning systems shipping today are overwhelmingly pipelines.",[376,542,543,544,548],{},"The upcoming LLM-Solve workshop, set for the 2026 Federated Logic Conference in Lisbon, captures the current mood. It frames the work as a two-way street. Models help non-experts build formal specifications, and solvers supply verification and structure for model-driven agents. As for production beyond research demos, the honest answer is that it is thin. Planning and scheduling look closest, given how directly they map onto classical solvers, and the engineering bill is real, covering translation latency, solver timeout policies, schema upkeep, and monitoring for the stealthy narration failures described earlier ",[390,545,546],{},[393,547,467],{"href":466},". The appeal of the idea is that it offers reasoning you can check. The work that remains is making sure the part you check is the part that matters.",[347,550,351,554,351,557],{"className":551},[552,553],"references","mt-8",[359,555,556],{"id":552},"References",[558,559,368,565,368,583,368,595,368,606,368,617,368,628,368,640,368,650,368,662,368,673,368,683,368,695,351],"ol",{"className":560},[561,562,563,564],"list-decimal","list-inside","space-y-2","mt-4",[566,567,569,570,574,575],"li",{"id":568},"source-1","L. Pan, A. Albalak, X. Wang, and W. Y. Wang, \"Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning,\" in ",[571,572,573],"em",{},"Findings of the Association for Computational Linguistics (EMNLP)",", 2023. DOI: ",[393,576,582],{"href":577,"target":578,"className":579},"https:\u002F\u002Fdoi.org\u002F10.18653\u002Fv1\u002F2023.findings-emnlp.248","_blank",[580,581],"text-blue-600","underline","[Online]",[566,584,586,587,590,591],{"id":585},"source-2","X. Ye, Q. Chen, I. Dillig, and G. Durrett, \"SatLM: Satisfiability-Aided Language Models Using Declarative Prompting,\" in ",[571,588,589],{},"Advances in Neural Information Processing Systems (NeurIPS)",", 2023, ",[393,592,582],{"href":593,"target":578,"className":594},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2305.09656",[580,581],[566,596,598,599,590,602],{"id":597},"source-3","T. X. Olausson et al., \"LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers,\" in ",[571,600,601],{},"Proceedings of the Conference on Empirical Methods in Natural Language Processing (EMNLP)",[393,603,582],{"href":604,"target":578,"className":605},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2310.15164",[580,581],[566,607,609,610,590,613],{"id":608},"source-4","B. Liu et al., \"LLM+P: Empowering Large Language Models with Optimal Planning Proficiency,\" ",[571,611,612],{},"arXiv",[393,614,582],{"href":615,"target":578,"className":616},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2304.11477",[580,581],[566,618,620,621,623,624],{"id":619},"source-5","H. Ryu, G. Kim, H. S. Lee, and E. Yang, \"Divide and Translate: Compositional First-Order Logic Translation and Verification for Complex Logical Reasoning,\" ",[571,622,612],{},", 2024, ",[393,625,582],{"href":626,"target":578,"className":627},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2410.08047",[580,581],[566,629,631,632,635,636],{"id":630},"source-6","R. R. Putra, R. S. P. Basuki, Y. Cheng, and P. Gao, \"NL2Logic: AST-Guided Translation of Natural Language into First-Order Logic with Large Language Models,\" in ",[571,633,634],{},"Findings of the Association for Computational Linguistics (EACL)",", 2026, ",[393,637,582],{"href":638,"target":578,"className":639},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2602.13237",[580,581],[566,641,643,644,635,646],{"id":642},"source-7","Z. Huang and S. Deng, \"Analyzing the Narration Gap in LLM-Solver Loops,\" ",[571,645,612],{},[393,647,582],{"href":648,"target":578,"className":649},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2606.19588",[580,581],[566,651,653,654,657,658],{"id":652},"source-8","Z. Wang, J. Liu, Q. Bao, H. Rong, and J. Zhang, \"ChatLogic: Integrating Logic Programming with Large Language Models for Multi-Step Reasoning,\" in ",[571,655,656],{},"Proceedings of the International Joint Conference on Neural Networks (IJCNN)",", 2024. DOI: ",[393,659,582],{"href":660,"target":578,"className":661},"https:\u002F\u002Fdoi.org\u002F10.1109\u002FIJCNN60899.2024.10650138",[580,581],[566,663,665,666,635,669],{"id":664},"source-9","A. Ishay and J. Lee, \"LLMs as ASP Programmers: Self-Correction Enables Task-Agnostic Nonmonotonic Reasoning,\" in ",[571,667,668],{},"Findings of the Association for Computational Linguistics (ACL)",[393,670,582],{"href":671,"target":578,"className":672},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2604.27960",[580,581],[566,674,676,677,623,679],{"id":675},"source-10","X. Tan, Y. Deng, X. Qiu, W. Xu, C. Qu, W. Chu, Y. Xu, and