Paclitaxel and BKM120 Before Surgery in Treating Patients With Stage II or III Estrogen Receptor-Positive and HER2-Negative Breast Cancer

Inclusion Criteria:

* Clinical stage II or III ER-positive, HER2-negative breast cancer with complete surgical excision of the breast cancer as the treatment goal.
* Tumor size at least 2cm in one dimension by clinical or radiographic examination (WHO criteria).
* Received at least 2 weeks of neoadjuvant endocrine therapy.
* Ki67 after 2 to 12 weeks of neoadjuvant endocrine therapy is \> 10% confirmed by central testing at Washington University.
* At least 18 years of age.
* ECOG performance status ≤ 2
* Normal bone marrow and organ function as defined below:

  * Absolute neutrophil count ≥ 1,500/mcl
  * Platelets ≥ 100,000/mcl
  * Hemoglobin \> 9.0 g/dL
  * AST(SGOT)/ALT(SGPT) \<= IULN
  * Serum bilirubin within normal limits (OR total bilirubin ≤ 3.0 x IULN with direct bilirubin within normal range in patients with well documented Gilbert Syndrome)
  * Creatinine ≤ 1.5 x IULN OR Creatinine clearance ≥ 50 mL/min/1.73 m2
  * plasma glucose ≤ 120 mg/dL (6.7 mmol/L)
* Patient may be pre- or post-menopausal. Women of childbearing potential must agree to use adequate contraception prior to study entry, for the duration of study participation, and for up to 30 days following completion of treatment. Should a woman become pregnant or suspect she is pregnant while participating in this study, she must inform her treating physician immediately.
* Ability to understand and willingness to sign an IRB approved written informed consent document (or that of legally authorized representative, if applicable).

Exclusion Criteria:

* Prior therapy with a PI3K inhibitor for the indexed breast cancer.
* Sentinel lymph node dissection prior to neoadjuvant therapy.
* Currently receiving any other investigational agents.
* Acute or chronic liver disease, renal disease, or pancreatitis.
* A history of allergic reactions attributed to compounds of similar chemical or biologic composition to BKM120 or paclitaxel or other agents used in the study.
* Presence of one of the following mood disorders (as judged by the physician or a psychiatrist or as a result of the patient's mood assessment questionnaire):

  * Medically documented history of or active major depressive episode, bipolar disorder (I or II), obsessive-compulsive disorder, schizophrenia, or a history of suicidal attempt/ideation or homicidal ideation (immediate risk of doing harm to others) or patients with active severe personality disorders (defined according to DSM- IV) are not eligible. Note: for patients with psychotropic treatments ongoing at baseline, the dose and the schedule should not be modified within the previous 6 weeks prior to start of study drug.

    \*≥ CTCAE grade 3 anxiety
  * Meets the cut-off score of ≥ 12 in the PHQ-9 or a cut-off of ≥ 15 in the GAD-7 mood scale, respectively, or selects a positive response of "1, 2, or 3" to question number 9 regarding potential for suicidal thoughts in the PHQ-9 (independent of the total score of the PHQ-9)

    * CTCAE grade 2 diarrhea.
* Presence of active cardiac disease, including any of the following:

  * Left ventricular ejection fraction (LVEF) \< 50% as determined by MUGA or echocardiogram
  * QTC \> 480 msec on screening ECG (using the QTcF formula)
  * Angina pectoris that requires the use of anti-anginal medication
  * Ventricular arrhythmias except for benign premature ventricular contractions
  * Supraventricular and nodal arrhythmias requiring a pacemaker or not controlled with medication
  * Conduction abnormality requiring a pacemaker
  * Valvular disease with document compromise in cardiac function
  * Symptomatic pericarditis.
* History of cardiac dysfunction including any of the following:

  * Myocardial infarction within the last 6 months, documented by persistent elevated cardiac enzymes or persistent regional wall abnormalities of LVEF function
  * History of documented congestive heart failure (New York Heart Association function classification III-IV)
  * Documented cardiomyopathy.
* Poorly controlled diabetes mellitus or steroid-induced diabetes mellitus.
* Significant symptomatic deterioration of lung function. If clinically indicated, pulmonary function tests including measures of predicted lung volumes, DLco, O2 and/or saturation at rest on room air should be considered to exclude pneumonitis or pulmonary infiltrates.
* Other concurrent severe and/or uncontrolled concomitant medical conditions (e.g., active or uncontrolled infection) that could cause unacceptable safety risks or compromise compliance with the protocol.
* Impairment of gastrointestinal function or GI disease that may significantly alter the absorption of BKM120 (e.g., ulcerative disease, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or small bowel resection).
* Treatment with hematopoietic colon-stimulating growth factors (e.g., G-CSF, GM-CSF) within the 2 weeks prior to starting study drug. Erythropoietin or darbepoetin therapy, if initiated at least 2 weeks prior to enrollment, may be continued.
* Currently receiving treatment with medication which carries a known risk of prolonging QT interval or inducing Torsades de Pointes. If treatment with this drug can be discontinued and the patient can be switched to a different medication prior to starting study drug, this is acceptable.
* Receiving chronic treatment with steroid or another immunosuppressive agent. Note that topical applications, inhaled sprays, eye drops, or local injections are allowed.
* Consumption of known CYP3A inhibitors such as Seville oranges, grapefruit, pummelos, exotic citrus fruits, St. John's wort, Kava, ephedra (ma huang), gingko biloba), dehydroepiandrosterone (DHEA), yohimbe, saw palmetto, and ginseng.
* Currently receiving treatment with medication known to be a moderate or strong inhibitor or inducer of isoenzyme CYP3A. If treatment with this drug can be discontinued and the patient can be switched to a different medication prior to starting study drug, this is acceptable. Please note that concomitant treatment with a weak inhibitor of CYP3A is allowed.
* Currently taking therapeutic doses of warfarin sodium or any other Coumadin-derivative anticoagulant.
* Pregnant and/or breastfeeding. Patient must have a negative serum pregnancy test within 72 hours of starting treatment.
* Known HIV-positivity.
* Inclusion of Women and Minorities
* Because breast cancer occurs predominantly in women, men will not be eligible for this trial. Women and members of all races and ethnic groups are eligible for this trial.