Y. Qi, \"Thought-Like-Pro: Enhancing Reasoning of Large Language Models through Self-Driven Prolog-based Chain-of-Thought,\" ",[571,678,612],{},[393,680,582],{"href":681,"target":578,"className":682},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2407.14562",[580,581],[566,684,686,687,690,691],{"id":685},"source-11","Z. Di, C. Zhang, H. Lv, L. Cui, and L. Liu, \"LoRP: LLM-based Logical Reasoning via Prolog,\" ",[571,688,689],{},"Knowledge-Based Systems",", 2025. DOI: ",[393,692,582],{"href":693,"target":578,"className":694},"https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.knosys.2025.114140",[580,581],[566,696,698,699,701,702],{"id":697},"source-12","J. Hu, J. Zhang, Y. Zhao, and T. Ringer, \"HybridProver: Augmenting Theorem Proving with LLM-Driven Proof Synthesis and Refinement,\" ",[571,700,612],{},", 2025, ",[393,703,582],{"href":704,"target":578,"className":705},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2505.15740",[580,581],{"title":707,"searchDepth":708,"depth":708,"links":709},"",2,[710,711,712,713,714,715,716],{"id":363,"depth":708,"text":364},{"id":384,"depth":708,"text":385},{"id":432,"depth":708,"text":433},{"id":471,"depth":708,"text":472},{"id":513,"depth":708,"text":514},{"id":527,"depth":708,"text":528},{"id":552,"depth":708,"text":556},"2026-06-27","Pairing a language model with a classical solver, an exact rule-crunching program, promises reasoning that is sound by construction, since the solver decides the hard step and returns an answer that can be checked independently. The catch is that trust does not disappear. It moves to the edges, into the act of turning a messy sentence into a precise spec and the act of reporting the result back, which is where most of the recent research now lives.","md",{"src":372},{"authors":722,"badge":728,"source":730},[723],{"avatar":724,"name":726,"to":727},{"src":725},"\u002Fimg\u002Fmark_avatar.png","Mark Williams","https:\u002F\u002Fthinkata.com",{"label":729},"Neurosymbolic AI",{"name":731,"url":727},"Thinkata Research",true,{"title":262,"description":718},"ATb_5AXa6afsQpQ4_-Tv8FigdS2lunOHmkmw_stWEL8",[736,984],{"id":737,"title":242,"body":738,"date":972,"description":973,"extension":719,"image":974,"meta":975,"navigation":732,"path":243,"seo":982,"stem":244,"__hash__":983,"_path":243},"insights\u002Fnews\u002Finsights\u002Fmulti-tenant-ai-isolation.md",{"type":344,"value":739,"toc":963},[740,752,758,761,764,767,771,779,782,790,794,800,803,811,819,823,829,832,845,853,857,865,875,879,882],[347,741,351,743,351,747],{"className":742},[350],[353,744,242],{"className":745,"id":746},[356],"one-model-many-customers-and-the-leak-nobody-tests-for",[359,748,751],{"className":749,"id":750},[362],"where-cross-tenant-data-leaks-in-shared-ai-systems-and-where-the-boundary-has-to-live","Where cross-tenant data leaks in shared AI systems, and where the boundary has to live",[347,753,368,754],{"style":367},[370,755],{"src":756,"alt":757,"style":374},"https:\u002F\u002Fimages.unsplash.com\u002Fphoto-1769117617809-cebd713b82bb?w=1200&auto=format&fit=crop","A long hotel hallway lined with identical guest room doors, analogous to a multi-tenant system where every customer looks safely separated until a shared mechanism, like a keycard coded for more than one room, quietly crosses the boundary",[376,759,760],{},"A hotel floor looks like strong isolation. Every room has its own door, its own number, and its own guest, and nobody expects one room's contents to turn up next door. The failure that matters is rarely a door left open. It is a keycard cut for one room that quietly opens the one beside it. That is the shape of the risk in shared AI systems. The separation between customers looks structural until something built for efficiency, a shared model, a shared index, or a shared cache, turns into a keycard that opens more than one room.",[376,762,763],{},"A B2B software company ships an AI feature. It summarizes contracts, answers questions over a customer's documents, or drafts replies from a customer's history. The demo lands, the feature works, usage climbs. One test rarely makes the plan. Can customer A pull customer B's data out of the same system. The feature working and the feature keeping customers apart are two different claims, and only the first one shows up in a product demo.",[376,765,766],{},"The word tenant here means one customer's isolated slice of a shared system, the same way a hotel gives each guest a private room inside one shared building. Most B2B AI products are multi-tenant by design, because running a separate model, database, and server stack for every customer is expensive. The saving comes from sharing, and sharing is exactly where the boundary between tenants can quietly disappear. Three surfaces tend to be shared, the model weights, the retrieval layer, and the serving cache. Each one has a documented way of moving one tenant's data into another tenant's output.",[359,768,770],{"id":769},"the-model-can-memorize-one-tenant-and-recite-it-to-another","The Model Can Memorize One Tenant and Recite It to Another",[376,772,773,774,778],{},"Language models memorize. One experiment extracted hundreds of verbatim sequences from a public model using only ordinary query access, including names, phone numbers, and other personal details, and some of those strings appeared in just a single training document ",[390,775,776],{},[393,777,396],{"href":395},". The finding that should worry anyone pooling customer data is that larger models memorized more, not less. A string does not need to be common to be recoverable.",[376,780,781],{},"The multi-tenant version of this risk shows up when a single model is fine-tuned on the combined data of every customer. Fine-tuning means continuing to train a base model on your own examples so it adapts to your domain. Do it on the pooled corpus of all tenants and the weights themselves become a shared surface. A prompt from tenant B can, at least in principle, surface a string that only tenant A ever provided, and no request-time permission check sees it happen, because the leak is baked into the parameters rather than pulled from a database.",[376,783,784,785,789],{},"There is a genuinely interesting counterpoint here. One study found that retrieval-augmented generation (RAG) can reduce a model's tendency to reproduce memorized training data, because the model leans on the freshly retrieved text instead of its own parameters ",[390,786,787],{},[393,788,403],{"href":402},". That is real, but it moves the risk rather than removing it. The retrieved text is the next shared surface.",[359,791,793],{"id":792},"retrieval-ranks-by-relevance-not-by-permission","Retrieval Ranks by Relevance, Not by Permission",[347,795,368,796],{"style":367},[370,797],{"src":798,"alt":799,"style":374},"https:\u002F\u002Fimages.unsplash.com\u002Fphoto-1762965119363-af950b523dca?w=1200&auto=format&fit=crop","Suitcases riding an airport baggage carousel, analogous to a retrieval step that surfaces whatever best matches the request as it comes around, without checking whether the person reaching for it is the rightful owner",[376,801,802],{},"Retrieval systems have one job, to find the most relevant text for a question, and they are good at it. Relevance is not permission. A baggage carousel sorts bags by the flight they arrived on and trusts travelers to claim the right one, which holds up until two bags look alike. A retrieval index sorts by semantic similarity, how close two pieces of text are in meaning, and by default carries no idea of who is allowed to see what. The index behind a shared RAG feature is usually one index for all tenants, kept that way for cost and for retrieval quality. The documents most similar to a question get pulled into the model's context before anything has checked whose documents they are.",[376,804,805,806,810],{},"One research group names this the relevance-authorization gap, and its measurements are stark. In a multitenant test setup, retrieval with no authorization gate leaked cross-tenant data in 98 to 100 percent of probes ",[390,807,808],{},[393,809,413],{"href":412},". The proposed fix is not a smarter filter placed after retrieval runs. It is a layered architecture that gates the candidate set at ingestion and at retrieval time, before the ranking step ever touches a document the requesting tenant should not see.",[376,812,813,814,818],{},"A follow-up test used a composite structured prompt, one part written to trigger retrieval and one part instructing the model to repeat the context it was given, and pulled 112 exact matches and 208 near matches from 250 prompts against a private email dataset ",[390,815,816],{},[393,817,403],{"href":402},". The common instinct, retrieve everything and then filter the results the user should not see, arrives too late. By the time the filter runs, the restricted text is already sitting in the context window.",[359,820,822],{"id":821},"the-cache-is-a-side-channel","The Cache Is a Side Channel",[347,824,368,825],{"style":367},[370,826],{"src":827,"alt":828,"style":374},"https:\u002F\u002Fimages.unsplash.com\u002Fphoto-1701187540994-054295adacc5?w=1200&auto=format&fit=crop","A wall of numbered mailboxes in a building lobby, analogous to a shared mailroom whose delivery speed for a repeated item quietly signals what a neighbor already received",[376,830,831],{},"To avoid recomputing work, serving systems store intermediate state, often the key-value cache that holds a request's attention data, and reuse it when a new request shares a prefix with an earlier one. Shared across tenants, a cache hit comes back faster than a cache miss, the way a mailroom hands over a familiar package quicker than a first-time delivery, and that timing gap is measurable from the outside. A watchful neighbor can learn what someone nearby received without ever seeing it.",[376,833,834,835,839,840,844],{},"One attack, in work now published in IEEE Transactions on Information Forensics and Security, turned that difference into a working exploit. It detected per-token cache hits at 86 percent accuracy, recovered prompt tokens at 92.3 percent, and a peeping neighbor variant identified another user's cached content above 95 percent accuracy after three trials ",[390,836,837],{},[393,838,420],{"href":419},". In another experiment, presented at the Network and Distributed System Security Symposium, the same idea ran against SGLang, a production serving framework, and reconstructed a stranger's entire prompt with no prior knowledge of its content at a 95 percent success rate, a figure that climbed to 99 percent once the attacker already knew the surrounding template. A case study inside that same paper recovered a health questionnaire's embedded gender, age, weight, and height fields in just 60 requests ",[390,841,842],{},[393,843,442],{"href":441},". None of this requires special access. The attacker just sends normal requests and measures how long the answers take.",[376,846,847,848,852],{},"This is not confined to research prototypes. An audit of live commercial APIs, presented at ICML 2025, detected global cache sharing across users in seven providers, including OpenAI, which means a fast response can carry information about a stranger's prompt ",[390,849,850],{},[393,851,457],{"href":456},". The optimization that makes shared inference affordable is the same one that opens the channel.",[359,854,856],{"id":855},"where-the-boundary-has-to-live","Where the Boundary Has to Live",[376,858,859,860,864],{},"The pattern across all three surfaces is the same. The boundary cannot be a filter at the end of the pipeline. It has to be enforced before the shared resource is touched. For retrieval, that means gating the candidate set before the model reads anything, not after, an approach validated earlier against ungated retrieval ",[390,861,862],{},[393,863,413],{"href":412},". For the model, pooling every customer into one fine-tune trades isolation for convenience, and per-tenant routing or per-tenant adapters keep one customer's data out of the surface another customer queries. For the cache, the same tension holds. Per-tenant cache isolation closes the timing channel entirely, but it gives up the throughput gains that shared caching exists to provide, and that tradeoff has to be sized against how sensitive the cached content is rather than defaulted away in either direction. Isolation is not free, and its cost belongs in the design, not in the incident report.",[376,866,867,868,872,873,404],{},"This is the case for carrying tenant context, the identity of the customer a request belongs to, through every layer of the system. Retrieval, model selection, cache, and logging each need to know which tenant they are serving, rather than trusting a single check at the front door. A boundary enforced at each layer is harder to build than a filter bolted onto the output, and it is close to what confidential computing work already argues for at the hardware level, where isolation is treated as a property of the whole path rather than a wrapper around it ",[390,869,870],{},[393,871,467],{"href":466},". The engineering effort is the difference between a feature that works and a feature that can prove it keeps customers apart. A platform should treat per-tenant isolation, model routing, and tenant context at every layer as the default rather than a retrofit, for exactly the reasons the research keeps surfacing. The related tradeoffs are discussed further in ",[393,874,286],{"href":287},[359,876,878],{"id":877},"what-to-actually-test","What to Actually Test",[376,880,881],{},"The useful test is adversarial and a little boring. Sit in tenant B and try to retrieve, extract, or time a path into tenant A's data. Ask the model to repeat the context it was handed. Send prompts that share long prefixes with a known tenant and watch the latency. Probe the retrieval index with a query only another tenant's documents could answer. The evidence across memorization, retrieval, and caching says these leaks are reachable with ordinary access, so the open question for any team shipping B2B AI is not whether the failure mode exists. It is how much isolation the product can afford while still hitting its latency and cost targets. That number is worth knowing before a customer's security review asks for it.",[347,883,351,885,351,887],{"className":884},[552,553],[359,886,556],{"id":552},[558,888,368,890,368,901,368,911,368,921,368,932,368,942,368,953,351],{"className":889},[561,562,563,564],[566,891,892,893,896,897],{"id":568},"N. Carlini et al., \"Extracting Training Data from Large Language Models,\" in ",[571,894,895],{},"Proc. 30th USENIX Security Symposium (USENIX Security '21)",", 2021, pp. 2633–2650. ",[393,898,582],{"href":899,"target":578,"className":900},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2012.07805",[580,581],[566,902,903,904,623,907],{"id":585},"S. Zeng et al., \"The Good and The Bad: Exploring Privacy Issues in Retrieval-Augmented Generation (RAG),\" in ",[571,905,906],{},"Findings of the Association for Computational Linguistics: ACL 2024",[393,908,582],{"href":909,"target":578,"className":910},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2402.16893",[580,581],[566,912,913,914,635,917],{"id":597},"F. J. Arceo and V. P. Narsing, \"Securing the Agent: Vendor-Neutral, Multitenant Enterprise Retrieval and Tool Use,\" in ",[571,915,916],{},"Proc. ACM Conf. on AI and Agentic Systems (CAIS '26)",[393,918,582],{"href":919,"target":578,"className":920},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2605.05287",[580,581],[566,922,923,924,927,928],{"id":608},"L. Song et al., \"The Early Bird Catches the Leak: Unveiling Timing Side Channels in LLM Serving Systems,\" ",[571,925,926],{},"IEEE Transactions on Information Forensics and Security",", vol. 20, pp. 11431–11446, 2025. DOI: ",[393,929,582],{"href":930,"target":578,"className":931},"https:\u002F\u002Fdoi.org\u002F10.1109\u002FTIFS.2025.3622954",[580,581],[566,933,934,935,690,938],{"id":619},"G. Wu et al., \"I Know What You Asked: Prompt Leakage via KV-Cache Sharing in Multi-Tenant LLM Serving,\" in ",[571,936,937],{},"Proc. Network and Distributed System Security Symposium (NDSS 2025)",[393,939,582],{"href":940,"target":578,"className":941},"https:\u002F\u002Fdoi.org\u002F10.14722\u002Fndss.2025.241772",[580,581],[566,943,944,945,948,949],{"id":630},"C. Gu et al., \"Auditing Prompt Caching in Language Model APIs,\" in ",[571,946,947],{},"Proc. 42nd International Conference on Machine Learning (ICML 2025)",", PMLR 267, 2025, ",[393,950,582],{"href":951,"target":578,"className":952},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2502.07776",[580,581],[566,954,955,956,690,959],{"id":642},"S. Zobaed and M. A. Salehi, \"Confidential Computing Across Edge-To-Cloud for Machine Learning: A Survey Study,\" ",[571,957,958],{},"Software: Practice and Experience",[393,960,582],{"href":961,"target":578,"className":962},"https:\u002F\u002Fdoi.org\u002F10.1002\u002Fspe.3398",[580,581],{"title":707,"searchDepth":708,"depth":708,"links":964},[965,966,967,968,969,970,971],{"id":750,"depth":708,"text":751},{"id":769,"depth":708,"text":770},{"id":792,"depth":708,"text":793},{"id":821,"depth":708,"text":822},{"id":855,"depth":708,"text":856},{"id":877,"depth":708,"text":878},{"id":552,"depth":708,"text":556},"2026-07-08","Your B2B AI feature works. The test that rarely makes the plan is whether customer A can pull customer B's data out of it. A shared model, a shared retrieval index, and a shared cache each have a documented way of letting one tenant's data surface in another tenant's output, and the boundary has to live earlier than most teams put it.",{"src":756},{"authors":976,"badge":979,"source":981},[977],{"avatar":978,"name":726,"to":727},{"src":725},{"label":980},"Multi-Tenant AI",{"name":731,"url":727},{"title":242,"description":973},"jC7ird3voL3pHj96Cu7vJ8AIRUrHnF3Yn944t89Oe54",{"id":985,"title":174,"body":986,"date":1238,"description":1239,"extension":719,"image":1240,"meta":1241,"navigation":732,"path":175,"seo":1248,"stem":176,"__hash__":1249,"_path":175},"insights\u002Fnews\u002Finsights\u002Fexperts-all-the-way.md",{"type":344,"value":987,"toc":1229},[988,1000,1006,1013,1016,1020,1026,1034,1042,1046,1054,1072,1076,1089,1093,1101,1109,1122,1126,1129],[347,989,351,991,351,995],{"className":990},[350],[353,992,174],{"className":993,"id":994},[356],"experts-all-the-way-down",[359,996,999],{"className":997,"id":998},[362],"recursive-hierarchical-gating-and-the-gap-between-a-1994-idea-and-todays-composed-models","Recursive Hierarchical Gating and the Gap Between a 1994 Idea and Today's Composed Models",[347,1001,368,1002],{"style":367},[370,1003],{"src":1004,"alt":1005,"style":374},"https:\u002F\u002Fimages.unsplash.com\u002Fphoto-1766364649443-9e6f73e71403?w=1200&auto=format&fit=crop","Bare tree branches dividing into ever finer twigs against the sky, analogous to a tree of gates that splits the input again at each level, with an expert waiting only at the final tip",[376,1007,1008,1009,1012],{},"A mixture-of-experts model holds many specialized sub-networks, called experts, and a small gating network that decides which of them handle a given input. In the usual design the gate fires once. It looks at a token, picks a few experts, and the rest of the layer sits out, a setup covered in an ",[393,1010,1011],{"href":239},"earlier overview of mixture-of-experts",". The idea worth examining keeps the gate but changes what happens after it decides. Rather than pick an expert and stop, the gate splits the incoming context into categories and forwards each piece to a more specialized system, and that system may carry its own gate, which splits again, to whatever depth helps. The decision becomes a tree rather than a single fork, and only at the leaves does an expert actually answer.",[376,1014,1015],{},"The structure branches the way a tree divides a trunk into limbs and limbs into twigs, each split finer than the last, with an expert waiting only at the final tip. Two features set it apart from a standard routing layer. The split is recursive rather than a single step, and the thing being routed is a chunk of meaning, a document or a sub-task, rather than an individual token. Whether that structure earns its added complexity, measured against a single flat model or a single flat routing step, is an open question with a longer history behind it than the recent interest suggests.",[359,1017,1019],{"id":1018},"a-soft-decision-tree-circa-1994","A Soft Decision Tree, Circa 1994",[347,1021,368,1022],{"style":367},[370,1023],{"src":1024,"alt":1025,"style":374},"https:\u002F\u002Fimages.unsplash.com\u002Fphoto-1601661783552-b125ad86e67d?w=1200&auto=format&fit=crop","Blue ink dispersing through water with no hard edge, analogous to a gating network whose region boundaries are soft, so an input can belong partly to several branches at once rather than landing in exactly one",[376,1027,1028,1029,1033],{},"The recursive version is not new. Jordan and Jacobs described it in 1994 as a tree-structured architecture in which gating networks sit at the branch points and experts sit at the leaves ",[390,1030,1031],{},[393,1032,396],{"href":395},". Each gate partitions the input space, except the boundaries are soft, the way ink dropped into water spreads into a shared zone instead of stopping at a clean line, so an input can belong partly to several branches at once rather than landing in exactly one. The same construction repeats at every level, which yields a tree of arbitrary depth. They named the result a hierarchical mixture of experts and fit the whole thing with the expectation-maximization algorithm, a standard method for learning models that contain hidden structure. Their own phrase remains the clearest handle on the idea, a soft decision tree, where each node asks a fuzzy question and the answers blend instead of committing to one path.",[376,1035,1036,1037,1041],{},"That 1994 model routed fixed-length numeric inputs through simple linear experts, a long way from variable-length natural language. The worked examples ran two levels deep, though the authors noted the method extends to arbitrary depth ",[390,1038,1039],{},[393,1040,396],{"href":395},". Whether the soft-partition mathematics survives the move to language, where the input is a long sequence with no fixed dimension and the categories are semantic rather than geometric, is the part that does not carry over for free.",[359,1043,1045],{"id":1044},"expert-layers-versus-expert-models","Expert Layers Versus Expert Models",[376,1047,1048,1049,1053],{},"A distinction matters before going further. In a transformer mixture-of-experts the experts are feed-forward blocks inside one network, trained together, sharing a backbone, and routing picks among parts of a single model, which is the common case a recent survey of the area documents ",[390,1050,1051],{},[393,1052,403],{"href":402},". A different design treats each expert as a whole, separately trained, separately deployable model and puts a router in front of the collection. The literature calls this composition of experts, a model of models rather than a layer of them.",[376,1055,1056,1057,1061,1062,1066,1067,1071],{},"One such system uses a single router over a pool of expert language models and reaches the quality of a much larger model while keeping average active parameters low, around 31 billion on one benchmark ",[390,1058,1059],{},[393,1060,413],{"href":412},". Its routing runs in two steps, a category router first sorts the prompt into one of a fixed set of categories, then a lookup maps that category to the best expert ",[390,1063,1064],{},[393,1065,413],{"href":412},". That is close to the category-splitting idea, yet the routing still resolves to a single expert in one pass. A second design encodes each expert model as a special token in a controller model's vocabulary, so choosing an expert looks like generating the next token, and it reports a few percent gain over earlier multi-model methods ",[390,1068,1069],{},[393,1070,420],{"href":419},". Useful as these are, the router in each is a flat dispatch to one of several models. The recursive part, a chosen branch that is itself another gated system, is absent.",[359,1073,1075],{"id":1074},"hierarchical-recursive-and-the-difference","Hierarchical, Recursive, and the Difference",[376,1077,1078,1079,1083,1084,1088],{},"Two recent lines of work carry the words hierarchical and recursive, and both deserve pinning down, because neither is the recursive category dispatch sketched above. One groups a model's experts and applies routing control at two coupled levels, balancing traffic across groups while encouraging specialization within them, and reports a modest perplexity gain and much better expert balance at the seven-billion scale ",[390,1080,1081],{},[393,1082,442],{"href":441},". That is hierarchy inside one model's router, still operating on tokens. The other reuses a single shared stack of layers several times and lets a lightweight router decide how many passes each token takes, which saves parameters and compute ",[390,1085,1086],{},[393,1087,457],{"href":456},". Its recursion is over depth of computation, how often a token revisits the same block, not over which specialized model handles which category of content. Recursive computation and recursive routing are easy to conflate and are not the same idea.",[359,1090,1092],{"id":1091},"whether-the-extra-structure-pays","Whether the Extra Structure Pays",[376,1094,1095,1096,1100],{},"A prior question hides under all of this. If routing by meaning is valuable, do large models already do it on their own? A 2025 study probed several open mixture-of-experts models and found clear, statistically significant evidence that routing is sensitive to semantics, with expert overlap rising when meaning is preserved and falling when it changes, an effect strongest in the middle layers and growing with model size ",[390,1097,1098],{},[393,1099,467],{"href":466},". The behavior looks learned and emergent rather than designed in. If category-like specialization arises on its own during ordinary training, a hand-built category gate has to justify itself against a baseline that already routes semantically without being asked to.",[376,1102,1103,1104,1108],{},"The statistical theory is encouraging but conditional. A recent analysis of hierarchical mixtures shows that the choice of gating function changes the outcome, that the familiar softmax gate creates parameter interactions which slow expert convergence, and that a different gating function removes them and sharpens specialization ",[390,1105,1106],{},[393,1107,486],{"href":485},". A hierarchical gate can provably help, in other words, but only under the right design, and the wrong gate blunts the advantage the structure was meant to provide.",[376,1110,1111,1112,1116,1117,1121],{},"The simple version of the pattern already ships, though rarely more than two levels deep. A production audio assistant routes a query with a lightweight intent classifier to one of several specialized models, speech recognition, speaker identification, music tagging, then lets a small language model assemble the answer, and the cheap classifier beats a large model at the routing step ",[390,1113,1114],{},[393,1115,493],{"href":492},". Nesting these systems further, a classifier whose chosen branch is itself a classifier-plus-experts system, is uncommon in published work. The closest the agent-orchestration literature comes is a hierarchical scheme that decomposes a task with a planning agent, instantiates specialized worker agents per sub-task, and searches over their arrangements, with double-digit accuracy gains reported on reasoning benchmarks ",[390,1118,1119],{},[393,1120,503],{"href":502},". The decomposition there is genuinely multi-level, though it splits tasks rather than routing categories of context to standing expert models.",[359,1123,1125],{"id":1124},"what-this-suggests","What This Suggests",[376,1127,1128],{},"The thirty-year arc is tidy in outline and unfinished in substance. The recursive, tree-structured gate was written down in 1994, and the modern pieces exist in scattered form, composition across whole models, hierarchical control inside one model, recursion over compute, emergent semantic routing, and conditional theory about when gating helps. What is missing is the join, a system that splits context by category and dispatches recursively across separately specialized models, more than two levels deep, with evidence that it beats a flat router. A recursive gate that dispatches to separate models would also inherit hard questions about where each leaf actually runs, since every leaf is a model that has to be served somewhere. The appeal of the idea is its plainness, a small classifier asking a question and asking it again. Whether that plainness holds once the splits are semantic, the experts are full models, and the tree is more than shallow, is still closer to a promising hypothesis than a settled result.",[347,1130,351,1132,351,1134],{"className":1131},[552,553],[359,1133,556],{"id":552},[558,1135,368,1137,368,1148,368,1157,368,1166,368,1175,368,1184,368,1193,368,1202,368,1211,368,1220,351],{"className":1136},[561,562,563,564],[566,1138,1139,1140,1143,1144],{"id":568},"M. I. Jordan and R. A. Jacobs, \"Hierarchical Mixtures of Experts and the EM Algorithm,\" ",[571,1141,1142],{},"Neural Computation",", vol. 6, no. 2, pp. 181–214, 1994. DOI: ",[393,1145,582],{"href":1146,"target":578,"className":1147},"https:\u002F\u002Fdoi.org\u002F10.1162\u002Fneco.1994.6.2.181",[580,581],[566,1149,1150,1151,623,1153],{"id":585},"W. Cai et al., \"A Survey on Mixture of Experts in Large Language Models,\" ",[571,1152,612],{},[393,1154,582],{"href":1155,"target":578,"className":1156},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2407.06204",[580,581],[566,1158,1159,1160,623,1162],{"id":597},"S. Jain et al., \"Composition of Experts: A Modular Compound AI System Leveraging Large Language Models,\" ",[571,1161,612],{},[393,1163,582],{"href":1164,"target":578,"className":1165},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2412.01868",[580,581],[566,1167,1168,1169,623,1171],{"id":608},"Z. Chai et al., \"An Expert is Worth One Token: Synergizing Multiple Expert LLMs as Generalist via Expert Token Routing,\" ",[571,1170,612],{},[393,1172,582],{"href":1173,"target":578,"className":1174},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2403.16854",[580,581],[566,1176,1177,1178,635,1180],{"id":619},"G. Molodtsov et al., \"Hierarchical Mixture-of-Experts with Two-Stage Optimization,\" ",[571,1179,612],{},[393,1181,582],{"href":1182,"target":578,"className":1183},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2605.08292",[580,581],[566,1185,1186,1187,701,1189],{"id":630},"S. Bae et al., \"Mixture-of-Recursions: Learning Dynamic Recursive Depths for Adaptive Token-Level Computation,\" ",[571,1188,612],{},[393,1190,582],{"href":1191,"target":578,"className":1192},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2507.10524",[580,581],[566,1194,1195,1196,701,1198],{"id":642},"M. L. Olson et al., \"Probing Semantic Routing in Large Mixture-of-Expert Models,\" in ",[571,1197,573],{},[393,1199,582],{"href":1200,"target":578,"className":1201},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2502.10928",[580,581],[566,1203,1204,1205,623,1207],{"id":652},"H. Nguyen et al., \"On Expert Estimation in Hierarchical Mixture of Experts: Beyond Softmax Gating Functions,\" ",[571,1206,612],{},[393,1208,582],{"href":1209,"target":578,"className":1210},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2410.02935",[580,581],[566,1212,1213,1214,623,1216],{"id":664},"V. Naveen et al., \"Comprehensive Audio Query Handling System with Integrated Expert Models and Contextual Understanding,\" ",[571,1215,612],{},[393,1217,582],{"href":1218,"target":578,"className":1219},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2412.03980",[580,581],[566,1221,1222,1223,701,1225],{"id":675},"Z. Hou et al., \"HALO: Hierarchical Autonomous Logic-Oriented Orchestration for Multi-Agent LLM Systems,\" ",[571,1224,612],{},[393,1226,582],{"href":1227,"target":578,"className":1228},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2505.13516",[580,581],{"title":707,"searchDepth":708,"depth":708,"links":1230},[1231,1232,1233,1234,1235,1236,1237],{"id":998,"depth":708,"text":999},{"id":1018,"depth":708,"text":1019},{"id":1044,"depth":708,"text":1045},{"id":1074,"depth":708,"text":1075},{"id":1091,"depth":708,"text":1092},{"id":1124,"depth":708,"text":1125},{"id":552,"depth":708,"text":556},"2026-06-21","A small gate that does not just pick an expert but splits the input and asks again, recursively, before any expert answers, is an old idea with a 1994 pedigree. Today's composition-of-experts and hierarchical mixture-of-experts systems borrow pieces of it, though most still dispatch in a single flat step, which leaves the genuinely recursive, category-by-category version more proposed than proven.",{"src":1004},{"authors":1242,"badge":1245,"source":1247},[1243],{"avatar":1244,"name":726,"to":727},{"src":725},{"label":1246},"AI Architecture",{"name":731,"url":727},{"title":174,"description":1239},"yh_SiF9JOWkyPEOEqGOXIaLJT_axwrB3lZYihkn7syM",1792582876378]